In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed. The algorithm proposed operates with a user defined number of arbitrary shaped or NACA airfoil sections, and employs arbitrary degree NURBS to represent the chord, pitch, skew and rake distribution as a function of the blade radial coordinate. The control points of such curves have been modified to generate, in a fully automated way, a family of blade geometries depending on as many as 20 shape parameters. Such geometries have then been used to carry out potential flow simulations with the Boundary Element Method based software PROCAL. Given the high number of parameters considered, such a preliminary stage allowed for a fast evaluation of the performance of several hundreds of shapes. In addition, the data obtained from the potential flow simulation allowed for the application of a parameter space reduction methodology based on active subspaces (AS) property, which suggested that the main propeller performance indices are, at a first but rather accurate approximation, only depending on a single parameter which is a linear combination of all the original geometric ones. AS analysis has also been used to carry out a constrained optimization exploiting response surface method in the reduced parameter space, and a sensitivity analysis based on such surrogate model. The few selected shapes were finally used to set up high fidelity RANS simulations and select an optimal shape.

%B VIII International Conference on Computational Methods in Marine Engineering %G eng %0 Journal Article %J Stochastic Processes and their Applications %D 2019 %T An entropic interpolation proof of the HWI inequality %A Ivan Gentil %A Christian Léonard %A Luigia Ripani %A Luca Tamanini %K Entropic interpolations %K Fisher information %K Relative entropy %K Schrödinger problem %K Wasserstein distance %XThe HWI inequality is an “interpolation”inequality between the Entropy H, the Fisher information I and the Wasserstein distance W. We present a pathwise proof of the HWI inequality which is obtained through a zero noise limit of the Schrödinger problem. Our approach consists in making rigorous the Otto–Villani heuristics in Otto and Villani (2000) taking advantage of the entropic interpolations, which are regular both in space and time, rather than the displacement ones.

%B Stochastic Processes and their Applications %G eng %U http://www.sciencedirect.com/science/article/pii/S0304414918303454 %R https://doi.org/10.1016/j.spa.2019.04.002 %0 Journal Article %J Phil. Trans. R. Soc. A %D 2019 %T On the existence of elastic minimizers for initially stressed materials %A Davide Riccobelli %A A. Agosti %A Pasquale Ciarletta %B Phil. Trans. R. Soc. A %I The Royal Society %V 377 %G eng %0 Journal Article %J Journal of Physics A: Mathematical and Theoretical %D 2018 %T Effective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate %A Alessandro Michelangeli %A Alessandro Olgiati %XWe derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.

%B Journal of Physics A: Mathematical and Theoretical %I IOP Publishing %V 51 %P 405201 %8 sep %G eng %U https://doi.org/10.1088%2F1751-8121%2Faadbc2 %R 10.1088/1751-8121/aadbc2 %0 Conference Proceedings %B The 28th International Ocean and Polar Engineering Conference %D 2018 %T An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment %A Nicola Demo %A Marco Tezzele %A Andrea Mola %A Gianluigi Rozza %K Active subspaces %K Boundary element method %K Dynamic mode decomposition %K Fluid structure interaction %K Free form deformation %K Fully nonlinear potential %K Numerical towing tank %X In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Given the high number of parameters involved - which might result in a high number of time consuming hydrodynamic simulations - assessing whether the parameters space can be reduced would lead to considerable computational cost reduction. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is which is a common benchmark in ship hydrodynamics simulations. %B The 28th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %C Sapporo, Japan %G eng %U https://www.onepetro.org/conference-paper/ISOPE-I-18-481 %0 Generic %D 2018 %T The Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows %A Saddam Hijazi %A Shafqat Ali %A Giovanni Stabile %A Francesco Ballarin %A Gianluigi Rozza %G eng %0 Report %D 2018 %T Energy-dissipation balance of a smooth moving crack %A Maicol Caponi %A Ilaria Lucardesi %A Emanuele Tasso %X 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. %G en %U http://preprints.sissa.it/handle/1963/35320 %1 35630 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-08-01T09:36:30Z No. of bitstreams: 1 CLT-preprint.pdf: 455925 bytes, checksum: 931583a37609035d6be19feceb41142d (MD5) %0 Report %D 2018 %T Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping %A Lorenzo Nardini %A Filippo Riva %XIn this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.

%G en %U http://preprints.sissa.it/handle/1963/35319 %1 35629 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-07-16T13:11:24Z No. of bitstreams: 1 PREPRINT_28_2018_mate.pdf: 600708 bytes, checksum: 04321c1f671175dc8cf001c358699cba (MD5) %0 Report %D 2018 %T Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks. %G en %U http://preprints.sissa.it/handle/1963/35308 %1 35616 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-19T09:02:45Z No. of bitstreams: 1 DM-Lar-Toa-sissa.pdf: 429343 bytes, checksum: 82817f96da6dcabff29c2c322590fb66 (MD5) %0 Report %D 2018 %T Existence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation %A Maicol Caponi %X 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. %G en %U http://preprints.sissa.it/handle/1963/35307 %1 35614 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-03-05T16:29:01Z No. of bitstreams: 1 PhFiMo_Caponi.pdf: 418992 bytes, checksum: 6bf6de00d58052411ec3a588e2f7933e (MD5) %0 Journal Article %J The Journal of Open Source Software %D 2018 %T EZyRB: Easy Reduced Basis method %A Nicola Demo %A Marco Tezzele %A Gianluigi Rozza %B The Journal of Open Source Software %V 3 %P 661 %G eng %U https://joss.theoj.org/papers/10.21105/joss.00661 %R 10.21105/joss.00661 %0 Report %D 2017 %T On the effect of interactions beyond nearest neighbours on non-convex lattice systems %A Roberto Alicandro %A Giuliano Lazzaroni %A Mariapia Palombaro %X We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation. %G en %U http://urania.sissa.it/xmlui/handle/1963/35268 %1 35574 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-16T12:38:33Z No. of bitstreams: 1 Lazzaroni_preprint_57_2016.pdf: 249941 bytes, checksum: e60963aab015e1fc146068240f824f79 (MD5) %0 Book Section %B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %D 2017 %T Effective Non-linear Dynamics of Binary Condensates and Open Problems %A Alessandro Olgiati %E Alessandro Michelangeli %E Gianfausto Dell'Antonio %XWe report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Schödinger equations. After reviewing and commenting our proof in the mean-field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.

%B Advances in Quantum Mechanics: Contemporary Trends and Open Problems %I Springer International Publishing %C Cham %P 239–256 %@ 978-3-319-58904-6 %G eng %U https://doi.org/10.1007/978-3-319-58904-6_14 %R 10.1007/978-3-319-58904-6_14 %0 Report %D 2017 %T Elliptic diffeomorphisms of symplectic 4-manifolds %A Vsevolod Shevchishin %A Gleb Smirnov %G eng %U https://arxiv.org/pdf/1708.01518.pdf %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %T Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening %A Stefano Almi %XIn the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

%B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %V 23 %P 791–826 %8 05/2017 %G eng %U https://www.esaim-cocv.org/component/article?access=doi&doi=10.1051/cocv/2016014 %R 10.1051/cocv/2016014 %0 Report %D 2016 %T Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces %A Nicola Gigli %A Enrico Pasqualetto %G eng %0 Journal Article %J JOURNAL OF SCIENTIFIC COMPUTING %D 2016 %T Error Estimates of B-spline based finite-element method for the wind-driven ocean circulation %A Rotundo, N. %A Kim, T. -Y. %A Jiang, W. %A Luca Heltai %A Fried, E. %B JOURNAL OF SCIENTIFIC COMPUTING %V 69 %P 430–459 %G eng %R 10.1007/s10915-016-0201-1 %0 Report %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non convex flux II %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %G en %U http://urania.sissa.it/xmlui/handle/1963/35197 %1 35494 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-06-21T11:33:07Z No. of bitstreams: 1 file2ABCottobre2015.pdf: 486411 bytes, checksum: cbdd0bce26d338707c03a61c42ec725e (MD5) %0 Journal Article %J Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %D 2016 %T Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux I %A Giovanni Alberti %A Stefano Bianchini %A Laura Caravenna %B Journal of Differential Equations, vol. 261, issue 8 (2016): 4298-4337 %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35207 %1 35507 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-09-05T15:06:32Z No. of bitstreams: 1 1512.04863v2_Caravenna.pdf: 1192837 bytes, checksum: 15e7fc975989af0ea19654f4eafd84a7 (MD5) %R 10.1016/j.jde.2016.06.026 %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants %A Mikhail Bershtein %A Giulio Bonelli %A Massimiliano Ronzani %A Alessandro Tanzini %XWe provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

%B Journal of High Energy Physics %V 2016 %P 23 %8 Jul %G eng %U https://doi.org/10.1007/JHEP07(2016)023 %R 10.1007/JHEP07(2016)023 %0 Journal Article %J Journal of Functional Analysis %D 2016 %T Existence and non-existence results for the SU(3) singular Toda system on compact surfaces %A Luca Battaglia %A Andrea Malchiodi %K Liouville-type equations %K Min–max solutions %K Non-existence results %K Toda system %XWe consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."

%B Journal of Functional Analysis %V 270 %P 3750 - 3807 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022123615004942 %R https://doi.org/10.1016/j.jfa.2015.12.011 %0 Journal Article %J Journal of Differential Equations %D 2016 %T Existence and uniqueness of dynamic evolutions for a peeling test in dimension one %A Gianni Dal Maso %A Giuliano Lazzaroni %A Lorenzo Nardini %K Dynamic debonding %K Dynamic energy release rate %K Dynamic fracture %K Griffith's criterion %K Maximum dissipation principle %K Wave equation in time-dependent domains %XIn this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

%B Journal of Differential Equations %V 261 %P 4897 - 4923 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616301772 %R https://doi.org/10.1016/j.jde.2016.07.012 %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 2015 %T Existence and multiplicity result for the singular Toda system %A Luca Battaglia %K Existence result %K Liouville-type equations %K Multiplicity result %K PDEs on compact surfaces %K Toda system %XWe consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

%B Journal of Mathematical Analysis and Applications %V 424 %P 49 - 85 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022247X14010191 %R https://doi.org/10.1016/j.jmaa.2014.10.081 %0 Report %D 2015 %T Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions. %G en %U http://urania.sissa.it/xmlui/handle/1963/35045 %1 35277 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2015-11-18T15:46:32Z No. of bitstreams: 1 DM-Lar-Toa-SISSA.pdf: 313034 bytes, checksum: 76419fd2c8c435ae7deeca773b424667 (MD5) %0 Journal Article %J Adv. Differential Equations 20 (2015), 937–982. %D 2015 %T Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems %A Guglielmo Feltrin %A Fabio Zanolin %XWe prove the existence of positive periodic solutions for the second order nonlinear equation u'' + a(x) g(u) = 0, where g(u) has superlinear growth at zero and at infinity. The weight function a(x) is allowed to change its sign. Necessary and sufficient conditions for the existence of nontrivial solutions are obtained. The proof is based on Mawhin's coincidence degree and applies also to Neumann boundary conditions. Applications are given to the search of positive solutions for a nonlinear PDE in annular domains and for a periodic problem associated to a non-Hamiltonian equation.

%B Adv. Differential Equations 20 (2015), 937–982. %I Khayyam Publishing %G en %U http://projecteuclid.org/euclid.ade/1435064518 %1 35388 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-18T08:49:04Z No. of bitstreams: 1 FeltrinZanolin_ade2015.pdf: 321052 bytes, checksum: 38a45a1515a02fc86751b5f088bbfbfb (MD5) %0 Journal Article %J Conference Publications %D 2015 %T Existence of positive solutions of a superlinear boundary value problem with indefinite weight %A Guglielmo Feltrin %K boundary value problem %K indefinite weight %K Positive solution; existence result. %K superlinear equation %XWe deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change sign. We assume that the function $g\colon\mathopen[0,+∞\mathclose[\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, including the superlinear case $g(s)=s^p$, with $p>1$. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.

%B Conference Publications %V 2015 %P 436 %G eng %U http://aimsciences.org//article/id/b3c1c765-e8f5-416e-8130-05cc48478026 %R 10.3934/proc.2015.0436 %0 Conference Paper %B International Conference on Parallel Processing and Applied Mathematics %D 2015 %T Experience on vectorizing lattice Boltzmann kernels for multi-and many-core architectures %A Calore, Enrico %A Nicola Demo %A Schifano, Sebastiano Fabio %A Tripiccione, Raffaele %B International Conference on Parallel Processing and Applied Mathematics %I Springer %P 53–62 %G eng %0 Report %D 2015 %T Explicit formulas for relaxed disarrangement densities arising from structured deformations %A Ana Cristina Barroso %A Jose Matias %A Marco Morandotti %A David R. Owen %X Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disarrangements) at submacroscopic levels. For each (first-order) structured deformation (g,G) of a continuous body, the tensor field G is known to be a measure of deformations without disarrangements, and M:=∇g−G is known to be a measure of deformations due to disarrangements. The tensor fields G and M together deliver not only standard notions of plastic deformation, but M and its curl deliver the Burgers vector field associated with closed curves in the body and the dislocation density field used in describing geometrical changes in bodies with defects. Recently, Owen and Paroni [13] evaluated explicitly some relaxed energy densities arising in Choksi and Fonseca’s energetics of structured deformations [4] and thereby showed: (1) (trM)+ , the positive part of trM, is a volume density of disarrangements due to submacroscopic separations, (2) (trM)−, the negative part of trM, is a volume density of disarrangements due to submacroscopic switches and interpenetrations, and (3) trM, the absolute value of trM, is a volume density of all three of these non-tangential disarrangements: separations, switches, and interpenetrations. The main contribution of the present research is to show that a different approach to the energetics of structured deformations, that due to Ba\'{i}a, Matias, and Santos [1], confirms the roles of (trM)+, (trM)−, and trM established by Owen and Paroni. In doing so, we give an alternative, shorter proof of Owen and Paroni’s results, and we establish additional explicit formulas for other measures of disarrangements. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34492 %1 34687 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-08-28T10:09:53Z No. of bitstreams: 1 SISSA_Preprint_37_2015_MATE.pdf: 315599 bytes, checksum: 2bd676c192205d3a2edd7c48bf53c11c (MD5) %0 Report %D 2015 %T Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials %A Boris Dubrovin %A Ian A.B. Strachan %A Youjin Zhang %A Dafeng Zuo %X For the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35316 %1 35625 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-05-23T10:53:54Z No. of bitstreams: 1 1510.08690.pdf: 433692 bytes, checksum: 0cd6111d36bb3b57262400e1f1cebe3a (MD5) %0 Journal Article %D 2014 %T Editorial %A Ciro Ciliberto %A Gianni Dal Maso %A Pasquale Vetro %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34712 %1 34926 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T10:50:12Z (GMT) No. of bitstreams: 0 %R 10.1007/s12215-014-0172-8 %0 Journal Article %D 2014 %T An effective model for nematic liquid crystal composites with ferromagnetic inclusions %A Maria Carme Calderer %A Antonio DeSimone %A Dmitry Golovaty %A Alexander Panchenko %X 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. %I Society for Industrial and Applied Mathematics Publications %G en %U http://urania.sissa.it/xmlui/handle/1963/34940 %1 35194 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-09T09:28:26Z No. of bitstreams: 1 preprint2014.pdf: 284611 bytes, checksum: ef4123b4aefb1a36fa198c1207a6f021 (MD5) %R 10.1137/130910348 %0 Report %D 2014 %T An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier-Stokes flows %A Andrea Manzoni %K Reduced Basis Method, parametrized Navier-Stokes equations, steady incompressible fluids, a posteriori error estimation, approximation stability %X We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier-Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [Deparis, Veroy & Patera, Quarteroni & Rozza] to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled Offline/Online procedure in order to speedup the solution of the reduced-order problem. This is particularly suitable for real-time and many-query contexts, which are both part of our final goal. Furthermore, we present an efficient numerical implementation for treating nonlinear advection terms in a convenient way. A residual-based a posteriori error estimation with respect to a truth, full-order Finite Element approximation is provided for joint pressure/velocity errors, according to the Brezzi-Rappaz-Raviart stability theory. To do this, we take advantage of an extension of the Successive Constraint Method for the estimation of stability factors and of a suitable fixed-point algorithm for the approximation of Sobolev embedding constants. Finally, we present some numerical test cases, in order to show both the approximation properties and the computational efficiency of the derived framework. %G en %1 7291 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Andrea Manzoni (amanzoni@sissa.it) on 2014-02-12T17:36:11Z No. of bitstreams: 1 AM_2014_M2AN_preprint.pdf: 5678588 bytes, checksum: 9589729cb84fffc5229b4b071e5e69fb (MD5) %0 Journal Article %J International Journal of Computational Fluid Dynamics %D 2014 %T Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems %A Forti, D. %A Gianluigi Rozza %X We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid–structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid–structure applications in several fields. The examples provided deal with aeronautics and wind engineering. %B International Journal of Computational Fluid Dynamics %V 28 %P 158–169 %G eng %R 10.1080/10618562.2014.932352 %0 Journal Article %D 2014 %T Existence and uniqueness of the gradient flow of the Entropy in the space of probability measures %A Stefano Bianchini %A Alexander Dabrowski %X After a brief introduction on gradient flows in metric spaces and on geodesically convex functionals, we give an account of the proof (following the outline of [3, 7]) of the existence and uniqueness of the gradient flow of the Entropy in the space of Borel probability measures over a compact geodesic metric space with Ricci curvature bounded from below. %I EUT Edizioni Universita di Trieste %G en %U http://urania.sissa.it/xmlui/handle/1963/34693 %1 34907 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-10-22T09:22:40Z No. of bitstreams: 1 ExUniqGFEntropy.pdf: 344636 bytes, checksum: a918d50ab5d6b9ce9cb8683238f402e6 (MD5) %0 Journal Article %J Annales de l'Institut Henri Poincare (C) Non Linear Analysis %D 2014 %T Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds %A Andrea Mondino %A Johannes Schygulla %K Direct methods in the calculus of variations %K General Relativity %K Geometric measure theory %K second fundamental form %K Willmore functional %XWe study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric with perturbation small in $C^1$ norm and of compact support, we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>0$ then there exists a smooth embedding $ f:\mathbb{S}^2 \hookrightarrow M$ minimizing the Willmore functional $\frac{1}{4}\int |H|^2$, where $H$ is the mean curvature. Second, assuming that $(M,h)$ is of bounded geometry (i.e. bounded sectional curvature and strictly positive injectivity radius) and asymptotically euclidean or hyperbolic we prove that if there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$ then there exists a smooth immersion $f:\mathbb{S}^2\hookrightarrow M$ minimizing the functional $\int (\frac{1}{2}|A|^2+1)$, where $A$ is the second fundamental form. Finally, adding the bound $K^M \leq 2$ to the last assumptions, we obtain a smooth minimizer $f:\mathbb{S}^2 \hookrightarrow M$ for the functional $\int \frac{1}{4}(|H|^2+1)$. The assumptions of the last two theorems are satisfied in a large class of 3-manifolds arising as spacelike timeslices solutions of the Einstein vacuum equation in case of null or negative cosmological constant.

%B Annales de l'Institut Henri Poincare (C) Non Linear Analysis %V 31 %P 707 - 724 %G eng %U http://www.sciencedirect.com/science/article/pii/S0294144913000851 %R https://doi.org/10.1016/j.anihpc.2013.07.002 %0 Journal Article %J Mathematische Annalen %D 2014 %T Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds %A Kuwert, Ernst %A Andrea Mondino %A Johannes Schygulla %XWe study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold $M$. Under the assumption that the sectional curvature $K^M$ is strictly positive, we prove the existence of a smooth immersion $f:{\mathbb{S}}^2 \rightarrow M$ minimizing the $L^2$ integral of the second fundamental form. Assuming instead that $K^M \leq 2 $ and that there is some point $\bar{x}\in M$ with scalar curvature $R^M(\bar{x})>6$, we obtain a smooth minimizer $f:{\mathbb{S}}^2 \rightarrow M$ for the functional $\int \frac{1}{4}|H|^2+1$, where $H$ is the mean curvature.

%B Mathematische Annalen %V 359 %P 379–425 %8 Jun %G eng %U https://doi.org/10.1007/s00208-013-1005-3 %R 10.1007/s00208-013-1005-3 %0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2014 %T Existence of integral m-varifolds minimizing $\int |A|^p $ and $\int |H|^p$ , p>m, in Riemannian manifolds %A Andrea Mondino %XWe prove existence of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2 \leq m<n$ and $p>m$ under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in ${\mathbb{R }^S}$ involving $\int |H|^p$to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.

%B Calculus of Variations and Partial Differential Equations %V 49 %P 431–470 %8 Jan %G eng %U https://doi.org/10.1007/s00526-012-0588-y %R 10.1007/s00526-012-0588-y %0 Journal Article %J PloS one. Volume 8, Issue 7, July 2013 : e68078 %D 2013 %T Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus %A Giovanni Iacono %A Claudio Altafini %A Vincent Torre %X Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box. %B PloS one. Volume 8, Issue 7, July 2013 : e68078 %I Public Library of Science %G en %U http://hdl.handle.net/1963/7287 %1 7332 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-14T11:26:18Z No. of bitstreams: 1 journal.pone.0068078.pdf: 1188661 bytes, checksum: 29e83864b33fd1a072fe4ab4da6fcc17 (MD5) %R 10.1371/journal.pone.0068078 %0 Journal Article %J ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189 %D 2013 %T Epitaxially strained elastic films: the case of anisotropic surface energies %A Marco Bonacini %XIn the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer of the total energy. The main tool used to obtain these results is a minimality criterion based on the positivity of the second variation.

%B ESAIM Control. Optim. Calc. Var. 19 (2013) 167-189 %I EDP Sciences %G en %U http://hdl.handle.net/1963/4268 %1 3999 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T15:17:45Z\\r\\nNo. of bitstreams: 1\\r\\nbonacini_31_M.pdf: 278252 bytes, checksum: ae2b293dfe841dc6e68fcdf2bea68578 (MD5) %R 10.1051/cocv/2012003 %0 Report %D 2013 %T Equilibrium measures for a class of potentials with discrete rotational symmetries %A Ferenc Balogh %A Dario Merzi %X In this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.

%B Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216 %I University of Catania %G en %1 7318 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-11T16:07:36Z No. of bitstreams: 1 1202.0576v1.pdf: 219939 bytes, checksum: 822c73753d6d4194cf48cb0ff9ad0e48 (MD5) %0 Journal Article %J Proceedings of the Royal Society of Edinburgh: Section A Mathematics %D 2013 %T An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime %A Aleks Jevnikar %B Proceedings of the Royal Society of Edinburgh: Section A Mathematics %I Royal Society of Edinburgh Scotland Foundation %V 143 %P 1021–1045 %G eng %R 10.1017/S030821051200042X %0 Journal Article %J Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386 %D 2013 %T Expanded degenerations and pairs %A Dan Abramovich %A Charles Cadman %A Barbara Fantechi %A Jonathan Wise %K Expanded pairs %X 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. %B Communications in Algebra. Volume 41, Issue 6, May 2013, Pages 2346-2386 %I Taylor and Francis %G en %U http://hdl.handle.net/1963/7383 %1 7431 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-18T09:55:33Z No. of bitstreams: 1 1110.2976v1.pdf: 418919 bytes, checksum: 61308c478c1e11ea1c389bd98e227cd2 (MD5) %R 10.1080/00927872.2012.658589 %0 Journal Article %J Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %D 2012 %T Exploring the low-energy landscape of large-scale signed social networks %A Giuseppe Facchetti %A Giovanni Iacono %A Claudio Altafini %X Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers. %B Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %I SISSA %G en %U http://hdl.handle.net/1963/6504 %1 6451 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:27:42Z (GMT) No. of bitstreams: 0 %R 10.1103/PhysRevE.86.036116 %0 Journal Article %J Journal of Differential Equations %D 2011 %T Embedding theorems and existence results for nonlinear Schrödinger–Poisson systems with unbounded and vanishing potentials %A Bonheure, Denis %A Mercuri, Carlo %XMotivated by existence results for positive solutions of non-autonomous nonlinear Schrödinger–Poisson systems with potentials possibly unbounded or vanishing at infinity, we prove embedding theorems for weighted Sobolev spaces. We both consider a general framework and spaces of radially symmetric functions when assuming radial symmetry of the potentials.

%B Journal of Differential Equations %I Elsevier %V 251 %P 1056–1085 %G eng %U https://doi.org/10.1016/j.jde.2011.04.010 %R 10.1016/j.jde.2011.04.010 %0 Journal Article %J Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 %D 2011 %T Energy release rate and stress intensity factor in antiplane elasticity %A Giuliano Lazzaroni %A Rodica Toader %X In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks. %B Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3780 %1 546 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-17T11:50:32Z\\r\\nNo. of bitstreams: 2\\r\\nLazzaroni_67M_2009.pdf: 259616 bytes, checksum: 3c3adef52607bc6238c11a84904a9fb9 (MD5)\\r\\nLazzaroni_67M_2009: 259616 bytes, checksum: 3c3adef52607bc6238c11a84904a9fb9 (MD5) %R 10.1016/j.matpur.2011.01.001 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %D 2011 %T Ennio De Giorgi and Γ-convergence %A Gianni Dal Maso %X Γ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/5308 %1 5138 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-31T12:04:34Z\\nNo. of bitstreams: 0 %R 10.3934/dcds.2011.31.1017 %0 Journal Article %J Communications in Partial Differential Equations 36 (2011) 777-796 %D 2011 %T An Estimate on the Flow Generated by Monotone Operators %A Stefano Bianchini %A Matteo Gloyer %B Communications in Partial Differential Equations 36 (2011) 777-796 %I Taylor & Francis %G en_US %U http://hdl.handle.net/1963/3646 %1 658 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-10T13:06:54Z\\r\\nNo. of bitstreams: 1\\r\\n29_2009M.pdf: 209332 bytes, checksum: b30a32046e7a3c3c30436e84c03dc6d3 (MD5) %R 10.1080/03605302.2010.534224 %0 Journal Article %J SIAM J. Math. Anal. %D 2011 %T An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

%B SIAM J. Math. Anal. %I Society for Industrial and Applied Mathematics %V 43 %P 1345-1368 %G en_US %U http://hdl.handle.net/1963/3894 %1 815 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T11:44:06Z\\r\\nNo. of bitstreams: 1\\r\\nMorandotti_44M.pdf: 217358 bytes, checksum: 4c362016bb2220e7a97805254b7fb870 (MD5) %R 10.1137/10080083X %0 Journal Article %J Rend. Lincei Mat. Appl. 22 (2011) 387-408 %D 2011 %T Existence for wave equations on domains with arbitrary growing cracks %A Gianni Dal Maso %A Cristopher J. Larsen %K Wave equation %X In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation. %B Rend. Lincei Mat. Appl. 22 (2011) 387-408 %I European Mathematical Society %G en %U http://hdl.handle.net/1963/4284 %1 4015 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-27T09:09:30Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Lar_32_M.pdf: 223891 bytes, checksum: 7c6c66b6d21936b33ed0c21574928e24 (MD5) %R 10.4171/RLM/606 %0 Journal Article %J J. Phys. A 43 (2010) 474014 %D 2010 %T Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs %A Gianfausto Dell'Antonio %A Emanuele Costa %X We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph. %B J. Phys. A 43 (2010) 474014 %I IOP Publishing %G en_US %U http://hdl.handle.net/1963/4106 %1 298 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-12-06T13:09:12Z\\nNo. of bitstreams: 1\\n1004.4750v2.pdf: 273649 bytes, checksum: ff34b6647ba206615715d6c764115064 (MD5) %R 10.1088/1751-8113/43/47/474014 %0 Journal Article %J SIAM J. Math. Anal. 42 (2010) 1179-1217 %D 2010 %T Estimates on path functionals over Wasserstein Spaces %A Stefano Bianchini %A Alessio Brancolini %X In this paper we consider the class a functionals (introduced in [Brancolini, Buttazzo, and Santambrogio, J. Eur. Math. Soc. (JEMS), 8 (2006), pp. 415-434] $\\\\mathcal{G}_{r,p}$ defined on Lipschitz curves $\\\\gamma$ valued in the $p$-Wasserstein space. The problem considered is the following: given a measure $\\\\mu$, give conditions in order to assure the existence of a curve $\\\\gamma$ such that $\\\\gamma(0)=\\\\mu$, $\\\\gamma(1)=\\\\delta_{x_0}$, and $\\\\mathcal{G}_{r,p}(\\\\gamma)<+\\\\infty$. To this end, new estimates on $\\\\mathcal{G}_{r,p}(\\\\mu)$ are given, and a notion of dimension of a measure (called path dimension) is introduced: the path dimension specifies the values of the parameters $(r,p)$ for which the answer to the previous reachability problem is positive. Finally, we compare the path dimension with other known dimensions. %B SIAM J. Math. Anal. 42 (2010) 1179-1217 %G en_US %U http://hdl.handle.net/1963/3583 %1 717 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T09:05:25Z\\nNo. of bitstreams: 1\\nestimates_path_functionals.prerint.pdf: 356623 bytes, checksum: 6bc99a8752ef3aae9d1b91d05e8a2f8e (MD5) %R 10.1137/100782693 %0 Journal Article %J Math. Z. 265 (2010) 889-923 %D 2010 %T On the Euler-Lagrange equation for a variational problem : the general case II %A Stefano Bianchini %A Matteo Gloyer %B Math. Z. 265 (2010) 889-923 %G en_US %U http://hdl.handle.net/1963/2551 %1 1568 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-14T09:52:10Z\\nNo. of bitstreams: 1\\ngeneralcase.final.pdf: 315418 bytes, checksum: dee89d593fb956f4a377db9221520eb6 (MD5) %R 10.1007/s00209-009-0547-2 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331 %D 2010 %T Exact reconstruction of damaged color images using a total variation model %A Irene Fonseca %A Giovanni Leoni %A Francesco Maggi %A Massimiliano Morini %X In this paper the reconstruction of damaged piecewice constant color images is studied using a RGB total variation based model for colorization/inpainting. In particular, it is shown that when color is known in a uniformly distributed region, then reconstruction is possible with maximal fidelity. %B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 1291-1331 %I Elsevier %G en_US %U http://hdl.handle.net/1963/4039 %1 363 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-06T09:54:56Z\\nNo. of bitstreams: 1\\nflmm.pdf: 434739 bytes, checksum: f315d8807349e077c524fe14a1619a56 (MD5) %R 10.1016/j.anihpc.2010.06.004 %0 Journal Article %J Proc. Steklov Inst. Math. 270 (2010) 43-56 %D 2010 %T Existence of planar curves minimizing length and curvature %A Ugo Boscain %A Grégoire Charlot %A Francesco Rossi %X 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. %B Proc. Steklov Inst. Math. 270 (2010) 43-56 %I Springer %G en_US %U http://hdl.handle.net/1963/4107 %1 297 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-12-06T13:30:01Z\\nNo. of bitstreams: 1\\n0906.5290v2.pdf: 305594 bytes, checksum: 3966f5a798b69743ce88a29bf73edc47 (MD5) %R 10.1134/S0081543810030041 %0 Journal Article %J Funct. Anal. Appl. 43 (2009) 18-29 %D 2009 %T Equivariant cohomology and localization for Lie algebroids %A Ugo Bruzzo %A Lucio Cirio %A Paolo Rossi %A Vladimir Rubtsov %X 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. %B Funct. Anal. Appl. 43 (2009) 18-29 %@ 978-981-270-377-4 %G en_US %U http://hdl.handle.net/1963/1724 %1 2427 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-26T15:10:18Z\\nNo. of bitstreams: 1\\nmathDG0506392.pdf: 223181 bytes, checksum: bb9437e12cfd3d7cc5c14904aaeebe7d (MD5) %R 10.1007/s10688-009-0003-4 %0 Journal Article %J Bioinformatics 25 (2009) 2853-2854 %D 2009 %T ERNEST: a toolbox for chemical reaction network theory %A Nicola Soranzo %A Claudio Altafini %X Summary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox. %B Bioinformatics 25 (2009) 2853-2854 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3826 %1 501 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-22T11:56:56Z\\nNo. of bitstreams: 1\\nSoAl09.pdf: 30345 bytes, checksum: a3c73c1a74eb623da69be9a9eba3ca72 (MD5) %R 10.1093/bioinformatics/btp513 %0 Journal Article %J Comm. Math. Phys. 289 (2009) 205-252 %D 2009 %T Exact results for topological strings on resolved Yp,q singularities %A Andrea Brini %A Alessandro Tanzini %B Comm. Math. Phys. 289 (2009) 205-252 %G en_US %U http://hdl.handle.net/1963/2631 %1 1492 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-16T11:13:40Z\\nNo. of bitstreams: 1\\npicard-b.pdf: 387933 bytes, checksum: 2261a0d091c9829eb1d1b55b77b1a42e (MD5) %R 10.1007/s00220-009-0814-4 %0 Journal Article %J Nonlinear Anal. 70 (2009) 3002-3007 %D 2009 %T Existence of extremals for the Maz\\\'ya and for the Caffarelli-Kohn-Nirenberg inequalities %A Roberta Musina %X This paper deals with some Sobolev-type inequalities with weights that were proved by Maz\\\'ya in 1980 and by Caffarelli-Kohn-Nirenberg in 1984. %B Nonlinear Anal. 70 (2009) 3002-3007 %G en_US %U http://hdl.handle.net/1963/2739 %1 1961 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-27T08:18:23Z\\nNo. of bitstreams: 1\\nMusinaCortona2.pdf: 220927 bytes, checksum: aeec20cde67e9e00bc1109988f192159 (MD5) %R 10.1016/j.na.2008.12.024 %0 Report %D 2009 %T An existence result for the Monge problem in R^n with norm cost %A Laura Caravenna %G en_US %U http://hdl.handle.net/1963/3647 %1 657 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-10T13:31:00Z\\nNo. of bitstreams: 1\\nMonge.sel.pdf: 1037029 bytes, checksum: 3f852fb5f7d74223ddee50818368c3f5 (MD5) %0 Journal Article %J Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %D 2009 %T On the extremality, uniqueness and optimality of transference plans %A Stefano Bianchini %A Laura Caravenna %X 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. %B Bull. Inst. Math. Acad. Sin. (N.S.) 4 (2009) 353-458 %G en_US %U http://hdl.handle.net/1963/3692 %1 613 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-24T11:10:18Z\\nNo. of bitstreams: 1\\n46M2009.pdf: 485239 bytes, checksum: ebe15dc163dd6bdffcbe875730432b12 (MD5) %0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 %D 2008 %T Entire solutions of autonomous equations on Rn with nontrivial asymptotics %A Andrea Malchiodi %X We prove existence of a new type of solutions for the semilinear equation $- \\\\D u + u = u^p$ on $\\\\R^n$, with $1 < p < \\\\frac{n+2}{n-2}$. These solutions are positive, bounded, decay exponentially to zero away from three half-lines with a common origin, and at infinity are asymptotically periodic. %B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008) 65-72 %G en_US %U http://hdl.handle.net/1963/2640 %1 1483 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-04-30T08:06:29Z\\nNo. of bitstreams: 1\\ngluingnote.pdf: 178833 bytes, checksum: eca0da57985e983d19aac5964c9a1e55 (MD5) %0 Journal Article %J J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %D 2008 %T An entropy based Glimm-type functional %A Laura Caravenna %B J. Hyperbolic Differ. Equ. 5 (2008) 643-662 %I World Scientific %G en_US %U http://hdl.handle.net/1963/4051 %1 351 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-09T11:15:30Z\\nNo. of bitstreams: 1\\nglimm.potential.pdf: 405855 bytes, checksum: e2a5f3fed36ffe727c6d43240482aa6d (MD5) %R 10.1142/S0219891608001635 %0 Journal Article %J Nuovo Cimento B 123 (2008) 181-192 %D 2008 %T Equivalent definitions of asymptotic 100% B.E.C. %A Alessandro Michelangeli %X In the mathematical analysis Bose-Einstein condensates, in particular in the study of the quantum dynamics, some kind of factorisation property has been recently proposed as a convenient technical assumption of condensation. After having surveyed both the standard definition of complete Bose-Einstein condensation in the limit of infinitely many particles and some forms of asymptotic factorisation, we prove that these characterisations are equivalent. %B Nuovo Cimento B 123 (2008) 181-192 %G en_US %U http://hdl.handle.net/1963/2546 %1 1573 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-10T13:15:49Z\\nNo. of bitstreams: 1\\nsissa_preprint102_07.pdf: 215355 bytes, checksum: a09c310627ed3ed9acf1156596e7dd7e (MD5) %R 10.1393/ncb/i2008-10521-y %0 Journal Article %J SIAM J. Math. Anal. 40 (2008) 1104-1122 %D 2008 %T Eulerian calculus for the displacement convexity in the Wasserstein distance %A Sara Daneri %A Giuseppe Savarè %X In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space. %B SIAM J. Math. Anal. 40 (2008) 1104-1122 %I SIAM %G en_US %U http://hdl.handle.net/1963/3413 %1 922 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-09T12:32:55Z\\nNo. of bitstreams: 1\\n0801.2455v1.pdf: 504916 bytes, checksum: 7ccfac515ef559e376c7e7d213bd4091 (MD5) %R 10.1137/08071346X %0 Journal Article %J Ann. of Math. 168 (2008) 813-858 %D 2008 %T Existence of conformal metrics with constant $Q$-curvature %A Zindine Djadli %A Andrea Malchiodi %X Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author. %B Ann. of Math. 168 (2008) 813-858 %G en_US %U http://hdl.handle.net/1963/2308 %1 1708 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:05:55Z\\nNo. of bitstreams: 1\\nDjadliMalchiodiFinal.pdf: 342979 bytes, checksum: fc2b0b8e4e01a5327ed8e01dc1bae6c5 (MD5) %0 Journal Article %J Int. Math. Res. Not. IMRN %D 2007 %T Effective inverse spectral problem for rational Lax matrices and applications %A Marco Bertola %A Gekhtman, M. %B Int. Math. Res. Not. IMRN %P Art. ID rnm103, 39 %G eng %0 Journal Article %J Arch. Ration. Mech. Anal. 186 (2007) 477-537 %D 2007 %T Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results %A Irene Fonseca %A Nicola Fusco %A Giovanni Leoni %A Massimiliano Morini %X Strained epitaxial films grown on a relatively thick substrate are considered in the context of plane linear elasticity. The total free energy of the system is assumed to be the sum of the energy of the free surface of the film and the strain energy. Because of the lattice mismatch between film and substrate, flat configurations are in general energetically unfavorable and a corrugated or islanded morphology is the preferred growth mode of the strained film. After specifying the functional setup in which the existence problem can be properly framed, a study of the qualitative properties of the solutions is undertaken. New regularity results for volume-constrained local minimizers of the total free energy are established, leading, as a byproduct, to a rigorous proof of the zero-contact-angle condition between islands and wetting layers. %B Arch. Ration. Mech. Anal. 186 (2007) 477-537 %G en_US %U http://hdl.handle.net/1963/2350 %1 1666 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-06T11:41:16Z\\nNo. of bitstreams: 1\\nwetting-december-30-06.pdf: 1519775 bytes, checksum: 40f435ddce013b1017d5c3e2369fa7c8 (MD5) %R 10.1007/s00205-007-0082-4 %0 Journal Article %J Discrete Contin. Dynam. Systems A 17 (2007) 449-480 %D 2007 %T On the Euler-Lagrange equation for a variational problem %A Stefano Bianchini %B Discrete Contin. Dynam. Systems A 17 (2007) 449-480 %G en_US %U http://hdl.handle.net/1963/1792 %1 2752 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-04T12:40:27Z\\nNo. of bitstreams: 1\\n95M-2005.pdf: 317685 bytes, checksum: 614765edebc7f0ed216ce0759aeb3de5 (MD5) %0 Journal Article %J ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 %D 2006 %T An estimation of the controllability time for single-input systems on compact Lie Groups %A Andrei A. Agrachev %A Thomas Chambrion %X 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. %B ESAIM Control Optim. Calc. Var. 12 (2006) 409-441 %G en_US %U http://hdl.handle.net/1963/2135 %1 2108 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-24T13:09:42Z\\nNo. of bitstreams: 1\\ncocv0452.pdf: 441157 bytes, checksum: 7c8ead7c835051e17567fe9bb8a60fbe (MD5) %R 10.1051/cocv:2006007 %0 Journal Article %J Molecular pharmacology. 2006 Jul; 70(1):373-82 %D 2006 %T Experimental and modeling studies of desensitization of P2X3 receptors. %A Elena Sokolova %A Andrei Skorinkin %A Igor Moiseev %A Andrei A. Agrachev %A Andrea Nistri %A Rashid Giniatullin %X The function of ATP-activated P2X3 receptors involved in pain sensation is modulated by desensitization, a phenomenon poorly understood. The present study used patch-clamp recording from cultured rat or mouse sensory neurons and kinetic modeling to clarify the properties of P2X3 receptor desensitization. Two types of desensitization were observed, a fast process (t1/2 = 50 ms; 10 microM ATP) following the inward current evoked by micromolar agonist concentrations, and a slow process (t1/2 = 35 s; 10 nM ATP) that inhibited receptors without activating them. We termed the latter high-affinity desensitization (HAD). Recovery from fast desensitization or HAD was slow and agonist-dependent. When comparing several agonists, there was analogous ranking order for agonist potency, rate of desensitization and HAD effectiveness, with 2-methylthioadenosine triphosphate the strongest and beta,gamma-methylene-ATP the weakest. HAD was less developed with recombinant (ATP IC50 = 390 nM) than native P2X3 receptors (IC50 = 2.3 nM). HAD could also be induced by nanomolar ATP when receptors seemed to be nondesensitized, indicating that resting receptors could express high-affinity binding sites. Desensitization properties were well accounted for by a cyclic model in which receptors could be desensitized from either open or closed states. Recovery was assumed to be a multistate process with distinct kinetics dependent on the agonist-dependent dissociation rate from desensitized receptors. Thus, the combination of agonist-specific mechanisms such as desensitization onset, HAD, and resensitization could shape responsiveness of sensory neurons to P2X3 receptor agonists. By using subthreshold concentrations of an HAD-potent agonist, it might be possible to generate sustained inhibition of P2X3 receptors for controlling chronic pain. %B Molecular pharmacology. 2006 Jul; 70(1):373-82 %I the American Society for Pharmacology and Experimental Therapeutics %G en %U http://hdl.handle.net/1963/4974 %1 4799 %2 Neuroscience %3 Neurobiology %4 -1 %$ Submitted by Alireza Alemi-neissi (alemi@sissa.it) on 2011-10-30T18:23:32Z\\nNo. of bitstreams: 0 %R 10.1124/mol.106.023564 %0 Report %D 2006 %T Extended affine Weyl groups and Frobenius manifolds -- II %A Boris Dubrovin %A Zhang Youjin %A Zuo Dafeng %X For the root system of type $B_l$ and $C_l$, we generalize the result of \\\\cite{DZ1998} by showing the existence of a Frobenius manifold structure on the orbit space of the extended affine Weyl group that corresponds to any vertex of the Dynkin diagram instead of a particular choice of \\\\cite{DZ1998}. %G en_US %U http://hdl.handle.net/1963/1787 %1 2757 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-03-30T13:34:27Z\\nNo. of bitstreams: 1\\n90FM-2005.pdf: 254524 bytes, checksum: abdf833c0cf0b01fb79663489dd6acc2 (MD5) %0 Journal Article %J Systems and Control Letters, 54 (11):1121-1130, 2005 %D 2005 %T Explicit Wei–Norman formulae for matrix Lie groups via Putzer\\\'s method %A Claudio Altafini %X The Wei–Norman formula locally relates the Magnus solution of a system of linear time-varying ODEs with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions. A closed form expression of such formula is proposed based on the use of Putzer\\\'s method. %B Systems and Control Letters, 54 (11):1121-1130, 2005 %I Elsevier %G en %U http://hdl.handle.net/1963/4538 %1 4299 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-06T12:04:23Z\\nNo. of bitstreams: 1\\nwei-norman.pdf: 201660 bytes, checksum: 6081c4fd935c318f831c791518f8b9c9 (MD5) %R 10.1016/j.sysconle.2005.03.006 %0 Conference Proceedings %B Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 %D 2004 %T The elliptic representation of the sixth Painlevé equation. %A Davide Guzzetti %K Painlevé equation %X We find a class of solutions of the sixth Painlev´e equation corresponding\r\nto almost all the monodromy data of the associated linear system; actually, all data\r\nbut one point in the space of data. We describe the critical behavior close to the\r\ncritical points by means of the elliptic representation, and we find the relation among\r\nthe parameters at the different critical points (connection problem). %B Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 %I Societe Matematique de France %@ 978-2-85629-229-7 %G en %U http://hdl.handle.net/1963/6529 %1 6482 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:22:07Z\nNo. of bitstreams: 1\n10-SemCongSMF06.pdf: 299143 bytes, checksum: dc2b0ca561808604467132b9b5942fe3 (MD5) %0 Journal Article %J M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %D 2004 %T Energetics and switching of quasi-uniform states in small ferromagnetic particles %A François Alouges %A Sergio Conti %A Antonio DeSimone %A Ivo Pokern %X 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. %B M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/2999 %1 1334 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:25:50Z\\nNo. of bitstreams: 1\\npreprint2003_88.pdf: 297354 bytes, checksum: d907d5a9d74d0a3dcb244e26ff2af68a (MD5) %R 10.1051/m2an:2004011 %0 Journal Article %J Rev. Mat. Iberoamericana 20 (2004) 611-626 %D 2004 %T Existence of H-bubbles in a perturbative setting %A Paolo Caldiroli %A Roberta Musina %X 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. %B Rev. Mat. Iberoamericana 20 (2004) 611-626 %I SISSA Library %G en %U http://hdl.handle.net/1963/1606 %1 2512 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2002 %0 Journal Article %J Moscow Math. J. 4 (2004)\\n313-332. %D 2004 %T The Extended Toda Hierarchy %A Guido Carlet %A Boris Dubrovin %A Zhang Youjin %B Moscow Math. J. 4 (2004)\\n313-332. %G en_US %U http://hdl.handle.net/1963/2542 %1 1577 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-21T12:22:27Z\\nNo. of bitstreams: 1\\n0306060v2.pdf: 242352 bytes, checksum: 7a4fc53dbf549eb7046e75be6c087368 (MD5) %0 Journal Article %D 2003 %T Effective dynamics for Bloch electrons: Peierls substitution and beyond %A Gianluca Panati %A Herbert Spohn %A Stefan Teufel %X We consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, $\\\\phi(\\\\epsi x)$, and vector potential $A(\\\\epsi x)$, with $x \\\\in \\\\R^d$ and $\\\\epsi \\\\ll 1$. We prove that associated to an isolated family of Bloch bands there exists an almost invariant subspace of $L^2(\\\\R^d)$ and an effective Hamiltonian governing the evolution inside this subspace to all orders in $\\\\epsi$. To leading order the effective Hamiltonian is given through the Peierls substitution. We explicitly compute the first order correction. From a semiclassical analysis of this effective quantum Hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics. %I Springer %G en_US %U http://hdl.handle.net/1963/3040 %1 1293 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-08T12:11:51Z\\nNo. of bitstreams: 1\\n0212041v2.pdf: 395908 bytes, checksum: 7b198d3311402d34945989b8f6edd8b8 (MD5) %0 Journal Article %J Communications on Pure and Applied Mathematics, Volume 55, Issue 10, October 2002, Pages 1280-1363 %D 2002 %T The Elliptic Representation of the General Painlevé 6 Equation %A Davide Guzzetti %X We study the analytic properties and the critical behavior of the elliptic\r\nrepresentation of solutions of the Painlev\\\'e 6 equation. We solve the\r\nconnection problem for elliptic representation in the generic case and in a\r\nnon-generic case equivalent to WDVV equations of associativity. %B Communications on Pure and Applied Mathematics, Volume 55, Issue 10, October 2002, Pages 1280-1363 %I SISSA %G en %U http://hdl.handle.net/1963/6523 %1 6475 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-12T10:59:59Z\nNo. of bitstreams: 1\nmath_0108073v2.pdf: 604540 bytes, checksum: 7e39c5af49afe1e1539cb4c3140cca6e (MD5) %R 10.1002/cpa.10045 %0 Conference Proceedings %B Deformation of differential equations and asymptotic analysis / Yoshishige Haraoka. - Kyōto : Kyoto University, Research Institute for Mathematical Sciences, 2002. - RIMS kokyuroku, volume 1296 . - page: 112-123 %D 2002 %T The Elliptic Representation of the Painleve 6 Equation %A Davide Guzzetti %K Painleve equations %X We review our results on the elliptic representation of the sixth Painleve’ equation %B Deformation of differential equations and asymptotic analysis / Yoshishige Haraoka. - Kyōto : Kyoto University, Research Institute for Mathematical Sciences, 2002. - RIMS kokyuroku, volume 1296 . - page: 112-123 %I Kyoto University, Research Institute for Mathematical Sciences %G en %U http://hdl.handle.net/1963/6530 %1 6481 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:18:28Z\nNo. of bitstreams: 1\n07-RIMSKokyuroku02.pdf: 1194417 bytes, checksum: 4710ff5d2a123d59ae61aea637048ddc (MD5) %0 Journal Article %J Commun. Contemp. Math. 4 (2002) 177-209 %D 2002 %T Existence of minimal H-bubbles %A Paolo Caldiroli %A Roberta Musina %B Commun. Contemp. Math. 4 (2002) 177-209 %I SISSA Library %G en %U http://hdl.handle.net/1963/1525 %1 2638 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:37Z (GMT). No. of bitstreams: 1\\nmath.AP0006157.pdf: 242337 bytes, checksum: ad4f345871a0c7fb33e9c4bc361ce4d8 (MD5)\\n Previous issue date: 2000 %R 10.1142/S021919970200066X %0 Journal Article %J Adv. Differential Equations 6 (2001), no. 3, 303-326 %D 2001 %T Existence and nonexistence results for a class of nonlinear, singular Sturm-Liouville equations %A Paolo Caldiroli %A Roberta Musina %B Adv. Differential Equations 6 (2001), no. 3, 303-326 %I SISSA Library %G en %U http://hdl.handle.net/1963/1319 %1 3136 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:56:13Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %0 Journal Article %J J. Dynam. Control Systems, 2001, 7, 209 %D 2001 %T Extremal synthesis for generic planar systems %A Ugo Boscain %A Benedetto Piccoli %B J. Dynam. Control Systems, 2001, 7, 209 %I SISSA Library %G en %U http://hdl.handle.net/1963/1503 %1 2660 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:19Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %R 10.1023/A:1013003204923 %0 Journal Article %J Theor. Math. Phys. 122 (2000) 17-28 %D 2000 %T An elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy %A Gregorio Falqui %A Franco Magri %A Marco Pedroni %A Jorge P. Zubelli %X We give an elementary construction of the solutions of the KP hierarchy associated with polynomial τ-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a consequence, we establish a Wronskian formula for the polynomial τ-functions of the KP hierarchy. This formula, known in the literature, is obtained very directly. %B Theor. Math. Phys. 122 (2000) 17-28 %I Springer %G en_US %U http://hdl.handle.net/1963/3223 %1 1078 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-31T11:53:05Z\\nNo. of bitstreams: 1\\npolynomial.pdf: 207747 bytes, checksum: 1df27acfb336a4df11658f6c011546da (MD5) %R 10.1007/BF02551166 %0 Journal Article %J J. Differential Equations 168 (2000), no. 1, 10--32 %D 2000 %T Elliptic variational problems in $ R\\\\sp N$ with critical growth %A Antonio Ambrosetti %A Jesus Garcia Azorero %A Ireneo Peral %B J. Differential Equations 168 (2000), no. 1, 10--32 %I SISSA Library %G en %U http://hdl.handle.net/1963/1258 %1 3197 %$ Made available in DSpace on 2004-09-01T12:55:25Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1006/jdeq.2000.3875 %0 Journal Article %J Rend. Mat. Appl., 2000, 20, 167 %D 2000 %T Existence and multiplicity results for some nonlinear elliptic equations: a survey. %A Antonio Ambrosetti %A Jesus Garcia Azorero %A Ireneo Peral %B Rend. Mat. Appl., 2000, 20, 167 %I SISSA Library %G en %U http://hdl.handle.net/1963/1462 %1 3078 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:44Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Thesis %D 2000 %T Existence and multiplicity results for some problems in Riemannian geometry %A Andrea Malchiodi %K Yamabe problem %I SISSA %G en %U http://hdl.handle.net/1963/5948 %1 5808 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-06-22T10:18:59Z\\nNo. of bitstreams: 1\\nPhD_Malchiodi.pdf: 25528908 bytes, checksum: dd49ac5ec54366bb2daf7288eb10f483 (MD5) %] 1 Introduction\\r\\n2 The Yamabe problem: first multiplicity results\\r\\n3 Infinitely many solutions for the Yamabe problem\\r\\n4 The scalar curvature problem: an approach via Morse theory\\r\\n5 The scalar curvature problem: the symmetric case\\r\\n6 Prescribing scalar curvature and boundary mean curvature %0 Journal Article %J Phys.Lett. B452 (1999) 244-250 %D 1999 %T Enhanced gauge symmetries on elliptic K3 %A Loriano Bonora %A Cesare Reina %A Alessandro Zampa %X We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s. %B Phys.Lett. B452 (1999) 244-250 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3366 %1 964 %2 Physics %3 Elementary Particle Theory %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-27T13:09:53Z\\nNo. of bitstreams: 1\\nEnhanced_gauge.pdf: 155859 bytes, checksum: 8dbf403648387d04a1923181897b6ea1 (MD5) %R 10.1016/S0370-2693(99)00295-6 %0 Journal Article %J Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %D 1999 %T Evans-Vasilesco theorem in Dirichlet spaces %A Gianni Dal Maso %A Virginia De Cicco %B Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %I SISSA %G en %U http://hdl.handle.net/1963/6436 %1 6376 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:39:11Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5) %0 Journal Article %J J. Math. Anal. Appl. 231 (1999) 301-318 %D 1999 %T Extremal faces of the range of a vector measure and a theorem of Lyapunov %A Stefano Bianchini %B J. Math. Anal. Appl. 231 (1999) 301-318 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3370 %1 960 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-28T16:59:08Z\\nNo. of bitstreams: 1\\nExtremal_faces.pdf: 1484685 bytes, checksum: 8866c1e71c362e06ebd3719a5f44e894 (MD5) %R 10.1006/jmaa.1998.6260 %0 Journal Article %J Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176 %D 1998 %T Error bounds for a deterministic version of the Glimm scheme %A Andrea Marson %A Alberto Bressan %X Consider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let $u$ be the unique viscosity solution with initial condition $u(0,x)=\\\\bar u(x)$ and let $u^\\\\varepsilon$ be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\\\\Delta x,\\\\Delta t=O(\\\\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$ %B Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176 %I Springer %G en %U http://hdl.handle.net/1963/1045 %1 2811 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:05Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1007/s002050050088 %0 Journal Article %J Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219 %D 1998 %T Extended affine Weyl groups and Frobenius manifolds %A Boris Dubrovin %A Youjin Zhang %B Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219 %I Kluwer %G en %U http://hdl.handle.net/1963/6486 %1 6424 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:13:49Z\\nNo. of bitstreams: 1\\ndubrovin_zhang_1998_compositio.pdf: 321250 bytes, checksum: 49608b8d8e6245677c302db09170d85e (MD5) %R 10.1023/A:1000258122329 %0 Thesis %D 1997 %T On Existence and Continuous Dependence for Systems of Conservation Laws %A Paolo Baiti %K Conservation laws %I SISSA %G en %U http://hdl.handle.net/1963/5588 %1 5418 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-03-08T13:48:00Z\\nNo. of bitstreams: 1\\nPhD_Baiti_Paolo.pdf: 5888073 bytes, checksum: fadab5be3940cd6a300d30600eb61194 (MD5) %0 Journal Article %D 1995 %T An existence result in a problem of the vectorial case of the calculus of variations %A Arrigo Cellina %A Sandro Zagatti %X SIAM J. Control Optim. 33 (1995) 960-970 %I SIAM %G en_US %U http://hdl.handle.net/1963/3513 %1 751 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-12T14:55:58Z\\nNo. of bitstreams: 1\\ncellina.pdf: 925141 bytes, checksum: d75c968d00d2e76a821d8ff4e31987ad (MD5) %0 Journal Article %J Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311 %D 1990 %T Existence and continuous dependence for discontinuous O.D.E.s %A Alberto Bressan %A Giovanni Colombo %B Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311 %I SISSA Library %G en %U http://hdl.handle.net/1963/716 %1 3210 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:40Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76 %D 1990 %T Existence of solutions for a class of non-convex differential inclusions %A Fabio Ancona %A Giovanni Colombo %B Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76 %I SISSA Library %G en %U http://hdl.handle.net/1963/792 %1 2999 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:01Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1989 %0 Journal Article %J Phys. Lett. B 210 (1988), no. 1-2, 68--72. %D 1988 %T Einstein algebras and the algebraic Kaluza-Klein monopole. %A Giovanni Landi %A Giuseppe Marmo %B Phys. Lett. B 210 (1988), no. 1-2, 68--72. %I SISSA Library %G en %U http://hdl.handle.net/1963/603 %1 3301 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:35:21Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %R 10.1016/0370-2693(88)90351-6 %0 Journal Article %J Phys. Lett. B 193 (1987), no. 1, 61-66. %D 1987 %T Extensions of Lie superalgebras and supersymmetric Abelian gauge fields. %A Giovanni Landi %A Giuseppe Marmo %B Phys. Lett. B 193 (1987), no. 1, 61-66. %I SISSA Library %G en %U http://hdl.handle.net/1963/507 %1 3397 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:33:45Z (GMT). No. of bitstreams: 1\\n26_87.pdf: 406704 bytes, checksum: e30da04d568e051692076b40861772e7 (MD5)\\n Previous issue date: 1987 %R 10.1016/0370-2693(87)90456-4