Publications related to The Momentum Map, Symplectic Reduction and an Introduction to Brownian Motion

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

Noether Theorems and Quantum Anomalies

Tudor Ratiu

A quantum anomaly is the breaking of symmetry with respect to some transformations after the quantization of a classical Hamiltonian or Lagrangian system. It is shown that both the Noether theorems (including their infinite-dimensional versions) and the ex ...

Springer Verlag2017

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

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

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Jan Sickmann Hesthaven, Babak Maboudi Afkham

Reduced basis methods are popular for approximately solving large and complex systems of dierential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present ...

2017

Multisymplectic variational integrators and space/time symplecticity

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

Multisymplectic variational integrators are structure-preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and spatial discrete evo ...

World Scientific Publ Co Pte Ltd2016

Bloch theorem with revised boundary conditions applied to glide and screw symmetric, quasi-one-dimensional structures

Florian Paul Robert Maurin

Bloch theorem is useful for analyzing wave propagation in periodic systems. It has been widely used to determine the energy bands of various translationally-periodic crystals and with the advent of nanoscale structures like nanotubes, it has been extended ...

Elsevier2016

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

Aparajita Dasgupta

In this paper we give a global characterisation of classes of ultradi_erentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. Thi ...

2016

The Momentum Map, Symplectic Reduction and an Introduction to Brownian Motion

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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

Noether Theorems and Quantum Anomalies

Structure preserving model reduction of parametric Hamiltonian systems

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

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Multisymplectic variational integrators and space/time symplecticity

Bloch theorem with revised boundary conditions applied to glide and screw symmetric, quasi-one-dimensional structures

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

Symplectic Model-Reduction with a Weighted Inner Product

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

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Noether Theorems and Quantum Anomalies

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Structure preserving model reduction of parametric Hamiltonian systems

Multisymplectic variational integrators and space/time symplecticity

Bloch theorem with revised boundary conditions applied to glide and screw symmetric, quasi-one-dimensional structures

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

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