Computer simulations of immobile particles

Computer simulations of bimolecular reactions for a system of immobile particles (incorporating their production) has a long history see, e.g., [18-22]. For the first time computer simulation as a test of analytical methods in the reaction kinetics was carried out by Zhdanov [23, 24] for d = 3. Despite the fact that his simulations were performed up to rather small reaction depths, To 1, it was established that of all empirical equations presented for the tunnelling recombination kinetics (those of linear approximation - (4.1.42) or (4.1.43)) turned out to be mostly correct (note that equations (5.1.14) to (5.1.16) of the complete superposition approximation were not considered.) On the other hand, irrespective of the initial reactant densities and space dimension d for reaction depths T Jb his theoretical curves deviate from those computer simulated by 10%. Accuracy of the superposition approximation in d = 3 case was first questioned by Kuzovkov [25], it was also 

According to (3.2.15) the probability for a given AB pair to survive t seconds is 

It means that time intervals Tm between decay of a given AB pair and another similar decay are distributed exponentially with the mean decay time T = Ylj Probability u ab that a given AB pair will recombine 

Computer simulations consist of the following steps, (i) Calculating of the time-step t = E, 7(rij)] . (ii) Making use of random numbers and a set of weighting factors wab = cr rij)T. (iii) A given AB pair recombines and reaction time t is increased by r. (iv) Passage to (i). 

Note some essential details of the simulation scheme. A choice of a particles pair to disappear consists of two steps with the help of the weighting factors wa = Yhj ab a single A particle was chosen, whereas particle B was sought respectively amongst B s with the help of weights wab- Since 

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