How the canonical distribution is realized in simulations based on deterministic dynamical
equations is explained in this review. Basic formulations and their recent extensions of two …

During recent decades it has become feasible to simulate the dynamics of molecular
systems on a computer. The method of molecular dynamics (MD) solves Newton's equations …

A third-order algorithm for stochastic dynamics (SD) simulations is proposed, identical to the
powerful molecular dynamics leap-frog algorithm in the limit of infinitely small friction …

Analytic expressions for mean squared positions and velocities of a harmonic oscillator are
derived for Langevin dynamics algorithms valid in the high and low friction limits, and for the …

Manufacturing processes that can create extremely small machines have been developed in
recent years. Microelectromechanical systems (MEMS) refer to devices that have …

Computing (ratios of) normalizing constants of probability models is a fundamental
computational problem for many statistical and scientific studies. Monte Carlo simulation is …

We propose a new effective Monte Carlo (MC) procedure for direct calculation of the free
energy in a single MC run. The partition function of the expanded ensemble is introduced …

Recent developments of meshfree and particle methods and their applications in applied
mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed …

Meshfree Particle Methods is a comprehensive and systematic exposition of particle
methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods …

Chaos: from simple models to complex systems aims to guide science and engineering
students through chaos and nonlinear dynamics from classical examples to the most recent …