Related Experiment Video
Updated: Aug 9, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Mapping the Monte Carlo scheme to Langevin dynamics: a Fokker-Planck approach
X Z Cheng1, M B A Jalil, Hwee Kuan Lee
1Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576, Singapore.
Abstract:
We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors alpha, unlike previous time-quantified MC methods which break down at low alpha, where precessional motion dominates.
Related Concept Videos
Maxwell-Boltzmann Distribution: Problem Solving
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Reaction Mechanisms: The Steady-State Approximation
Fermi Level Dynamics
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Poisson's And Laplace's Equation
Mean free path and Mean free time
Partial Derivatives and Gas Laws
