ISSN:
1572-9613
Keywords:
Diffusion theory
;
chemical reactions
;
fluctuations
;
instabilities
;
master equations
;
phase transitions
;
stochastic processes
;
nonequilibrium thermodynamics
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A comprehensive study of correlations in linear and nonlinear chemical reactions is presented using coupled chemical and diffusion master equations. As a consequence of including correlations in linear reactions the approach to the steady-state Poisson distribution from an initial non-Poissonian distribution is given by a power law rather than the exponential predicted by neglecting correlations. In nonlinear reactions we show that a steadystate Poisson distribution is achieved in small volumes, whereas in large volumes a non-Poissonian distribution is built up via the correlation. The spatial correlation function is calculated for two examples, one which exhibits an instability, the other which exhibits a second-order phase transition, and correlation length and correlation time are calculated and shown to become infinite as the critical point is approached. The critical exponents are found to be classical.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01030197
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