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Related papers: Discrete nonlinear elastodynamics in a port-Hamilt…

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We introduce a new definition of discrete-time port-Hamiltonian systems (PHS), which results from structure-preserving discretization of explicit PHS in time. We discretize the underlying continuous-time Dirac structure with the collocation…

Dynamical Systems · Mathematics 2018-11-20 Paul Kotyczka , Laurent Lefèvre

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Systems and Control · Computer Science 2019-03-01 Ibrahim Ayed , Emmanuel de Bézenac , Arthur Pajot , Julien Brajard , Patrick Gallinari

Elastodynamic equations have been formulated with either Newton's second law of motion, Lagrange's equation, or Hamilton's principle for over 150 years. In this work, contrary to classical continuum mechanics, a novel strategic methodology…

Classical Physics · Physics 2025-01-08 Yinqiu Zhou , Xiumei Zhang , Lin Liu , Tingting Liu , Xiuming Wang

In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the…

Numerical Analysis · Mathematics 2016-01-20 Arvind Baskaran , Zhen Guan , John Lowengrub

We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy-Green deformation…

Numerical Analysis · Mathematics 2022-10-19 François Demoures , François Gay-Balmaz

The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing…

Systems and Control · Electrical Eng. & Systems 2024-11-26 Muhammad Zakwan , Giancarlo Ferrari-Trecate

In the present work, advanced spatial and temporal discretization techniques are tailored to hyperelastic physics-augmented neural networks, i.e., neural network based constitutive models which fulfill all relevant mechanical conditions of…

Computational Engineering, Finance, and Science · Computer Science 2023-06-19 Marlon Franke , Dominik K. Klein , Oliver Weeger , Peter Betsch

We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…

Statistical Mechanics · Physics 2023-12-04 Kui Cao , Su-Peng Kou

We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of…

Quantum Physics · Physics 2025-07-31 Pei Wang

We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…

Systems and Control · Electrical Eng. & Systems 2025-05-28 Martine Dyring Hansen , Elena Celledoni , Benjamin Kwanen Tapley

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisation of the relative equilibrium point notion to a…

Mathematical Physics · Physics 2021-10-04 J. de Lucas , B. M. Zawora

This thesis deals with the formulation and analysis of two systems of conservation laws defined on two complementary intervals and coupled by some moving interface as a single infinite-dimensional port-Hamiltonian system. This approach may…

Analysis of PDEs · Mathematics 2023-01-19 Alexander Kilian

We derive an exact deterministic nonlinear observer to compute the continuous state of an inertial navigation system based on partial discrete measurements, the so-called strapdown problem. Nonlinear contraction is used as the main analysis…

Optimization and Control · Mathematics 2007-05-23 Yong Zhao , Jean-Jacques E. Slotine

Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy…

Numerical Analysis · Mathematics 2024-12-17 Andreas Bartel , Manuel Schaller

We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…

General Relativity and Quantum Cosmology · Physics 2023-10-18 Nishita Jadoo , J. David Brown , Charles R. Evans

This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…

Numerical Analysis · Mathematics 2026-05-12 Patrick Bammer , Lothar Banz , Miriam Schönauer , Andreas Schröder

We investigate finite-strain elastoplastic evolution in the nonassociative setting. The constitutive material model is formulated in variational terms and coupled with the quasistatic equilibrium system. We introduce measure-valued…

Analysis of PDEs · Mathematics 2025-05-08 Ulisse Stefanelli , Andreas Vikelis

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

Analysis of PDEs · Mathematics 2022-03-14 Federico Califano , Ramy Rashad , Frederic P. Schuller , Stefano Stramigioli

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

Mathematical Physics · Physics 2015-06-12 Raphael Lefevere