K. J. Mork

Unification of the methods of Onsager and Monchick for calculating the probabilities of various fates in diffusion‐controlled reactions, with applications to diffusion in space and in a plane

We have unified the methods of Onsager and Monchick for calculating the probabilities for the various fates (reaction, escape, re‐encounter, etc.) of a particle undergoing a diffusion‐controlled reaction in three dimensions; the unified treatment applies also to diffusion in a plane and leads easily to some results which have either not been derived before or have required considerable labor. Finally, explicit solutions for a specific force field representing both attraction and repulsion are given.

Thirteen-moment solution of the steady-state fokker—planck equation for Brownian motion in a homogeneous medium occupying the region bounded internally by an absorbing sphere

Abstract The steady, centrally symmetric motion of Brownian particles in a homogeneous medium occupying the region bounded internally by an absorbing sphere of radius R is considered. The distribution function of the particles, assumed to obey the generalized fokker—Planck equation, is found (in three successive approximations) by applying Grads method of moments, which consists in expanding the distribution function in Hermitean tensors and truncating the series after the term of N th order. Approximations up to and including the so-called 13-moment approximation (corresponding to N = 1, 2,and3) are studied, and a previous 13-moment analysis is criticized; it is stressed that the results furnished by the N th-order approximation are valid to O ( Λ/ R ) N , where Λ is the velocity persistence length.

On the rate of absorption of Brownian particles by a black sphere: The connection between the Fokker–Planck equation and the diffusion equation

It is shown that, if one takes the first two moments of the Fokker–Planck equation, one obtains, in the lowest order, the telegraph equation irrespective of whether one uses a full‐range or a half‐range decomposition of the distribution function; it is pointed out that the exact boundary condition, according to which the distribution function for emerging particles vanishes at the surface of an absorbing (black) sphere of radius R, may be replaced, in either case, by Marshak’s boundary condition j+(R, t) =0, where j+ is the outward radial current. Drawing on Wilemski’s work, the second moment equation is finally replaced by Fick’s law, obtaining thereby the diffusion equation and the radiation boundary condition.

Symmetric random walk on a regular lattice with an elastic barrier: diffusion equation and the boundary condition

Abstract We examine here the symmetric random-walk model in which a particle can jump only to adjacent sites on a regular lattice, and discuss, in the light of the works of Chandrasekhar, Goodrich, van Kampen, and Oppenheim, the reduction of the problem of random walk in the presence of an elastic barner to a boundary value problem.

On describing the steady absorption of brownian particles by a restricted random walk

Abstract This paper is concerned with idealizing brownian motion as a random walk, using the diffusion equation, and finding the boundary condition at an absorbing surface - all with an eye towards chemical kinetics. Three models of random walk (due to Smoluchowski, Fermi, and Lorentz) are considered, and it is concluded that the lorentzian model is the most appropriate.

Comment on ‘‘The reactivity dependence of the recombination probability’’

The author’s previous work2 is reexamined. Especially the definition of diffusion controlled reaction. It is argued that the author’s definition of diffusion‐controlled reactions is substantially different from that of Pedersen1. (AIP)

Comment on ‘‘Steady, one‐dimensional Brownian motion with an absorbing boundary’’

Some comments on Harris’s1 paper regarding the Brownian motion with an absorbing boundary are presented. Harris’s solution of Ni Fokker‐Planck equation is discussed. (AIP)