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This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
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…
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and…
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…
Classical polarizable approaches have become the gold standard for simulating complex systems and processes in the condensed phase. These methods describe intrinsically dissipative polarizable media, requiring a formal definition within the…
In this short note, we derive dissipative conditions with slack variables for a linear coupled differential-difference (CDDS) via constructing a Krasovskii functional. The approach can be interpreted as a generalization of the Finsler Lemma…
In this paper we present energy-conserving, mixed discontinuous Galerkin (DG) and continuous Galerkin (CG) schemes for the solution of a broad class of physical systems described by Hamiltonian evolution equations. These systems often arise…
The idea of dissipative mechanical system with delay is proposed. The paper studies the phenomenon of dissipation with delay for Euler-Poincare systems on Lie algebras or equivalently, for Lie-Poisson systems on the duals of Lie algebras.…
Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a…
Recently, Morrison and Updike showed that many dissipative systems are naturally described as possessing a Riemann curvature-like bracket, which similar to the Poisson bracket, generates the dissipative equations of motion once suitable…
This paper is concerned with a stochastic dissipativity theory using quadratic-exponential storage functions for open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations. The…
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation…
We construct linear Hamilton systems without usual dichotomy property. The Ljapunov spectra of these systems are unfamiliar and conflicting, the behaviour of trajectories is very complicated. The paper's subject refers to some problems of…
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the…
Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
The fluctuation-dissipation (F-D) theorem is a fundamental result for systems near thermodynamic equilibrium, and justifies studies between microscopic and macroscopic properties. It states that the nonequilibrium relaxation dynamics is…
In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential…
The quantum dynamics away from equilibrium is of fundamental interest for interacting many-body systems. In this letter, we study tilted many-body systems using the effective Hamiltonian derived from the microscopic description. We first…