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We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian and multihamiltonian representations for some important nonlinear…

High Energy Physics - Theory · Physics 2016-09-06 Oleg Mokhov

Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…

Computational Physics · Physics 2020-08-24 Vasileios Chatziioannou

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

A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the…

Fluid Dynamics · Physics 2021-05-05 Federico Califano , Ramy Rashad , Frederic P. Schuller , Stefano Stramigioli

This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…

Numerical Analysis · Mathematics 2016-03-14 Liqian Peng , Kamran Mohseni

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

We introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…

Numerical Analysis · Mathematics 2024-12-10 R. Altmann , P. Schulze

A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…

Fluid Dynamics · Physics 2023-07-26 R. Camassa , G. Falqui , G. Ortenzi , M. Pedroni , T. T. Vu Ho

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…

Quantum Physics · Physics 2009-11-11 V. G. Kupriyanov , S. L. Lyakhovich , A. A. Sharapov

In this work, the multiplier method is extended to obtain a general lower bound of the exponential decay rate in terms of the physical parameters for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical…

Analysis of PDEs · Mathematics 2023-03-17 Luis A. Mora , Kirsten Morris

In this paper a method of controlling nonholonomic systems within the port-Hamiltonian (pH) framework is presented. It is well known that nonholonomic systems can be represented as pH systems without Lagrange multipliers by considering a…

Systems and Control · Computer Science 2018-01-23 Joel Ferguson , Alejandro Donaire , Christopher Renton , Richard H. Middleton

We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…

Numerical Analysis · Mathematics 2019-03-06 Wietse M. Boon , Jan M. Nordbotten

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

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

This paper aims at developing exactly energy-conservative and structure-preserving finite volume schemes for the discretisation of first-order symmetric-hyperbolic and thermodynamically compatible (SHTC) systems of partial differential…

Numerical Analysis · Mathematics 2026-01-01 Alessia Lucca , Michael Dumbser

A general framework for the numerical approximation of evolution problems is presented that allows to preserve exactly an underlying Hamiltonian- or gradient structure. The approach relies on rewriting the evolution problem in a particular…

Numerical Analysis · Mathematics 2018-12-12 Herbert Egger

The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…

Systems and Control · Computer Science 2012-10-31 Giovanni Marro

This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an…

Numerical Analysis · Mathematics 2025-07-04 C. Núñez , M. A. Sánchez

Recently, a new family of integrators (Hamiltonian Boundary ValueMethods) has been introduced, which is able to precisely conserve the energy function of polynomial Hamiltonian systems and to provide a practical conservation of the energy…

Numerical Analysis · Mathematics 2010-10-19 Luigi Brugnano , Felice Iavernaro , Donato Trigiante

Molecular representations are of fundamental importance for the modeling and analysis of molecular systems. Representation models and in general approaches based on topological data analysis (TDA) have demonstrated great success in various…

Biomolecules · Quantitative Biology 2025-11-26 JunJie Wee , Ginestra Bianconi , Kelin Xia