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<html>
<head>
<title>
BROWNIAN_MOTION_SIMULATION - Simulation of Brownian Motion in M Dimensions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BROWNIAN_MOTION_SIMULATION <br> Simulation of Brownian Motion in M Dimensions
</h1>
<hr>
<p>
<b>BROWNIAN_MOTION_SIMULATION</b>
is a C++ library which
simulates Brownian motion in an M-dimensional region,
creating graphics files for processing by gnuplot.
</p>
<p>
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.
</p>
<p>
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.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>BROWNIAN_MOTION_SIMULATON</b> is available in
<a href = "../../c_src/brownian_motion_simulation/brownian_motion_simulation.html">a C version</a> and
<a href = "../../cpp_src/brownian_motion_simulation/brownian_motion_simulation.html">a C++ version</a> and
<a href = "../../f77_src/brownian_motion_simulation/brownian_motion_simulation.html">a FORTRAN77 version</a> and
<a href = "../../f_src/brownian_motion_simulation/brownian_motion_simulation.html">a FORTRAN90 version</a> and
<a href = "../../m_src/brownian_motion_simulation/brownian_motion_simulation.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/correlation/correlation.html">
CORRELATION</a>,
a C++ library which
contains examples of statistical correlation functions.
</p>
<p>
<a href = "../../cpp_src/duel_simulation/duel_simulation.html">
DUEL_SIMULATION</a>,
a C++ program which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
</p>
<p>
<a href = "../../cpp_src/fair_dice_simulation/fair_dice_simulation.html">
FAIR_DICE_SIMULATION</a>,
a C++ program which
simulates N tosses of 2 dice, making a histogram of the results.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
</p>
<p>
<a href = "../../cpp_src/high_card_simulation/high_card_simulation.html">
HIGH_CARD_SIMULATION</a>,
a C++ 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.
</p>
<p>
<a href = "../../cpp_src/ising_2d_simulation/ising_2d_simulation.html">
ISING_2D_SIMULATION</a>,
a C++ 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.
</p>
<p>
<a href = "../../cpp_src/ornstein_uhlenbeck/ornstein_uhlenbeck.html">
ORNSTEIN_UHLENBECK</a>,
a C++ library which
approximates solutions of the Ornstein-Uhlenbeck
stochastic differential equation (SDE) using the Euler method
and the Euler-Maruyama method.
</p>
<p>
<a href = "../../cpp_src/poisson_simulation/poisson_simulation.html">
POISSON_SIMULATION</a>,
a C++ library which
simulates a Poisson process in which events randomly occur with an
average waiting time of Lambda.
</p>
<p>
<a href = "../../cpp_src/reactor_simulation/reactor_simulation.html">
REACTOR_SIMULATION</a>,
a C++ 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."
</p>
<p>
<a href = "../../cpp_src/three_body_simulation/three_body_simulation.html">
THREE_BODY_SIMULATION</a>,
a C++ 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.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "brownian_motion_simulation.cpp">brownian_motion_simulation.cpp</a>, the source code.
</li>
<li>
<a href = "brownian_motion_simulation.hpp">brownian_motion_simulation.hpp</a>, the include file.
</li>
<li>
<a href = "brownian_motion_simulation.sh">brownian_motion_simulation.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "brownian_motion_simulation_prb.cpp">brownian_motion_simulation_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "brownian_motion_simulation_prb.sh">brownian_motion_simulation_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "brownian_motion_simulation_prb_output.txt">brownian_motion_simulation_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
Some data files and plots are made by the test program.
<ul>
<li>
<a href = "motion_1d_data.txt">motion_1d_data.txt</a>,
data for a Brownian motion trajectory in 1D.
</li>
<li>
<a href = "motion_1d_commands.txt">motion_1d_commands.txt</a>,
gnuplot commands to plot data for a Brownian motion trajectory in 1D.
</li>
<li>
<a href = "motion_1d.png">motion_1d.png</a>,
a plot of a Brownian motion trajectory in 1D, with time as second dimension.
</li>
<li>
<a href = "motion_2d_data.txt">motion_2d_data.txt</a>,
data for a Brownian motion trajectory in 2D.
</li>
<li>
<a href = "motion_2d_commands.txt">motion_2d_commands.txt</a>,
gnuplot commands to plot data for a Brownian motion trajectory in 2D.
</li>
<li>
<a href = "motion_2d.png">motion_2d.png</a>,
a plot of a Brownian motion trajectory in 2D.
</li>
<li>
<a href = "displacement_1d_data.txt">displacement_1d_data.txt</a>,
data for Brownian displacements in 1D.
</li>
<li>
<a href = "displacement_1d_commands.txt">displacement_1d_commands.txt</a>,
gnuplot commands to plot Brownian displacements in 1D.
</li>
<li>
<a href = "displacement_1d.png">displacement_1d.png</a>,
a plot of squared displacements, averaged over several 1D Brownian motions.
</li>
<li>
<a href = "displacement_2d_data.txt">displacement_2d_data.txt</a>,
data for Brownian displacements in 2D.
</li>
<li>
<a href = "displacement_2d_commands.txt">displacement_2d_commands.txt</a>,
gnuplot commands to plot Brownian displacements in 2D.
</li>
<li>
<a href = "displacement_2d.png">displacement_2d.png</a>,
a plot of squared displacements, averaged over several 2D Brownian motions.
</li>
<li>
<a href = "displacement_3d_data.txt">displacement_3d_data.txt</a>,
data for Brownian displacements in 3D.
</li>
<li>
<a href = "displacement_3d_commands.txt">displacement_3d_commands.txt</a>,
gnuplot commands to plot Brownian displacements in 3D.
</li>
<li>
<a href = "displacement_3d.png">displacement_3d.png</a>,
a plot of squared displacements, averaged over several 3D Brownian motions.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 02 October 2012.
</i>
<!-- John Burkardt -->
</body>
</html>