TY - JOUR

T1 - Communication

T2 - A full solution of the annihilation reaction A B → based on time-subordination

AU - Benson, David A.

AU - Bolster, Diogo

AU - Paster, Amir

PY - 2013/4/7

Y1 - 2013/4/7

N2 - The connection between the governing equations of chemical reaction and the underlying stochastic processes of particle collision and transformation have been developed previously along two end-member conditions: perfectly mixed and maximally diffusion-limited. The complete governing equation recognizes that in the perfectly mixed case, the particle (i.e., molecular or macro-particle) number state evolution is Markovian, but that spatial self-organization of reactants decreases the probability of reactant pairs finding themselves co-located. This decreased probability manifests itself as a subordination of the clock time: as reactant concentrations become spatially variable (unmixed), the time required for reactants to find each other increases and the random operational time that particles spend in the active reaction process is less than the clock time. For example, in the system A + B → ø, a simple approximate calculation for the return time of a Brownian motion to a moving boundary allows a calculation of the operational time density, and the total solution is a subordination integral of the perfectly-mixed solution with a modified inverse Gaussian subordinator. The system transitions from the well-mixed solution to the asymptotic diffusion-limited solution that decays as t-d4 in d-dimensions.

AB - The connection between the governing equations of chemical reaction and the underlying stochastic processes of particle collision and transformation have been developed previously along two end-member conditions: perfectly mixed and maximally diffusion-limited. The complete governing equation recognizes that in the perfectly mixed case, the particle (i.e., molecular or macro-particle) number state evolution is Markovian, but that spatial self-organization of reactants decreases the probability of reactant pairs finding themselves co-located. This decreased probability manifests itself as a subordination of the clock time: as reactant concentrations become spatially variable (unmixed), the time required for reactants to find each other increases and the random operational time that particles spend in the active reaction process is less than the clock time. For example, in the system A + B → ø, a simple approximate calculation for the return time of a Brownian motion to a moving boundary allows a calculation of the operational time density, and the total solution is a subordination integral of the perfectly-mixed solution with a modified inverse Gaussian subordinator. The system transitions from the well-mixed solution to the asymptotic diffusion-limited solution that decays as t-d4 in d-dimensions.

UR - http://www.scopus.com/inward/record.url?scp=84876152006&partnerID=8YFLogxK

U2 - 10.1063/1.4800799

DO - 10.1063/1.4800799

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C2 - 23574201

AN - SCOPUS:84876152006

SN - 0021-9606

VL - 138

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 13

M1 - 131101

ER -