BROWNIAN_MOTION_SIMULATION
Simulation of Brownian Motion in M Dimensions

BROWNIAN_MOTION_SIMULATION is a FORTRAN77 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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

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.

Related Data and Programs:

CORRELATION, a FORTRAN77 library which contains examples of statistical correlation functions.

DUEL_SIMULATION, a FORTRAN77 program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

FAIR_DICE_SIMULATION, a FORTRAN77 program which simulates N tosses of 2 dice, making a histogram of the results.

GNUPLOT, FORTRAN77 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 FORTRAN77 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 FORTRAN77 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.

POISSON_SIMULATION, a FORTRAN77 library which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.

REACTOR_SIMULATION, a FORTRAN77 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 FORTRAN77 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.

Source Code:

• brownian_motion_simulation.f, the source code.
• brownian_motion_simulation.sh, BASH commands to compile the source code.

Examples and Tests:

• brownian_motion_simulation_prb.f, a sample calling program.
• brownian_motion_simulation_prb.sh, BASH commands to compile and run the sample program.
• brownian_motion_simulation_prb_output.txt, the output file.

Some data files and plots are made by the test program.

• motion_1d_data.txt, data for a Brownian motion trajectory in 1D.
• motion_1d_commands.txt, gnuplot commands to plot data for a Brownian motion trajectory in 1D.
• motion_1d.png, a plot of a Brownian motion trajectory in 1D, with time as second dimension.
• motion_2d_data.txt, data for a Brownian motion trajectory in 2D.
• motion_2d_commands.txt, gnuplot commands to plot data for a Brownian motion trajectory in 2D.
• motion_2d.png, a plot of a Brownian motion trajectory in 2D.
• displacement_1d_data.txt, data for Brownian displacements in 1D.
• displacement_1d_commands.txt, gnuplot commands to plot Brownian displacements in 1D.
• displacement_1d.png, a plot of squared displacements, averaged over several 1D Brownian motions.
• displacement_2d_data.txt, data for Brownian displacements in 2D.
• displacement_2d_commands.txt, gnuplot commands to plot Brownian displacements in 2D.
• displacement_2d.png, a plot of squared displacements, averaged over several 2D Brownian motions.
• displacement_3d_data.txt, data for Brownian displacements in 3D.
• displacement_3d_commands.txt, gnuplot commands to plot Brownian displacements in 3D.
• displacement_3d.png, a plot of squared displacements, averaged over several 3D Brownian motions.

You can go up one level to the FORTRAN77 source codes.