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Related papers: Port-Hamiltonian systems on discrete manifolds

200 papers

In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…

Mathematical Physics · Physics 2025-10-10 C. Sardón , X. Zhao

We consider two systems of two conservation laws that are defined on complementary, one-dimensional spatial intervals and coupled by an interface as a single port-Hamiltonian system. In case of a fixed interface position, we characterize…

Analysis of PDEs · Mathematics 2025-01-22 Alexander Kilian , Bernhard Maschke , Andrii Mironchenko , Fabian Wirth

This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…

Dynamical Systems · Mathematics 2023-11-08 Cristobal Ponce , Yongxin Wu , Yann Le Gorrec , Hector Ramirez

A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a list of consistency criteria with the geometric setting of…

Symplectic Geometry · Mathematics 2025-11-11 François Gay-Balmaz , Álvaro Rodríguez Abella , Hiroaki Yoshimura

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…

Mathematical Physics · Physics 2015-06-11 Vit Jakubsky

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…

Systems and Control · Computer Science 2015-01-22 Fernando Castaños , Hannah Michalska , Dmitry Gromov , Vincent Hayward

We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrained variational calculus, optimal control, Lagrangian…

Mathematical Physics · Physics 2018-04-17 M. Barbero-Liñán , H. Cendra , E. García-Toraño Andrés , D. Martín de Diego

We extend the correspondence between Poisson maps and actions of symplectic groupoids, which generalizes the one between momentum maps and hamiltonian actions, to the realm of Dirac geometry. As an example, we show how hamiltonian…

Differential Geometry · Mathematics 2007-05-23 Henrique Bursztyn , Marius Crainic

We define the topological Dirac equation describing the evolution of a topological wave function on networks or on simplicial complexes. On networks, the topological wave function describes the dynamics of topological signals or cochains,…

Disordered Systems and Neural Networks · Physics 2021-09-27 Ginestra Bianconi

In this paper, we consider infinite-dimensional port-Hamiltonian systems with in-domain actuation by means of an approach based on Stokes-Dirac structures as well as in a framework that exploits an underlying jet-bundle structure. In both…

Optimization and Control · Mathematics 2021-07-29 Tobias Malzer , Jesús Toledo , Yann Le Gorrec , Markus Schöberl

The port-Hamiltonian modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as port-Hamiltonian systems and the inputs are…

Numerical Analysis · Mathematics 2023-01-06 Andreas Bartel , Markus Clemens , Michael Günther , Birgit Jacob , Timo Reis

This paper provides a first contribution to port-Hamiltonian modeling of district heating networks. By introducing a model hierarchy of flow equations on the network, this work aims at a thermodynamically consistent port-Hamiltonian…

After recalling standard nonlinear port-Hamiltonian systems and their algebraic constraint equations, called here Dirac algebraic constraints, an extended class of port-Hamiltonian systems is introduced. This is based on replacing the…

Optimization and Control · Mathematics 2019-09-17 Arjan van der Schaft , Bernhard Maschke

The purpose of this paper is to define the concept of multi-Dirac structures and to describe their role in the description of classical field theories. We begin by outlining a variational principle for field theories, referred to as the…

Mathematical Physics · Physics 2010-10-22 Joris Vankerschaver , Hiroaki Yoshimura , Jerrold E. Marsden

Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…

Exactly Solvable and Integrable Systems · Physics 2015-06-23 B. G. Konopelchenko , W. K. Schief

A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…

Functional Analysis · Mathematics 2023-02-03 Bálint Farkas , Birgit Jacob , Timo Reis , Merlin Schmitz

A complete structure-preserving learning scheme for single-input/single-output (SISO) linear port-Hamiltonian systems is proposed. The construction is based on the solution, when possible, of the unique identification problem for these…

Dynamical Systems · Mathematics 2023-03-29 Juan-Pablo Ortega , Daiying Yin

In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for…

Classical Physics · Physics 2009-11-07 Sonnet Q H Nguyen , Lukasz A Turski

In this paper we discuss singular Lagrangian systems on the framework of contact geometry. These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic…

Mathematical Physics · Physics 2019-11-14 Manuel de León , Manuel Lainz Valcázar

We investigate an energy-based formulation of the two-field poroelasticity model and the related multiple-network model as they appear in geosciences or medical applications. We propose a port-Hamiltonian formulation of the system…

Dynamical Systems · Mathematics 2021-04-13 Robert Altmann , Volker Mehrmann , Benjamin Unger