2,083 research outputs found
Infinite-dimensional port-Hamiltonian systems with a stationary interface
We consider two systems of two conservation laws that are defined on
complementary spatial intervals and coupled by an interface as a single
port-Hamiltonian system. In case of a fixed interface position, we characterize
the boundary and interface conditions for which the associated port-Hamiltonian
operator generates a contraction semigroup. Furthermore, we present sufficient
conditions for the exponential stability of the generated -semigroup. The
results are illustrated by the example of two acoustic waveguides coupled by an
interface consisting of some membrane.Comment: arXiv admin note: text overlap with arXiv:2301.0734
On the relevance of the dam break problem in the context of nonlinear shallow water equations
The classical dam break problem has become the de facto standard in
validating the Nonlinear Shallow Water Equations (NSWE) solvers. Moreover, the
NSWE are widely used for flooding simulations. While applied mathematics
community is essentially focused on developing new numerical schemes, we tried
to examine the validity of the mathematical model under consideration. The main
purpose of this study is to check the pertinence of the NSWE for flooding
processes. From the mathematical point of view, the answer is not obvious since
all derivation procedures assumes the total water depth positivity. We
performed a comparison between the two-fluid Navier-Stokes simulations and the
NSWE solved analytically and numerically. Several conclusions are drawn out and
perspectives for future research are outlined.Comment: 20 pages, 15 figures. Accepted to Discrete and Continuous Dynamical
Systems. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutyk
A hydrodynamic approach to non-equilibrium conformal field theories
We develop a hydrodynamic approach to non-equilibrium conformal field theory.
We study non-equilibrium steady states in the context of one-dimensional
conformal field theory perturbed by the irrelevant operator. By
direct quantum computation, we show, to first order in the coupling, that a
relativistic hydrodynamic emerges, which is a simple modification of
one-dimensional conformal fluids. We show that it describes the steady state
and its approach, and we provide the main characteristics of the steady state,
which lies between two shock waves. The velocities of these shocks are modified
by the perturbation and equal the sound velocities of the asymptotic baths.
Pushing further this approach, we are led to conjecture that the approach to
the steady state is generically controlled by the power law , and
that the widths of the shocks increase with time according to .Comment: 24 page
Twenty years of distributed port-Hamiltonian systems:A literature review
The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups
Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics
This paper develops the foundations of the multisymplectic
formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in
computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. The present formulation also includes solid-fluid interactions and material interfaces and, in addition, lays
the groundwork for a treatment of shocks
Nonlocal magnetization dynamics in ferromagnetic heterostructures
Two complementary effects modify the GHz magnetization dynamics of nanoscale
heterostructures of ferromagnetic and normal materials relative to those of the
isolated magnetic constituents: On the one hand, a time-dependent ferromagnetic
magnetization pumps a spin angular-momentum flow into adjacent materials and,
on the other hand, spin angular momentum is transferred between ferromagnets by
an applied bias, causing mutual torques on the magnetizations. These phenomena
are manifestly nonlocal: they are governed by the entire spin-coherent region
that is limited in size by spin-flip relaxation processes. We review recent
progress in understanding the magnetization dynamics in ferromagnetic
heterostructures from first principles, focusing on the role of spin pumping in
layered structures. The main body of the theory is semiclassical and based on a
mean-field Stoner or spin-density--functional picture, but quantum-size effects
and the role of electron-electron correlations are also discussed. A growing
number of experiments support the theoretical predictions. The formalism should
be useful to understand the physics and to engineer the characteristics of
small devices such as magnetic random-access memory elements.Comment: 48 pages, 21 figures (3 in color
Energetic decomposition of Distributed Systems with Moving Material Domains:the port-Hamiltonian model of Fluid-Structure Interaction
We introduce the geometric structure underlying the port-Hamiltonian models
for distributed parameter systems exhibiting moving material domains
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