Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

VL - 2 UR - http://dx.doi.org/10.3934/mine.2020011 ER - TY - RPRT T1 - A dynamic model for viscoelastic materials with prescribed growing cracks Y1 - 2019 A1 - Maicol Caponi A1 - Francesco Sapio AB -In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

UR - http://preprints.sissa.it:8180/xmlui/handle/1963/35334 ER - TY - JOUR T1 - On the existence of elastic minimizers for initially stressed materials JF - Phil. Trans. R. Soc. A Y1 - 2019 A1 - Davide Riccobelli A1 - A. Agosti A1 - Pasquale Ciarletta PB - The Royal Society VL - 377 ER - TY - JOUR T1 - Isomonodromy deformations at an irregular singularity with coalescing eigenvalues JF - Duke Math. J. Y1 - 2019 A1 - Giordano Cotti A1 - Boris Dubrovin A1 - Davide Guzzetti AB -We consider an n×n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=∞, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=∞ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=∞ is a resonant irregular singularity for t∈Δ. We analyse the case when the leading matrix remains diagonalisable at Δ. We discuss the existence of fundamental matrix solutions, their asymptotics, Stokes phenomenon and monodromy data as t varies in the polydisc, and their limits for t tending to points of Δ. When the deformation is isomonodromic away from Δ, it is well known that a fundamental matrix solution has singularities at Δ. When the system also has a Fuchsian singularity at z=0, we show under minimal vanishing conditions on the residue matrix at z=0 that isomonodromic deformations can be extended to the whole polydisc, including Δ, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisc. These data can be computed just by considering the system at fixed t=0. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisc not intersecting Δ, if the entries of the Stokes matrices with indices corresponding to coalescing eigenvalues vanish, then we show that Δ is not a branching locus for the fundamental matrix solutions. The importance of these results for the analytic theory of Frobenius Manifolds is explained. An application to Painlev\'e equations is discussed.

PB - Duke University Press VL - 168 UR - https://doi.org/10.1215/00127094-2018-0059 ER - TY - RPRT T1 - Canonical Surfaces and Hypersurfaces in Abelian Varieties Y1 - 2018 A1 - Luca Cesarano UR - https://arxiv.org/abs/1808.05302 ER - TY - JOUR T1 - Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue JF - Mathematical Models and Methods in Applied Sciences Y1 - 2018 A1 - Vito Crismale A1 - Giuliano Lazzaroni A1 - Gianluca Orlando AB -In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

VL - 28 UR - https://doi.org/10.1142/S0218202518500379 ER - TY - CHAP T1 - Computational methods in cardiovascular mechanics T2 - Cardiovascular Mechanics Y1 - 2018 A1 - Auricchio, Ferdinando A1 - Conti, Michele A1 - Lefieux, Adrian A1 - Morganti, Simone A1 - Alessandro Reali A1 - Gianluigi Rozza A1 - Veneziani, Alessandro ED - Michel F. Labrosse AB -The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

JF - Cardiovascular Mechanics PB - CRC Press UR - https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-5 ER - TY - RPRT T1 - Energy-dissipation balance of a smooth moving crack Y1 - 2018 A1 - Maicol Caponi A1 - Ilaria Lucardesi A1 - Emanuele Tasso AB - In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures. UR - http://preprints.sissa.it/handle/1963/35320 U1 - 35630 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Existence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation Y1 - 2018 A1 - Maicol Caponi AB - We propose a phase-field model of dynamic crack propagation based on the Ambrosio-Tortorelli approximation, which takes in account dissipative effects due to the speed of the crack tips. In particular, adapting the time discretization scheme contained in [Bourdin et al., Int. J. Fracture 168 (2011), 133-143] and [Larsen et al., Math. Models Methods Appl. Sci. 20 (2010), 1021-1048], we show the existence of a dynamic crack evolution satisfying an energy dissipation balance, according to Griffith's criterion. UR - http://preprints.sissa.it/handle/1963/35307 U1 - 35614 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - On Krylov solutions to infinite-dimensional inverse linear problems Y1 - 2018 A1 - Noe Caruso A1 - Alessandro Michelangeli A1 - Paolo Novati AB - We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35327 U1 - 35638 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Local moduli of semisimple Frobenius coalescent structures Y1 - 2018 A1 - Giordano Cotti A1 - Boris Dubrovin A1 - Davide Guzzetti AB -There is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.

PB - SISSA UR - http://preprints.sissa.it/handle/1963/35304 U1 - 35610 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - JOUR T1 - Morpho-elastic model of the tortuous tumour vessels JF - Int. J. Non-Linear Mech. Y1 - 2018 A1 - Davide Riccobelli A1 - Pasquale Ciarletta PB - Elsevier BV VL - 107 ER - TY - JOUR T1 - Noncommutative Painlevé Equations and Systems of Calogero Type JF - Comm. Math. Phys Y1 - 2018 A1 - Marco Bertola A1 - Mattia Cafasso A1 - V. Rubtsov ER - TY - RPRT T1 - Observables in the equivariant A-model Y1 - 2018 A1 - Bonechi, F. A1 - Cattaneo, A.S. A1 - Riccardo Iraso A1 - Maxim Zabzine UR - https://arxiv.org/abs/1807.08659 ER - TY - JOUR T1 - Shape transitions in a soft incompressible sphere with residual stresses JF - Math. Mech. Solids Y1 - 2018 A1 - Davide Riccobelli A1 - Pasquale Ciarletta PB - SAGE Publications Sage UK: London, England VL - 23 ER - TY - RPRT T1 - Stochastic homogenisation of free-discontinuity problems Y1 - 2018 A1 - Filippo Cagnetti A1 - Gianni Dal Maso A1 - Lucia Scardia A1 - Caterina Ida Zeppieri AB - In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas. UR - http://preprints.sissa.it/handle/1963/35309 U1 - 35617 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Truncation and convergence issues for bounded linear inverse problems in Hilbert space Y1 - 2018 A1 - Noe Caruso A1 - Alessandro Michelangeli A1 - Paolo Novati AB - We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35326 U1 - 35637 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Analytic geometry of semisimple coalescent Frobenius structures JF - Random Matrices: Theory and Applications Y1 - 2017 A1 - Giordano Cotti A1 - Davide Guzzetti AB -We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop “Asymptotic and Computational Aspects of Complex Differential Equations” at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians.

VL - 06 UR - https://doi.org/10.1142/S2010326317400044 ER - TY - RPRT T1 - Complex Friedrichs systems and applications Y1 - 2017 A1 - Nenad Antonić A1 - Krešimir Burazin A1 - Ivana Crnjac A1 - Marko Erceg AB - We provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper. UR - http://urania.sissa.it/xmlui/handle/1963/35270 U1 - 35576 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Gamma-Convergence of Free-discontinuity problems Y1 - 2017 A1 - Filippo Cagnetti A1 - Gianni Dal Maso A1 - Lucia Scardia A1 - Caterina Ida Zeppieri AB - We study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35276 U1 - 35583 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Globally stable quasistatic evolution for strain gradient plasticity coupled with damage JF - Annali di Matematica Pura ed Applicata (1923 -) Y1 - 2017 A1 - Vito Crismale AB -We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin–Anand formulation (J Mech Phys Solids 53:1624–1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material's degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).

VL - 196 UR - https://doi.org/10.1007/s10231-016-0590-7 ER - TY - JOUR T1 - The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon JF - Comm. Math. Phys Y1 - 2017 A1 - Marco Bertola A1 - Mattia Cafasso VL - DOI 10.1007/s00220-017-2856-3 UR - http://arxiv.org/abs/1603.06420 ER - TY - RPRT T1 - Linear hyperbolic systems in domains with growing cracks Y1 - 2017 A1 - Maicol Caponi AB - We consider the hyperbolic system $\ddot u-{\rm div}\,(\mathbb A\nabla u)=f$ in the time varying cracked domain $\Omega\setminus\Gamma_t$, where the set $\Omega\subset\mathbb R^d$ is open, bounded, and with Lipschitz boundary, the cracks $\Gamma_t$, $t\in[0,T]$, are closed subsets of $\overline\Omega$, increasing with respect to inclusion, and $u(t):\Omega\setminus\Gamma_t\to\mathbb R^d$ for every $t\in[0,T]$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system $\ddot v-{\rm div}\,(\mathbb B\nabla v)+\mathbf a\nabla v -2\nabla\dot vb=g$ on the fixed domain $\Omega\setminus\Gamma_0$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions $v$, which allows us to prove a continuous dependence result for both systems. UR - http://urania.sissa.it/xmlui/handle/1963/35271 U1 - 35577 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Model Reduction Methods T2 - Encyclopedia of Computational Mechanics Second Edition Y1 - 2017 A1 - Francisco Chinesta A1 - Antonio Huerta A1 - Gianluigi Rozza A1 - Karen Willcox AB -This chapter presents an overview of model order reduction – a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control – critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1&isAllowed=y

JF - Encyclopedia of Computational Mechanics Second Edition PB - John Wiley & Sons ER - TY - JOUR T1 - Quasistatic crack growth based on viscous approximation: a model with branching and kinking JF - Nonlinear Differential Equations and Applications NoDEA Y1 - 2017 A1 - Vito Crismale A1 - Giuliano Lazzaroni AB -Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.

VL - 24 UR - https://doi.org/10.1007/s00030-016-0426-6 ER - TY - JOUR T1 - Rayleigh–Taylor instability in soft elastic layers JF - Phil. Trans. R. Soc. A Y1 - 2017 A1 - Davide Riccobelli A1 - Pasquale Ciarletta PB - The Royal Society VL - 375 ER - TY - JOUR T1 - Reduced Basis Methods for Uncertainty Quantification JF - SIAM/ASA Journal on Uncertainty Quantification Y1 - 2017 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB -In this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuška, F. Nobile, and R. Tempone, *SIAM Rev.*, 52 (2010), pp. 317--355]. We demonstrate its computational efficiency and accuracy for a benchmark problem with parameters ranging from a few to a few hundred dimensions. Generalizations to more complex models and applications to uncertainty quantification problems in risk prediction, evaluation of statistical moments, Bayesian inversion, and optimal control under uncertainty are also presented to illustrate how to use the reduced basis method in practice. Further challenges, advancements, and research opportunities are outlined.

Read More: http://epubs.siam.org/doi/abs/10.1137/151004550

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

JF - Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering, PB - ECCOMAS CY - Crete, Greece U1 - 35466 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers Y1 - 2016 A1 - Giordano Cotti ER - TY - JOUR T1 - Comparing Poisson Sigma Model with A-model JF - Journal of High Energy Physics Y1 - 2016 A1 - Bonechi, F. A1 - Cattaneo, A.S. A1 - Riccardo Iraso AB -We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

VL - 2016 UR - https://doi.org/10.1007/JHEP10(2016)133 ER - TY - RPRT T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna UR - http://urania.sissa.it/xmlui/handle/1963/35197 U1 - 35494 U2 - Mathematics ER - TY - JOUR T1 - Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I JF - Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 Y1 - 2016 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35207 U1 - 35507 U2 - Mathematics ER - TY - JOUR T1 - Globally stable quasistatic evolution for a coupled elastoplastic–damage model JF - ESAIM: Control, Optimisation and Calculus of Variations Y1 - 2016 A1 - Vito Crismale AB -We show the existence of globally stable quasistatic evolutions for a rate-independent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

PB - EDP Sciences VL - 22 UR - https://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html ER - TY - CHAP T1 - Model Order Reduction: a survey T2 - Wiley Encyclopedia of Computational Mechanics, 2016 Y1 - 2016 A1 - Francisco Chinesta A1 - Antonio Huerta A1 - Gianluigi Rozza A1 - Karen Willcox JF - Wiley Encyclopedia of Computational Mechanics, 2016 PB - Wiley UR - http://urania.sissa.it/xmlui/handle/1963/35194 U1 - 35470 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Motion planning and motility maps for flagellar microswimmers JF - The European Physical Journal E Y1 - 2016 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone AB -We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

VL - 39 UR - https://doi.org/10.1140/epje/i2016-16072-y ER - TY - JOUR T1 - A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel JF - Annals of Nuclear Energy, 87, 2 (2016): pp. 198-208 Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings. In order to address the potential of such approach, two different kinds of varying parameters have been considered, namely one related to a geometric quantity (i.e., the inner radius of the fuel pellet) and one related to a physical quantity (i.e., the inlet lead velocity). The capabilities of the presented reduced order model (ROM) have been tested and compared with a high-fidelity finite element model (upon which the ROM has been constructed) on different aspects. In particular, the comparison focused on the system reactivity prediction (with and without thermal feedbacks on neutronics), the neutron flux and temperature field reconstruction, and on the computational time. The outcomes provided by the reduced order model are in good agreement with the high-fidelity finite element ones, and a computational speed-up of at least three orders of magnitude is achieved as well. PB - Elsevier VL - 87 UR - http://urania.sissa.it/xmlui/handle/1963/35191 U1 - 35471 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - CHAP T1 - Pimsner Algebras and Circle Bundles T2 - Noncommutative Analysis, Operator Theory and Applications Y1 - 2016 A1 - Francesca Arici A1 - Francesco D'Andrea A1 - Giovanni Landi ED - Alpay, Daniel ED - Cipriani, Fabio ED - Colombo, Fabrizio ED - Guido, Daniele ED - Sabadini, Irene ED - Sauvageot, Jean-Luc AB -We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

JF - Noncommutative Analysis, Operator Theory and Applications PB - Springer International Publishing CY - Cham SN - 978-3-319-29116-1 UR - https://doi.org/10.1007/978-3-319-29116-1_1 ER - TY - JOUR T1 - POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations Y1 - 2016 A1 - Stefano Lorenzi A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - Numerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods. PB - Computer Methods in Applied Mechanics and Engineering, Elsevier U1 - 35502 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods JF - NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB - This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased. PB - ASME VL - 2 UR - http://urania.sissa.it/xmlui/handle/1963/35192 IS - 2 N1 - 8 pages U1 - 35473 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods JF - Communications in Computational Physics Y1 - 2016 A1 - Alberto Sartori A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB -In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a “staircase” strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as “truth” solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine “truth” finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.

PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34963 IS - in press U1 - 35188 U2 - Mathematics ER - TY - THES T1 - Some results on quasistatic evolution problems for unidirectional processes Y1 - 2016 A1 - Vito Crismale PB - SISSA U1 - 35522 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - On the third critical speed for rotating Bose-Einstein condensates JF - Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 Y1 - 2016 A1 - Daniele Dimonte A1 - Michele Correggi AB - We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε−4, with ε−2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer. PB - AIP Publisher UR - http://urania.sissa.it/xmlui/handle/1963/35246 U1 - 35557 U2 - Mathematics ER - TY - JOUR T1 - Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model JF - Calculus of Variations and Partial Differential Equations Y1 - 2016 A1 - Vito Crismale A1 - Giuliano Lazzaroni AB -Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.

VL - 55 UR - https://doi.org/10.1007/s00526-015-0947-6 ER - TY - JOUR T1 - Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems JF - Computers and Mathematics with Applications 69 (2015) 1167–1188 Y1 - 2015 A1 - Roy Saswati A1 - Luca Heltai A1 - Francesco Costanzo AB - We present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks. U1 - 34633 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - A class of Hamiltonians for a three-particle fermionic system at unitarity Y1 - 2015 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide. UR - http://urania.sissa.it/xmlui/handle/1963/34469 N1 - This SISSA preprint is composed of 29 pages and is recorded in PDF format U1 - 34644 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Dispersive deformations of the Hamiltonian structure of Euler's equations Y1 - 2015 A1 - Matteo Casati AB - Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson brackets of 2d hydrodynamics of ideal fluids as a reduction from the one associated to the full algebra of vector fields. Motivated by some recent results about the deformations of Lie-Poisson brackets of vector fields, we study the dispersive deformations of the Poisson brackets of Euler's equation and show that, up to the second order, they are trivial. U1 - 34700 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - CONF T1 - Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures T2 - International Conference on Parallel Processing and Applied Mathematics Y1 - 2015 A1 - Calore, Enrico A1 - Nicola Demo A1 - Schifano, Sebastiano Fabio A1 - Tripiccione, Raffaele JF - International Conference on Parallel Processing and Applied Mathematics PB - Springer ER - TY - THES T1 - Mathematical Models of Locomotion: Legged Crawling, Snake-like Motility, and Flagellar Swimming Y1 - 2015 A1 - Giancarlo Cicconofri KW - Motility PB - SISSA U1 - 34743 U2 - Mathematics U4 - 1 U5 - FIS/02 ER - TY - JOUR T1 - Motility of a model bristle-bot: A theoretical analysis JF - International Journal of Non-Linear Mechanics Y1 - 2015 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone KW - Bristle-robots KW - Crawling motility KW - Frictional interactions AB -Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

VL - 76 UR - http://www.sciencedirect.com/science/article/pii/S0020746215000025 ER - TY - THES T1 - Multidimensional Poisson Vertex Algebras and Poisson cohomology of Hamiltonian operators of hydrodynamic type Y1 - 2015 A1 - Matteo Casati KW - Poisson Vertex Algebras, Poisson brackets, Hamiltonian operators, Integrable Systems AB - The Poisson brackets of hydrodynamic type, also called Dubrovin-Novikov brackets, constitute the Hamiltonian structure of a broad class of evolutionary PDEs, that are ubiquitous in the theory of Integrable Systems, ranging from Hopf equation to the principal hierarchy of a Frobenius manifold. They can be regarded as an analogue of the classical Poisson brackets, defined on an infinite dimensional space of maps Σ → M between two manifolds. Our main problem is the study of Poisson-Lichnerowicz cohomology of such space when dim Σ > 1. We introduce the notion of multidimensional Poisson Vertex Algebras, generalizing and adapting the theory by A. Barakat, A. De Sole, and V. Kac [Poisson Vertex Algebras in the theory of Hamiltonian equations, 2009]; within this framework we explicitly compute the first nontrivial cohomology groups for an arbitrary Poisson bracket of hydrodynamic type, in the case dim Σ = dim M = 2. For the case of the so-called scalar brackets, namely the ones for which dim M = 1, we give a complete description on their Poisson–Lichnerowicz cohomology. From this computations it follows, already in the particular case dim Σ = 2, that the cohomology is infinite dimensional. PB - SISSA N1 - 161 pages U1 - 34902 U2 - Mathematics U4 - 1 U5 - MAT/07 ER - TY - JOUR T1 - Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations JF - Numerische Mathematik, (2015), 36 p. Article in Press Y1 - 2015 A1 - Gianluigi Rozza A1 - Peng Chen A1 - Alfio Quarteroni AB - In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve. In order to reduce the unaffordable computational effort, we propose a reduced basis method using a multilevel greedy algorithm in combination with isotropic and anisotropic sparse-grid techniques. A weighted a posteriori error bound highlights the contribution stemming from each method. Numerical tests on stochastic dimensions ranging from 10 to 100 demonstrate that our method is very efficient, especially for solving high-dimensional and large-scale optimization problems. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34491 U1 - 34680 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - RPRT T1 - Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets Y1 - 2015 A1 - Guido Carlet A1 - Matteo Casati A1 - Sergey Shadrin AB - We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial. U1 - 35389 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - JOUR T1 - A study of snake-like locomotion through the analysis of a flexible robot model JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2015 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone AB -We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

VL - 471 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 ER - TY - JOUR T1 - An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds Y1 - 2014 A1 - Massimiliano Berti A1 - Livia Corsi A1 - Michela Procesi AB - We prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34651 U1 - 34858 U2 - Mathematics ER - TY - JOUR T1 - Comparison between reduced basis and stochastic collocation methods for elliptic problems Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - The stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34727 U1 - 34916 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics JF - Annals of Nuclear Energy Y1 - 2014 A1 - Alberto Sartori A1 - Davide Baroli A1 - Antonio Cammi A1 - Davide Chiesa A1 - Lelio Luzzi A1 - Roberto R. Ponciroli A1 - Ezio Previtali A1 - Marco E. Ricotti A1 - Gianluigi Rozza A1 - Monica Sisti AB -In this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

PB - Elsevier VL - 71 UR - http://urania.sissa.it/xmlui/handle/1963/35039 U1 - 35270 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription Y1 - 2014 A1 - Rod R. Gover A1 - Yaiza Canzani A1 - Dmitry Jakobson A1 - Raphaël Ponge A1 - Andrea Malchiodi AB - In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures. PB - Oxford University Press UR - http://urania.sissa.it/xmlui/handle/1963/35128 U1 - 35366 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Darboux Transformations and Random Point Processes JF - IMRN Y1 - 2014 A1 - Marco Bertola A1 - Mattia Cafasso VL - rnu122 ER - TY - JOUR T1 - Editorial Y1 - 2014 A1 - Ciro Ciliberto A1 - Gianni Dal Maso A1 - Pasquale Vetro PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34712 U1 - 34926 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - An effective model for nematic liquid crystal composites with ferromagnetic inclusions Y1 - 2014 A1 - Maria Carme Calderer A1 - Antonio DeSimone A1 - Dmitry Golovaty A1 - Alexander Panchenko AB - Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature. PB - Society for Industrial and Applied Mathematics Publications UR - http://urania.sissa.it/xmlui/handle/1963/34940 U1 - 35194 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Local and global minimality results for a nonlocal isoperimetric problem on R^N JF - SIAM Journal on Mathematical Analysis Y1 - 2014 A1 - Marco Bonacini A1 - Riccardo Cristoferi KW - Nonlocal isoperimetric problem AB -We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

PB - SIAM Publications VL - 46 UR - http://hdl.handle.net/1963/6984 IS - 4 U1 - 6976 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - On the Lp-differentiability of certain classes of functions Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa AB - We prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation. PB - European Mathematical Society UR - http://urania.sissa.it/xmlui/handle/1963/34695 U1 - 34909 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - Generic T1 - A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics T2 - 22nd International Conference on Nuclear Engineering ICONE22 Y1 - 2014 A1 - Alberto Sartori A1 - Davide Baroli A1 - Antonio Cammi A1 - Lelio Luzzi A1 - Gianluigi Rozza AB -In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity "truth" finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the "truth" model.

JF - 22nd International Conference on Nuclear Engineering ICONE22 PB - American Society of Mechanical Engineers (ASME) CY - Prague, Czech Republic SN - 978-079184595-0 UR - http://urania.sissa.it/xmlui/handle/1963/35123 N1 - 2014 22nd International Conference on Nuclear Engineering, ICONE 2014; Prague; Czech Republic; 7 July 2014 through 11 July 2014; Code 109131; U1 - 35360 U2 - Mathematics U4 - 1 ER - TY - CHAP T1 - Reduction on characteristics for continuous of a scalar balance law T2 - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Laura Caravenna KW - Method of characteristics JF - AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 PB - SISSA UR - http://hdl.handle.net/1963/6562 U1 - 6516 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Some remarks on the seismic behaviour of embedded cantilevered retaining walls Y1 - 2014 A1 - Riccardo Conti A1 - F. Burali D'Arezzo A1 - Giulia M.B. Viggiani AB - This paper is a numerical investigation of the physical phenomena that control the dynamic behaviour of embedded cantilevered retaining walls. Recent experimental observations obtained from centrifuge tests have shown that embedded cantilevered retaining walls experience permanent displacements even before the acceleration reaches its critical value, corresponding to full mobilisation of the soil strength. The motivation for this work stems from the need to incorporate these observations in simplified design procedures. A parametric study was carried out on a pair of embedded cantilevered walls in dry sand, subjected to real earthquakes scaled at different values of the maximum acceleration. The results of these analyses indicate that, for the geotechnical design of the wall, the equivalent acceleration to be used in pseudo-static calculations can be related to the maximum displacement that the structure can sustain, and can be larger than the maximum acceleration expected at the site. For the structural design of the wall, it is suggested that the maximum bending moments of the wall can be computed using a realistic distribution of contact stress and a conservative value of the pseudo-static acceleration, taking into account two-dimensional amplification effects near the walls. PB - Thomas Telford UR - http://urania.sissa.it/xmlui/handle/1963/35073 U1 - 35308 U2 - Physics U4 - 2 ER - TY - JOUR T1 - A uniqueness result for the continuity equation in two dimensions: dedicated to constantine dafermos on the occasion of his 70th birthday Y1 - 2014 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa AB - We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation ∂tu +div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence. PB - European Mathematical Society; Springer Verlag UR - http://urania.sissa.it/xmlui/handle/1963/34692 U1 - 34906 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A weighted empirical interpolation method: A priori convergence analysis and applications Y1 - 2014 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis is provided for the proposed method and the error bound by Kolmogorov N-width is improved from the recent work [Y. Maday, N.C. Nguyen, A.T. Patera and G.S.H. Pau, A general, multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2009) 383-404]. We apply our method to geometric Brownian motion, exponential Karhunen-Loève expansion and reduced basis approximation of non-affine stochastic elliptic equations. We demonstrate its improved accuracy and efficiency over the empirical interpolation method, as well as sparse grid stochastic collocation method. PB - EDP Sciences UR - http://urania.sissa.it/xmlui/handle/1963/35021 U1 - 35253 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Connected Sum Construction for σk-Yamabe Metrics JF - Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 Y1 - 2013 A1 - Giovanni Catino A1 - Lorenzo Mazzieri AB - In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation. PB - Springer UR - http://hdl.handle.net/1963/6441 N1 - This article has not yet been published. U1 - 6366 U2 - Mathematics U4 - -1 ER - TY - RPRT T1 - On deformations of multidimensional Poisson brackets of hydrodynamic type Y1 - 2013 A1 - Matteo Casati KW - Hamiltonian operator AB - The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consist of a pair $(\mathcal{A},\{\cdot_{\lambda}\cdot\})$ of a differential algebra $\mathcal{A}$ and a bilinear operation called the $\lambda$-bracket. We extend the definition to the class of algebras $\mathcal{A}$ endowed with $d\geq 1$ commuting derivations. We call this structure a multidimensional PVA: it is a suitable setting to the study of deformations of the Poisson bracket of hydrodynamic type associated to the Euler's equation of motion of $d$-dimensional incompressible fluids. We prove that for $d=2$ all the first order deformations of such class of Poisson brackets are trivial. PB - SISSA UR - http://hdl.handle.net/1963/7235 U1 - 7271 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Expanded degenerations and pairs JF - Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386 Y1 - 2013 A1 - Dan Abramovich A1 - Charles Cadman A1 - Barbara Fantechi A1 - Jonathan Wise KW - Expanded pairs AB - Since Jun Li's original definition, several other definitions of expanded pairs and expanded degenerations have appeared in the literature. We explain how these definitions are related and introduce several new variants and perspectives. Among these are the twisted expansions used by Abramovich and Fantechi as a basis for orbifold techniques in degeneation formulas. PB - Taylor and Francis UR - http://hdl.handle.net/1963/7383 N1 - This article is composed of 41 pages and is recorded in PDF format U1 - 7431 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation JF - Random Matrices: Theory and Applications Y1 - 2013 A1 - Marco Bertola A1 - Mattia Cafasso VL - 02 UR - http://www.worldscientific.com/doi/abs/10.1142/S2010326313500032 ER - TY - JOUR T1 - Genus stabilization for moduli of curves with symmetries Y1 - 2013 A1 - Fabrizio Catanese A1 - Michael Lönne A1 - Fabio Perroni KW - group actions KW - mapping class group KW - Moduli space of curves KW - Teichmüller space AB - In a previous paper, arXiv:1206.5498, we introduced a new homological\r\ninvariant $\\e$ for the faithful action of a finite group G on an algebraic\r\ncurve.\r\n We show here that the moduli space of curves admitting a faithful action of a\r\nfinite group G with a fixed homological invariant $\\e$, if the genus g\' of the\r\nquotient curve is sufficiently large, is irreducible (and non empty iff the\r\nclass satisfies the condition which we define as \'admissibility\'). In the\r\nunramified case, a similar result had been proven by Dunfield and Thurston\r\nusing the classical invariant in the second homology group of G, H_2(G, \\ZZ).\r\n We achieve our result showing that the stable classes are in bijection with\r\nthe set of admissible classes $\\e$. PB - SISSA UR - http://hdl.handle.net/1963/6509 N1 - 21 pages, 2 figures U1 - 6461 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces JF - Journal of Geometric Analysis Y1 - 2013 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Mario Sigalotti AB -Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot–Carathéodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

VL - 23 UR - https://doi.org/10.1007/s12220-011-9262-4 ER - TY - JOUR T1 - Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations JF - ESAIM: Mathematical Modelling and Numerical Analysis Y1 - 2013 A1 - Cacace, S. A1 - Antonin Chambolle A1 - Antonio DeSimone A1 - Livio Fedeli PB - EDP Sciences VL - 47 ER - TY - JOUR T1 - The Monge Problem for Distance Cost in Geodesic Spaces JF - Communications in Mathematical Physics Y1 - 2013 A1 - Stefano Bianchini A1 - Fabio Cavalletti AB -We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dLis a geodesic Borel distance which makes (X, dL) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by dL. It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting dL-cyclical monotonicity is not sufficient for optimality.

VL - 318 UR - https://doi.org/10.1007/s00220-013-1663-8 ER - TY - JOUR T1 - A note on non-homogeneous hyperbolic operators with low-regularity coefficients Y1 - 2013 A1 - Ferruccio Colombini A1 - Francesco Fanelli AB -In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

ER - TY - JOUR T1 - Stochastic optimal robin boundary control problems of advection-dominated elliptic equations JF - SIAM Journal on Numerical Analysis Y1 - 2013 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection field and consider a stochastic Robin boundary condition as control function. A stochastic saddle point system is formulated and proved to be equivalent to the first order optimality system for the optimal control problem, based on which we provide the existence and uniqueness of the optimal solution as well as some results on stochastic regularity with respect to the random variables. Stabilized finite element approximations in physical space and collocation approximations in stochastic space are applied to discretize the optimality system. A global error estimate in the product of physical space and stochastic space for the numerical approximation is derived. Illustrative numerical experiments are provided. VL - 51 ER - TY - JOUR T1 - A weighted reduced basis method for elliptic partial differential equations with random input data JF - SIAM Journal on Numerical Analysis Y1 - 2013 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems. VL - 51 ER - TY - JOUR T1 - On the behaviour of flexible retaining walls under seismic actions JF - Geotechnique, Volume 62, Issue 12, December 2012, Pages 1081-1094 Y1 - 2012 A1 - Riccardo Conti A1 - G.S.P. Madabhushi A1 - Giulia M.B. Viggiani KW - Centrifuge modelling AB - This paper describes an experimental investigation of the behaviour of embedded retaining walls under seismic actions. Nine centrifuge tests were carried out on reduced-scale models of pairs of retaining walls in dry sand, either cantilevered or with one level of props near the top. The experimental data indicate that, for maximum accelerations that are smaller than the critical limit equilibrium value, the retaining walls experience significant permanent displacements under increasing structural loads, whereas for larger accelerations the walls rotate under constant internal forces. The critical acceleration at which the walls start to rotate increases with increasing maximum acceleration. No significant displacements are measured if the current earthquake is less severe than earthquakes previously experienced by the wall. The increase of critical acceleration is explained in terms of redistribution of earth pressures and progressive mobilisation of the passive strength in front of the wall. The experimental data for cantilevered retaining walls indicate that the permanent displacements of the wall can be reasonably predicted adopting a Newmark-type calculation with a critical acceleration that is a fraction of the limit equilibrium value. PB - ICE Publishing UR - http://hdl.handle.net/1963/6933 U1 - 6912 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. JF - Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 Y1 - 2012 A1 - Andrea Malchiodi A1 - Paul Yang A1 - Jih-Hsin Cheng A1 - JennFang Hwang AB - In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1 PB - SISSA UR - http://hdl.handle.net/1963/6556 U1 - 6490 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis JF - Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 Y1 - 2012 A1 - Q Beg A1 - Mattia Zampieri A1 - N Klitgord A1 - S Collins A1 - M Serres A1 - Daniel Segrè A1 - Claudio Altafini AB - The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems PB - SISSA UR - http://hdl.handle.net/1963/6506 U1 - 6452 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation JF - Comm. Math. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Mattia Cafasso VL - 309 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x ER - TY - RPRT T1 - A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library Y1 - 2012 A1 - Luca Heltai A1 - Saswati Roy A1 - Francesco Costanzo KW - Finite Element Method KW - Immersed Boundary Method KW - Immersed Finite Element Method AB - We present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method. PB - SISSA UR - http://hdl.handle.net/1963/6255 N1 - 28 pages, 9 figures U1 - 6172 U2 - Mathematics U3 - Functional Analysis and Applications U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment JF - Nanoscale. 2012 Mar; 4(5):1734-41 Y1 - 2012 A1 - Alessandro Bosco A1 - Fouzia Bano A1 - Pietro Parisse A1 - Loredana Casalis A1 - Antonio DeSimone A1 - Cristian Micheletti AB - Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters. PB - Royal Society of Chemistry U1 - 6998 U2 - Physics U4 - -1 ER - TY - JOUR T1 - The KdV hierarchy: universality and a Painleve transcendent JF - International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 Y1 - 2012 A1 - Tom Claeys A1 - Tamara Grava KW - Small-Dispersion limit AB - We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the solution to the hyperbolic transport equation which corresponds to $\e=0$. Near the time of gradient catastrophe for the transport equation, we show that the solution to the KdV hierarchy is approximated by a particular Painlev\'e transcendent. This supports Dubrovins universality conjecture concerning the critical behavior of Hamiltonian perturbations of hyperbolic equations. We use the Riemann-Hilbert approach to prove our results. PB - Oxford University Press UR - http://hdl.handle.net/1963/6921 N1 - This article was published in "International Mathematics Research Notices, vol. 22 (2012) , page 5063-5099 U1 - 6902 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - The Monge problem in Wiener space JF - Calculus of Variations and Partial Differential Equations Y1 - 2012 A1 - Fabio Cavalletti AB -We address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure γ.

VL - 45 UR - https://doi.org/10.1007/s00526-011-0452-5 ER - TY - JOUR T1 - Numerical modelling of installation effects for diaphragm walls in sand JF - Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237 Y1 - 2012 A1 - Riccardo Conti A1 - Luca de Sanctis A1 - Giulia M.B. Viggiani KW - Constitutive relations AB - The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic. PB - Springer UR - http://hdl.handle.net/1963/6934 U1 - 6916 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Optimal Transport with Branching Distance Costs and the Obstacle Problem JF - SIAM Journal on Mathematical Analysis Y1 - 2012 A1 - Fabio Cavalletti VL - 44 UR - https://doi.org/10.1137/100801433 ER - TY - JOUR T1 - Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases JF - Physica D: Nonlinear Phenomena Y1 - 2012 A1 - Marco Bertola A1 - Mattia Cafasso KW - Integrable kernels VL - 241 UR - http://www.sciencedirect.com/science/article/pii/S0167278912000115 N1 - Integrable Systems in Pure and Applied Mathematics ER - TY - JOUR T1 - SBV regularity for genuinely nonlinear, strictly hyperbolic systems of conservation laws in one space dimension JF - Communications in Mathematical Physics 313 (2012) 1-33 Y1 - 2012 A1 - Stefano Bianchini A1 - Laura Caravenna PB - Springer UR - http://hdl.handle.net/1963/4091 U1 - 313 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Simulation-based uncertainty quantification of human arterial network hemodynamics JF - International Journal Numerical Methods Biomedical Engineering Y1 - 2012 A1 - Peng Chen A1 - Alfio Quarteroni A1 - Gianluigi Rozza KW - uncertainty quantification, mathematical modelling of the cardiovascular system, fluid-structure interaction AB - This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular\r\nsystem based on stochastic simulation of a one dimensional arterial network. A general analysis of\r\ndifferent uncertainties and probability characterization with log-normal distribution of these uncertainties\r\nis introduced. Deriving from a deterministic one dimensional fluid structure interaction model, we establish\r\nthe stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe\r\nthe blood flow and pressure wave propagation in the arterial network. By applying a stochastic collocation\r\nmethod with sparse grid technique, we study systemically the statistics and sensitivity of the solution with\r\nrespect to many different uncertainties in a relatively complete arterial network with potential physiological\r\nand pathological implications for the first time. PB - Wiley U1 - 6467 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions JF - Rev. Math. Phys. 24 (2012), 1250017 Y1 - 2012 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Domenico Finco A1 - Alessandro Michelangeli A1 - Alessandro Teta AB - We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs. PB - World Scientific UR - http://hdl.handle.net/1963/6069 U1 - 5955 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Variational implementation of immersed finite element methods JF - Computer Methods in Applied Mechanics and Engineering. Volume 229-232, 1 July 2012, Pages 110-127 Y1 - 2012 A1 - Luca Heltai A1 - Francesco Costanzo KW - Turbulent flow AB -Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

PB - Elsevier UR - http://hdl.handle.net/1963/6462 N1 - 42 pages, 5 figures, Revision 1 U1 - 6389 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Weighted barycentric sets and singular Liouville equations on compact surfaces JF - Journal of Functional Analysis 262 (2012) 409-450 Y1 - 2012 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - Given a closed two dimensional manifold, we prove a general existence result\\r\\nfor a class of elliptic PDEs with exponential nonlinearities and negative Dirac\\r\\ndeltas on the right-hand side, extending a theory recently obtained for the\\r\\nregular case. This is done by global methods: since the associated Euler\\r\\nfunctional is in general unbounded from below, we need to define a new model\\r\\nspace, generalizing the so-called space of formal barycenters and\\r\\ncharacterizing (up to homotopy equivalence) its very low sublevels. As a\\r\\nresult, the analytic problem is reduced to a topological one concerning the\\r\\ncontractibility of this model space. To this aim, we prove a new functional\\r\\ninequality in the spirit of [16] and then we employ a min-max scheme based on a cone-style construction, jointly with the blow-up analysis given in [5] (after\\r\\n[6] and [8]). This study is motivated by abelian Chern- Simons theory in\\r\\nself-dual regime, or from the problem of prescribing the Gaussian curvature in\\r\\npresence of conical singularities (hence generalizing a problem raised by\\r\\nKazdan and Warner in [26]). PB - Elsevier UR - http://hdl.handle.net/1963/5218 U1 - 5040 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - A class of existence results for the singular Liouville equation JF - Comptes Rendus Mathematique 349 (2011) 161-166 Y1 - 2011 A1 - Alessandro Carlotto A1 - Andrea Malchiodi AB - We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional. PB - Elsevier UR - http://hdl.handle.net/1963/5793 U1 - 5648 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Cones of divisors of blow-ups of projective spaces JF - Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 Y1 - 2011 A1 - Alessio Lo Giudice A1 - Salvatore Cacciola A1 - M. Donten-Bury A1 - O. Dumitrescu A1 - J. Park KW - Mori dream space AB - We investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points. PB - Università degli Studi di Catania. Dipartimento di matematica UR - http://hdl.handle.net/1963/6613 U1 - 6462 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions JF - PNAS 108 (2011) 13978 Y1 - 2011 A1 - Luca Cardamone A1 - Alessandro Laio A1 - Rajesh Shahapure A1 - Antonio DeSimone PB - National Academy of Sciences UR - http://hdl.handle.net/1963/4358 U1 - 4066 U2 - Physics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems JF - Matematische Annalen 349 (2011) 75-115 Y1 - 2011 A1 - Guido Carlet A1 - Boris Dubrovin A1 - Luca Philippe Mertens AB - We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold. PB - Springer UR - http://hdl.handle.net/1963/3584 U1 - 716 U2 - Mathematics U3 - Mathematical Physics ER - TY - CONF T1 - The Monge Problem in Geodesic Spaces T2 - Nonlinear Conservation Laws and Applications Y1 - 2011 A1 - Stefano Bianchini A1 - Fabio Cavalletti ED - Alberto Bressan ED - Chen, Gui-Qiang G. ED - Marta Lewicka ED - Wang, Dehua AB -We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on each geodesic are continuous. It is known that this regularity is sufficient for the construction of an optimal transport map.

JF - Nonlinear Conservation Laws and Applications PB - Springer US CY - Boston, MA SN - 978-1-4419-9554-4 ER - TY - JOUR T1 - A proof of Sudakov theorem with strictly convex norms JF - Mathematische Zeitschrift 268 (2011) 371-407 Y1 - 2011 A1 - Laura Caravenna AB - We establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem. PB - Springer UR - http://hdl.handle.net/1963/2967 U1 - 1733 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications JF - Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 Y1 - 2011 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. UR - http://hdl.handle.net/1963/4065 U1 - 337 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach JF - ESAIM: COCV 17 (2011) 1-27 Y1 - 2011 A1 - Filippo Cagnetti A1 - Rodica Toader AB - A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [6] is recovered. In this case, the convergence of the discrete time approximations is improved. PB - Cambridge University Press / EDP Sciences UR - http://hdl.handle.net/1963/2355 U1 - 1662 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Singular perturbation models in phase transitions for second order materials JF - Indiana Univ. Math. J. 60 (2011) 367-409 Y1 - 2011 A1 - Milena Chermisi A1 - Gianni Dal Maso A1 - Irene Fonseca A1 - Giovanni Leoni AB - A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained. PB - Indiana University UR - http://hdl.handle.net/1963/3858 U1 - 851 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry JF - Journal of Dynamical and Control Systems Y1 - 2011 A1 - Bernard Bonnard A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Gabriel Janin AB -We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

PB - Springer VL - 17 UR - http://hdl.handle.net/1963/4914 U1 - 4692 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Structure of level sets and Sard-type properties of Lipschitz maps Y1 - 2011 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa PB - SISSA UR - http://hdl.handle.net/1963/4657 U1 - 4424 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - The Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach JF - International Mathematics Research Notices Y1 - 2011 A1 - Marco Bertola A1 - Mattia Cafasso VL - doi: 10.1093/imrn/rnr066 ER - TY - RPRT T1 - A uniqueness result for the continuity equation in two dimensions Y1 - 2011 A1 - Giovanni Alberti A1 - Stefano Bianchini A1 - Gianluca Crippa PB - SISSA UR - http://hdl.handle.net/1963/4663 U1 - 4425 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - The disintegration of the Lebesgue measure on the faces of a convex function JF - J. Funct. Anal. 258 (2010) 3604-3661 Y1 - 2010 A1 - Laura Caravenna A1 - Sara Daneri AB -We consider the disintegration of the Lebesgue measure on the graph of a convex function f:\\\\Rn-> \\\\R w.r.t. the partition into its faces, which are convex sets and therefore have a well defined linear dimension, and we prove that each conditional measure is equivalent to the k-dimensional Hausdorff measure of the k-dimensional face on which it is concentrated. The remarkable fact is that a priori the directions of the faces are just Borel and no Lipschitz regularity is known. Notwithstanding that, we also prove that a Green-Gauss formula for these directions holds on special sets.

UR - http://hdl.handle.net/1963/3622 U1 - 682 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Dynamics control by a time-varying feedback JF - Journal of Dynamical and Control Systems. Volume 16, Issue 2, April 2010, Pages :149-162 Y1 - 2010 A1 - Andrei A. Agrachev A1 - Marco Caponigro KW - Discrete-time dynamics AB - We consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable. PB - SISSA UR - http://hdl.handle.net/1963/6461 U1 - 6407 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs JF - J. Phys. A 43 (2010) 474014 Y1 - 2010 A1 - Gianfausto Dell'Antonio A1 - Emanuele Costa AB - We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph. PB - IOP Publishing UR - http://hdl.handle.net/1963/4106 U1 - 298 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Existence of planar curves minimizing length and curvature JF - Proc. Steklov Inst. Math. 270 (2010) 43-56 Y1 - 2010 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Francesco Rossi AB - In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional $\\\\int \\\\sqrt{1+K_\\\\gamma^2} ds$, depending both on length and curvature $K$. We fix starting and ending points as well as initial and final directions.\\nFor this functional we discuss the problem of existence of minimizers on various functional spaces. We find non-existence of minimizers in cases in which initial and final directions are considered with orientation. In this case, minimizing sequences of trajectories can converge to curves with angles.\\nWe instead prove existence of minimizers for the \\\"time-reparameterized\\\" functional $$\\\\int \\\\| \\\\dot\\\\gamma(t) \\\\|\\\\sqrt{1+K_\\\\ga^2} dt$$ for all boundary conditions if initial and final directions are considered regardless to orientation. In this case, minimizers can present cusps (at most two) but not angles. PB - Springer UR - http://hdl.handle.net/1963/4107 U1 - 297 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective JF - Systems and Control Letters, 59 (12):782-786, 2010 Y1 - 2010 A1 - Claudio Altafini A1 - Paola Cappellaro A1 - David Cory AB - In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated. PB - Elsevier UR - http://hdl.handle.net/1963/4384 U1 - 4132 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Gene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus. JF - The European journal of neuroscience. 2010 Oct; 32(8):1364-79 Y1 - 2010 A1 - Dario Motti A1 - Caroline Le Duigou A1 - Nicole Chemaly A1 - Lucia Wittner A1 - Dejan Lazarevic A1 - Helena Krmac A1 - Troels Torben Marstrand A1 - Eivind Valen A1 - Remo Sanges A1 - Elia Stupka A1 - Albin Sandelin A1 - Enrico Cherubini A1 - Stefano Gustincich A1 - Richard Miles AB -We report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

PB - Wiley UR - http://hdl.handle.net/1963/4480 U1 - 4244 U2 - Neuroscience U3 - Neurobiology U4 - -1 ER - TY - JOUR T1 - Homogeneous binary trees as ground states of quantum critical Hamiltonians JF - Phys. Rev. A 81 (2010) 062335 Y1 - 2010 A1 - Pietro Silvi A1 - Vittorio Giovannetti A1 - Simone Montangero A1 - Matteo Rizzi A1 - J. Ignacio Cirac A1 - Rosario Fazio AB -Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

PB - American Physical Society UR - http://hdl.handle.net/1963/3909 U1 - 800 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - A kinetic mechanism inducing oscillations in simple chemical reactions networks JF - Mathematical Biosciences and Engineering 7(2):301-312, 2010 Y1 - 2010 A1 - Julien Coatleven A1 - Claudio Altafini AB - It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/2393 U1 - 2304 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point JF - arXiv preprint arXiv:1008.5036 Y1 - 2010 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi ER - TY - JOUR T1 - On optimality of c-cyclically monotone transference plans JF - Comptes Rendus Mathematique 348 (2010) 613-618 Y1 - 2010 A1 - Stefano Bianchini A1 - Laura Caravenna AB - Abstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire. PB - Elsevier UR - http://hdl.handle.net/1963/4023 U1 - 379 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit JF - Comm. Pure Appl. Math. 63 (2010) 203-232 Y1 - 2010 A1 - Tom Claeys A1 - Tamara Grava AB - In the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach. PB - Wiley UR - http://hdl.handle.net/1963/3799 U1 - 527 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Positive solutions for some non-autonomous Schrödinger–Poisson systems JF - Journal of Differential Equations Y1 - 2010 A1 - Giovanna Cerami A1 - Giusi Vaira PB - Academic Press VL - 248 ER - TY - JOUR T1 - The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures JF - J. Phys. A 43 (2010) 045201 Y1 - 2010 A1 - Guido Carlet A1 - Paolo Lorenzoni A1 - Andrea Raimondo AB - We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov. PB - IOP Publishing UR - http://hdl.handle.net/1963/3846 U1 - 863 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit JF - SIAM J. Math. Anal. 42 (2010) 2132-2154 Y1 - 2010 A1 - Tamara Grava A1 - Tom Claeys AB - We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\\\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation. UR - http://hdl.handle.net/1963/3839 U1 - 488 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Two-dimensional almost-Riemannian structures with tangency points JF - Ann. Inst. H. Poincare Anal. Non Lineaire Y1 - 2010 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Mario Sigalotti AB -Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

PB - Elsevier VL - 27 UR - http://hdl.handle.net/1963/3870 U1 - 839 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Bubbles with prescribed mean curvature: the variational approach Y1 - 2009 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/3659 N1 - H-systems, prescribed mean curvature equation, blowup U1 - 646 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability of the discrete-spectrum Schrodinger equation driven by an external field JF - Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 Y1 - 2009 A1 - Thomas Chambrion A1 - Paolo Mason A1 - Mario Sigalotti A1 - Ugo Boscain AB - We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials. UR - http://hdl.handle.net/1963/2547 U1 - 1572 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability on the group of diffeomorphisms JF - Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Marco Caponigro AB - Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M. UR - http://hdl.handle.net/1963/3396 U1 - 936 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Differential geometry of curves in Lagrange Grassmannians with given Young diagram JF - Differential Geom. Appl. 27 (2009) 723-742 Y1 - 2009 A1 - Igor Zelenko A1 - Li Chengbo AB - Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure. The Pontryagin extremals of this optimal problem are integral curves of certain Hamiltonian system in the cotangent bundle. The dynamics of the fibers of the cotangent bundle w.r.t. this system along an extremal is described by certain curve in a Lagrange Grassmannian, called Jacobi curve of the extremal. Any symplectic invariant of the Jacobi curves produces the invariant of the original geometric structure. The basic characteristic of a curve in a Lagrange Grassmannian is its Young diagram. The number of boxes in its kth column is equal to the rank of the kth derivative of the curve (which is an appropriately defined linear mapping) at a generic point. We will describe the construction of the complete system of symplectic invariants for parameterized curves in a Lagrange Grassmannian with given Young diagram. It allows to develop in a unified way local differential geometry of very wide classes of geometric structures on manifolds, including both classical geometric structures such as Riemannian and Finslerian structures and less classical ones such as sub-Riemannian and sub-Finslerian structures, defined on nonholonomic distributions. PB - Elsevier UR - http://hdl.handle.net/1963/3819 U1 - 508 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers JF - Netw. Heterog. Media 4 (2009) 667-708 Y1 - 2009 A1 - Marco Cicalese A1 - Antonio DeSimone A1 - Caterina Ida Zeppieri AB - In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3788 U1 - 538 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - The Disintegration Theorem and Applications to Optimal Mass Transportation Y1 - 2009 A1 - Laura Caravenna PB - SISSA UR - http://hdl.handle.net/1963/5900 U1 - 5750 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Equivariant cohomology and localization for Lie algebroids JF - Funct. Anal. Appl. 43 (2009) 18-29 Y1 - 2009 A1 - Ugo Bruzzo A1 - Lucio Cirio A1 - Paolo Rossi A1 - Vladimir Rubtsov AB - Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula. SN - 978-981-270-377-4 UR - http://hdl.handle.net/1963/1724 U1 - 2427 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - An existence result for the Monge problem in R^n with norm cost Y1 - 2009 A1 - Laura Caravenna UR - http://hdl.handle.net/1963/3647 U1 - 657 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the extremality, uniqueness and optimality of transference plans JF - Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 Y1 - 2009 A1 - Stefano Bianchini A1 - Laura Caravenna AB - We consider the following standard problems appearing in optimal mass transportation theory: when a transference plan is extremal; when a transference plan is the unique transference plan concentrated on a set A,; when a transference plan is optimal. UR - http://hdl.handle.net/1963/3692 U1 - 613 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Jacobi Equations and Comparison Theorems for Corank 1 Sub-Riemannian structures with symmetries Y1 - 2009 A1 - Li Chengbo A1 - Igor Zelenko AB - The Jacobi curve of an extremal of optimal control problem is a curve in a Lagrangian Grassmannian defined up to a symplectic transformation and containing all information about the solutions of the Jacobi equations along this extremal. In our previous works we constructed the canonical\\nbundle of moving frames and the complete system of symplectic invariants, called curvature maps, for\\nparametrized curves in Lagrange Grassmannians satisfying very general assumptions. The structural\\nequation for a canonical moving frame of the Jacobi curve of an extremal can be interpreted as the\\nnormal form for the Jacobi equation along this extremal and the curvature maps can be seen as the\\n\\\"coefficients\\\"of this normal form. In the case of a Riemannian metric there is only one curvature map and it is naturally related to the Riemannian sectional curvature. In the present paper we study the curvature maps for a sub-Riemannian structure on a corank 1 distribution having an additional transversal infinitesimal symmetry. After the factorization by the integral foliation of this symmetry, such sub-Riemannian structure can be reduced to a Riemannian manifold equipped with a closed 2-form(a magnetic field). We obtain explicit expressions for the curvature maps of the original sub-Riemannian structure in terms of the curvature tensor of this Riemannian manifold and the magnetic field. We also estimate the number of conjugate points along the sub-Riemannian extremals in terms of the bounds for the curvature tensor of this Riemannian manifold and the magnetic field in the case of an uniform magnetic field. The language developed for the calculation of the curvature maps can be applied to more general sub-Riemannian structures with symmetries, including sub-Riemmannian structures appearing naturally in Yang-Mills fields. UR - http://hdl.handle.net/1963/3736 U1 - 581 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Strain-order coupling in nematic elastomers: equilibrium configurations JF - Math. Models Methods Appl. Sci. 19 (2009) 601-630 Y1 - 2009 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations. UR - http://hdl.handle.net/1963/2700 U1 - 1400 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach JF - Comm. Math. Phys. 286 (2009) 979-1009 Y1 - 2009 A1 - Tamara Grava A1 - Tom Claeys AB - We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation.\\nThe sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit. UR - http://hdl.handle.net/1963/2636 U1 - 1487 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - An entropy based Glimm-type functional JF - J. Hyperbolic Differ. Equ. 5 (2008) 643-662 Y1 - 2008 A1 - Laura Caravenna PB - World Scientific UR - http://hdl.handle.net/1963/4051 U1 - 351 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices JF - Phys. Rev. B 77 (2008) 245105 Y1 - 2008 A1 - Matteo Rizzi A1 - Marco Polini A1 - Miguel A. Cazalilla A1 - M.R. Bakhtiari A1 - Mario P. Tosi A1 - Rosario Fazio AB -Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

UR - http://hdl.handle.net/1963/2694 U1 - 1406 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Limit Time Optimal Syntheses for a control-affine system on S² JF - SIAM J. Control Optim. 47 (2008) 111-143 Y1 - 2008 A1 - Paolo Mason A1 - Rebecca Salmoni A1 - Ugo Boscain A1 - Yacine Chitour AB - For $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$. UR - http://hdl.handle.net/1963/1862 U1 - 2360 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Relaxation of some transversally isotropic energies and applications to smectic A elastomers JF - Math. Models Methods Appl. Sci. 18 (2008) 1-20 Y1 - 2008 A1 - James Adams A1 - Sergio Conti A1 - Antonio DeSimone A1 - Georg Dolzmann UR - http://hdl.handle.net/1963/1912 U1 - 2325 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A second order minimality condition for the Mumford-Shah functional JF - Calc. Var. Partial Differential Equations 33 (2008) 37-74 Y1 - 2008 A1 - Filippo Cagnetti A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\\\\Gamma)$, $\\\\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\\\\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given. UR - http://hdl.handle.net/1963/1955 U1 - 2318 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solitons of linearly coupled systems of semilinear non-autonomous equations on Rn JF - J. Funct. Anal. 254 (2008) 2816-2845 Y1 - 2008 A1 - Antonio Ambrosetti A1 - Giovanna Cerami A1 - David Ruiz AB - Using concentration compactness type arguments, we prove some results about the existence of positive ground and bound state of linearly coupled systems of nonlinear Schrödinger equations. UR - http://hdl.handle.net/1963/2175 U1 - 2069 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Symmetries of noncommutative spaces and equivariant cohomology Y1 - 2008 A1 - Lucio Cirio KW - Noncommutative spaces AB - As the title suggests, the main subject of this thesis is the study of symmetries of noncommutative spaces and related equivariant cohomologies. We focus on deformations of classical geometries coming from the action of some symmetry. A close relation between the deformation of the symmetry and the deformation of the space on which it acts is at the heart of our approach; we will use this idea to generate noncommutative geometries, and to de¯ne algebraic models for the equivariant cohomology of such actions. PB - SISSA UR - http://hdl.handle.net/1963/5254 U1 - 5077 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas JF - Phys. Rev. Lett. 98 (2007) 030404 Y1 - 2007 A1 - Gao Xianlong A1 - Matteo Rizzi A1 - Marco Polini A1 - Rosario Fazio A1 - Mario P. Tosi A1 - Vivaldo L. Jr. Campo A1 - Klaus Capelle AB -The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

UR - http://hdl.handle.net/1963/2056 U1 - 2140 U2 - Physics U3 - Condensed Matter Theory ER - TY - CHAP T1 - Massless scalar field in a two-dimensional de Sitter universe T2 - Rigorous quantum field theory Y1 - 2007 A1 - Marco Bertola A1 - Corbetta, Francesco A1 - Moschella, Ugo JF - Rigorous quantum field theory T3 - Progr. Math. PB - Birkhäuser CY - Basel VL - 251 ER - TY - RPRT T1 - Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations Y1 - 2007 A1 - Antonio Ambrosetti A1 - Eduardo Colorado A1 - David Ruiz JF - Calc. Var. Partial Differential Equations 30 (2007) 85-112 UR - http://hdl.handle.net/1963/1835 U1 - 2381 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Parametrized curves in Lagrange Grassmannians JF - C. R. Math. 345 (2007) 647-652 Y1 - 2007 A1 - Igor Zelenko A1 - Li Chengbo UR - http://hdl.handle.net/1963/2560 U1 - 1559 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Soft elasticity and microstructure in smectic C elastomers Y1 - 2007 A1 - Antonio DeSimone A1 - James Adams A1 - Sergio Conti AB - Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable. JF - Contin. Mech. Thermodyn. 18 (2007) 319-334 UR - http://hdl.handle.net/1963/1811 U1 - 2403 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Standing waves of some coupled Nonlinear Schrödinger Equations Y1 - 2007 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - We deal with a class of systems of NLS equations, proving the existence of bound and ground states provided the coupling parameter is small, respectively, large. JF - J. Lond. Math. Soc. 75 (2007) 67-82 UR - http://hdl.handle.net/1963/1821 U1 - 2393 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Twisted noncommutative equivariant Y1 - 2007 A1 - Lucio Cirio AB - We propose Weil and Cartan models for the equivariant cohomology of covariant actions on toric deformation manifolds. The construction is based on the noncommutative Weil algebra of Alekseev and Meinrenken; we show that one can implement a Drinfeld twist of their models in order to take into account the noncommutativity of the spaces we are acting on. UR - http://hdl.handle.net/1963/1991 U1 - 2205 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients JF - J. Hyperbolic Differ. Equ. 4 (2007) 771-795 Y1 - 2007 A1 - Giuseppe Maria Coclite A1 - Nils Henrik Risebro AB - We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to \\\"internal boundaries\\\". By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\\\infty$, and that the limits are viscosity solutions. PB - World Scientific UR - http://hdl.handle.net/1963/2907 U1 - 1793 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - 4e-condensation in a fully frustrated Josephson junction diamond chain JF - Phys. Rev. B 73 (2006) 100502(R) Y1 - 2006 A1 - Matteo Rizzi A1 - Vittorio Cataudella A1 - Rosario Fazio AB -Fully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\\\\c{c}ot and J. Vidal, Phys. Rev. Lett. {\\\\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.

UR - http://hdl.handle.net/1963/2400 U1 - 2297 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - Bound and ground states of coupled nonlinear Schrödinger equations JF - C. R. Acad. Sci. Paris, Ser. I 342 (2006) 453-458 Y1 - 2006 A1 - Antonio Ambrosetti A1 - Eduardo Colorado AB - We prove existence of bound and ground states of some systems of coupled nonlinear Schrodinger equations. UR - http://hdl.handle.net/1963/2149 U1 - 2094 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Common Polynomial Lyapunov Functions for Linear Switched Systems JF - SIAM J. Control Optim. 45 (2006) 226-245 Y1 - 2006 A1 - Paolo Mason A1 - Ugo Boscain A1 - Yacine Chitour AB - In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given. UR - http://hdl.handle.net/1963/2181 U1 - 2063 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Dirichlet problem for H-systems with small boundary data: blowup phenomena and nonexistence results JF - Arch. Ration. Mech. Anal. 181 (2006) 1-42 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina UR - http://hdl.handle.net/1963/2252 U1 - 1995 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An estimation of the controllability time for single-input systems on compact Lie Groups JF - ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 Y1 - 2006 A1 - Andrei A. Agrachev A1 - Thomas Chambrion AB - Geometric control theory and Riemannian techniques are used to describe the reachable set at time t of left invariant single-input control systems on semi-simple compact Lie groups and to estimate the minimal time needed to reach any point from identity. This method provides an effective way to give an upper and a lower bound for the minimal time needed to transfer a controlled quantum system with a drift from a given initial position to a given final position. The bounds include diameters of the flag manifolds; the latter are also explicitly computed in the paper. UR - http://hdl.handle.net/1963/2135 U1 - 2108 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On Palais-Smale sequences for H-systems: some examples JF - Adv. Differential Equations 11 (2006) 931-960 Y1 - 2006 A1 - Paolo Caldiroli A1 - Roberta Musina AB - We exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour. UR - http://hdl.handle.net/1963/2157 U1 - 2087 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Stability of planar nonlinear switched systems Y1 - 2006 A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Mario Sigalotti AB - We consider the time-dependent nonlinear system ˙ q(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R2, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uniform with respect to u(.). Such conditions can be verified without any integration or construction of a Lyapunov function, and they are robust under small perturbations of the vector fields. JF - Discrete Contin. Dyn. Syst. 15 (2006) 415-432 UR - http://hdl.handle.net/1963/1710 U1 - 2441 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Asymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$ JF - Comm. Anal. Geom. 13 (2005) 187-252 Y1 - 2005 A1 - Sagun Chanillo A1 - Andrea Malchiodi AB - Given a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron. PB - International Press UR - http://hdl.handle.net/1963/3533 U1 - 731 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the attainable set for Temple class systems with boundary controls JF - SIAM J. Control Optim. 43 (2005) 2166-2190 Y1 - 2005 A1 - Fabio Ancona A1 - Giuseppe Maria Coclite AB - Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology. PB - SISSA Library UR - http://hdl.handle.net/1963/1581 U1 - 2537 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Conservation laws with time dependent discontinuous coefficients JF - SIAM J. Math. Anal. 36 (2005) 1293-1309 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Nils Henrik Risebro AB - We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11]. PB - SISSA Library UR - http://hdl.handle.net/1963/1666 U1 - 2452 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals JF - J. Dyn. Control Syst. 11 (2005) 297-327 Y1 - 2005 A1 - Andrei A. Agrachev A1 - Natalia N. Chtcherbakova A1 - Igor Zelenko AB - Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem. UR - http://hdl.handle.net/1963/2254 U1 - 1993 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Decay of a bound state under a time-periodic perturbation: a toy case JF - J. Phys. A 38 (2005) 4769-4781 Y1 - 2005 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio AB - We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength\\\'\\\' (\\\\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\\\\alpha(t)), we prove complete ionization as (t \\\\to \\\\infty). We prove also that, under the same conditions, all the states of the system are scattering states. UR - http://hdl.handle.net/1963/2298 U1 - 1718 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Global solutions of the Hunter-Saxton equation JF - SIAM J. Math. Anal. 37 (2005) 996-1026 Y1 - 2005 A1 - Alberto Bressan A1 - Adrian Constantin AB - We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data. UR - http://hdl.handle.net/1963/2256 U1 - 1991 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Ionization for Three Dimensional Time-dependent Point Interactions JF - Comm. Math. Phys. 257 (2005) 169-192 Y1 - 2005 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Andrea Mantile AB - We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states. UR - http://hdl.handle.net/1963/2297 U1 - 1719 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Minimal surfaces in pseudohermitian geometry JF - Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (5), 4 (2005) 129-177. Y1 - 2005 A1 - Jih-Hsin Cheng A1 - JennFang Hwang A1 - Andrea Malchiodi A1 - Paul Yang AB - We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold. PB - Scuola Normale Superiore UR - http://hdl.handle.net/1963/4579 U1 - 4347 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy JF - Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990 Y1 - 2005 A1 - Ugo Boscain A1 - Thomas Chambrion A1 - Grégoire Charlot AB - We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed. UR - http://hdl.handle.net/1963/2259 U1 - 1988 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Self-similar folding patterns and energy scaling in compressed elastic sheets JF - Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 Y1 - 2005 A1 - Sergio Conti A1 - Antonio DeSimone A1 - Stefan Müller AB - Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves. PB - Elsevier UR - http://hdl.handle.net/1963/3000 U1 - 1333 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stability of solutions of quasilinear parabolic equations JF - J. Math. Anal. Appl. 308 (2005) 221-239 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Helge Holden AB - We bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth. PB - Elsevier UR - http://hdl.handle.net/1963/2892 U1 - 1808 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Time Optimal Synthesis for Left-Invariant Control Systems on SO(3) JF - SIAM J. Control Optim. 44 (2005) 111-139 Y1 - 2005 A1 - Ugo Boscain A1 - Yacine Chitour AB - Consider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations. UR - http://hdl.handle.net/1963/2258 U1 - 1989 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Traffic flow on a road network JF - SIAM J. Math. Anal. 36 (2005) 1862-1886 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Benedetto Piccoli A1 - Mauro Garavello AB - This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights. PB - SISSA Library UR - http://hdl.handle.net/1963/1584 U1 - 2534 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Energetics and switching of quasi-uniform states in small ferromagnetic particles JF - M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 Y1 - 2004 A1 - François Alouges A1 - Sergio Conti A1 - Antonio DeSimone A1 - Ivo Pokern AB - We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size. PB - EDP Sciences UR - http://hdl.handle.net/1963/2999 U1 - 1334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of H-bubbles in a perturbative setting JF - Rev. Mat. Iberoamericana 20 (2004) 611-626 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a $C^{1}$ function $H: \\\\mathbb{R}^3 \\\\to \\\\mathbb{R}$, we look for $H$-bubbles, i.e., surfaces in $\\\\mathbb{R}^3$ parametrized by the sphere $\\\\mathbb{S}^2$ with mean curvature $H$ at every regular point. Here we study the case $H(u)=H_{0}(u)+\\\\epsilon H_{1}(u)$ where $H_{0}$ is some \\\"good\\\" curvature (for which there exist $H_{0}$-bubbles with minimal energy, uniformly bounded in $L^{\\\\infty}$), $\\\\epsilon$ is the smallness parameter, and $H_{1}$ is {\\\\em any} $C^{1}$ function. PB - SISSA Library UR - http://hdl.handle.net/1963/1606 U1 - 2512 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Extended Toda Hierarchy JF - Moscow Math. J. 4 (2004)\\n313-332. Y1 - 2004 A1 - Guido Carlet A1 - Boris Dubrovin A1 - Zhang Youjin UR - http://hdl.handle.net/1963/2542 U1 - 1577 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - H-bubbles in a perturbative setting: the finite-dimensional reduction\\\'s method JF - Duke Math. J. 122 (2004), no. 3, 457--484 Y1 - 2004 A1 - Paolo Caldiroli A1 - Roberta Musina AB - Given a regular function $H\\\\colon\\\\mathbb{R}^{3}\\\\to\\\\mathbb{R}$, we look for $H$-bubbles, that is, regular surfaces in $\\\\mathbb{R}^{3}$ parametrized on the sphere $\\\\mathbb{S}+^{2}$ with mean curvature $H$ at every point. Here we study the case of $H(u)=H_{0}+\\\\varepsilon H_{1}(u)=:H_{\\\\varepsilon}(u)$, where $H_{0}$ is a nonzero constant, $\\\\varepsilon$ is the smallness parameter, and $H_{1}$ is any $C^{2}$-function. We prove that if $\\\\bar p\\\\in\\\\mathbb{R}^{3}$ is a ``good\\\'\\\' stationary point for the Melnikov-type function $\\\\Gamma(p)=-\\\\int_{|q-p|<|H_{0}|^{-1}}H_{1}(q)\\\\,dq$, then for $|\\\\varepsilon|$ small there exists an $H_{\\\\varepsilon}$-bubble $\\\\omega^{\\\\varepsilon}$ that converges to a sphere of radius $|H_{0}|^{-1}$ centered at $\\\\bar p$, as $\\\\varepsilon\\\\to 0$. PB - SISSA Library UR - http://hdl.handle.net/1963/1607 U1 - 2511 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - Generic T1 - On the minimal degree of a common Lyapunov function for planar switched systems T2 - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 Y1 - 2004 A1 - Paolo Mason A1 - Ugo Boscain A1 - Yacine Chitour AB - In this paper, we consider linear switched systems x(t) = Au(t)x(t), x ε Rn, u ε U, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a polynomial common Lyapunov function. Then our main result is that the degree of that the common polynomial Lyapunov function is not uniformly bounded over all the UAS systems. This result answers a question raised by Dayawansa and Martin. JF - 43rd IEEE Conference on Decision and Control, 2004, 2786 - 2791 Vol.3 PB - IEEE UR - http://hdl.handle.net/1963/4834 U1 - 4611 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Resonance of minimizers for n-level quantum systems with an arbitrary cost JF - ESAIM COCV 10 (2004) 593-614 Y1 - 2004 A1 - Ugo Boscain A1 - Grégoire Charlot AB - We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system.\\nFor a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists a minimizer in resonance. This permits to justify some strategies used in experimental physics. It is also quite important because it permits to reduce remarkably the complexity of the problem (and extend some of our previous results for $n=2$ and $n=3$): instead of looking for minimizers on the sphere $S^{2n-1}\\\\subset\\\\C^n$ one is reduced to look just for minimizers on the sphere $S^{n-1}\\\\subset \\\\R^n$. Moreover, for the reduced problem, we investigate on the question of existence of strict abnormal minimizer. PB - EDP Sciences UR - http://hdl.handle.net/1963/2910 U1 - 1790 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Rotating Singular Perturbations of the Laplacian JF - Ann. Henri Poincare 5 (2004) 773-808 Y1 - 2004 A1 - Michele Correggi A1 - Gianfausto Dell'Antonio AB - We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for their unitary semigroups. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as (\\\\omega \\\\to \\\\infty). PB - Springer UR - http://hdl.handle.net/1963/2945 U1 - 1755 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Solitary waves for Maxwell Schrodinger equations JF - Electron. J. Differential Equations (2004) 94 Y1 - 2004 A1 - Giuseppe Maria Coclite A1 - Vladimir Georgiev AB - In this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated. PB - SISSA Library UR - http://hdl.handle.net/1963/1582 U1 - 2536 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Time-dependent singular interactions Y1 - 2004 A1 - Michele Correggi KW - Rotating singular interactions PB - SISSA UR - http://hdl.handle.net/1963/5310 U1 - 5135 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - THES T1 - Control Problems for Systems of Conservation Laws Y1 - 2003 A1 - Giuseppe Maria Coclite KW - Asymptotic Stabilization PB - SISSA UR - http://hdl.handle.net/1963/5325 U1 - 5154 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An interior estimate for a nonlinear parabolic equation JF - J.Math.Anal.Appl. 284 (2003) no.1, 49 Y1 - 2003 A1 - Giuseppe Maria Coclite PB - SISSA Library UR - http://hdl.handle.net/1963/1622 U1 - 2496 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Some results on the boundary control of systems of conservation laws JF - SIAM J.Control Optim. 41 (2003),no.2, 607 Y1 - 2003 A1 - Alberto Bressan A1 - Fabio Ancona A1 - Giuseppe Maria Coclite PB - SISSA Library UR - http://hdl.handle.net/1963/1615 U1 - 2503 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Boundary Control of Systems of Conservation Laws JF - SIAM J. Control Optim. 41 (2002) 607-622 Y1 - 2002 A1 - Alberto Bressan A1 - Giuseppe Maria Coclite AB - The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand, we give an example showing that exact controllability in finite time cannot be achieved, in general. PB - SIAM UR - http://hdl.handle.net/1963/3070 U1 - 1263 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems JF - Nonlinear Anal. 48 (2002) 481-504 Y1 - 2002 A1 - Massimiliano Berti A1 - Carlo Carminati PB - Elsevier UR - http://hdl.handle.net/1963/1279 U1 - 3176 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of minimal H-bubbles JF - Commun. Contemp. Math. 4 (2002) 177-209 Y1 - 2002 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1525 U1 - 2638 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the K+P problem for a three-level quantum system: optimality implies resonance JF - J.Dynam. Control Systems 8 (2002),no.4, 547 Y1 - 2002 A1 - Ugo Boscain A1 - Thomas Chambrion A1 - Jean-Paul Gauthier PB - SISSA Library UR - http://hdl.handle.net/1963/1601 U1 - 2517 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A multiplicity result for the Schrodinger-Maxwell equations with negative potential JF - Ann. Pol. Math. 79 (2002) 21-30 Y1 - 2002 A1 - Giuseppe Maria Coclite AB - We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential. PB - IMPAN UR - http://hdl.handle.net/1963/3053 U1 - 1280 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quantum mechanics and stochastic mechanics for compatible observables at different times JF - Ann.Physics 296 (2002), no.2, 371 Y1 - 2002 A1 - Michele Correggi A1 - Giovanni Morchio PB - SISSA Library UR - http://hdl.handle.net/1963/1577 U1 - 2541 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Singular elliptic problems with critical growth JF - Comm. Partial Differential Equations 27 (2002), no. 5-6, 847-876 Y1 - 2002 A1 - Paolo Caldiroli A1 - Andrea Malchiodi PB - Dekker UR - http://hdl.handle.net/1963/1268 U1 - 3187 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the Stability of the Standard Riemann Semigroup JF - P. Am. Math. Soc., 2002, 130, 1961 Y1 - 2002 A1 - Stefano Bianchini A1 - Rinaldo M. Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/1528 U1 - 2635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Controllability for discrete systems with a finite control set JF - Math. Control Signals Systems 14 (2001) 173-193 Y1 - 2001 A1 - Yacine Chitour A1 - Benedetto Piccoli PB - Springer UR - http://hdl.handle.net/1963/3114 U1 - 1219 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations JF - Adv. Differential Equations 6 (2001), no. 3, 303-326 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1319 U1 - 3136 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - S^2 type parametric surfaces with prescribed mean curvature and minimal energy T2 - Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina JF - Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77 PB - Birkhauser UR - http://hdl.handle.net/1963/1605 U1 - 2513 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stationary states for a two-dimensional singular Schrodinger equation JF - Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 4 (2001), no. 3, 609-633. Y1 - 2001 A1 - Paolo Caldiroli A1 - Roberta Musina PB - SISSA Library UR - http://hdl.handle.net/1963/1249 U1 - 3206 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On a Steffen\\\'s result about parametric surfaces with prescribed mean curvature Y1 - 2000 A1 - Roberta Musina A1 - Paolo Caldiroli PB - SISSA Library UR - http://hdl.handle.net/1963/1558 U1 - 2560 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - BOOK T1 - Well-posedness of the Cauchy problem for n x n systems of conservation laws T2 - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. Y1 - 2000 A1 - Alberto Bressan A1 - Graziano Crasta A1 - Benedetto Piccoli JF - Mem. Amer. Math. Soc. 146 (2000), no. 694, 134 p. PB - American Mathematical Society UR - http://hdl.handle.net/1963/3495 N1 - Chapter 1 and 2 U1 - 769 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete approximation of the Mumford-Shah functional in dimension two JF - M2AN 33 (1999) 651-672 Y1 - 1999 A1 - Antonin Chambolle A1 - Gianni Dal Maso PB - EDP Sciences UR - http://hdl.handle.net/1963/3588 U1 - 712 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A note on fractional KDV hierarchies. II. The bihamiltonian approach Y1 - 1999 A1 - Paolo Casati A1 - Gregorio Falqui A1 - Marco Pedroni PB - SISSA Library UR - http://hdl.handle.net/1963/1220 U1 - 2723 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws JF - Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5 Y1 - 1997 A1 - Graziano Crasta A1 - Benedetto Piccoli PB - SISSA Library UR - http://hdl.handle.net/1963/969 U1 - 3485 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - An existence result in a problem of the vectorial case of the calculus of variations Y1 - 1995 A1 - Arrigo Cellina A1 - Sandro Zagatti AB - SIAM J. Control Optim. 33 (1995) 960-970 PB - SIAM UR - http://hdl.handle.net/1963/3513 U1 - 751 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Special functions of bounded deformation Y1 - 1995 A1 - Giovanni Bellettini A1 - Alessandra Coscia A1 - Gianni Dal Maso PB - SISSA Library UR - http://hdl.handle.net/1963/978 U1 - 3476 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Unique solutions of 2x2 conservation laws with large data JF - Indiana Univ. Math. J. 44 (1995), no. 3, 677-725 Y1 - 1995 A1 - Alberto Bressan A1 - Rinaldo M. Colombo AB - For a 2x2 hyperbolic system of conservation laws, we first consider a Riemann problem with arbitrarily large data. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. We then establish a uniqueness result for large BV solutions, valid within the same class of functions where a local existence theorem can be proved. PB - Indiana University Mathematics Journal UR - http://hdl.handle.net/1963/975 U1 - 3479 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A version of Olech\\\'s lemma in a problem of the calculus of variations JF - SIAM J. Control Optim. 32 (1994) 1114-1127 Y1 - 1994 A1 - Arrigo Cellina A1 - Sandro Zagatti AB - This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data. PB - SIAM UR - http://hdl.handle.net/1963/3514 U1 - 750 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A class of absolute retracts of dwarf spheroidal galaxies JF - Proc.Amer.Math.Soc. 112 (1991), no.2, 413 Y1 - 1991 A1 - Alberto Bressan A1 - Arrigo Cellina A1 - Andrzej Fryszkowski PB - SISSA Library UR - http://hdl.handle.net/1963/837 U1 - 2954 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence and continuous dependence for discontinuous O.D.E.s JF - Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311 Y1 - 1990 A1 - Alberto Bressan A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/716 U1 - 3210 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence of solutions for a class of non-convex differential inclusions JF - Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76 Y1 - 1990 A1 - Fabio Ancona A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/792 U1 - 2999 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - G-convergence of monotone operators JF - Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160 Y1 - 1990 A1 - Valeria Chiadò Piat A1 - Gianni Dal Maso A1 - Anneliese Defranceschi PB - SISSA Library UR - http://hdl.handle.net/1963/680 U1 - 3246 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Limits of obstacle problems for the area functional. JF - Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309 Y1 - 1989 A1 - Gianni Dal Maso A1 - Michele Carriero A1 - Antonio Leaci A1 - Eduardo Pascali PB - SISSA Library UR - http://hdl.handle.net/1963/577 U1 - 3327 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Upper semicontinuous differential inclusions without convexity JF - Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775 Y1 - 1989 A1 - Alberto Bressan A1 - Arrigo Cellina A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/670 U1 - 3256 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Generalized Baire category and differential inclusions in Banach spaces. JF - J. Differential Equations 76 (1988), no. 1, 135-158. Y1 - 1988 A1 - Alberto Bressan A1 - Giovanni Colombo PB - SISSA Library UR - http://hdl.handle.net/1963/538 U1 - 3366 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Solutions with minimal period for Hamiltonian systems in a potential well. JF - Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296 Y1 - 1987 A1 - Antonio Ambrosetti A1 - Vittorio Coti Zelati PB - SISSA Library UR - http://hdl.handle.net/1963/466 U1 - 3437 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Symmetry breaking in Hamiltonian systems JF - J. Differential Equations 67 (1987), no. 2, 165-184 Y1 - 1987 A1 - Antonio Ambrosetti A1 - Vittorio Coti Zelati A1 - Ivar Ekeland PB - SISSA Library UR - http://hdl.handle.net/1963/409 U1 - 3558 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Maximal acceleration and Sakharov's limiting temperature JF - Lett. Nuovo Cim. 42 (1985) 70-72 Y1 - 1985 A1 - Eduardo R. Caianiello A1 - Giovanni Landi AB -It is shown that Sakharov's maximal temperature, derived by him from astrophysical considerations, is a straightforward consequence of the maximal acceleration introduced by us in previous works.

PB - Società Italiana di Fisica UR - http://hdl.handle.net/1963/372 U1 - 3595 U2 - Physics U3 - Elementary Particle Theory ER -