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In this paper, we propose and analyse a reconstruction technique which enables one to design high-order conservative semi-Lagrangian schemes for kinetic equations. The proposed reconstruction can be obtained by taking the sliding average of…
The total angular momentum of a close system is a conserved quantity, which should remain constant in time for any excitation experiment once the pumping signal has extinguished. Such conservation, however, is never satisfied in practice in…
The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…
This paper presents decentralized algorithms for formation control of multiple robots in three dimensions. Specifically, we leverage the mathematical properties of cyclic pursuit along with results from contraction and partial contraction…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…
Several recent works in online optimization and game dynamics have established strong negative complexity results including the formal emergence of instability and chaos even in small such settings, e.g., $2\times 2$ games. These results…
The exact equation of spin motion in a cylindrical coordinate system with allowance for electric dipole moments of particles has been derived. This equation is convenient for analytical calculations of spin dynamics in circular storage…
In this article, we consider fixed spin-1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give approximate evolutions of coherent states. This uses spins-photon classical Hamiltonian…
A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping…
We provide an algorithm and a publicly available code to numerically evolve multicomponent Schr\"{o}dinger-Poisson (SP) systems with a SO($n$) symmetry, including attractive or repulsive self-interactions in addition to gravity. Focusing on…
A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-BMT equation formulated in the Clifford algebra representation of Baylis. It is…
Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such approach based on…
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…
In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the…
Elegant integration schemes of second and fourth order for simulations of rigid body systems are presented which treat translational and rotational motion on the same footing. This is made possible by a recent implementation of the exact…