Diffusion Form of LG Model Equations

In case of movable adsorbate in some applications it is more convenient to present the migration operator in the equation (6.1.19) in diffusion approximation. For the sake of simplicity, let us consider this question on the example of structmeless particles when the equation (6.1.19) with an eye to (7.1.8)-(7.1.10) and (8.2.12) takes on the form 

Suppose that the probabilities of jrnnps R- R + Rf m the operator M vary strongly with R compared to more smooth dependence of the quasiequilibrium distribution fmiction 0n(R) On(R) 6ji(R -t- It ) and rewrite this operator in the form 

Using standard algorithm (Dubrovskiy 1982) for the transformation of discrete operator (8.5.10) to diffusion fomi and taking into accoimt (8.5.7) yield the following Fokker-Planck representation for Mf  

12) the diffusion tensor is expressed through q(9) and m R, R ), the particle drift potential V - through q 8) and the quasiequilibrium distribution function Or (that is defined up to an arbitrary function see next chap.). For isotropic 

The diffusion tensor D(j that is proportional to q(6) vanishes in the points where 0 P, R,t) = 1 and 6 /3 - 1, JJ, t) = 0 (/ 3). In these points V oo, thus occupied cells and cells lying over unoccupied ones (y0 3) are automaticeJly excluded from diffusion field that matches the basic postulates of the model. Operator M (0) vanishes when 9 = Or similetr to its discrete aneJogue. 

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