BROWNIAN_MOTION_SIMULATION is a FORTRAN90 library 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.
CORRELATION, a FORTRAN90 library 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.
GNUPLOT, FORTRAN90 programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program 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 library which approximates solutions of the Ornstein-Uhlenbeck stochastic differential equation (SDE) using the Euler method and the Euler-Maruyama method.
POISSON_SIMULATION, a FORTRAN90 library 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.
Some data files and plots are made by the test program.
You can go up one level to the FORTRAN90 source codes.