2,083 research outputs found

    Infinite-dimensional port-Hamiltonian systems with a stationary interface

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    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 C0C_0-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

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    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

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    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 TTˉT\bar T 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 t1/2t^{-1/2}, and that the widths of the shocks increase with time according to t1/3t^{1/3}.Comment: 24 page

    Twenty years of distributed port-Hamiltonian systems:A literature review

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    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

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    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

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    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

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    We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains
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