Brownian sampling in an unbounded space

Darrell Velegol

doi:10.1016/j.jcis.2004.02.020

Brownian sampling in an unbounded space

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Abstract

As a particle undergoes translational Brownian motion in an unbounded space, the particle samples the space. Traditionally the sampling in N dimensions is quantified in terms of average squared distance traversed (〈x·x〉). However, another quantitative measure of the sampled space is the total number (n) of equispaced regions (of size L^N) sampled after a particle moves with a diffusion coefficient (D) for a time (t). Calculations show that the average 〈n〉=a(Dt/L²) ^b. Results are given for a and b for 1, 2, 3, and 4 dimensions.

Original language	English (US)
Pages (from-to)	334-336
Number of pages	3
Journal	Journal of Colloid And Interface Science
Volume	274
Issue number	1
DOIs	https://doi.org/10.1016/j.jcis.2004.02.020
State	Published - Jun 1 2004

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Biomaterials
Surfaces, Coatings and Films
Colloid and Surface Chemistry

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10.1016/j.jcis.2004.02.020

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abstract = "As a particle undergoes translational Brownian motion in an unbounded space, the particle samples the space. Traditionally the sampling in N dimensions is quantified in terms of average squared distance traversed (〈x·x〉). However, another quantitative measure of the sampled space is the total number (n) of equispaced regions (of size LN) sampled after a particle moves with a diffusion coefficient (D) for a time (t). Calculations show that the average 〈n〉=a(Dt/L2) b. Results are given for a and b for 1, 2, 3, and 4 dimensions.",

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Brownian sampling in an unbounded space

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