Related papers: Metric-tensor flexible-cell algorithm for isotherm…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
Atomistic simulations of heat transport in complex materials are costly and hard to converge. This has led to the development of several noise-reduction techniques applicable to equilibrium molecular-dynamics (MD) simulations. We analyze…
A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the…
In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with…
A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a…
It is well known that symplectic integrators lose their near energy preservation properties when variable step sizes are used. The most common approach to combine adaptive step sizes and symplectic integrators involves the Poincar\'e…
We present a set of second-order, time-reversible algorithms for the isothermal (NVT) molecular-dynamics (MD) simulation of systems with mixed hard-core/continuous potentials. The methods are generated by combining real-time Nose'…
We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a powerful method of Bayesian inference that exploits underlying geometric information of the posterior distribution in order to efficiently traverse the parameter space. However, the…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
Metriplectic dynamics is applied to compute equilibria of fluid dynamical systems. The result is a relaxation method in which Hamiltonian dynamics (symplectic structure) is combined with dissipative mechanisms (metric structure) that…
The leapfrog integrator is widely used because of its excellent stability in molecular dynamics simulation. This is recognized as being due to the existence of a discrete variational structure of the equations. We introduce a modified…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
A simple technique is proposed for numerically determining equilibrium ion distribution functions belonging to free energies of the Poisson-Boltzmann type. The central idea is to perform a conventional Monte-Carlo simulation using the free…
We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to…
Metriplectic dynamics couple a Poisson bracket of the Hamiltonian description with a kind of metric bracket, for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a…
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform…