BROWNIAN_MOTION_SIMULATION, a FORTRAN90 code which simulates Brownian motion in an M-dimensional region, creating graphics files for processing by gnuplot.
Brownian motion is a physical phenomenon which can be observed, for instance, when a small particle is immersed in a liquid. The particle will move as though under the influence of random forces of varying direction and magnitude.
There is a mathematical idealization of this motion, and from there a computational discretization that allows us to simulate the successive positions of a particle undergoing Brownian motion.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
BROWNIAN_MOTION_SIMULATON is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
CORRELATION, a FORTRAN90 code which contains examples of statistical correlation functions.
DUEL_SIMULATION, a FORTRAN90 program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.
FAIR_DICE_SIMULATION, a FORTRAN90 program which simulates N tosses of 2 dice, making a histogram of the results.
HIGH_CARD_SIMULATION, a FORTRAN90 program which simulates a situation in which you see the cards in a deck one by one, and must select the one you think is the highest and stop; the program uses GNUPLOT for graphics.
ISING_2D_SIMULATION, a FORTRAN90 program which carries out a Monte Carlo simulation of an Ising model. a 2D array of positive and negative charges, each of which is likely to flip to be in agreement with neighbors.
ISING_3D_SIMULATION, a FORTRAN90 program which carries out a Monte Carlo simulation of an Ising model, a 3D array of positive and negative charges, each of which is likely to flip to be in agreement with neighbors.
ORNSTEIN_UHLENBECK, a FORTRAN90 code which approximates solutions of the Ornstein-Uhlenbeck stochastic differential equation (SDE) using the Euler method and the Euler-Maruyama method.
POISSON_SIMULATION, a FORTRAN90 code which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.
REACTOR_SIMULATION, a FORTRAN90 program which a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This program was provided as an example with the book "Numerical Methods and Software."
THREE_BODY_SIMULATION, a FORTRAN90 program which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.
TWO_BODY_SIMULATION, a FORTRAN90 program which simulates the behavior of two bodies, constrained to lie in a plane, moving under the influence of gravity, with one body much more massive than the other, creating graphics files for processing by gnuplot.