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Symplectic dynamical low rank approximation of wave equations with random parameters

Publications associées (62)

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The radial wave operator in similarity coordinates

Roland Donninger

We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyze linear stability of the fundamental self-similar solution of the wave equation with a focusing power nonlinearity. T ...

American Institute of Physics2010

Hamiltonian approach to hybrid plasma models

Cesare Tronci

The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ord ...

2010

Slow Blow up solutions for certain critical wave equations

Joachim Krieger

We describe in this article two recent results [11], [12], obtained by the author jointly with W. Schlag and D. Tataru, about singular solutions for the critical wave maps equation, as well as the critical focussing semilinear wave equation. Specifically, ...

2010

Nonlinear Stability of Self-Similar Solutions for Semilinear Wave Equations

Roland Donninger

We prove nonlinear stability of the fundamental self-similar solution of the wave equation with a focusing power nonlinearity tt-=p for [image omitted] in the radial case. The proof is based on a semigroup formulation of the wave equation in similarity coo ...

Taylor & Francis2010

The geometric structure of complex fluids

Tudor Ratiu, François Gay-Balmaz

This paper develops the theory of affine Euler-Poincare and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microf ...

Elsevier2009

Asymptotics and analytic modes for the wave equation in similarity coordinates

Roland Donninger

We consider the radial wave equation in similarity coordinates within the semigroup formalism. It is known that the generator of the semigroup exhibits a continuum of eigenvalues and embedded in this continuum there exists a discrete set of eigenvalues wit ...

Springer Verlag2009

Differential geometry: a natural tool for describing symmetry operations

Gervais Chapuis, Kurt Schenk, Philippe Kocian

Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group o ...

2009

The Momentum Map In Poisson Geometry

Tudor Ratiu, Juan-Pablo Ortega

Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in reduction. ...

2009

Applying combined field integral equation technique to analyze quasi-waveguide structures

Juan Ramon Mosig, Michael Mattes, Laleh Golestanirad

In this paper a detailed mathematical procedure is described to evaluate modal scattering parameters conventionally defined in planar multilayered structures excited by wave ports. Combined Field Integral Equation technique is implemented and solved using ...

2009

The non-linear stochastic wave equation in high dimensions

Daniel Conus

The main topic of this thesis is the study of the non-linear stochastic wave equation in spatial dimension greater than 3 driven by spatially homogeneous Gaussian noise that is white in time. We are interested in questions of existence and uniqueness of so ...

EPFL2008