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RandomWalk1D

20,000 1-D random walks are taken, the summation of Gaussian distributed steps with mean of 0 and variance = 1 or uniformly distributed steps from -1 to 1. The positions at a specific step number are

Model number: 0184

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Description

``` 1 DIMENSIONAL DIFFUSION, RANDOM DIRECTION, RANDOM STEP SIZE

N walks (nwalks) are taken consisting of N steps (nsteps). Each
walk starts at x=0. The steps are either left or right depending
on a uniform random number(0 to 1) being greater than 1/2; the
step lengths are taken from a uniform random distribution from
0 to 1. The final positions are gridded into bins of width xL.delta.
The distribution and the cumulative distributions are plotted along
the expected Gaussian distribution and the expected cumulative
distribution. The Gaussian distribution is given by

Gaussian distribution = (A/(sigma*sqrt(2*PI))*exp(-(xL-xmean)^2/(2*sigma^2)));

where A= xL.delta, tmean=0, and sigma = sqrt(ntime/3) for steps drawn from
the uniform distribution from -1 to 1, or sigma = sqrt(ntime) for
steps drawn from the Gaussian distribution with mean = 0 and variance = 1.

```

A Gaussian model fitting the end positions of a 1-D Random Walk.

Ten 1D random walks.

Equations

None.

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

References

```	None.

```

name="Related Models" id="Related Models">Related Models

Key Terms

Diffusion, Random walk, Stochastic, one dimension, 1-D, Transport Physiology

Model History

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Posted by: GMR

Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.