Molecular discreteness in reaction-diffusion systems yields steady states not seen in the continuum limit

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 70, Issue 2, 2004, Pages 4-

  Togashi, Yuichi ^a   Kaneko, Kunihiko ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONTINUUM MECHANICS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ESTIMATION; MOLECULAR DYNAMICS;

CHEMICAL SPECIES; KURAMOTO LENGTH; MOLECULAR DISCRETENESS; REACTION-DIFFUSION SYSTEMS;

DIFFUSION;

ARTICLE; BIOPHYSICS; DIFFUSION; METHODOLOGY; NORMAL DISTRIBUTION; STATISTICAL MODEL; STATISTICS; TIME;

BIOPHYSICS; DIFFUSION; MODELS, STATISTICAL; NORMAL DISTRIBUTION; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 42749100047     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.020901     Document Type: Article

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12. In, this is expressed as (Formula presented), (Formula presented), where, the concentrations of (Formula presented), (Formula presented), (Formula presented), and (Formula presented) are taken to be constant in order to make an analysis of the equations possible.
13. Here, only the (Formula presented) species is relevant to this reaction, so that it is not necessary to consider detailed structures smaller than the typical distance between (Formula presented) molecules and the total rate of the reaction can therefore be described by a smoothened distribution.
14. The acceleration factor (Formula presented) is estimated as follows. We assume that the distribution of localized (Formula presented) molecules is Gaussian with a standard deviation (Formula presented) around the (Formula presented) molecules. That is, (Formula presented), where (Formula presented) is the position of each (Formula presented) molecule. The total distribution (concentration) of (Formula presented) is (Formula presented), and (Formula presented). Since the molecules (Formula presented) are randomly distributed, (Formula presented). Thus, (Formula presented) Consequently, we obtain (Formula presented).