Steady-state diffusion-controlled A+A-->0 reaction in Euclidean and fractal dimensions: Rate laws and particle self-ordering

by: Eric Clément, Leonard M Sander, Raoul Kopelman

Physical Review A, Vol. 39, No. 12. (15 June 1989), 6472.

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Abstract

For diffusion-limited reactions of the type A+A→0; we present a theory for the pair correlation function and the macroscopic reaction law for the Euclidean dimensions d =1; 2; 3 and for self-similar fractal structures with spectral dimension such that 1≤ d s ≤2. In any dimension we define a length Λ ; which is the typical size of the depletion zone around each particle. Λ is expressed as a function of a fundamental size ξ= √ρD/R ; where ρ is the steady-state density; R the external source rate; and D the microscopic diffusion constant. For d s ≤2; we obtain the ‘‘fractal’’ reaction order X=1+2/ d s and a mesoscopic; density-dependent depletion zone around each particle. We give an interpretation of the particle self-ordering and anomalous rate laws in terms of the random-walk topological properties.

@article{citeulike:1569846, abstract = {For diffusion-limited reactions of the type A+A→0; we present a theory for the pair correlation function and the macroscopic reaction law for the Euclidean dimensions d =1; 2; 3 and for self-similar fractal structures with spectral dimension such that 1≤ d s ≤2. In any dimension we define a length Λ ; which is the typical size of the depletion zone around each particle. Λ is expressed as a function of a fundamental size ξ= √ρD/R ; where ρ is the steady-state density; R the external source rate; and D the microscopic diffusion constant. For d s ≤2; we obtain the ‘‘fractal’’ reaction order X=1+2/ d s and a mesoscopic; density-dependent depletion zone around each particle. We give an interpretation of the particle self-ordering and anomalous rate laws in terms of the random-walk topological properties.}, author = {Cl\'{e}ment, Eric and Sander, Leonard M. and Kopelman, Raoul }, citeulike-article-id = {1569846}, doi = {10.1103/PhysRevA.39.6472}, journal = {Physical Review A}, keywords = {203}, month = {June}, number = {12}, pages = {6472+}, posted-at = {2007-08-16 19:04:51}, priority = {2}, publisher = {American Physical Society}, title = {Steady-state diffusion-controlled A+A--\>0 reaction in Euclidean and fractal dimensions: Rate laws and particle self-ordering}, url = {http://dx.doi.org/10.1103/PhysRevA.39.6472}, volume = {39}, year = {1989} }

RIS record

TY - JOUR ID - citeulike:1569846 L3 - citeulike-article-id:1569846 TI - Steady-state diffusion-controlled A+A-->0 reaction in Euclidean and fractal dimensions: Rate laws and particle self-ordering JF - Physical Review A VL - 39 IS - 12 SP - 6472 PB - American Physical Society N2 - For diffusion-limited reactions of the type A+A→0; we present a theory for the pair correlation function and the macroscopic reaction law for the Euclidean dimensions d =1; 2; 3 and for self-similar fractal structures with spectral dimension such that 1≤ d s ≤2. In any dimension we define a length Λ ; which is the typical size of the depletion zone around each particle. Λ is expressed as a function of a fundamental size ξ= √ρD/R ; where ρ is the steady-state density; R the external source rate; and D the microscopic diffusion constant. For d s ≤2; we obtain the ‘‘fractal’’ reaction order X=1+2/ d s and a mesoscopic; density-dependent depletion zone around each particle. We give an interpretation of the particle self-ordering and anomalous rate laws in terms of the random-walk topological properties. KW - 203 AU - Clément, Eric AU - Sander, Leonard AU - Kopelman, Raoul PY - 1989/06/15/ UR - http://dx.doi.org/10.1103/PhysRevA.39.6472 ER -

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