We present a free energy lattice Boltzmann approach to modelling the dynamics of liquid drops on chemically patterned substrates. We start by describing a choice of free energy that reproduces the bulk behaviour of a liquid–gas system together with the varying contact angles on surfaces with...

We present a method for computer simulation of diffusion. The method uses quasi-random walk of particles. We consider a pure initial value problem for a simple diffusion equation in s space dimensions. We introduce s spatial steps Δxi. A semi-discrete approximation to the equation is obtained...

We present a particle method for solving initial-value problems for convection–diffusion equations with constant diffusion coefficients. We sample N particles at locations xj(0) from the initial data. We discretize time into intervals of length Δt. We represent the solution at time tn=nΔt by...

The paper deals with photosynthetic microorganism growth modelling and simulation in a distributed parameter system. Main result concerns the development and comparison of two modeling frameworks for photo-bioreactor modelling. The first “classical” approach is based on PDE...

It is well known that there is no analytic expression for the electrical capacitance of the unit cube. However, there are several Monte Carlo methods that have been used to numerically estimate this capacitance to high accuracy. These include a Brownian dynamics algorithm [H.-X. Zhou, A. Szabo,...

In this article we study the return transmission among stock markets in Greater China – Mainland China (Shanghai, Shenzhen), Hong Kong and Taiwan – a region which has been enjoying tremendous growth and expansion in the economies and capital markets in the last decade. Using a multiple time...

Probabilistic methods are presented to solve one-dimensional nonlinear reaction–diffusion equations. Computational particles are used to approximate the spatial derivative of the solution. The random walk principle is used to model the diffusion term. We investigate the effect of replacing...