We study the average condition number for polynomial eigenvalues of collections of matrices drawn from some random matrix ensembles. In particular, we prove that polynomial eigenvalue problems defined by matrices with random Gaussian entries are very well conditioned on the average.

%B Foundations of Computational Mathematics %8 May %G eng %U https://doi.org/10.1007/s10208-019-09414-2 %R 10.1007/s10208-019-09414-2 %0 Journal Article %J Journal of Functional Analysis %D 2019 %T Reducibility of first order linear operators on tori via Moser's theorem %A Roberto Feola %A Filippo Giuliani %A Riccardo Montalto %A Michela Procesi %K Hyperbolic PDEs %K KAM theory %K Nash–Moser %K Reducibility %XIn this paper we prove reducibility of a class of first order, quasi-linear, quasi-periodic time dependent PDEs on the torus∂tu+ζ⋅∂xu+a(ωt,x)⋅∂xu=0,x∈Td,ζ∈Rd,ω∈Rν. As a consequence we deduce a stability result on the associated Cauchy problem in Sobolev spaces. By the identification between first order operators and vector fields this problem can be formulated as the problem of finding a change of coordinates which conjugates a weakly perturbed constant vector field on Tν+d to a constant diophantine flow. For this purpose we generalize Moser's straightening theorem: considering smooth perturbations we prove that the corresponding straightening torus diffeomorphism is smooth, under the assumption that the perturbation is small only in some given Sobolev norm and that the initial frequency belongs to some Cantor-like set. In view of applications in KAM theory for PDEs we provide also tame estimates on the change of variables.

%B Journal of Functional Analysis %V 276 %P 932 - 970 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123618303793 %R https://doi.org/10.1016/j.jfa.2018.10.009 %0 Journal Article %J Annali di Matematica Pura ed Applicata (1923 -) %D 2019 %T On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions %A Giovanni Bellettini %A Alaa Elshorbagy %A Maurizio Paolini %A Riccardo Scala %XIn this paper, we estimate from above the area of the graph of a singular map u taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2$-embedded curves that meet transversely at only one point of the disk. We show that the singular part of the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to ``fill the hole'' in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of u, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of u cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.

%B Annali di Matematica Pura ed Applicata (1923 -) %8 Jul %G eng %U https://doi.org/10.1007/s10231-019-00887-0 %R 10.1007/s10231-019-00887-0 %0 Report %D 2018 %T On real resonances for the three-dimensional, multi-centre point interaction %A Alessandro Michelangeli %A Raffaele Scandone %G eng %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2018 %T Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group %A Nicola Gigli %A Chiara Rigoni %XWe prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

%B Calculus of Variations and Partial Differential Equations %V 57 %P 104 %8 Jun %G eng %U https://doi.org/10.1007/s00526-018-1377-z %R 10.1007/s00526-018-1377-z %0 Generic %D 2018 %T A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to fluid dynamics %A Efthymios N. Karatzas %A Giovanni Stabile %A Leo Nouveau %A Guglielmo Scovazzi %A Gianluigi Rozza %G eng %0 Generic %D 2018 %T A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries %A Efthymios N. Karatzas %A Giovanni Stabile %A N. Atallah %A Guglielmo Scovazzi %A Gianluigi Rozza %G eng %0 Report %D 2018 %T Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation %A Roberto Feola %A Filippo Giuliani %A Michela Procesi %G eng %0 Journal Article %J Journal of Hyperbolic Differential Equations %D 2018 %T Regularity estimates for scalar conservation laws in one space dimension %A Elio Marconi %XWe deal with the regularizing effect that, in scalar conservation laws in one space dimension, the nonlinearity of the flux function f has on the entropy solution. More precisely, if the set w : f″(w)≠0 is dense, the regularity of the solution can be expressed in terms of BVΦ spaces, where Φ depends on the nonlinearity of f. If moreover the set w : f″(w) = 0 is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that f′∘ u(t) ∈BV loc(ℝ) for every t > 0 and that this can be improved to SBVloc(ℝ) regularity except an at most countable set of singular times. Finally, we present some examples that show the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.

%B Journal of Hyperbolic Differential Equations %V 15 %P 623-691 %G eng %U https://doi.org/10.1142/S0219891618500200 %R 10.1142/S0219891618500200 %0 Report %D 2017 %T Random spectrahedra %A Paul Breiding %A Khazhgali Kozhasov %A Antonio Lerario %G eng %0 Journal Article %J Phil. Trans. R. Soc. A %D 2017 %T Rayleigh–Taylor instability in soft elastic layers %A Davide Riccobelli %A Pasquale Ciarletta %B Phil. Trans. R. Soc. A %I The Royal Society %V 375 %G eng %0 Journal Article %J Journal of High Energy Physics %D 2017 %T Real topological string amplitudes %A Narain, K. S. %A Nicolò Piazzalunga %A Alessandro Tanzini %XWe discuss the physical superstring correlation functions in type I theory (or equivalently type II with orientifold) that compute real topological string amplitudes. We consider the correlator corresponding to holomorphic derivative of the real topological amplitude $\mathcal{G_\chi}$, at fixed worldsheet Euler characteristic $\chi$. This corresponds in the low-energy effective action to $\mathcal{N}=2$ Weyl multiplet, appropriately reduced to the orientifold invariant part, and raised to the power $g'= −\chi+ 1$. We show that the physical string correlator gives precisely the holomorphic derivative of topological amplitude. Finally, we apply this method to the standard closed oriented case as well, and prove a similar statement for the topological amplitude $\mathcal{F}_g$.

%B Journal of High Energy Physics %V 2017 %P 80 %8 Mar %G eng %U https://doi.org/10.1007/JHEP03(2017)080 %R 10.1007/JHEP03(2017)080 %0 Journal Article %J SIAM/ASA Journal on Uncertainty Quantification %D 2017 %T Reduced Basis Methods for Uncertainty Quantification %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %XIn 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

POD–Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

%B Model Reduction of Parametrized Systems %I Springer International Publishing %P 149–167 %G eng %& Reduced-order semi-implicit schemes for fluid-structure interaction problems %R 10.1007/978-3-319-58786-8_10 %0 Report %D 2017 %T Regularity estimates for scalar conservation laws in one space dimension %A Elio Marconi %X In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces. %G en %U http://preprints.sissa.it/handle/1963/35291 %1 35597 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-08-16T06:45:14Z No. of bitstreams: 1 Regularity_preprint.pdf: 603969 bytes, checksum: 29e1eefa4da3dc5272a6e9c6119108a5 (MD5) %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian %A Alessandro Olgiati %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XThe effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation. We elucidate the steps needed to adapt to the magnetic case the proof of the derivation of the Gross-Pitaevskii equation within the ``projection counting'' scheme.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 257–266 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_15 %R 10.1007/978-3-319-58904-6_15 %0 Journal Article %J NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %D 2016 %T A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X 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. %B NERS-14-1062; ASME J of Nuclear Rad Sci, 2, 2 (2016) 021019 %I ASME %V 2 %P 8 %8 02/2016 %G en %U http://urania.sissa.it/xmlui/handle/1963/35192 %N 2 %1 35473 %2 Mathematics %4 1 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-05-30T00:18:10Z No. of bitstreams: 1 sartori_post-icone.pdf: 1377810 bytes, checksum: 5c09a1296518bbbd4b61b709ced8dbca (MD5) %R 10.1115/1.4031945 %0 Journal Article %J Communications in Computational Physics %D 2016 %T Reduced basis approaches in time-dependent noncoercive settings for modelling the movement of nuclear reactor control rods %A Alberto Sartori %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %XIn 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.

%B Communications in Computational Physics %I SISSA %8 2016 %G en %U http://urania.sissa.it/xmlui/handle/1963/34963 %N in press %1 35188 %2 Mathematics %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-11-05T15:06:51Z No. of bitstreams: 1 manuscript.pdf: 2056729 bytes, checksum: 2a2fad22dc931e8c4094642e21c479cd (MD5) %0 Journal Article %J Computers and Mathematics with Applications %D 2016 %T Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries %A Laura Iapichino %A Alfio Quarteroni %A Gianluigi Rozza %X The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed. %B Computers and Mathematics with Applications %I Elsevier %V 71 %P 430 %8 01/2016 %G en %N 1 %1 35187 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2015-11-05T14:59:46Z No. of bitstreams: 1 RDF2_reduced.pdf: 3254431 bytes, checksum: 508b8775e27dfb868f1b39c270cb4a6f (MD5) %& 408 %0 Journal Article %J Communications in Number Theory and Physics %D 2016 %T Refined node polynomials via long edge graphs %A Lothar Göttsche %A Benjamin Kipkirui Kikwai %XThe generating functions of the Severi degrees for sufficiently ample line bundles on algebraic surfaces are multiplicative in the topological invariants of the surface and the line bundle. Recently new proofs of this fact were given for toric surfaces by Block, Colley, Kennedy and Liu, Osserman, using tropical geometry and in particular the combinatorial tool of long-edged graphs. In the first part of this paper these results are for $\mathbb{P}^2$ and rational ruled surfaces generalised to refined Severi degrees. In the second part of the paper we give a number of mostly conjectural generalisations of this result to singular surfaces, and curves with prescribed multiple points. The formulas involve modular forms and theta functions.

%B Communications in Number Theory and Physics %I International Press of Boston %V 10 %P 193–234 %G eng %U http://dx.doi.org/10.4310/CNTP.2016.v10.n2.a2 %R 10.4310/CNTP.2016.v10.n2.a2 %0 Journal Article %J SIAM Journal on Mathematical Analysis %D 2016 %T Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions %A Stefano Bianchini %A Paolo Bonicatto %A N.A. Gusev %XGiven a bounded autonomous vector field $b \colon \mathbb{R}^d \to \mathbb{R}^d$, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation \begin{equation*} \partial_t u + b \cdot \nabla u= 0. \end{equation*} We are interested in the case where $b$ is of class BV and it is nearly incompressible. Assuming that the ambient space has dimension $d=2$, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [7] (where the steady case is treated). Our proof is based on splitting the equation onto a suitable partition of the plane: this technique was introduced in [3], using the results on the structure of level sets of Lipschitz maps obtained in [1]. Furthermore, in order to construct the partition, we use Ambrosio's superposition principle [4].

%B SIAM Journal on Mathematical Analysis %V 48 %P 1-33 %G eng %U https://doi.org/10.1137/15M1007380 %R 10.1137/15M1007380 %0 Journal Article %J Proc. A. %D 2016 %T Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation %A Marco Bertola %A Gennady El %A Alexander Tovbis %B Proc. A. %V 472 %P 20160340, 12 %G eng %U http://dx.doi.org/10.1098/rspa.2016.0340 %R 10.1098/rspa.2016.0340 %0 Journal Article %J Advances in Computational Mathematics %D 2015 %T Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system %A Immanuel Martini %A Gianluigi Rozza %A Bernard Haasdonk %K Domain decomposition %K Error estimation %K Non-coercive problem %K Porous medium equation %K Reduced basis method %K Stokes flow %XThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

%B Advances in Computational Mathematics %V special issue for MoRePaS 2012 %G eng %N in press %R 10.1007/s10444-014-9396-6 %0 Journal Article %J Lecture Notes in Computational Science and Engineering %D 2015 %T Reduced basis approximation of parametrized advection-diffusion PDEs with high Péclet number %A Pacciarini, P. %A Gianluigi Rozza %XIn this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

%B Lecture Notes in Computational Science and Engineering %V 103 %P 419–426 %G eng %R 10.1007/978-3-319-10705-9__41 %0 Journal Article %J Computers and Mathematics with Applications %D 2015 %T Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations %A Federico Negri %A Andrea Manzoni %A Gianluigi Rozza %XThis paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties-with particular emphasis on the stability of the resulting double nested saddle-point problems and on aggregated error estimates-and the computational aspects of the method. Then, we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three-dimensional flow through boundary control, demonstrating the effectivity of the methodology.

%B Computers and Mathematics with Applications %V 69 %P 319–336 %G eng %R 10.1016/j.camwa.2014.12.010 %0 Journal Article %J Comput Methods Appl Mech Eng. 2015;284:1147–1180 %D 2015 %T Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils %A Andrea Manzoni %A Filippo Salmoiraghi %A Luca Heltai %X We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement. %B Comput Methods Appl Mech Eng. 2015;284:1147–1180 %G en %1 34587 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Luca Heltai (heltai@sissa.it) on 2015-03-03T16:15:31Z No. of bitstreams: 1 RB_IGA_BEM.pdf: 725470 bytes, checksum: e2fe6fabfdbe6118e9ef07fb185113af (MD5) %R 10.1016/j.cma.2014.11.037 %0 Thesis %D 2015 %T The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces. %A Lucia Tealdi %K Area functional %X In this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided. %I SISSA %G en %1 34732 %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-09-21T12:23:44Z No. of bitstreams: 1 Tealdi_PhD_thesis.pdf: 917244 bytes, checksum: a6bfc90b8457a030be4c7314ee1f426f (MD5) %0 Report %D 2015 %T Results on the minimization of the Dirichlet functional among semicartesian parametrizations %A Lucia Tealdi %A Giovanni Bellettini %A Maurizio Paolini %XWe start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau's problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34488 %1 34671 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Lucia Tealdi (ltealdi@sissa.it) on 2015-08-07T16:12:37Z No. of bitstreams: 1 bellettini_paolini_tealdi_semicart.pdf: 338138 bytes, checksum: c689a5b64d30dc600fe0429b72996c7d (MD5) %0 Report %D 2015 %T Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires %A Giuliano Lazzaroni %A Mariapia Palombaro %A Anja Schlomerkemper %X In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7494 %1 7623 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-01-30T07:54:33Z No. of bitstreams: 1 LaPaSc-3dim.pdf: 249836 bytes, checksum: 8b8edddc952b9a4a084c1c0c85514051 (MD5) %0 Report %D 2014 %T Rate-independent damage in thermo-viscoelastic materials with inertia %A Giuliano Lazzaroni %A Riccarda Rossi %A Marita Thomas %A Rodica Toader %X We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is Independent of temperature. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/7444 %1 7542 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-10-15T09:00:07Z No. of bitstreams: 1 LRTT-SISSA-preprint-14_10_15.pdf: 498065 bytes, checksum: 0de0c4a77dafb5df12747fd9947cec5c (MD5) %0 Thesis %D 2014 %T Rational curves and instantons on the Fano threefold Y_5 %A Giangiacomo Sanna %K Moduli space of vector bundles %X This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-Mülich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it. %I arXiv preprint %G en %U http://urania.sissa.it/xmlui/handle/1963/7482 %1 7594 %2 Mathematics %4 1 %# MAT/02 %$ Submitted by gggsanna@sissa.it (gggsanna@sissa.it) on 2014-12-01T10:51:46Z No. of bitstreams: 1 (Official) G. Sanna - Rational curves and instantons on the Fano threefold Y5 copia.pdf: 2005901 bytes, checksum: bd001232412f102490968ba3b21e1c20 (MD5) %0 Conference Paper %B ECMI 2014 proceedings %D 2014 %T Reduced basis method for the Stokes equations in decomposable domains using greedy optimization %A Laura Iapichino %A Alfio Quarteroni %A Gianluigi Rozza %A Volkwein, Stefan %B ECMI 2014 proceedings %P 1–7 %G eng %0 Book %B MS&A %D 2014 %T Reduced Order Methods for Modeling and Computational Reduction %A Alfio Quarteroni %A Gianluigi Rozza %K reduced order methods, MOR, ROM, POD, RB, greedy, CFD, Numerical Analysis %XThis monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

%B MS&A %7 1 %I Springer %C Milano %V 9 %P 334 %G eng %6 1 %R 10.1007/978-3-319-02090-7 %0 Conference Proceedings %B 22nd International Conference on Nuclear Engineering ICONE22 %D 2014 %T A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics %A Alberto Sartori %A Davide Baroli %A Antonio Cammi %A Lelio Luzzi %A Gianluigi Rozza %X

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.

%B 22nd International Conference on Nuclear Engineering ICONE22 %7 American Society Mechanical Engineering %I American Society of Mechanical Engineers (ASME) %C Prague, Czech Republic %P V005T17A048-V005T17A048 %8 07/2014 %@ 978-079184595-0 %G en %U http://urania.sissa.it/xmlui/handle/1963/35123 %1 35360 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T10:06:02Z (GMT) No. of bitstreams: 0 %R 10.1115/ICONE22-30707 %0 Book Section %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %D 2014 %T Reduction on characteristics for continuous of a scalar balance law %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %K Method of characteristics %B AIMS Series on Applied Mathematics, vol. 8 (2014): 399 - 406 %I SISSA %G en %U http://hdl.handle.net/1963/6562 %1 6516 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-04-03T07:48:04Z No. of bitstreams: 1 Alberti_11.pdf: 330968 bytes, checksum: a5f69e2a1d0afcfe139cf17ebcaf0f2d (MD5) %0 Journal Article %D 2014 %T A Review of the Sixth Painlevé Equation %A Davide Guzzetti %X For the Painlevé VI transcendents, we provide a unitary description of the critical behaviours, the connection formulae, their complete tabulation, and the asymptotic distribution of poles close to a critical point. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34658 %1 34868 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-20T13:13:55Z No. of bitstreams: 1 preprint2014.pdf: 283505 bytes, checksum: d5f401efb5eec8b4689b090dbcca6d84 (MD5) %R 10.1007/s00365-014-9250-6 %0 Journal Article %J Proceedings of the Royal Society A 470, 20140333 (2014) %D 2014 %T A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model %A Giovanni Noselli %A Antonio DeSimone %X We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations. %B Proceedings of the Royal Society A 470, 20140333 (2014) %I Royal Society Publishing %G en %1 34594 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T18:10:10Z No. of bitstreams: 1 bristle_crawlers.pdf: 9309327 bytes, checksum: 10f6df9814dd01c888aa9ec7836f1dff (MD5) %R 10.1098/rspa.2014.0333 %0 Journal Article %J Numerische Mathematik, 2013 %D 2013 %T Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants %A Gianluigi Rozza %A Phuong Huynh %A Andrea Manzoni %K parametrized Stokes equations %X In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle. %B Numerische Mathematik, 2013 %I Springer %G en %U http://hdl.handle.net/1963/6339 %1 6269 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T17:19:05Z\\nNo. of bitstreams: 1\\nStokes_HMR10_SISSA_report.pdf: 4641267 bytes, checksum: 82a163163a62d0b9deef8d5d6590f8d7 (MD5) %0 Book Section %B CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches %D 2013 %T Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA) %A Denis Devaud %A Gianluigi Rozza %B CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches %V 48 %P 98-115 %G eng %R http://dx.doi.org/10.1051/proc/201448004 %0 Journal Article %J SIAM Journal on Scientific Computing %D 2013 %T Reduced basis method for parametrized elliptic optimal control problems %A Federico Negri %A Gianluigi Rozza %A Andrea Manzoni %A Alfio Quarteroni %X We propose a suitable model reduction paradigm-the certified reduced basis method (RB)-for the rapid and reliable solution of parametrized optimal control problems governed by partial differential equations. In particular, we develop the methodology for parametrized quadratic optimization problems with elliptic equations as a constraint and infinite-dimensional control variable. First, we recast the optimal control problem in the framework of saddle-point problems in order to take advantage of the already developed RB theory for Stokes-type problems. Then, the usual ingredients of the RB methodology are called into play: a Galerkin projection onto a low-dimensional space of basis functions properly selected by an adaptive procedure; an affine parametric dependence enabling one to perform competitive offline-online splitting in the computational procedure; and an efficient and rigorous a posteriori error estimate on the state, control, and adjoint variables as well as on the cost functional. Finally, we address some numerical tests that confirm our theoretical results and show the efficiency of the proposed technique. %B SIAM Journal on Scientific Computing %V 35 %P A2316–A2340 %G eng %R 10.1137/120894737 %0 Report %D 2013 %T A Reduced Computational and Geometrical Framework for Inverse Problems in Haemodynamics %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %I SISSA %G en %1 6571 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-04-30T14:47:07Z No. of bitstreams: 1 LMQR_inverse_problems_Haemo.pdf: 2913600 bytes, checksum: 9bff594072e6c7b4a664bdade361a1a9 (MD5) %0 Report %D 2013 %T A reduced-order strategy for solving inverse Bayesian identification problems in physiological flows %A Toni Lassila %A Andrea Manzoni %A Alfio Quarteroni %A Gianluigi Rozza %I SISSA %G en %1 6555 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-04-12T10:16:42Z\nNo. of bitstreams: 1\nHanoi_RQML_2012_REVISED.pdf: 1360222 bytes, checksum: 4cb9ffaaf9fd67e3eacf4d9c060d0940 (MD5) %0 Report %D 2013 %T Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics %A Toni Lassila %A Andrea Manzoni %A Gianluigi Rozza %I SISSA %G en %1 6554 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2013-04-12T09:59:54Z\nNo. of bitstreams: 1\n03910397-1.pdf: 531448 bytes, checksum: 0ec611490748bed35d10f612e8296f27 (MD5) %0 Journal Article %J Advances in Nonlinear Analysis %D 2013 %T Remarks on the Moser–Trudinger inequality %A Gabriele Mancini %A Luca Battaglia %XWe extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

%B Advances in Nonlinear Analysis %I Advances in Nonlinear Analysis %V 2 %P 389-425 %G en %U http://edoc.unibas.ch/43974/ %N 4 %1 34666 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-07T13:45:19Z No. of bitstreams: 1 articolo1.pdf: 526978 bytes, checksum: 941a2e14ae2d0ff88b198a2e8c8c153e (MD5) %R 10.1515/anona-2013-0014 %0 Conference Proceedings %B European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 %D 2012 %T Reduction strategies for PDE-constrained oprimization problems in Haemodynamics %A Gianluigi Rozza %A Andrea Manzoni %A Federico Negri %K inverse problems %X Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems. This framework is based on a suitable saddle-point formulation of the optimal control problem and exploits the reduced basis method for the rapid and reliable solution of parametrized PDEs, leading to a relevant computational reduction with respect to traditional discretization techniques such as the finite element method. This allows a very efficient evaluation of state solutions and cost functionals, leading to an effective solution of repeated optimal control problems, even on domains of variable shape, for which a further (geometrical) reduction is pursued, relying on flexible shape parametrization techniques. This setting is applied to the solution of two problems arising from haemodynamics, dealing with both data reconstruction and data assimilation over domains of variable shape,\\r\\nwhich can be recast in a common PDE-constrained optimization formulation. %B European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.), Vienna, Austria, 10-14 sept. 2012 %G en %U http://hdl.handle.net/1963/6338 %1 6268 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2012-12-13T16:30:48Z\\r\\nNo. of bitstreams: 1\\r\\npaper_ECCOMAS2012_AM_SISSAreport.pdf: 4599005 bytes, checksum: 014a5a01276f25177386ad374a5917c8 (MD5) %0 Journal Article %J Differential Integral Equations %D 2012 %T Resonance at the first eigenvalue for first-order systems in the plane: vanishing Hamiltonians and the Landesman-Lazer condition %A Maurizio Garrione %B Differential Integral Equations %I Khayyam Publishing, Inc. %V 25 %P 505–526 %8 05 %G eng %U https://projecteuclid.org:443/euclid.die/1356012676 %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %D 2012 %T Reverse engineering the euglenoid movement %A Marino Arroyo %A Luca Heltai %A Daniel Millán %A Antonio DeSimone %K microswimmers %X Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics. %B Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 %G en %U http://hdl.handle.net/1963/6444 %1 6380 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:29:31Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1213977109 %0 Journal Article %D 2012 %T A Review on The Sixth Painlevé Equation %A Davide Guzzetti %K Painlevé equation %XFor the Painlev\\\'e 6 transcendents, we provide a unitary description of the\r\ncritical behaviours, the connection formulae, their complete tabulation, and\r\nthe asymptotic distribution of the poles close to a critical point.

%I SISSA %G en %U http://hdl.handle.net/1963/6525 %1 6470 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:24:43Z\nNo. of bitstreams: 1\n1210.0311v1.pdf: 283505 bytes, checksum: d5f401efb5eec8b4689b090dbcca6d84 (MD5) %0 Journal Article %J Physica D: Nonlinear Phenomena %D 2012 %T Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases %A Marco Bertola %A Mattia Cafasso %K Integrable kernels %B Physica D: Nonlinear Phenomena %V 241 %P 2237 - 2245 %G eng %U http://www.sciencedirect.com/science/article/pii/S0167278912000115 %R 10.1016/j.physd.2012.01.003 %0 Journal Article %J Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353 %D 2012 %T On robust Lie-algebraic stability conditions for switched linear systems %A Andrei A. Agrachev %A Yurij Baryshnikov %A Daniel Liberzon %X This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novelty feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. %B Systems and Control Letters. Volume 61, Issue 2, February 2012, Pages 347-353 %G en %U http://hdl.handle.net/1963/6455 %1 6400 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:15:25Z\\nNo. of bitstreams: 0 %R 10.1016/j.sysconle.2011.11.016 %0 Journal Article %J Le Matematiche %D 2011 %T Resonance and Landesman-Lazer conditions for first order systems in R^2 %A Maurizio Garrione %XThe first part of the paper surveys the concept of resonance for $T$-periodic nonlinear problems. In the second part, some new results about existence conditions for nonlinear planar systems are presented. In particular, the Landesman-Lazer conditions are generalized to systems in $\mathbbR^2$ where the nonlinearity interacts with two resonant Hamiltonians. Such results apply to second order equations, generalizing previous theorems by Fabry [4] (for the undamped case), and Frederickson-Lazer [9] (for the case with friction). The results have been obtained with A. Fonda, and have been published in [8].

%B Le Matematiche %V 66 %P 153–160 %G eng %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2011 %T Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincaré–Birkhoff theorem %A Alberto Boscaggin %A Maurizio Garrione %K Multiple periodic solutions %K Poincaré–Birkhoff theorem %K Resonance %K Rotation number %XIn the general setting of a planar first order system (0.1)u′=G(t,u),u∈R2, with G:[0,T]×R2→R2, we study the relationships between some classical nonresonance conditions (including the Landesman–Lazer one) — at infinity and, in the unforced case, i.e. G(t,0)≡0, at zero — and the rotation numbers of “large” and “small” solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincaré–Birkhoff fixed point theorem, new multiplicity results for T-periodic solutions of unforced planar Hamiltonian systems Ju′=∇uH(t,u) and unforced undamped scalar second order equations x″+g(t,x)=0. In particular, by means of the Landesman–Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 4166 - 4185 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X11001817 %R https://doi.org/10.1016/j.na.2011.03.051 %0 Journal Article %J J. Phys. A 43 (2010) 045201 %D 2010 %T The reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures %A Guido Carlet %A Paolo Lorenzoni %A Andrea Raimondo %X 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. %B J. Phys. A 43 (2010) 045201 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/3846 %1 863 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-02-17T09:13:18Z\\nNo. of bitstreams: 1\\n0910.1210v1.pdf: 183431 bytes, checksum: 90f5253ca8e81822f6ffb26ece621075 (MD5) %R 10.1088/1751-8113/43/4/045201 %0 Journal Article %J Geom. Topol. 14 (2010) 83-115 %D 2010 %T Riemann-Roch theorems and elliptic genus for virtually smooth schemes %A Barbara Fantechi %A Lothar Göttsche %X For a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth case. We prove virtual versions of the Grothendieck-Riemann-Roch and Hirzebruch-Riemann-Roch theorems. We show that the virtual chi y-genus is a polynomial, and use this to define a virtual topological Euler characteristic. We prove that the virtual elliptic genus satisfies a Jacobi modularity property; we state and prove a localization theorem in the toric equivariant case. We show how some of our results apply to moduli spaces of stable sheaves. %B Geom. Topol. 14 (2010) 83-115 %I Mathematical Sciences Publishers %G en_US %U http://hdl.handle.net/1963/3888 %1 821 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T07:35:11Z\\nNo. of bitstreams: 1\\n0706.0988v1.pdf: 396801 bytes, checksum: 640403457a0a02c4166b8c684d8af419 (MD5) %R 10.2140/gt.2010.14.83 %0 Report %D 2010 %T The role of membrane viscosity in the dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %A Luca Heltai %X Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3. %G en_US %U http://hdl.handle.net/1963/3930 %1 471 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:13:35Z\\nNo. of bitstreams: 1\\nArroyo_55M.pdf: 4419667 bytes, checksum: ca8a9c175a457ad33996d46a08e85e44 (MD5) %0 Journal Article %J J. Approx. Theory %D 2009 %T Regularity of a vector potential problem and its spectral curve %A Ferenc Balogh %A Marco Bertola %B J. Approx. Theory %V 161 %P 353–370 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2008.10.010 %R 10.1016/j.jat.2008.10.010 %0 Journal Article %J Phys. Rev. E 79 (2009) 031915 %D 2009 %T Relaxation dynamics of fluid membranes %A Marino Arroyo %A Antonio DeSimone %X We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest. %B Phys. Rev. E 79 (2009) 031915 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/3618 %1 686 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-04-22T08:29:29Z\\nNo. of bitstreams: 1\\nmembrane_dynamics_PRE_2.pdf: 1000677 bytes, checksum: e7ab0f6e2046800e154d399808ea314c (MD5) %R 10.1103/PhysRevE.79.031915 %0 Journal Article %J Math. Models Methods Appl. Sci. 18 (2008) 1-20 %D 2008 %T Relaxation of some transversally isotropic energies and applications to smectic A elastomers %A James Adams %A Sergio Conti %A Antonio DeSimone %A Georg Dolzmann %B Math. Models Methods Appl. Sci. 18 (2008) 1-20 %G en_US %U http://hdl.handle.net/1963/1912 %1 2325 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-02-02T14:15:25Z\\nNo. of bitstreams: 1\\nsma_Preprint_SISSA.pdf: 271875 bytes, checksum: eb0cf2c367021718506356a73bda219a (MD5) %R 10.1142/S0218202508002693 %0 Journal Article %J J. Phys. A 40 (2007) 10769-10790 %D 2007 %T Reciprocal transformations and flat metrics on Hurwitz spaces %A Simonetta Abenda %A Tamara Grava %X We consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian structures. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltonian structure of Dubrovin-Novikov type. We show that, under our hypotheses, bi-hamiltonicity is preserved by the reciprocal transformation. Finally we apply such results to reciprocal systems of genus g Whitham-KdV modulation equations. %B J. Phys. A 40 (2007) 10769-10790 %G en_US %U http://hdl.handle.net/1963/2210 %1 2034 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-12T09:26:01Z\\nNo. of bitstreams: 1\\n0704.1779v2.pdf: 286756 bytes, checksum: 3d2d03a6f16be9191b242adb35638601 (MD5) %R 10.1088/1751-8113/40/35/004 %0 Report %D 2007 %T Reduced density matrices and Bose-Einstein condensation %A Alessandro Michelangeli %X Emergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the level of marginals.\\nThe topic of correlations in the condensed state is addressed in order to show their influence at this level of marginals, both in the true condensed state and in the suitable trial functions one introduces to approximate the many-body structure and energy. Complete condensation is shown to be equivalently defined at any fixed k-body level, both for pure and mixed states. Further, it is proven to be equivalent to some other characterizations in terms of asymptotic factorization of the many-body state, which are currently present in the literature. %G en_US %U http://hdl.handle.net/1963/1986 %1 2210 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-07T12:22:30Z\\nNo. of bitstreams: 1\\n39-2007MP.pdf: 563889 bytes, checksum: b6688b840128220a2e61def6a60ff7d9 (MD5) %0 Journal Article %J Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187 %D 2007 %T On the reductions and classical solutions of the Schlesinger equations %A Boris Dubrovin %A Marta Mazzocco %X The Schlesinger equations S(n,m) describe monodromy preserving\\r\\ndeformations of order m Fuchsian systems with n+1 poles. They\\r\\ncan be considered as a family of commuting time-dependent Hamiltonian\\r\\nsystems on the direct product of n copies of m×m matrix algebras\\r\\nequipped with the standard linear Poisson bracket. In this paper we address\\r\\nthe problem of reduction of particular solutions of “more complicated”\\r\\nSchlesinger equations S(n,m) to “simpler” S(n′,m′) having n′ < n\\r\\nor m′ < m. %B Differential equations and quantum groups, IRMA Lect. Math. Theor. Phys. 9 (2007) 157-187 %I SISSA %G en %U http://hdl.handle.net/1963/6472 %1 6418 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T14:52:15Z\\nNo. of bitstreams: 1\\ndubrovin_mazzocco_2007_irma.pdf: 300042 bytes, checksum: 85252eedf7d0fbbdf06061c20b471d44 (MD5) %0 Journal Article %J Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219 %D 2007 %T On the regularity of weak solutions to H-systems %A Roberta Musina %X Abstract. In this paper we prove that every weak solution to the H-surface equation is locally bounded, provided the prescibed mean curvatore H is asymptotic to a constant at infinity (with a suitable decay rate). No smoothness ssumptions are required on H. We consider also the Dirichlet problem.... %B Atti .Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 18 (2007) 209-219 %G en_US %U http://hdl.handle.net/1963/1753 %1 2791 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-20T11:28:05Z\\nNo. of bitstreams: 1\\n36M.pdf: 150157 bytes, checksum: 61fa8ec27fb7c35396978c1aa4dd26fd (MD5) %0 Journal Article %J J. Math. Phys. 48 (2007) 102102 %D 2007 %T Role of scaling limits in the rigorous analysis of Bose-Einstein condensation %A Alessandro Michelangeli %X In the context of the rigorous analysis of Bose-Einstein condensation, recent achievements have been obtained in the form of asymptotic results when some appropriate scaling is performed in the Hamiltonian, and the limit of infinite number of particles is taken. In particular, two modified thermodynamic limits of infinite dilution turned out to provide an insight in this analysis, the so-\\ncalled Gross-Pitaevskii limit and the related Tomas-Fermi limit. Here such scalings are discussed with respect to their physical and mathematical motivations, and to the currently known results obtained within this framework. %B J. Math. Phys. 48 (2007) 102102 %G en_US %U http://hdl.handle.net/1963/1984 %1 2212 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-07-26T14:30:55Z\\nNo. of bitstreams: 1\\n14-2007-MP.pdf: 485881 bytes, checksum: 3cf7764eded7853d876ad4793569bdfa (MD5) %R 10.1063/1.2783114 %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907 %D 2006 %T Radial solutions concentrating on spheres of nonlinear Schrödinger equations with vanishing potentials %A Antonio Ambrosetti %A David Ruiz %X We prove the existence of radial solutions of 1.2) concentrating at a sphere for potentials which might be zero and might decay to zero at\\r\\ninfinity. The proofs use a perturbation technique in a variational setting, through a Lyapunov-Schmidt reduction. %B Proc. Roy. Soc. Edinburgh Sect. A 136 (2006) 889-907 %G en_US %U http://hdl.handle.net/1963/1755 %1 2789 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-20T13:11:31Z\\r\\nNo. of bitstreams: 1\\r\\n38M.pdf: 251285 bytes, checksum: e0773652a2fcb13cab0758778b6ea906 (MD5) %R 10.1017/S0308210500004789 %0 Book Section %B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. %D 2006 %T Recent analytical developments in micromagnetics %A Antonio DeSimone %A Robert V. Kohn %A Stefan Müller %A Felix Otto %B The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. %@ 978-0-12-480874-4 %G en_US %U http://hdl.handle.net/1963/2230 %1 2014 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T15:16:57Z\\nNo. of bitstreams: 1\\nDKMO.pdf: 1644450 bytes, checksum: 4c1079e4854e372d31af9a285f87f400 (MD5) %0 Journal Article %J J. Math. Phys. 47 (2006) 032104 %D 2006 %T Reflection symmetries for multiqubit density operators %A Claudio Altafini %A Timothy F. Havel %X For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states. %B J. Math. Phys. 47 (2006) 032104 %G en_US %U http://hdl.handle.net/1963/2121 %1 2122 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T06:51:45Z\\nNo. of bitstreams: 1\\n0405123v2.pdf: 247264 bytes, checksum: c504f911bff46e503941a0298617759a (MD5) %R 10.1063/1.2181827 %0 Journal Article %J Journal of Mathematical Sciences 126 (2005) 1561-1573 %D 2005 %T Regularity properties of optimal trajectories of single-input control systems in dimension three %A Mario Sigalotti %X Let q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories. %B Journal of Mathematical Sciences 126 (2005) 1561-1573 %I Springer %G en %U http://hdl.handle.net/1963/4794 %1 4564 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-17T08:06:19Z\\nNo. of bitstreams: 1\\nsuz.pdf: 199707 bytes, checksum: 1d18998eb7281177da4a442135d9b77d (MD5) %R 10.1007/s10958-005-0044-z %0 Journal Article %J ESAIM: COCV 10 (2004) 526-548 %D 2004 %T Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric %A Claudio Altafini %X For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential map and the Lie group exponential map do not coincide. The consequence is that the reduced equations look more complicated than the original ones. The main scope of this paper is to treat the reduction of second order variational problems (corresponding to geometric splines) on such semidirect products of Lie groups. Due to the semidirect structure, a number of extra terms appears in the reduction, terms that are calculated explicitely. The result is used to compute the necessary conditions of an optimal control problem for a simple mechanical control system having invariant Lagrangian equal to the kinetic energy corresponding to the metric tensor. As an example, the case of a rigid body on the Special Euclidean group is considered in detail. %B ESAIM: COCV 10 (2004) 526-548 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3521 %1 743 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-18T11:36:09Z\\nNo. of bitstreams: 1\\ncocv0318.pdf: 296243 bytes, checksum: d9c2fc54e6a7b051fd350dfc5556c06e (MD5) %R 10.1051/cocv:2004018 %0 Journal Article %J Phys. Rev. A 70 (2004) 032331 %D 2004 %T Representing multiqubit unitary evolutions via Stokes tensors %A Claudio Altafini %X For the Stokes tensor parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at the infinitesimal level. The main advantage of this formalism (clearly reminiscent of the ideas of ``coherences\\\'\\\' and ``coupling Hamiltonians\\\'\\\' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows to compute explicitly a Rodrigues\\\' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows to express the Cartan decomposition of unitary propagators as a linear action directly in terms of the infinitesimal generators. %B Phys. Rev. A 70 (2004) 032331 %G en_US %U http://hdl.handle.net/1963/2307 %1 1709 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T12:24:28Z\\nNo. of bitstreams: 1\\n0404006v2.pdf: 225292 bytes, checksum: 7e44f5dc452e09ecabe9744c757b4b03 (MD5) %R 10.1103/PhysRevA.70.032331 %0 Journal Article %J ESAIM COCV 10 (2004) 593-614 %D 2004 %T Resonance of minimizers for n-level quantum systems with an arbitrary cost %A Ugo Boscain %A Grégoire Charlot %X 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. %B ESAIM COCV 10 (2004) 593-614 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2910 %1 1790 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:22:45Z\\nNo. of bitstreams: 1\\n0308103v2.pdf: 290972 bytes, checksum: 2195a0a0002da9f91cbc9fff24262981 (MD5) %R 10.1051/cocv:2004022 %0 Journal Article %J J. Anal. Math. 94 (2004) 265-291 %D 2004 %T The role of the spectrum of the Laplace operator on \\\\S2 in the H-bubble problem %A Roberta Musina %B J. Anal. Math. 94 (2004) 265-291 %I Hebrew University Magnes Press %G en_US %U http://hdl.handle.net/1963/2894 %1 1806 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T08:25:18Z\\nNo. of bitstreams: 1\\n30-03.pdf: 329914 bytes, checksum: 3895c2d75f9be226052e7d4797d7cd9c (MD5) %R 10.1007/BF02789050 %0 Journal Article %J Ann. Henri Poincare 5 (2004) 773-808 %D 2004 %T Rotating Singular Perturbations of the Laplacian %A Michele Correggi %A Gianfausto Dell'Antonio %X 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). %B Ann. Henri Poincare 5 (2004) 773-808 %I Springer %G en_US %U http://hdl.handle.net/1963/2945 %1 1755 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-15T08:20:31Z\\nNo. of bitstreams: 1\\nmath-ph0307056.pdf: 360658 bytes, checksum: 16a12ce4dfd525b63e0a6e703ef9d7bf (MD5) %R 10.1007/s00023-004-0182-8 %0 Journal Article %J IEEE Trans. Automat. Contr. 47 (2002) 546-563 %D 2002 %T On the reachability of quantized control systems %A Antonio Bicchi %A Alessia Marigo %A Benedetto Piccoli %X In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed. %B IEEE Trans. Automat. Contr. 47 (2002) 546-563 %I SISSA Library %G en %U http://hdl.handle.net/1963/1501 %1 2662 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:18Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1109/9.995034 %0 Journal Article %J Systems Control Lett. 47 (2002) 343-353 %D 2002 %T The reachable set of a linear endogenous switching system %A Claudio Altafini %X In this work, switching systems are named endogenous when their switching pattern is controllable. Linear endogenous switching systems can be considered as a particular class of bilinear control systems. The key idea is that both types of systems are equivalent to polysystems, i.e. to systems whose flow is piecewise smooth. The reachable set of a linear endogenous switching system can be studied consequently. The main result is that, in general, it has the structure of a semigroup, even when the Lie algebra rank condition is satisfied since the logic inputs cannot reverse the direction of the flow. The adaptation of existing controllability criteria for bilinear systems is straightforward. %B Systems Control Lett. 47 (2002) 343-353 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3142 %1 1191 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-20T10:54:15Z\\nNo. of bitstreams: 1\\nreachswitch.pdf: 196896 bytes, checksum: 2682b7b9d90c38e08cffe3e8e9228d73 (MD5) %R 10.1016/S0167-6911(02)00228-1 %0 Journal Article %J Math. Nachr. 238 (2002) 23-36 %D 2002 %T Relatively stable bundles over elliptic fibrations %A Claudio Bartocci %A Ugo Bruzzo %A Daniel Hernandez Ruiperez %A Jose M. Munoz Porras %X We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah\\\'s and Tu\\\'s results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree. %B Math. Nachr. 238 (2002) 23-36 %I Wiley %G en_US %U http://hdl.handle.net/1963/3132 %1 1201 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-17T07:37:19Z\\nNo. of bitstreams: 1\\n0109123v2.pdf: 199719 bytes, checksum: b8757f4871a0f0fd621bc8f115792a5c (MD5) %0 Book Section %B Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 %D 2000 %T Reachability Analysis for a Class of Quantized Control Systems %A Alessia Marigo %A Benedetto Piccoli %A Antonio Bicchi %X We study control systems whose input sets are quantized. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some results on the reachable set of linear quantized systems, and study in detail an interesting class of nonlinear systems, forming the discrete counterpart of driftless nonholonomic continuous systems. For such systems, we provide a complete characterization of the reachable set, and, in the case the set is discrete, a computable method to describe its lattice structure. %B Proc. 39th IEEE Int. Conf. on Decision and Control 4 (2000) 3963-3968 %I IEEE %G en_US %U http://hdl.handle.net/1963/3518 %1 746 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-18T10:49:16Z\\nNo. of bitstreams: 1\\nquantized-CDC00.pdf: 249884 bytes, checksum: b54871be602650ae79a8f293167c1a1c (MD5) %R 10.1109/CDC.2000.912333 %0 Journal Article %J Theor. Math. Phys. 122 (2000) 176-192 %D 2000 %T Reduction of bi-Hamiltonian systems and separation of variables: an example from the Boussinesq hierarchy %A Gregorio Falqui %A Franco Magri %A G. Tondo %X We discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel\\\'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations. %B Theor. Math. Phys. 122 (2000) 176-192 %I Springer %G en_US %U http://hdl.handle.net/1963/3219 %1 1082 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T17:15:49Z\\nNo. of bitstreams: 1\\n9906009v1.pdf: 207707 bytes, checksum: 488733797e10a7277aa5f36438c6b2d8 (MD5) %R 10.1007/BF02551195 %0 Journal Article %J SIAM J. Control Optim. 39 (2000) 359-410 %D 2000 %T Regular Synthesis and Sufficiency Conditions for Optimality %A Benedetto Piccoli %A Hector J. Sussmann %X We propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side. %B SIAM J. Control Optim. 39 (2000) 359-410 %I SIAM %G en_US %U http://hdl.handle.net/1963/3213 %1 1088 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T10:03:13Z\\nNo. of bitstreams: 1\\npiccolisussmann.pdf: 302609 bytes, checksum: 5cd7041b7e00172b4670a5e17f815e63 (MD5) %R 10.1137/S0363012999322031 %0 Journal Article %J Int. J. Mod. Phys. B 14 (2000) 721-727 %D 2000 %T A Remark on One-Dimensional Many-Body Problems with Point Interactions %A Sergio Albeverio %A Ludwik Dabrowski %A Shao-Ming Fei %X The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\\\\delta$-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics. %B Int. J. Mod. Phys. B 14 (2000) 721-727 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3214 %1 1087 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T11:10:07Z\\nNo. of bitstreams: 1\\n0001089v1.pdf: 116474 bytes, checksum: e9cac488b17f06674f7abc822769dc6a (MD5) %R 10.1142/S0217979200000601 %0 Report %D 1999 %T Recurrent procedure for the determination of the free energy ε^2 expansion in the topological string theory %A Boris Dubrovin %A Andrei Ya A Maltsev %XWe present here the iteration procedure for the determination of free energy ǫ2-expansion using the theory of KdV - type equations. In our approach we use the conservation laws for KdV - type equations depending explicitly on times t1, t2, . . . to find the ǫ2-expansion of u(x, t1, t2, . . .) after the infinite number of shifts of u(x, 0, 0, . . .) ≡ x along t1, t2, . . . in recurrent form. The formulas for the free energy expansion are just obtained then as a result of quite simple integration procedure applied to un(x).

%B arXiv:solv-int/990400 %I SISSA %G en %U http://hdl.handle.net/1963/6489 %1 6421 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:03:06Z No. of bitstreams: 1 dubrovin_maltsev_1999.pdf: 156918 bytes, checksum: b8e98c45d6ed83c8762446339a79418a (MD5) %0 Journal Article %J Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 %D 1999 %T Renormalized solutions of elliptic equations with general measure data %A Gianni Dal Maso %A Francois Murat %A Luigi Orsina %A Alain Prignet %B Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 741-808 %I Scuola Normale Superiore di Pisa %G en %U http://hdl.handle.net/1963/1236 %1 2707 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:08Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J Advances in Hamiltonian systems (Rome, 1981), 1--22, Ann. CEREMADE, Birkhauser Boston, Boston, MA, 1983. %D 1981 %T Recent advances in the study of the existence of periodic orbits of Hamiltonian systems %A Antonio Ambrosetti %B Advances in Hamiltonian systems (Rome, 1981), 1--22, Ann. CEREMADE, Birkhauser Boston, Boston, MA, 1983. %I SISSA Library %G en %U http://hdl.handle.net/1963/159 %1 3808 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:26:05Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1982