Related papers: A novel energy-based modeling framework
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…
A port-Hamiltonian (pH) system formulation is a geometrical notion used to formulate conservation laws for various physical systems. The distributed parameter port-Hamiltonian formulation models infinite dimensional Hamiltonian dynamical…
In this paper, energy-preserving methods are formulated and studied for solving charged-particle dynamics. We first formulate the scheme of energy-preserving methods and analyze its basic properties including algebraic order and symmetry.…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure,…
In [Bonito et al., J. Comput. Phys. (2022)], a local discontinuous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IMA J. Numer. Anal. (2023)] the numerical properties of this…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
The present work address the problem of energy shaping for stochastic port-Hamiltonian system. Energy shaping is a powerful technique that allows to systematically find feedback law to shape the Hamiltonian of a controlled system so that,…
We develop two local energy methods for distributed parameter port-Hamiltonian (pH) systems on one-dimensional spatial domains. The methods are applied to derive a characterization of exponential stability directly in terms of the energy…
Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our…
We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains.
This paper discusses energy-conserving time-discretizations for finite element particle-in-cell discretizations of the Vlasov--Maxwell system. A geometric spatially discrete system can be obtained using a standard particle-in-cell…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic…
Transient gas network simulations can significantly assist in design and operational aspects of gas networks. Models used in these simulations require a detailed framework integrating various models of the network constituents - pipes and…
We generalize the energy-based discontinuous Galerkin method proposed in [SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave equations. A stability and convergence analysis is presented along with numerical…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…
We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the…
If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionary Gamma-convergence that relates the…