Brownian sampling in an unbounded space

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)334-336
Number of pages3
JournalJournal of Colloid and Interface Science
Volume274
Issue number1
DOIs
StatePublished - Jun 1 2004

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Brownian movement
sampling
Sampling
diffusion coefficient

All Science Journal Classification (ASJC) codes

  • Colloid and Surface Chemistry
  • Physical and Theoretical Chemistry
  • Surfaces and Interfaces

Cite this

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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. / Velegol, Darrell.

In: Journal of Colloid and Interface Science, Vol. 274, No. 1, 01.06.2004, p. 334-336.

Research output: Contribution to journalArticle

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