Random walk with nonuniform angular distribution biased by an external periodic pulse
| Autor: | Aranyak Acharyya |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
0301 basic medicine
Physics Mathematical analysis Zero (complex analysis) General Physics and Astronomy Motion (geometry) Probability density function Random walk 01 natural sciences Displacement (vector) Pulse (physics) Mean squared displacement 03 medical and health sciences 030104 developmental biology Classical mechanics Random walker algorithm 0103 physical sciences 010306 general physics |
| Zdroj: | European Journal of Physics. 37:065104 |
| ISSN: | 1361-6404 0143-0807 |
| DOI: | 10.1088/0143-0807/37/6/065104 |
| Popis: | We studied the motion of a random walker in two dimensions with nonuniform angular distribution biased by an external periodic pulse. Here, we analytically calculated the mean square displacement (end-to-end distance of a walk after n time steps), without bias and with bias. We determined the average x-component of the final displacement of the walker. Interestingly, we noted that for a particular periodicity of the bias, this average x-component of the final displacement becomes approximately zero. The average y-component of the final displacement is found to be zero for any perodicity of the bias, and its reason can be attributed to the nature of the probability density function of the angle (subtended by the displacement vector with the x-axis). These analytical results are also supported by computer simulations. The present study may be thought of as a model for arresting the bacterial motion (along a preferred direction) by an external periodic bias. This article will be useful for undergraduate students of physics, statistics and biology as an example of an interdisciplinary approach to understand a way to control bacterial motion. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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