Critical dimensions of the diffusion equation

T. J. Newman; Will Loinaz

doi:10.1103/PhysRevLett.86.2712

Critical dimensions of the diffusion equation

T. J. Newman (Lead / Corresponding author), Will Loinaz (Lead / Corresponding author)

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

Abstract

The persistence properties of the diffusion equation in arbitrary dimensions were studied using a simple algorithm. It was found that there exist two critical dimensions in the behavior of the sign-time distribution (STD). For dimensions below d ? 26 the STD is purely concave, while for dimensions above d ? 46 the STD is purely convex.

Original language	English
Pages (from-to)	2712-2715
Number of pages	4
Journal	Physical Review Letters
Volume	86
Issue number	13
DOIs	https://doi.org/10.1103/PhysRevLett.86.2712
Publication status	Published - 26 Mar 2001

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10.1103/PhysRevLett.86.2712

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abstract = "The persistence properties of the diffusion equation in arbitrary dimensions were studied using a simple algorithm. It was found that there exist two critical dimensions in the behavior of the sign-time distribution (STD). For dimensions below d ? 26 the STD is purely concave, while for dimensions above d ? 46 the STD is purely convex.",

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AB - The persistence properties of the diffusion equation in arbitrary dimensions were studied using a simple algorithm. It was found that there exist two critical dimensions in the behavior of the sign-time distribution (STD). For dimensions below d ? 26 the STD is purely concave, while for dimensions above d ? 46 the STD is purely convex.

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Critical dimensions of the diffusion equation

Abstract

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