Publications related to Analysis of adiabatic trapping for quasi-integrable area-preserving maps

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

Motivic and p-adic Localization Phenomena

Dimitri Stelio Wyss

In this thesis we compute motivic classes of hypertoric varieties, Nakajima quiver varieties and open de Rham spaces in a certain localization of the Grothendieck ring of varieties. Furthermore we study the

p

-adic pushforward of the Haar measure under a ...

EPFL2017

Structure preserving model reduction of parametric Hamiltonian systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

While reduced-order models (ROMs) are popular for approximately solving large systems of differential equations, the stability of reduced models over long-time integration remains an open question. We present a greedy approach for ROM generation of paramet ...

2017

The tropical momentum map: a classification of toric log symplectic manifolds

Tudor Ratiu

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...

Springer Verlag2017

Multisymplectic Variational Integrators For Nonsmooth Lagrangian Continuum Mechanics

Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

This paper develops the theory of multisymplectic variational integrators for nonsmooth continuum mechanics with constraints. Typical problems are the impact of an elastic body on a rigid plate or the collision of two elastic bodies. The integrators are ob ...

Cambridge Univ Press2016

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

We reformulate the equation characterizing the critical points of the hypersymplectic action functional as solutions of a Hamiltonian system on the iterated loop space. The intent is to gain more insight into dynamics of hyperkahler Floer theory. ...

American Mathematical Society2015

Discrete variational Lie group formulation of geometrically exact beams dynamics

Yves Weinand, Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resultin ...

Springer Verlag2015

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

Analysis of adiabatic trapping for quasi-integrable area-preserving maps

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Symplectic Dynamical Low Rank approximation of wave equations with random parameters

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Dynamical Low Rank approximation of PDEs with random parameters

Motivic and p-adic Localization Phenomena

Structure preserving model reduction of parametric Hamiltonian systems

The tropical momentum map: a classification of toric log symplectic manifolds

Multisymplectic Variational Integrators For Nonsmooth Lagrangian Continuum Mechanics

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

Discrete variational Lie group formulation of geometrically exact beams dynamics

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

The tropical momentum map: a classification of toric log symplectic manifolds

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Multisymplectic Variational Integrators For Nonsmooth Lagrangian Continuum Mechanics

Dynamical Low Rank approximation of PDEs with random parameters

Motivic and p-adic Localization Phenomena

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

Structure preserving model reduction of parametric Hamiltonian systems

Discrete variational Lie group formulation of geometrically exact beams dynamics