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The high volatility of renewable energies calls for more energy efficiency. Thus, different physical systems need to be coupled efficiently although they run on various time scales. Here, the port-Hamiltonian (pH) modeling framework comes…

Numerical Analysis · Mathematics 2024-04-09 Sarah-Alexa Hauschild , Nicole Marheineke

A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…

Analysis of PDEs · Mathematics 2023-11-29 Ansgar Jüngel , Martin Vetter

We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and Galilean transformations, we define a…

Mathematical Physics · Physics 2022-06-29 Alexei A. Mailybaev

To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the…

Mesoscale and Nanoscale Physics · Physics 2019-11-04 Weiqi Chu , Xiantao Li

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation…

Numerical Analysis · Mathematics 2022-10-19 Andrea Brugnoli , Ramy Rashad , Stefano Stramigioli

We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. We show that this equation predicts…

Statistical Mechanics · Physics 2021-12-10 Joseph Durnin , Andrea De Luca , Jacopo De Nardis , Benjamin Doyon

We present a flexible discretization technique for computational models of thin tubular networks embedded in a bulk domain, for example a porous medium. These systems occur in the simulation of fluid flow in vascularized biological tissue,…

Computational Engineering, Finance, and Science · Computer Science 2022-02-01 Timo Koch

Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for…

Numerical Analysis · Mathematics 2020-02-07 Michael Kraus , Tomasz M. Tyranowski

We show that the $m$-dimensional Euler--Manakov top on $so^*(m)$ can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety $\bar{\cal V}(k,m)$, and present its Lax representation…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 Yuri N. Fedorov

We integrate in closed implicit form the Navier-Stokes equations for an incompressible fluid and the kinematical dynamo equation, in smooth manifolds and Euclidean space. This integration is carried out by applying Stochastic Differential…

Mathematical Physics · Physics 2007-05-23 Diego L. Rapoport

In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…

Mathematical Physics · Physics 2011-03-09 Tianshu Luo , Yimu Guo

We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…

Analysis of PDEs · Mathematics 2007-12-27 Jerry L. Bona , David Lannes , Jean-Claude Saut

We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D generalization allows one to invert the total divergence…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Willy Hereman , Michael Colagrosso , Ryan Sayers , Adam Ringler , Bernard Deconinck , Michael Nivala , Mark S. Hickman

A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…

Numerical Analysis · Mathematics 2024-07-23 William Barham , Philip J. Morrison

In this article we study port-Hamiltonian partial differential equations on certain one-dimensional manifolds. We classify those boundary conditions that give rise to contraction semigroups. As an application we study port-Hamiltonian…

Functional Analysis · Mathematics 2021-11-09 Marcus Waurick , Sven-Ake Wegner

In this work the issue of whether key energetic properties (nonlinear, exponential-type dissipation in the abscence of forcing and long-term stability under conditions of time dependent loading) are automatically inherited by deforming…

Fluid Dynamics · Physics 2015-06-26 S. J. Childs

We propose a semismooth Newton method for non-Newtonian models of incompressible flow where the constitutive relation between the shear stress and the symmetric velocity gradient is given implicitly; this class of constitutive relations…

Numerical Analysis · Mathematics 2021-10-18 P. A. Gazca-Orozco

Most organic and inorganic surfaces (e.g., glass, nucleic acids or lipid membranes) become charged in aqueous solutions. The resulting ionic distribution induces effective interactions between the charged surfaces. Stacks of like-charged…

In this paper, the semiclassical limit of Davey-Stewartson systems are studied. It shows that these dispersionless limited integrable systems of hydrodynamic type, which are defined as dDS (dispersionless Davey-Stewartson) systems, are…

Exactly Solvable and Integrable Systems · Physics 2021-01-19 G. Yi

We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component…

Exactly Solvable and Integrable Systems · Physics 2022-05-18 M. B. Sheftel , D. Yazıcı