In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

}, url = {https://arxiv.org/abs/1901.02285}, author = {Saddam Hijazi and Giovanni Stabile and Andrea Mola and Gianluigi Rozza}, editor = {van Brummelen, Harald and Corsini, Alessandro and Perotto, Simona and Rozza, Gianluigi} } @article {Dal-MasoHeltai-2020-a, title = {A numerical study of the jerky crack growth in elastoplastic materials with localized plasticity}, journal = {Journal of Convex Analysis}, year = {2020}, note = {To appear}, url = {https://arxiv.org/abs/2004.12705}, author = {Gianni Dal Maso and Luca Heltai} } @article {Agostinelli2020.07.06.188987, title = {Nutations in plant shoots: endogenous and exogenous factors in the presence of mechanical deformations}, year = {2020}, institution = {Cold Spring Harbor Laboratory}, type = {preprint}, abstract = {We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots, as driven by differential growth at the tip. We discuss the evolution laws for endogenous oscillators, straightening mechanisms and reorientations to directional cues, such as phototropic responses to a far light source and gravitropic reactions governed by the statoliths avalanche dynamics. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of a Hopf bifurcation reminiscent of flutter instabilities exhibited by structural systems under nonconservative loads. When also oscillations due to endogenous cues are present, their weight relative to those associated with the Hopf instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the flutter induced oscillations becomes dominant. Our findings suggest that the relative importance of the two mechanisms is an emergent property of the system that is affected by the amplitude of elastic deformations, and highlight the crucial role of elasticity in the analysis of circumnutations.Competing Interest StatementThe authors have declared no competing interest.

}, doi = {10.1101/2020.07.06.188987}, url = {https://www.biorxiv.org/content/early/2020/07/06/2020.07.06.188987}, author = {Daniele Agostinelli and Antonio DeSimone and Giovanni Noselli} } @article {Bawane:2017gjf, title = {N=2 gauge theories on unoriented/open four-manifolds and their AGT counterparts}, journal = {JHEP}, volume = {07}, year = {2019}, pages = {040}, doi = {10.1007/JHEP07(2019)040}, url = {http://inspirehep.net/record/1631219/}, author = {Aditya Bawane and Benvenuti, Sergio and Giulio Bonelli and Muteeb, Nouman and Alessandro Tanzini} } @article {gigli_rigoni_2019, title = {A Note About the Strong Maximum Principle on RCD Spaces}, journal = {Canadian Mathematical Bulletin}, volume = {62}, number = {2}, year = {2019}, pages = {259{\textendash}266}, publisher = {Canadian Mathematical Society}, abstract = {We give a direct proof of the strong maximum principle on finite dimensional RCD spaces based on the Laplacian comparison of the squared distance.

}, doi = {10.4153/CMB-2018-022-9}, author = {Nicola Gigli and Chiara Rigoni} } @article {Kozhasov2019, title = {On the Number of Flats Tangent to Convex Hypersurfaces in Random Position}, journal = {Discrete \& Computational Geometry}, year = {2019}, month = {Mar}, issn = {1432-0444}, doi = {10.1007/s00454-019-00067-0}, url = {https://doi.org/10.1007/s00454-019-00067-0}, author = {Khazhgali Kozhasov and Antonio Lerario} } @article {AGOSTINELLI2019103702, title = {Nutations in growing plant shoots: The role of elastic deformations due to gravity loading}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2019}, pages = {103702}, abstract = {The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin{\textquoteright}s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

}, keywords = {Circumnutations, Flutter instability, Gravitropism, Hopf bifurcation}, issn = {0022-5096}, doi = {10.1016/j.jmps.2019.103702}, url = {https://doi.org/10.1016/j.jmps.2019.103702}, author = {Daniele Agostinelli and Alessandro Lucantonio and Giovanni Noselli and Antonio DeSimone} } @article {BeCaRu, title = {Noncommutative Painlev{\'e} Equations and Systems of Calogero Type}, journal = {Comm. Math. Phys}, year = {2018}, author = {Marco Bertola and Mattia Cafasso and V. Rubtsov} } @article {2018, title = {Non-linear Gross-Pitaevskii dynamics of a 2D binary condensate: a numerical analysis}, number = {SISSA;35/2018/MATE}, year = {2018}, abstract = {We present a numerical study of the two-dimensional Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.}, url = {http://preprints.sissa.it/handle/1963/35323}, author = {Alessandro Michelangeli and Giuseppe Pitton} } @article {1803.05374, title = {On the notion of parallel transport on RCD spaces}, year = {2018}, author = {Nicola Gigli and Enrico Pasqualetto} } @article {Stabile2018, title = {A novel reduced order model for vortex induced vibrations of long flexible cylinders}, volume = {156}, year = {2018}, month = {may}, pages = {191{\textendash}207}, publisher = {Elsevier {BV}}, doi = {10.1016/j.oceaneng.2018.02.064}, url = {https://doi.org/10.1016/j.oceaneng.2018.02.064}, author = {Giovanni Stabile and Hermann G. Matthies and Claudio Borri} } @article {doi:10.1098/rspa.2017.0458, title = {Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {474}, number = {2210}, year = {2018}, pages = {20170458}, abstract = {A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev{\textendash}Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schr{\"o}dinger equation in the semiclassical limit.

}, doi = {10.1098/rspa.2017.0458}, url = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2017.0458}, author = {Tamara Grava and Christian Klein and Giuseppe Pitton} } @article {20.500.11767_81737, title = {NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, volume = {338}, year = {2018}, pages = {440{\textendash}462}, doi = {10.1016/j.cma.2018.04.039}, url = {https://arxiv.org/abs/1804.08271}, author = {Giuseppe Pitton and Luca Heltai} } @article {20.500.11767_11953, title = {A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling}, journal = {COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, volume = {316}, year = {2017}, pages = {522{\textendash}546}, doi = {10.1016/j.cma.2016.08.008}, url = {http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H}, author = {Luca Heltai and Kiendl, J. and Antonio DeSimone and Alessandro Reali} } @article {12163, title = {A note on a fixed point theorem on topological cylinders}, journal = {Ann. Mat. Pura Appl.}, number = {Annali di Matematica Pura ed Applicata;}, year = {2017}, note = {AMS Subject Classification: 47H10, 37C25, 47H11, 54H25.}, publisher = {Springer Verlag}, abstract = {We present a fixed point theorem on topological cylinders in normed linear spaces for maps satisfying a property of stretching a space along paths. This result is a generalization of a similar theorem obtained by D. Papini and F. Zanolin. In view of the main result, we discuss the existence of fixed points for maps defined on different types of domains and we propose alternative proofs for classical fixed point theorems, as Brouwer, Schauder and Krasnosel{\textquoteright}skii ones.

}, doi = {10.1007/s10231-016-0623-2}, url = {http://urania.sissa.it/xmlui/handle/1963/35263}, author = {Guglielmo Feltrin} } @article {Nardini2017, title = {A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations}, journal = {Journal of Dynamics and Differential Equations}, volume = {29}, number = {2}, year = {2017}, month = {Jun}, pages = {783{\textendash}797}, issn = {1572-9222}, doi = {10.1007/s10884-015-9461-y}, url = {https://doi.org/10.1007/s10884-015-9461-y}, author = {Lorenzo Nardini} } @article {2017, title = {Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts}, journal = {Biomechanics and Modeling in Mechanobiology}, volume = {16}, year = {2017}, pages = {1373-1399}, doi = {10.1007/s10237-017-0893-7}, url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015065851\&doi=10.1007\%2fs10237-017-0893-7\&partnerID=40\&md5=c388f20bd5de14187bad9ed7d9affbd0}, author = {Francesco Ballarin and Elena Faggiano and Andrea Manzoni and Alfio Quarteroni and Gianluigi Rozza and Sonia Ippolito and Roberto Scrofani} } @article {jevnikar_2016, title = {New existence results for the mean field equation on compact surfaces via degree theory}, journal = {Rend. Sem. Mat. Univ. Padova}, volume = {136}, year = {2016}, pages = {11{\textendash}17}, doi = {10.4171/RSMUP/136-2}, author = {Aleks Jevnikar} } @article {2016, title = {Non-linear Schr{\"o}dinger system for the dynamics of a binary condensate: theory and 2D numerics}, number = {SISSA;63/2016/MATE}, year = {2016}, abstract = {We present a comprehensive discussion of the mathematical framework for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.}, url = {http://urania.sissa.it/xmlui/handle/1963/35266}, author = {Alessandro Michelangeli and Giuseppe Pitton} } @article {jevnikar2016note, title = {A note on a multiplicity result for the mean field equation on compact surfaces}, journal = {Advanced Nonlinear Studies}, volume = {16}, year = {2016}, pages = {221{\textendash}229}, publisher = {De Gruyter}, doi = {10.1515/ans-2015-5009}, author = {Aleks Jevnikar} } @article {Bawane2015, title = {N=2 supersymmetric gauge theories on S^2xS^2 and Liouville Gravity}, journal = {Journal of High Energy Physics}, volume = {2015}, number = {7}, year = {2015}, month = {Jul}, pages = {54}, abstract = {We consider $\mathcal{N}=2$ supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a $U(1)$ isometry. This is used to explicitly compute the supersymmetric path integral on $S^2 \times S^2$ via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2015)054}, url = {https://doi.org/10.1007/JHEP07(2015)054}, author = {Aditya Bawane and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} } @mastersthesis {2015, title = {Normal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries}, year = {2015}, school = {SISSA}, abstract = {In this thesis we are going to study normal random matrix models which generalize naturally the polynomially perturbed Ginibre ensamble, focusing in particular on their eigenvalue distribution and on the asymptotics of the associated orthogonal polynomials. \\ The main result we are going to present are the following: \begin{itemize} \item we describe the explicit derivation of the equilibrium measure for a class of potentials with discrete rotational symmetries, namely of the form \[V(z)=|z|^{2n}-t(z^{d}+\bar{z}^{d})\qquad n,d\in\mathbb{N},\ \ d\leq2n\ \ t>0 .\] \item We obtain the strong asymptotics for the orthogonal polynomials associated to the weight \[ e^{-NV(z)},\quad V(z)=|z|^{2s}-t(z^s+\bar{z}^{s}) \qquad z \in \mathbb{C},\;s\in \mathbb{N},\quad t>0,\] and we will show how the density of their zeroes is related to the eigenvalue distribution of the corresponding matrix model; \item We show how the conformal maps used to describe the support of the equilibrium measure for polynomial perturbation of the potential $V(z)=|z|^{2n}$ lead to a natural generalization of the concept of polynomial curves introduced in by Elbau. \end{itemize}}, keywords = {Mathematical Physics}, author = {Dario Merzi} } @article {2015, title = {A note on compactness properties of the singular Toda system}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. }, volume = {26}, number = {Rendiconti Lincei. Mathematics and Applications;vol. 26, Issue 3}, year = {2015}, pages = {299-307}, abstract = {In this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

}, doi = {10.4171/RLM/708}, author = {Luca Battaglia and Gabriele Mancini} } @article {2014, title = {N = 2 Quiver Gauge Theories on A-type ALE Spaces}, number = {Letters in mathematical physics;volume 105; issue 3; pages 401-445;}, year = {2014}, publisher = {Springer}, abstract = {We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg{\textendash}Witten geometry.}, doi = {10.1007/s11005-014-0734-x}, url = {http://urania.sissa.it/xmlui/handle/1963/34719}, author = {Ugo Bruzzo and Francesco Sala and Richard J. Szabo} } @article {2012, title = {New results on Gamma-limits of integral functionals}, number = {Annales de l{\textquoteright}Institut Henri Poincare. Analyse Non Lineaire}, year = {2014}, publisher = {Elsevier}, keywords = {Gamma-convergence}, doi = {10.1016/j.anihpc.2013.02.005}, url = {http://hdl.handle.net/1963/5880}, author = {Nadia Ansini and Gianni Dal Maso and Caterina Ida Zeppieri} } @mastersthesis {2014, title = {Non-commutative integration for spectral triples associated to quantum groups}, year = {2014}, school = {SISSA}, abstract = {This thesis is dedicated to the study of non-commutative integration, in the sense of spectral triples, for some non-commutative spaces associated to quantum groups.}, keywords = {Non-commutative geometry}, author = {Marco Matassa} } @article {2012, title = {Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D}, number = {Computer Methods in Applied Mechanics and Engineering}, year = {2014}, publisher = {Elsevier}, abstract = {Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.}, keywords = {Isogeometric Analysis}, doi = {10.1016/j.cma.2013.09.017}, url = {http://hdl.handle.net/1963/6326}, author = {Luca Heltai and Marino Arroyo and Antonio DeSimone} } @article {2013, title = {N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae}, number = {arXiv:1208.0790;}, year = {2013}, note = {33 pages, 1 figure; v2: discussions on U(1) gauge theory and\r\n Frenkel-Kac construction have been added in section 5.1, and typos corrected;\r\n v3: published version; v4: typos corrected}, institution = {SISSA}, abstract = {We compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories.}, url = {http://hdl.handle.net/1963/6577}, author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagi} } @article {modena2013, title = {A New Quadratic Potential for Scalar Conservation Laws}, journal = {Oberwolfach Reports}, volume = {29}, year = {2013}, author = {Stefano Bianchini and Stefano Modena} } @article {11011, title = {Nonabelian Lie algebroid extensions}, number = {SISSA preprint;06/2014/mate}, year = {2013}, abstract = {We classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

}, keywords = {Lie algebroids, nonabelian extensions, spectral sequences}, author = {Ugo Bruzzo and Igor Mencattini and Pietro Tortella and Vladimir Rubtsov} } @article {2013, title = {Noncommutative circle bundles and new Dirac operators}, journal = {Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130}, number = {arXiv:1012.3055v2;}, year = {2013}, note = {This article is composed of 25 pages and is recorded in PDF format}, publisher = {Springer}, abstract = {We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.}, keywords = {Quantum principal bundles}, doi = {10.1007/s00220-012-1550-8}, url = {http://hdl.handle.net/1963/7384}, author = {Ludwik Dabrowski and Andrzej Sitarz} } @article {2013, title = {The nonlinear multidomain model: a new formal asymptotic analysis.}, journal = {Geometry Partial Differential Equations {\textendash} proceedings, CRM Series (15), 2013.}, number = {SISSA preprint;SISSA 54/2013/MATE}, year = {2013}, abstract = {We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m- equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

}, keywords = {bidomain model, anisotropic mean curvature, star-shaped combination}, isbn = {8876424724}, author = {Stefano Amato and Giovanni Bellettini and Maurizio Paolini} } @article {2013, title = {A note on KAM theory for quasi-linear and fully nonlinear forced KdV}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 24 (2013), no. 3: 437{\textendash}450}, year = {2013}, publisher = {European Mathematical Society}, abstract = {We present the recent results in [3] concerning quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities the solutions are linearly stable. The proofs are based on a combination of di erent ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization procedure, which conjugates the linearized operator to a di erential operator with constant coe cients plus a bounded remainder. These transformations are obtained by changes of variables induced by di eomorphisms of the torus and pseudo-di erential operators. (iii) A reducibility KAM scheme, which completes the reduction to constant coe cients of the linearized operator, providing a sharp asymptotic expansion of the perturbed eigenvalues.}, keywords = {KAM for PDEs}, doi = {10.4171/RLM/660}, author = {P Baldi and Massimiliano Berti and Riccardo Montalto} } @article {1305.1133, title = {A note on non-homogeneous hyperbolic operators with low-regularity coefficients}, year = {2013}, abstract = {In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

}, author = {Ferruccio Colombini and Francesco Fanelli} } @article {2012, title = {Nonlinear thin-walled beams with a rectangular cross-section-Part I}, journal = {Math. Models Methods Appl. Sci. 22, 1150016 (2012)}, number = {SISSA;79/2010/M}, year = {2012}, publisher = {World Scientific}, abstract = {Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results.}, doi = {10.1142/S0218202511500163}, url = {http://hdl.handle.net/1963/4104}, author = {Lorenzo Freddi and Maria Giovanna Mora and Roberto Paroni} } @article {SFECCI20126191, title = {A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {75}, number = {16}, year = {2012}, pages = {6191 - 6202}, abstract = {We prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991) [2]. Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.

}, keywords = {Neumann problem, Nonresonance, Radial solutions, Time-map}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2012.06.023}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X12002659}, author = {Andrea Sfecci} } @article {2012, title = {Non-uniqueness results for critical metrics of regularized determinants in four dimensions}, journal = {Communications in Mathematical Physics, Volume 315, Issue 1, September 2012, Pages 1-37}, number = {arXiv:1105.3762;}, year = {2012}, note = {35 pages, title changed, added determinant of half-torsion, references added. Comm. Math. Phys., to appear}, publisher = {Springer}, abstract = {The regularized determinant of the Paneitz operator arises in quantum gravity (see Connes 1994, IV.4.$\gamma$). An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in Branson (1996). A similar formula holds for Cheeger{\textquoteright}s half-torsion, which plays a role in self-dual field theory (see Juhl, 2009), and is defined in terms of regularized determinants of the Hodge laplacian on $p$-forms ($p < n/2$). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in Chang and Yang (1995), Branson, Chang, and Yang (1992), and Gursky (1997). We also study entire solutions of the Euler-Lagrange equation of $\log \det P$ and the half-torsion $\tau_h$ on $\mathbb{R}^4 \setminus {0}$, and show the existence of two families of periodic solutions. One of these families includes Delaunay-type solutions.}, doi = {10.1007/s00220-012-1535-7}, url = {http://hdl.handle.net/1963/6559}, author = {Matthew Gursky and Andrea Malchiodi} } @article {2012, title = {Numerical modelling of installation effects for diaphragm walls in sand}, journal = {Acta Geotechnica, Volume 7, Issue 3, September 2012, Pages 219-237}, year = {2012}, publisher = {Springer}, abstract = {The scopes of this work are to study the mechanisms of load transfer and the deformations of the ground during slurry trenching and concreting in dry sand and to evaluate their effects on service structural loads, wall deflections and ground displacements behind the wall caused by subsequent excavation. A series of three-dimensional finite element analyses was carried out modelling the installation of diaphragm walls consisting of panels of different length. The soil was modelled as either linearly elastic-perfectly plastic or incrementally non-linear (hypoplastic) with elastic strain range. Plane strain analyses of diaphragm walls of identical cross section were also carried out in which wall installation was either modelled or the wall was wished in place (WIP). The analyses predict ground movements consistent with the experimental observations both in magnitude and trend. The results also show that the maximum horizontal wall deflections and structural loads reduce with increasing panel aspect ratio towards a minimum which is about twice the value computed for WIP analyses. Panel aspect ratios should be larger than about three to take advantage of the three-dimensional effects. The pattern and magnitude of surface vertical displacements obtained from linearly elastic-perfectly plastic analyses, no matter whether three- or two-dimensional, are unrealistic.}, keywords = {Constitutive relations}, doi = {10.1007/s11440-011-0157-0}, url = {http://hdl.handle.net/1963/6934}, author = {Riccardo Conti and Luca de Sanctis and Giulia M.B. Viggiani} } @article {2012, title = {Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions}, journal = {Physica D 241, nr. 23-24 (2012): 2246-2264}, number = {arXiv:1202.0962;}, year = {2012}, publisher = {Elsevier}, abstract = {We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ for $\epsilon\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.}, keywords = {Korteweg-de Vries equation}, doi = {10.1016/j.physd.2012.04.001}, author = {Tamara Grava and Christian Klein} } @article {2011, title = {New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces}, journal = {Geometric and Functional Analysis 21 (2011) 1196-1217}, number = {SISSA;74/2010/M}, year = {2011}, publisher = {Springer}, abstract = {We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.}, doi = {10.1007/s00039-011-0134-7}, url = {http://hdl.handle.net/1963/4099}, author = {Andrea Malchiodi and David Ruiz} } @article {fonda2011nonlinear, title = {Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions}, journal = {Advanced Nonlinear Studies}, volume = {11}, number = {2}, year = {2011}, pages = {391{\textendash}404}, publisher = {Advanced Nonlinear Studies, Inc.}, abstract = {We show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

}, doi = {10.1515/ans-2011-0209}, author = {Alessandro Fonda and Maurizio Garrione} } @article {2011, title = {Nonlinear thin-walled beams with a rectangular cross-section - Part II}, number = {SISSA;14/2011/M}, year = {2011}, institution = {SISSA}, abstract = {In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..}, keywords = {Thin-walled cross-section beams}, url = {http://hdl.handle.net/1963/4169}, author = {Lorenzo Freddi and Maria Giovanna Mora and Roberto Paroni} } @article {2011, title = {Nonlinear wave and Schr{\"o}dinger equations on compact Lie groups and homogeneous spaces}, journal = {Duke Mathematical Journal}, volume = {159}, year = {2011}, month = {2011}, chapter = {479}, abstract = {We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relevant for the theory of evolutionary Hamiltonian PDEs. A basic tool is the theory of the highest weight for irreducible representations of compact Lie groups. This theory provides an accurate description of the eigenvalues of the Laplace-Beltrami operator as well as the multiplication rules of its eigenfunctions. As an application, we prove the existence of Cantor families of small amplitude time-periodic solutions for wave and Schr{\textasciidieresis}odinger equations with differentiable nonlinearities. We apply an abstract Nash-Moser implicit function theorem to overcome the small divisors problem produced by the degenerate eigenvalues of the Laplace operator. We provide a new algebraic framework to prove the key tame estimates for the inverse linearized operators on Banach scales of Sobolev functions.}, issn = {0012-7094}, doi = {10.1215/00127094-1433403}, author = {Massimiliano Berti and Michela Procesi} } @article {BOSCAGGIN2011259, title = {A note on a superlinear indefinite Neumann problem with multiple positive solutions}, journal = {Journal of Mathematical Analysis and Applications}, volume = {377}, number = {1}, year = {2011}, pages = {259 - 268}, abstract = {We prove the existence of three positive solutions for the Neumann problem associated to u"+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta-(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.

}, keywords = {Indefinite weight, Nonlinear boundary value problems, positive solutions, Shooting method}, issn = {0022-247X}, doi = {https://doi.org/10.1016/j.jmaa.2010.10.042}, url = {http://www.sciencedirect.com/science/article/pii/S0022247X10008796}, author = {Alberto Boscaggin} } @article {2011, title = {On the number of eigenvalues of a model operator related to a system of three particles on lattices}, journal = {J. Phys. A 44 (2011) 315302}, year = {2011}, publisher = {IOP Publishing}, doi = {10.1088/1751-8113/44/31/315302}, url = {http://hdl.handle.net/1963/5496}, author = {Gianfausto Dell{\textquoteright}Antonio and Zahriddin I. Muminov and Y.M. Shermatova} } @article {2011, title = {Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers}, journal = {Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387}, number = {SISSA;33/2009/M}, year = {2011}, publisher = {World Scientific}, abstract = {We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.}, keywords = {Optimal swimming}, doi = {10.1142/S0218202511005088}, url = {http://hdl.handle.net/1963/3657}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai} } @article {2011, title = {Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations}, journal = {SIAM J. Appl. Math. 71 (2011) 983-1008}, number = {arXiv:1101.0268;}, year = {2011}, publisher = {SIAM}, abstract = {This article is concerned with a conjecture in [B. Dubrovin, Comm. Math. Phys., 267 (2006), pp. 117{\textendash}139] on the formation of dispersive shocks in a class of Hamiltonian dispersive regularizations of the quasi-linear transport equation. The regularizations are characterized by two arbitrary functions of one variable, where the condition of integrability implies that one of these functions must not vanish. It is shown numerically for a large class of equations that the local behavior of their solution near the point of gradient catastrophe for the transport equation is described by a special solution of a Painlev{\'e}-type equation. This local description holds also for solutions to equations where blowup can occur in finite time. Furthermore, it is shown that a solution of the dispersive equations away from the point of gradient catastrophe is approximated by a solution of the transport equation with the same initial data, modulo terms of order $\\\\epsilon^2$, where $\\\\epsilon^2$ is the small dispersion parameter. Corrections up to order $\\\\epsilon^4$ are obtained and tested numerically.}, doi = {10.1137/100819783}, url = {http://hdl.handle.net/1963/4951}, author = {Boris Dubrovin and Tamara Grava and Christian Klein} } @mastersthesis {2010, title = {New approximation results for free discontinuity problems}, year = {2010}, type = {Master{\textquoteright}s thesis}, author = {Flaviana Iurlano} } @article {2010, title = {Nonlocal character of the reduced theory of thin films with higher order perturbations}, journal = {Adv. Calc. Var. 3 (2010) 287-319}, number = {SISSA;57/2009/M}, year = {2010}, doi = {10.1515/ACV.2010.012, /July/2010}, url = {http://hdl.handle.net/1963/3754}, author = {Gianni Dal Maso and Irene Fonseca and Giovanni Leoni} } @article {boscain2010normal, title = {A normal form for generic 2-dimensional almost-Riemannian structures at a tangency point}, journal = {arXiv preprint arXiv:1008.5036}, year = {2010}, author = {Ugo Boscain and Gr{\'e}goire Charlot and Roberta Ghezzi} } @article {2010, title = {On the number of positive solutions of some semilinear elliptic problems}, number = {SISSA;66/2010/M}, year = {2010}, url = {http://hdl.handle.net/1963/4083}, author = {Antonio Ambrosetti} } @article {2010, title = {Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions}, number = {SISSA;10/2010/FM}, year = {2010}, abstract = {The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....}, url = {http://hdl.handle.net/1963/3840}, author = {Simonetta Abenda and Tamara Grava and Christian Klein} } @article {2009, title = {A nonlinear theory for shells with slowly varying thickness}, journal = {C. R. Math. 347 (2009) 211-216}, number = {SISSA;23/2008/M}, year = {2009}, abstract = {We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.}, doi = {10.1016/j.crma.2008.12.017}, url = {http://hdl.handle.net/1963/2632}, author = {Marta Lewicka and Maria Giovanna Mora and Mohammad Reza Pakzad} } @article {2009, title = {A note on the paper \\\"Optimizing improved Hardy inequalities\\\" by S. Filippas and A. Tertikas}, journal = {J. Funct. Anal. 256 (2009) 2741-2745}, number = {SISSA;45/2008/M}, year = {2009}, doi = {10.1016/j.jfa.2008.08.009}, url = {http://hdl.handle.net/1963/2698}, author = {Roberta Musina} } @article {2008, title = {Noncommutative families of instantons}, journal = {Int. Math. Res. Not. vol. 2008, Article ID rnn038}, number = {arXiv.org;0710.0721v2}, year = {2008}, publisher = {Oxford University Press}, abstract = {We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.}, doi = {10.1093/imrn/rnn038}, url = {http://hdl.handle.net/1963/3417}, author = {Giovanni Landi and Chiara Pagani and Cesare Reina and Walter van Suijlekom} } @article {2008, title = {The Noncommutative Geometry of the Quantum Projective Plane}, journal = {Rev. Math. Phys. 20 (2008) 979-1006}, number = {SISSA;100/2007/MP}, year = {2008}, abstract = {We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).}, doi = {10.1142/S0129055X08003493}, url = {http://hdl.handle.net/1963/2548}, author = {Francesco D{\textquoteright}Andrea and Ludwik Dabrowski and Giovanni Landi} } @article {2008, title = {A note on the differentiability of Lipschitz functions and the chain rule in Sobolev spaces}, number = {SISSA;29/2008/M}, year = {2008}, url = {http://hdl.handle.net/1963/2654}, author = {Massimiliano Morini} } @article {2008, title = {Numerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlev{\'e}-II equation}, journal = {Proc. R. Soc. A 464 (2008) 733-757}, number = {arXiv.org;0708.0638v3}, year = {2008}, abstract = {The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\e^2$, $\\\\e\\\\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\\\\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\\\\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a multiscale expansion of the solution of KdV in terms of the Hastings-McLeod solution of the Painlev\\\\\\\'e-II equation. We show numerically that the resulting multiscale solution approximates the KdV solution, in the small dispersion limit, to the order $\\\\epsilon^{2/3}$.}, doi = {10.1098/rspa.2007.0249}, url = {http://hdl.handle.net/1963/2592}, author = {Tamara Grava and Christian Klein} } @article {2007, title = {Nearly time optimal stabilizing patchy feedbacks}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310}, number = {arXiv.org;math/0512531v1}, year = {2007}, abstract = {We consider the time optimal stabilization problem for a nonlinear control system $\\\\dot x=f(x,u)$. Let $\\\\tau(y)$ be the minimum time needed to steer the system from the state $y\\\\in\\\\R^n$ to the origin, and call $\\\\A(T)$ the set of initial states that can be steered to the origin in time $\\\\tau(y)\\\\leq T$. Given any $\\\\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\\\\dot x=f(x, U(x))$, $x(0)=y\\\\in \\\\A(T)$ reaches an $\\\\ve$-neighborhood of the origin within time $\\\\tau(y)+\\\\ve$.}, doi = {10.1016/j.anihpc.2006.03.010}, url = {http://hdl.handle.net/1963/2185}, author = {Fabio Ancona and Alberto Bressan} } @article {2007, title = {Necessary and sufficient conditions for the chainrule in W1,1loc(RN;Rd) and BVloc(RN;Rd)}, journal = {J. Eur. Math. Soc. (JEMS) 9 (2007) 219-252}, year = {2007}, abstract = {In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in Sobolev spaces and in the space of functions of bounded variation.

}, doi = {10.4171/JEMS/78}, url = {http://hdl.handle.net/1963/2037}, author = {Giovanni Leoni and Massimiliano Morini} } @article {2007, title = {A new model for contact angle hysteresis}, number = {SISSA;37/2006/M}, year = {2007}, abstract = {We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.}, url = {http://hdl.handle.net/1963/1848}, author = {Antonio DeSimone and Natalie Gruenewald and Felix Otto} } @mastersthesis {2007, title = {Noncommutative geometry and quantum group symmetries}, year = {2007}, school = {SISSA}, abstract = {It is a widespread belief that mathematics originates from the desire to understand (and eventually to formalize) some aspects of the real world. Quoting [Man07], {\guillemotleft}we are doing mathematics in order to understand, create, and handle things, and perhaps this understanding is mathematics{\guillemotright} . Let me thus begin with a brief discussion of the physical ideas that motivated the development of Noncommutative Geometry and Quantum Group Theory - the areas of mathematics to which this dissertation belongs. Some physicists believe, and Einstein himself expressed this view in [Ein98a], that physics progresses in stages: there is no {\textquoteleft}final\\\' theory of Nature, but simply a sequence of theories which provide more and more accurate descriptions of the real world...}, keywords = {Noncommutative geometry}, url = {http://hdl.handle.net/1963/5269}, author = {Francesco D{\textquoteright}Andrea} } @article {2007, title = {On a notion of unilateral slope for the Mumford-Shah functional}, journal = {NoDEA 13 (2007) 713-734}, number = {SISSA;78/2004/M}, year = {2007}, abstract = {In this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional.}, doi = {10.1007/s00030-006-4054-4}, url = {http://hdl.handle.net/1963/2059}, author = {Gianni Dal Maso and Rodica Toader} } @article {2007, title = {The number of eigenvalues of three-particle Schr{\"o}dinger operators on lattices}, journal = {J. Phys. A 40 (2007) 14819-14842}, number = {arXiv.org;math/0703191v1}, year = {2007}, abstract = {We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\\\\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\\\\\\\"{o}dinger operator $H_{\\\\gamma}(K),$ $K$ being the total quasi-momentum and $\\\\gamma>0$ the ratio of the mass of fermion and boson.\\nWe choose for $\\\\gamma>0$ the interaction $v(\\\\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance.\\nWe prove for any $\\\\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\\\\gamma}(0).$ We establish for the number $N(0,\\\\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$ \\\\lim_{z\\\\to 0-}\\\\frac{N(0,\\\\gamma;z)}{\\\\mid \\\\log \\\\mid z\\\\mid \\\\mid}={U} (\\\\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \\\\in T^3 $ we establish the finiteness of the number $ N(K,\\\\gamma;\\\\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\\\\gamma;0)$ of eigenvalues below zero.}, doi = {10.1088/1751-8113/40/49/015}, url = {http://hdl.handle.net/1963/2576}, author = {Sergio Albeverio and Gianfausto Dell{\textquoteright}Antonio and Saidakhmat N. Lakaev} } @article {2007, title = {Numerical solution of the small dispersion limit of Korteweg de Vries and Whitham equations}, number = {SISSA;91/2005/FM}, year = {2007}, abstract = {The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\\\\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\\\\epsilon$. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. In this manuscript we give a quantitative analysis of the discrepancy between the numerical solution of the KdV equation in the small dispersion limit and the corresponding approximate solution for values of $\\\\epsilon$ between $10^{-1}$ and $10^{-3}$. The numerical results are compatible with a difference of order $\\\\epsilon$ within the {\textquoteleft}interior\\\' of the Whitham oscillatory zone, of order $\\\\epsilon^{1/3}$ at the left boundary outside the Whitham zone and of order $\\\\epsilon^{1/2}$ at the right boundary outside the Whitham zone.}, doi = {10.1002/cpa.20183}, url = {http://hdl.handle.net/1963/1788}, author = {Tamara Grava and Christian Klein} } @article {2007, title = {Numerical study of a multiscale expansion of KdV and Camassa-Holm equation}, number = {arXiv.org;math-ph/0702038v1}, year = {2007}, abstract = {We study numerically solutions to the Korteweg-de Vries and Camassa-Holm equation close to the breakup of the corresponding solution to the dispersionless equation. The solutions are compared with the properly rescaled numerical solution to a fourth order ordinary differential equation, the second member of the Painlev\\\\\\\'e I hierarchy. It is shown that this solution gives a valid asymptotic description of the solutions close to breakup. We present a detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation}, url = {http://hdl.handle.net/1963/2527}, author = {Tamara Grava and Christian Klein} } @article {2007, title = {Numerically flat Higgs vector bundles}, number = {SISSA;39/2005/FM}, year = {2007}, abstract = {After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.}, doi = {10.1142/S0219199707002526}, url = {http://hdl.handle.net/1963/1757}, author = {Ugo Bruzzo and Beatriz Grana-Otero} } @article {2006, title = {N=1 superpotentials from multi-instanton calculus}, number = {SISSA;73/2005/FM}, year = {2006}, abstract = {In this paper we compute gaugino and scalar condensates in N = 1 supersymmetric gauge\\ntheories with and without massive adjoint matter, using localization formulae over the multi-instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the N = 1* theory and check this result against the multi-instanton computation finding agreement.}, doi = {10.1088/1126-6708/2006/01/031}, url = {http://hdl.handle.net/1963/1773}, author = {Francesco Fucito and Jose F. Morales and Rubik Poghossian and Alessandro Tanzini} } @article {2006, title = {Normal bundles to Laufer rational curves in local Calabi-Yau threefolds}, number = {SISSA;88/2005/FM}, year = {2006}, abstract = {We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.}, doi = {10.1007/s11005-006-0057-7}, url = {http://hdl.handle.net/1963/1785}, author = {Ugo Bruzzo and Antonio Ricco} } @article {2005, title = {Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy}, journal = {Discrete Contin. Dyn. Syst. Ser. B 5 (2005) 957-990}, number = {SISSA;56/2004/M}, year = {2005}, abstract = {We apply techniques of subriemannian geometry on Lie groups and of optimal synthesis on 2-D manifolds to the population transfer problem in a three-level quantum system driven by two laser pulses, of arbitrary shape and frequency. In the rotating wave approximation, we consider a nonisotropic model i.e. a model in which the two coupling constants of the lasers are different. The aim is to induce transitions from the first to the third level, minimizing 1) the time of the transition (with bounded laser amplitudes),\\n2) the energy of lasers (with fixed final time). After reducing the problem to real variables, for the purpose 1) we develop a theory of time optimal syntheses for distributional problem on 2-D-manifolds, while for the purpose 2) we use techniques of subriemannian geometry on 3-D Lie groups. The complete optimal syntheses are computed.}, url = {http://hdl.handle.net/1963/2259}, author = {Ugo Boscain and Thomas Chambrion and Gr{\'e}goire Charlot} } @article {2005, title = {Nonlinear Schr{\"o}dinger Equations with vanishing and decaying potentials}, number = {SISSA;52/2005/M}, year = {2005}, url = {http://hdl.handle.net/1963/1760}, author = {Antonio Ambrosetti and Wang Zhi-Qiang} } @article {2003, title = {Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces}, journal = {Mod. Phys. Lett. A 18 (2003) 2371-2379}, number = {arXiv.org;math/0309143v1}, year = {2003}, publisher = {World Scientific}, abstract = {We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.}, doi = {10.1142/S0217732303012593}, url = {http://hdl.handle.net/1963/3215}, author = {Ludwik Dabrowski and Thomas Krajewski and Giovanni Landi} } @article {2003, title = {A note on singular limits to hyperbolic systems of conservation laws}, journal = {Commun. Pure Appl. Ana., 2003, 2, 51-64}, number = {SISSA;85/00/M}, year = {2003}, publisher = {SISSA Library}, abstract = {In this note we consider two different singular limits to hyperbolic system of conservation laws, namely the standard backward schemes for non linear semigroups and the semidiscrete scheme. \\nUnder the assumption that the rarefaction curve of the corresponding hyperbolic system are straight lines, we prove the stability of the solution and the convergence to the perturbed system to the unique solution of the limit system for initial data with small total variation.}, url = {http://hdl.handle.net/1963/1542}, author = {Stefano Bianchini} } @article {2003, title = {A note on the integral representation of functionals in the space SBD(O)}, journal = {Rend. Mat. Appl. 23 (2003) 189-201}, number = {SISSA;14/2001/M}, year = {2003}, publisher = {Rendiconti di Matematica}, abstract = {In this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions.}, url = {http://hdl.handle.net/1963/3064}, author = {Francois Ebobisse and Rodica Toader} } @article {2001, title = {Non-compactness and multiplicity results for the Yamabe problem on Sn}, journal = {J. Funct. Anal. 180 (2001) 210-241}, number = {SISSA;130/99/M}, year = {2001}, publisher = {Elsevier}, doi = {10.1006/jfan.2000.3699}, url = {http://hdl.handle.net/1963/1345}, author = {Massimiliano Berti and Andrea Malchiodi} } @article {2001, title = {A note on the super Krichever map}, journal = {J. Geom. Phys. 37 (2001), no. 1-2, 169-181}, number = {SISSA;36/00/FM}, year = {2001}, publisher = {SISSA Library}, abstract = {We consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based\\non the Fa{\textquoteleft}a di Bruno recursion relations, considered as the cocycle condition for the natural double complex associated with the deformations of super Krichever data. Our approach is based on the construction of the universal super divisor (of degree g), and a local universal family of geometric data which give the map into the Super Grassmannian.}, doi = {10.1016/S0393-0440(00)00037-1}, url = {http://hdl.handle.net/1963/1494}, author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa} } @mastersthesis {2001, title = {Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence}, year = {2001}, school = {SISSA}, keywords = {Mumford-Shah functional}, url = {http://hdl.handle.net/1963/5399}, author = {Matteo Negri} } @article {2001, title = {Numerical minimization of the Mumford-Shah functional}, journal = {Calcolo, 2001, 38, 67}, number = {SISSA;3/00/M}, year = {2001}, publisher = {SISSA Library}, doi = {10.1007/s100920170004}, url = {http://hdl.handle.net/1963/1461}, author = {Matteo Negri and Maurizio Paolini} } @article {2000, title = {A note on the scalar curvature problem in the presence of symmetries}, journal = {Ricerche Mat. 49 (2000), suppl., 169-176}, number = {SISSA;150/99/M}, year = {2000}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1365}, author = {Antonio Ambrosetti and Li YanYan and Andrea Malchiodi} } @article {1999, title = {Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws}, journal = {J. Differential Equations 151 (1999) 345-372}, number = {SISSA;139/97/M}, year = {1999}, publisher = {Elsevier}, abstract = {The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.}, doi = {10.1006/jdeq.1998.3513}, url = {http://hdl.handle.net/1963/3312}, author = {Debora Amadori and Paolo Baiti and Philippe G. LeFloch and Benedetto Piccoli} } @article {1999, title = {A note on fractional KDV hierarchies. II. The bihamiltonian approach}, number = {SISSA;6/99/FM}, year = {1999}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1220}, author = {Paolo Casati and Gregorio Falqui and Marco Pedroni} } @article {1990, title = {N=2 super Riemann surfaces and algebraic geometry}, journal = {J. Math. Phys. 31 (1990), no.4, 948-952}, number = {SISSA;47/89/FM}, year = {1990}, publisher = {American Institute of Physics}, abstract = {The geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems.}, doi = {10.1063/1.528775}, url = {http://hdl.handle.net/1963/807}, author = {Cesare Reina and Gregorio Falqui} } @article {1990, title = {A note on the global structure of supermoduli spaces}, journal = {Comm.Math.Phys. 31 (1990), no.4, 948}, number = {SISSA;46/89/FM}, year = {1990}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/806}, author = {Cesare Reina and Gregorio Falqui} } @article {1989, title = {On the number of families of periodic solutions of a Hamiltonian system near equilibrium. II. (English. Italian summary)}, journal = {Boll. Un. Mat. Ital. B (7) 3 (1989), no. 3, 579-590}, number = {SISSA;13/88/FM}, year = {1989}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/609}, author = {Gianfausto Dell{\textquoteright}Antonio and Biancamaria D{\textquoteright}Onofrio} } @article {1986, title = {The natural spinor connection on $S\\\\sb 8$ is a gauge field}, journal = {Lett. Math. Phys. 11 (1986), no. 2, 171-175}, number = {SISSA;61/85/MP}, year = {1986}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/448}, author = {Giovanni Landi} }