Related papers: Velocity-Verlet-like algorithm for simulations of …
New explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the…
We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate…
We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds…
We present a mechanistic model for a Newtonian fluid called fluid particle dynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose an heuristic derivation of…
We present a new molecular-dynamics algorithm for integrating the equations of motion for a system of particles interacting with mixed continuous/impulsive forces. This method, which we call Impulsive Verlet, is constructed using operator…
The Verlet method is still widely used to integrate the equations of motion in ab initio molecular dynamics simulations. We show that the stability limit of the Verlet method may be significantly increased by setting an upper limit on the…
In ab initio molecular dynamics simulations of real-world problems, the simple Verlet method is still widely used for integrating the equations of motion, while more efficient algorithms are routinely used in classical molecular dynamics.…
The Discrete Element Method is widely employed for simulating granular flows, but conventional integration techniques may produce unphysical results for simulations with static friction when particle size ratios exceed $R \approx 3$. These…
We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which…
In this paper, a stochastic Hamiltonian formulation (SHF) is proposed and applied to dissipative particle dynamics (DPD) simulations. As an extension of Hamiltonian dynamics to stochastic dissipative systems, the SHF provides necessary…
A recent article in J. Chem. Phys. argues that the two algorithms, the velocity-Verlet, and position-Verlet integrators, commonly used in Molecular Dynamics (MD) simulations, are different \cite{Ni2024}. But not only are the two algorithms…
We define a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion via an $S$-transform approach. We investigate the properties of this stochastic integral, prove the Ito formula for functions of…
Stochastic integration \textit{wrt} Gaussian processes has raised strong interest in recent years, motivated in particular by its applications in Internet traffic modeling, biomedicine and finance. The aim of this work is to define and…
We present the complete set of stochastic Verlet-type algorithms that can provide correct statistical measures for both configurational and kinetic sampling in discrete-time Langevin systems. The approach is a brute-force general…
Brownian dynamics of colloidal particles on complex surfaces has found important applications in diverse physical, chemical and biological processes. However, current Brownian dynamics simulation algorithms mostly work for relatively simple…
We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
Classical molecular dynamics simulations are based on solving Newton's equations of motion. Using a small timestep, numerical integrators such as Verlet generate trajectories of particles as solutions to Newton's equations. We introduce…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…