Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/69129
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Type: | Journal article |
Title: | Quantifying evenly distributed states in exclusion and nonexclusion processes |
Author: | Binder, B. Landman, K. |
Citation: | Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2011; 83(4):041914-1-041914-9 |
Publisher: | American Physical Soc |
Issue Date: | 2011 |
ISSN: | 1539-3755 1550-2376 |
Statement of Responsibility: | Benjamin J. Binder and Kerry A. Landman |
Abstract: | Spatial-point data sets, generated from a wide range of physical systems and mathematical models, can be analyzed by counting the number of objects in equally sized bins. We find that the bin counts are related to the Pólya distribution. New measures are developed which indicate whether or not a spatial data set, generated from an exclusion process, is at its most evenly distributed state, the complete spatial randomness (CSR) state. To this end, we define an index in terms of the variance between the bin counts. Limiting values of the index are determined when objects have access to the entire domain and when there are subregions of the domain that are inaccessible to objects. Using three case studies (Lagrangian fluid particles in chaotic laminar flows, cellular automata agents in discrete models, and biological cells within colonies), we calculate the indexes and verify that our theoretical CSR limit accurately predicts the state of the system. These measures should prove useful in many biological applications. |
Rights: | ©2011 American Physical Society |
DOI: | 10.1103/PhysRevE.83.041914 |
Grant ID: | ARC |
Published version: | http://dx.doi.org/10.1103/physreve.83.041914 |
Appears in Collections: | Aurora harvest 5 Mathematical Sciences publications |
Files in This Item:
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hdl_69129.pdf | Published version | 1.02 MB | Adobe PDF | View/Open |
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