We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

VL - 59 UR - https://doi.org/10.1063/1.5033856 ER - TY - JOUR T1 - On fractional powers of singular perturbations of the Laplacian JF - Journal of Functional Analysis Y1 - 2018 A1 - Vladimir Georgiev A1 - Alessandro Michelangeli A1 - Raffaele Scandone KW - Point interactions KW - Regular and singular component of a point-interaction operator KW - Singular perturbations of the Laplacian AB -We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

VL - 275 UR - http://www.sciencedirect.com/science/article/pii/S0022123618301046 ER - TY - JOUR T1 - Framed symplectic sheaves on surfaces JF - International Journal of Mathematics Y1 - 2018 A1 - Jacopo Vittorio Scalise AB -A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D \subset X$ and a morphism $\Lambda^2 E \rightarrow \mathcal{O}_X$ satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for $X =\mathbb{P}_\mathbb{C}^2$. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

VL - 29 UR - https://doi.org/10.1142/S0129167X18500076 ER - TY - JOUR T1 - Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation JF - International Journal of Computational Fluid Dynamics Y1 - 2018 A1 - Filippo Salmoiraghi A1 - Scardigli, Angela A1 - Telib, Haysam A1 - Gianluigi Rozza AB -In this work, we provide an integrated pipeline for the model-order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, free-form deformation is applied for geometry parametrisation, whereas two different reduced-order models based on proper orthogonal decomposition (POD) are employed in order to speed-up the full-order simulations: the first method exploits POD with interpolation, while the second one is based on domain decomposition. For the sampling of the parameter space, we adopt a Greedy strategy coupled with Constrained Centroidal Voronoi Tessellations, in order to guarantee a good compromise between space exploration and exploitation. The proposed framework is tested on an industrially relevant application, i.e. the front-bumper morphing of the DrivAer car model, using the finite-volume method for the full-order resolution of the Reynolds-Averaged Navier–Stokes equations.

PB - Taylor & Francis VL - 32 ER - TY - JOUR T1 - On fully real eigenconfigurations of tensors JF - SIAM Journal on Applied Algebra and Geometry Y1 - 2018 A1 - Khazhgali Kozhasov AB -We construct generic real symmetric tensors with only real eigenvectors or, equivalently, real homogeneous polynomials with the maximum possible finite number of critical points on the sphere.

PB - SIAM VL - 2 UR - https://epubs.siam.org/doi/pdf/10.1137/17M1145902 ER - TY - RPRT T1 - Friedrichs systems in a Hilbert space framework: solvability and multiplicity Y1 - 2017 A1 - Nenad Antonić A1 - Marko Erceg A1 - Alessandro Michelangeli AB - The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples. UR - http://preprints.sissa.it/handle/1963/35280 U1 - 35587 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - A fast virtual surgery platform for many scenarios haemodynamics of patient-specific coronary artery bypass grafts Y1 - 2016 A1 - Francesco Ballarin A1 - Elena Faggiano A1 - Andrea Manzoni A1 - Gianluigi Rozza A1 - Alfio Quarteroni A1 - Sonia Ippolito A1 - Roberto Scrofani A1 - Carlo Antona AB - A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed. Complex surgical configurations employed in the clinical practice, such as Y-grafts and sequential grafts, are studied. A virtual surgery platform based on model reduction of unsteady Navier Stokes equations for blood dynamics is proposed to carry out sensitivity analyses in a very rapid and reliable way. A specialized geometrical parametrization is employed to compare the effect of stenosis and anastomosis variation on the outcome of the surgery in several relevant cases. PB - Submitted UR - http://urania.sissa.it/xmlui/handle/1963/35240 U1 - 35545 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case JF - Calculus of Variations and Partial Differential Equations Y1 - 2016 A1 - Gianni Dal Maso A1 - Gianluca Orlando A1 - Rodica Toader AB -We study the asymptotic behavior of a variational model for damaged elasto-plastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter $\varepsilon$, which forces damage concentration on regions of codimension one. We determine the $\Gamma$-limit as $\varepsilon$ tends to zero and show that it contains an energy term involving the crack opening.

VL - 55 UR - https://doi.org/10.1007/s00526-016-0981-z ER - TY - THES T1 - Frames symplectic sheaves on surfaces and their ADHM data Y1 - 2016 A1 - Jacopo Vittorio Scalise KW - moduli spaces AB - This dissertation is centered on the moduli space of what we call framed symplectic sheaves on a surface, compactifying the corresponding moduli space of framed principal SP−bundles. It contains the construction of the moduli space, which is carried out for every smooth projective surface X with a big and nef framing divisor, and a study of its deformation theory. We also develop an in-depth analysis of the examples X = P2 and X = Blp (P2 ), showing that the corresponding moduli spaces enjoy an ADHM-type description. In the former case, we prove irreducibility of the space and exhibit a relation with the space of framed ideal instantons on S4 in type C. PB - SISSA U1 - 35517 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - JOUR T1 - A Frobenius theorem for corank-1 continuous distributions in dimensions two and three JF - International Journal of Mathematics Y1 - 2016 A1 - Stefano Luzzatto A1 - Sina Türeli A1 - Khadim Mbacke War AB -We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive C1 distribution is uniquely integrable.

VL - 27 UR - https://doi.org/10.1142/S0129167X16500610 ER - TY - RPRT T1 - Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization Y1 - 2015 A1 - Francesco Ballarin A1 - Elena Faggiano A1 - Sonia Ippolito A1 - Andrea Manzoni A1 - Alfio Quarteroni A1 - Gianluigi Rozza A1 - Roberto Scrofani AB - In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach. UR - http://urania.sissa.it/xmlui/handle/1963/34623 U1 - 34824 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows JF - Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 Y1 - 2015 A1 - Nicola Giuliani A1 - Andrea Mola A1 - Luca Heltai A1 - L. Formaggia AB -In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

UR - http://urania.sissa.it/xmlui/handle/1963/34466 U1 - 34640 U2 - Mathematics U4 - 1 U5 - MAT/08 ER - TY - JOUR T1 - Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians Y1 - 2014 A1 - Ferenc Balogh A1 - Tiago Fonseca A1 - John P. Harnad AB - We study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function. PB - American Institute of Physics Inc. UR - http://urania.sissa.it/xmlui/handle/1963/34952 U1 - 35153 U2 - Mathematics U4 - 1 ER - TY - Generic T1 - A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures T2 - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 Y1 - 2014 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - ship hydrodynamics AB - We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed. JF - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 PB - SISSA U1 - 7357 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - CHAP T1 - Fundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications T2 - Separated representations and PGD-based model reduction : fundamentals and applications Y1 - 2014 A1 - Gianluigi Rozza KW - reduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs AB -In this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.

JF - Separated representations and PGD-based model reduction : fundamentals and applications T3 - CISM International Centre for Mechanical Sciences PB - Springer CY - Wien VL - 554 ER - TY - JOUR T1 - Fields of bounded deformation for mesoscopic dislocations Y1 - 2013 A1 - Nicolas Van Goethem AB - In this paper we discuss the consequences of the distributional approach to dislocations in terms of the mathematical properties\\r\\nof the auxiliary model fields such as displacement and displacement gradient which are obtained directly from \\r\\nthe main model field here considered as the linear strain. We show that these fields cannot be introduced rigourously without \\r\\nthe introduction of gauge fields, or equivalently, without cuts in the Riemann foliation associated to the dislocated crystal.\\r\\nIn a second step we show that the space of bounded deformations follows from the distributional approach in a natural way and \\r\\ndiscuss the reasons why it is adequate to model dislocations. The case of dislocation clusters is also addressed, as it represents an important issue in industrial crystal growth while from a mathematical point of view, peculiar phenomena might appear at the set of accumulation points. \\r\\nThe elastic-plastic decomposition of the strain within this approach is also given a precise meaning. PB - SISSA UR - http://hdl.handle.net/1963/6378 U1 - 6311 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Fracture models as Gamma-limits of damage models JF - Communications on Pure and Applied Analysis 12 (2013) 1657-1686 Y1 - 2013 A1 - Gianni Dal Maso A1 - Flaviana Iurlano AB -We analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/4225 U1 - 3952 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Framed sheaves on projective stacks Y1 - 2013 A1 - Ugo Bruzzo A1 - Francesco Sala AB - Given a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider {\em framed sheaves} on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent sheaf on $\mathscr X$ and $\phi_{\mathcal E}$ is a morphism from $\mathcal E$ to a fixed coherent sheaf $\mathcal F$. After introducing a suitable notion of (semi)stability, we construct a projective scheme, which is a moduli space for semistable framed sheaves with fixed Hilbert polynomial, and an open subset of it, which is a fine moduli space for stable framed sheaves. If $\mathscr X$ is a projective irreducible orbifold of dimension two and $\mathcal F$ a locally free sheaf on a smooth divisor $\mathscr D\subset \mathscr X$ satisfying certain conditions, we consider {\em $(\mathscr{D}, \mathcal{F})$-framed sheaves}, i.e., framed sheaves $(\mathcal E,\phi_{\mathcal E})$ with $\mathcal E$ a torsion-free sheaf which is locally free in a neighborhood of $\mathscr D$, and ${\phi_{\mathcal{E}}}_{\vert \mathscr{D}}$ an isomorphism. These pairs are $\mu$-stable for a suitable choice of a parameter entering the (semi)stability condition, and of the polarization of $\mathscr X$. This implies the existence of a fine moduli space parameterizing isomorphism classes of $(\mathscr{D}, \mathcal{F})$-framed sheaves on $\mathscr{X}$ with fixed Hilbert polynomial, which is a quasi-projective scheme. In an appendix we develop the example of stacky Hirzebruch surfaces. This is the first paper of a project aimed to provide an algebro-geometric approach to the study of gauge theories on a wide class of 4-dimensional Riemannian manifolds by means of framed sheaves on ``stacky" compactifications of them. In particular, in a subsequent paper \cite{art:bruzzopedrinisalaszabo2013} these results are used to study gauge theories on ALE spaces of type $A_k$. UR - http://urania.sissa.it/xmlui/handle/1963/7438 U1 - 7532 ER - TY - JOUR T1 - Free Form Deformation Techniques Applied to 3D Shape Optimization Problems JF - Communications in Applied and Industrial Mathematics Y1 - 2013 A1 - Anwar Koshakji A1 - Alfio Quarteroni A1 - Gianluigi Rozza AB - The purpose of this work is to analyse and study an efficient parametrization technique for a 3D shape optimization problem. After a brief review of the techniques and approaches already available in literature, we recall the Free Form Deformation parametrization, a technique which proved to be efficient and at the same time versatile, allowing to manage complex shapes even with few parameters. We tested and studied the FFD technique by establishing a path, from the geometry definition, to the method implementation, and finally to the simulation and to the optimization of the shape. In particular, we have studied a bulb and a rudder of a race sailing boat as model applications, where we have tested a complete procedure from Computer-Aided-Design to build the geometrical model to discretization and mesh generation. ER - TY - JOUR T1 - A formula for Popp\'s volume in sub-Riemannian geometry JF - Analysis and Geometry in Metric Spaces, vol. 1 (2012), pages : 42-57 Y1 - 2012 A1 - Luca Rizzi A1 - Davide Barilari KW - subriemannian, volume, Popp, control AB - For an equiregular sub-Riemannian manifold M, Popp\'s volume is a smooth\r\nvolume which is canonically associated with the sub-Riemannian structure, and\r\nit is a natural generalization of the Riemannian one. In this paper we prove a\r\ngeneral formula for Popp\'s volume, written in terms of a frame adapted to the\r\nsub-Riemannian distribution. As a first application of this result, we prove an\r\nexplicit formula for the canonical sub-Laplacian, namely the one associated\r\nwith Popp\'s volume. Finally, we discuss sub-Riemannian isometries, and we prove\r\nthat they preserve Popp\'s volume. We also show that, under some hypotheses on\r\nthe action of the isometry group of M, Popp\'s volume is essentially the unique\r\nvolume with such a property. PB - SISSA UR - http://hdl.handle.net/1963/6501 N1 - 16 pages, minor revisions U1 - 6446 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - JOUR T1 - Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation JF - Comm. Math. Phys. Y1 - 2012 A1 - Marco Bertola A1 - Mattia Cafasso VL - 309 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00220-011-1383-x ER - TY - JOUR T1 - Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation JF - Communications in Mathematical Physics 311 (2012) 557-594 Y1 - 2012 A1 - Andrea Raimondo AB - We consider a Frobenius structure associated with the dispersionless\\r\\nKadomtsev-Petviashvili equation. This is done, essentially, by applying a\\r\\ncontinuous analogue of the finite dimensional theory in the space of Schwartz\\r\\nfunctions on the line. The potential of the Frobenius manifold is found to be a\\r\\nlogarithmic potential with quadratic external field. Following the construction\\r\\nof the principal hierarchy, we construct a set of infinitely many commuting\\r\\nflows, which extends the classical dKP hierarchy. PB - Springer UR - http://hdl.handle.net/1963/6040 U1 - 5931 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - A Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library Y1 - 2012 A1 - Luca Heltai A1 - Saswati Roy A1 - Francesco Costanzo KW - Finite Element Method KW - Immersed Boundary Method KW - Immersed Finite Element Method AB - We present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method. PB - SISSA UR - http://hdl.handle.net/1963/6255 N1 - 28 pages, 9 figures U1 - 6172 U2 - Mathematics U3 - Functional Analysis and Applications U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Fracture and plastic models as Gamma-limits of damage models under different regimes JF - Advances in Calculus of Variations., to appear. Y1 - 2011 A1 - Flaviana Iurlano AB -We consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

PB - Walter de Gruyter UR - http://hdl.handle.net/1963/5069 U1 - 4883 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective JF - Systems and Control Letters, 59 (12):782-786, 2010 Y1 - 2010 A1 - Claudio Altafini A1 - Paola Cappellaro A1 - David Cory AB - In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated. PB - Elsevier UR - http://hdl.handle.net/1963/4384 U1 - 4132 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - First colonization of a hard-edge in random matrix theory JF - Constr. Approx. Y1 - 2010 A1 - Marco Bertola A1 - Lee, S. Y. VL - 31 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-009-9052-4 ER - TY - RPRT T1 - Families of Monads and Instantons from a Noncommutative ADHM Construction Y1 - 2009 A1 - Simon Brain A1 - Giovanni Landi AB - We give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent. UR - http://hdl.handle.net/1963/3478 U1 - 786 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - First colonization of a spectral outpost in random matrix theory JF - Constr. Approx. Y1 - 2009 A1 - Marco Bertola A1 - Lee, S. Y. VL - 30 UR - http://0-dx.doi.org.mercury.concordia.ca/10.1007/s00365-008-9026-y ER - TY - JOUR T1 - Foliations of small tubes in Riemannian manifolds by capillary minimal discs JF - Nonlinear Analysis: Theory, Methods & Applications Y1 - 2009 A1 - Fall, Mouhamed Moustapha A1 - Mercuri, Carlo AB -Letting be an embedded curve in a Riemannian manifold , we prove the existence of minimal disc-type surfaces centered at inside the surface of revolution of around , having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

PB - Elsevier VL - 70 UR - https://doi.org/10.1016/j.na.2008.10.024 ER - TY - JOUR T1 - Fluid–structure interaction problems in free surface flows: Application to boat dynamics JF - International Journal for Numerical Methods in Fluids Y1 - 2008 A1 - L. Formaggia A1 - Edie Miglio A1 - Andrea Mola A1 - N Parolini PB - Wiley VL - 56 UR - https://doi.org/10.1002/fld.1583 ER - TY - JOUR T1 - Forced Vibrations of a Nonhomogeneous String JF - SIAM J. Math. Anal. 40 (2008) 382-412 Y1 - 2008 A1 - P Baldi A1 - Massimiliano Berti AB - We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme. UR - http://hdl.handle.net/1963/2643 U1 - 1480 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Frobenius Manifolds and Central Invariants for the Drinfeld - Sokolov Bihamiltonian Structures JF - Adv. Math. 219 (2008) 780-837 Y1 - 2008 A1 - Boris Dubrovin A1 - Liu Si-Qi A1 - Zhang Youjin AB - The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the group of Miura type transformations. UR - http://hdl.handle.net/1963/2523 U1 - 1595 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices JF - Phys. Rev. B 77 (2008) 245105 Y1 - 2008 A1 - Matteo Rizzi A1 - Marco Polini A1 - Miguel A. Cazalilla A1 - M.R. Bakhtiari A1 - Mario P. Tosi A1 - Rosario Fazio AB -Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices.

UR - http://hdl.handle.net/1963/2694 U1 - 1406 U2 - Physics U3 - Condensed Matter Theory ER - TY - JOUR T1 - On feedback classification of control-affine systems with one and two-dimensional inputs JF - SIAM J. Control Optim. 46 (2007) 1431-1460 Y1 - 2007 A1 - Andrei A. Agrachev A1 - Igor Zelenko AB - The paper is devoted to the local classification of generic control-affine systems on an n-dimensional manifold with scalar input for any n>3 or with two inputs for n=4 and n=5, up to state-feedback transformations, preserving the affine structure. First using the Poincare series of moduli numbers we introduce the intrinsic numbers of functional moduli of each prescribed number of variables on which a classification problem depends. In order to classify affine systems with scalar input we associate with such a system the canonical frame by normalizing some structural functions in a commutative relation of the vector fields, which define our control system. Then, using this canonical frame, we introduce the canonical coordinates and find a complete system of state-feedback invariants of the system. It also gives automatically the micro-local (i.e. local in state-input space) classification of the generic non-affine n-dimensional control system with scalar input for n>2. Further we show how the problem of feedback-equivalence of affine systems with two-dimensional input in state space of dimensions 4 and 5 can be reduced to the same problem for affine systems with scalar input. In order to make this reduction we distinguish the subsystem of our control system, consisting of the directions of all extremals in dimension 4 and all abnormal extremals in dimension 5 of the time optimal problem, defined by the original control system. In each classification problem under consideration we find the intrinsic numbers of functional moduli of each prescribed number of variables according to its Poincare series. UR - http://hdl.handle.net/1963/2186 U1 - 2058 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Feedback control of spin systems Y1 - 2007 A1 - Claudio Altafini AB - The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems. JF - Quantum Inf. Process. 6 (2007) 9-36 UR - http://hdl.handle.net/1963/1808 N1 - Proc. of the 44th IEEE Conf. on Decision and Control,. Seville, Spain, December 2005 (to appear). U1 - 2406 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds JF - 45th IEEE Conference on Decision and Control (2007) 2471-2476 Y1 - 2007 A1 - Claudio Altafini AB - In an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a \\\"root-space\\\"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability. UR - http://hdl.handle.net/1963/1729 U1 - 2422 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On finite-dimensional projections of distributions for solutions of randomly forced PDE\\\'s JF - Ann. Inst. Henri Poincare-Prob. Stat. 43 (2007) 399-415 Y1 - 2007 A1 - Andrei A. Agrachev A1 - Sergei Kuksin A1 - Andrey Sarychev A1 - Armen Shirikyan AB - The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue measure and continuously depends on the map. The results obtained are applied to the 2D Navier-Stokes equations perturbed by various random forces of low dimension. UR - http://hdl.handle.net/1963/2012 U1 - 2184 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Forced vibrations of wave equations with non-monotone nonlinearities JF - Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 439-474 Y1 - 2006 A1 - Massimiliano Berti A1 - Luca Biasco AB - We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz. UR - http://hdl.handle.net/1963/2160 U1 - 2084 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Fundamental form and Cartan tensor of (2,5)-distributions coincide JF - J. Dyn. Control Syst. 12 (2006) 247-276 Y1 - 2006 A1 - Igor Zelenko AB - In our previous paper for generic rank 2 vector distributions on n-dimensional manifold (n greater or equal to 5) we constructed a special differential invariant, the fundamental form. In the case n=5 this differential invariant has the same algebraic nature, as the covariant binary biquadratic form, constructed by E.Cartan in 1910, using his ``reduction- prolongation\\\'\\\' procedure (we call this form Cartan\\\'s tensor). In the present paper we prove that our fundamental form coincides (up to constant factor -35) with Cartan\\\'s tensor. This result explains geometric reason for existence of Cartan\\\'s tensor (originally this tensor was obtained by very sophisticated algebraic manipulations) and gives the true analogs of this tensor in Riemannian geometry. In addition, as a part of the proof, we obtain a new useful formula for Cartan\\\'s tensor in terms of structural functions of any frame naturally adapted to the distribution. UR - http://hdl.handle.net/1963/2187 U1 - 2057 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A fourth order uniformization theorem on some four manifolds with large total Q-curvature JF - C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. Y1 - 2005 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. PB - Elsevier UR - http://hdl.handle.net/1963/4868 U1 - 4649 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Fredholm modules for quantum euclidean spheres JF - J. Geom. Phys. 49 (2004) 272-293 Y1 - 2004 A1 - Eli Hawkins A1 - Giovanni Landi AB - The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\\\\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres $S_q^{N-1}$. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i. e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra $A(S^{N-1}_q)$. PB - SISSA Library UR - http://hdl.handle.net/1963/1636 U1 - 2482 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - A finite element approximation of the Griffith\\\'s model in fracture mechanics JF - Numer. Math., 2003, 95, 653 Y1 - 2003 A1 - Matteo Negri AB - The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown. PB - SISSA Library UR - http://hdl.handle.net/1963/1548 U1 - 2570 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Free energy of the two-matrix model/dToda tau-function JF - Nuclear Phys. B Y1 - 2003 A1 - Marco Bertola VL - 669 ER - TY - JOUR T1 - Fast Arnold diffusion in systems with three time scales JF - Discrete Contin. Dyn. Syst. 8 (2002) 795-811 Y1 - 2002 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diffusion takes place with fast (polynomial) speed, even though the \\\"splitting determinant\\\" is exponentially small. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3058 U1 - 1275 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization JF - SIAM J. Control Optim. 41 (2002) 1455-1476 Y1 - 2002 A1 - Fabio Ancona A1 - Alberto Bressan AB - The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances. PB - SIAM UR - http://hdl.handle.net/1963/3073 U1 - 1260 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Following a path of varying curvature as an output regulation problem JF - IEEE Trans. Automatic Control 47 (2002) 1551-1556 Y1 - 2002 A1 - Claudio Altafini AB - Given a path of nonconstant curvature, local asymptotic stability can be proven for the general n trailer whenever the curvature can be considered as the output of an exogenous dynamical system. The controllers that provide convergence to zero of the tracking error chosen for the path-following problem are composed of a prefeedback that input-output linearizes the system, plus a linear controller. PB - IEEE UR - http://hdl.handle.net/1963/3143 U1 - 1190 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A functional analysis approach to Arnold diffusion JF - Ann. Inst. H. Poincare Anal. Non Lineaire 19 (2002) 395-450 Y1 - 2002 A1 - Massimiliano Berti A1 - Philippe Bolle AB - We discuss in the context of nearly integrable Hamiltonian systems a functional analysis approach to the \\\"splitting of separatrices\\\" and to the \\\"shadowing problem\\\". As an application we apply our method to the problem of Arnold Diffusion for nearly integrable partially isochronous systems improving known results. PB - Elsevier UR - http://hdl.handle.net/1963/3151 U1 - 1182 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Finite Difference Approximation of Free Discontinuity Problems JF - Proc. Royal Soc. Edinb. Ser. A 131 (2001), no. 3, 567-595 Y1 - 2001 A1 - Massimo Gobbino A1 - Maria Giovanna Mora PB - SISSA Library UR - http://hdl.handle.net/1963/1228 U1 - 2715 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A Fourier transform for sheaves on real tori. I. The equivalence Sky(T)~ Loc (T) JF - J. Geom. Phys. 39 (2001), no. 2, 174--182 Y1 - 2001 A1 - Ugo Bruzzo A1 - Giovanni Marelli A1 - Fabio Pioli PB - SISSA Library UR - http://hdl.handle.net/1963/1526 U1 - 2637 U2 - Mathematics U3 - Mathematical Physics ER - TY - THES T1 - Free-discontinuity problems: calibration and approximation of solutions Y1 - 2001 A1 - Massimiliano Morini KW - Calibration of solutions PB - SISSA UR - http://hdl.handle.net/1963/5398 U1 - 5223 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Frobenius manifold structure on orbit space of Jacobi groups. I JF - Differential Geom. Appl. Y1 - 2000 A1 - Marco Bertola VL - 13 ER - TY - JOUR T1 - Frobenius manifold structure on orbit space of Jacobi groups. II JF - Differential Geom. Appl. Y1 - 2000 A1 - Marco Bertola VL - 13 ER - TY - JOUR T1 - Functionals depending on curvatures with constraints JF - Rend. Sem. Mat. Univ. Padova 104 (2000), 173--199 Y1 - 2000 A1 - Maria Giovanna Mora A1 - Massimiliano Morini PB - SISSA Library UR - http://hdl.handle.net/1963/1299 U1 - 3156 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Frobenius manifolds and Virasoro constraints JF - Selecta Math. (N.S.) 5 (1999) 423-466 Y1 - 1999 A1 - Boris Dubrovin A1 - Zhang Youjin AB - For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. Particularly, the genus $\\\\leq 1$ Virasoro conjecture of T.Eguchi, K.Hori, M.Jinzenji, and C.-S.Xiong and of S.Katz is proved for smooth projective varieties having semisimple quantum cohomology. PB - Springer UR - http://hdl.handle.net/1963/2883 U1 - 1817 U2 - Mathematics U3 - Mathematical Physics ER - TY - CHAP T1 - Flat pencils of metrics and Frobenius manifolds T2 - Integrable systems and algebraic geometry : proceedings of the Taniguchi symposium 1997, Kobe, June 30 - July 4, 1997 and Research Institute for Mathematical Sciences, Kyoto University, July 7 - 11, 1997 / eds. M.-H. Saito, Y. Shimizu and K. Ueno. - Sing Y1 - 1997 A1 - Boris Dubrovin AB - This paper is based on the author\\\'s talk at 1997 Taniguchi Symposium \\\"Integrable Systems and Algebraic Geometry\\\". We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics. It is shown that, under certain homogeneity assumptions, these two objects are identical. The flat pencils of contravariant metrics on a manifold $M$ appear naturally in the classification of bihamiltonian structures of hydrodynamics type on the loop space $L(M)$. This elucidates the relations between Frobenius manifolds and integrable hierarchies. JF - Integrable systems and algebraic geometry : proceedings of the Taniguchi symposium 1997, Kobe, June 30 - July 4, 1997 and Research Institute for Mathematical Sciences, Kyoto University, July 7 - 11, 1997 / eds. M.-H. Saito, Y. Shimizu and K. Ueno. - Sing PB - World Scientific SN - 981-02-3266-7 UR - http://hdl.handle.net/1963/3237 U1 - 1065 U2 - Mathematics U3 - Mathematical Physics ER - TY - CHAP T1 - Functionals of the Peierls - Fröhlich Type and the Variational Principle for the Whitham Equations T2 - Solitons, geometry, and topology : on the crossroad / V. M. Buchstaber, S. P. Novikov editors.- Providence : American Mathematical Society, 1997. - ( American mathematical society translations. Series 2. - vol. 179). - pages : 35-44 Y1 - 1997 A1 - Boris Dubrovin JF - Solitons, geometry, and topology : on the crossroad / V. M. Buchstaber, S. P. Novikov editors.- Providence : American Mathematical Society, 1997. - ( American mathematical society translations. Series 2. - vol. 179). - pages : 35-44 PB - American Mathematical Society SN - 0821806661 UR - http://hdl.handle.net/1963/6485 U1 - 6425 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Flat connections for Lax hierarchies on coadjoint orbits JF - Phys. Lett. A 108 (1985), no. 7, 311-314 Y1 - 1985 A1 - Giovanni Landi A1 - Sergio De Filippo PB - SISSA Library UR - http://hdl.handle.net/1963/460 U1 - 3443 U2 - Mathematics U3 - Mathematical Physics ER -