Related papers: Port-Hamiltonian systems on discrete manifolds
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit…
This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and…
A simple Hamiltonian manifold is a closed connected symplectic manifold equipped with a Hamiltonian action of a torus T with moment map Phi: M-->t^*, such that the fixed set M^T has exactly two connected components, denoted M_0 and M_1. We…
In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…
We study the geometric structure of the drift dynamics of Irreversible port-Hamiltonian systems. This drift dynamics is defined with respect to a product of quasi-Poisson brackets, reflecting the interconnection structure and the…
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those…
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of…
In the first part of the paper we introduce some geometric tools needed to describe slow-fast Hamiltonian systems on smooth manifolds. We start with a smooth Poisson bundle $p: M\to B$ of a regular (i.e. of constant rank) Poisson manifold…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…
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,…
Hydrogen's growing role in the transition towards climate-neutral energy systems necessitates structured modeling frameworks. Existing gas network models, largely developed for natural gas, fail to capture hydrogen systems distinct…
In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature.…
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…
In this paper higher order mimetic discretizations are introduced which are firmly rooted in the geometry in which the variables are defined. The paper shows how basic constructs in differential geometry have a discrete counterpart in…
Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange--Dirac mechanical…
Dirac structures and Morse families are used to obtain a geometric formalism that unifies most of the scenarios in mechanics (constrained calculus, nonholonomic systems, optimal control theory, higher-order mechanics, etc.), as the examples…
We propose a new interconnection relation for infinite-dimensional port-Hamiltonian systems that enables the coupling of ports with different spatial dimensions by integrating over the the surplus dimensions. To show the practical…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
We study the system of first order PDEs for pseudo-Riemannian metrics governing the Hamiltonian formalism for systems of hydrodynamic type. In the diagonal setting the integrability conditions ensure the compatibility of this system and,…