Publications related to Geometry of nonabelian charged fluids

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

2018

Symplectic Model-Reduction with a Weighted Inner Product

Jan Sickmann Hesthaven, Babak Maboudi Afkham

In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems, symplectic model redu ...

2018

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

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

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 Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

Fabio Rinaldi

In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction, of strength beta, centred at 0 (the bottom of the confining parabolic potential), that was rigorou ...

Iop Publishing Ltd2016

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

Low rank differential equations for Hamiltonian matrix nearness problems

Daniel Kressner

For a Hamiltonian matrix with purely imaginary eigenvalues, we aim to determine the nearest Hamiltonian matrix such that some or all eigenvalues leave the imaginary axis. Conversely, for a Hamiltonian matrix with all eigenvalues lying off the imaginary axi ...

Springer Heidelberg2015

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

Cedric Jean-François Hernalsteens, Massimo Giovannozzi

Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinea ...

American Physical Society2014

Geometry of nonabelian charged fluids

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Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

Symplectic Model-Reduction with a Weighted Inner Product

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

Structure preserving model reduction of parametric Hamiltonian systems

The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

Low rank differential equations for Hamiltonian matrix nearness problems

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

The Hamiltonian of the harmonic oscillator with an attractive delta '-interaction centred at the origin as approximated by the one with a triple of attractive delta-interactions

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

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

Structure preserving model reduction of parametric Hamiltonian systems

Symplectic Model-Reduction with a Weighted Inner Product

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

Hyperkahler Floer Theory As Infinite Dimensional Hamiltonian System

Low rank differential equations for Hamiltonian matrix nearness problems