title: Lattice statistical theory of random walks on a fractal-like geometry.
abstract: We have designed a two-dimensional, fractal-like lattice and explored, both numerically and analytically, the differences between random walks on this lattice and a regular, square-planar Euclidean lattice. We study the efficiency of diffusion-controlled processes for flows from external sites to a centrosymmetric reaction center and, conversely, for flows from a centrosymmetric source to boundary sites. In both cases, we find that analytic expressions derived for the mean walk length on the fractal-like lattice have an algebraic dependence on system size, whereas for regular Euclidean lattices the dependence can be transcendental. These expressions are compared with those derived in the continuum limit using classical diffusion theory. Our analysis and the numerical results quantify the extent to which one paradigmatic class of spatial inhomogeneities can compromise the efficiency of adatom diffusion on solid supports and of surface-assisted self-assembly in metal-organic materials.
authors.affiliation: DePaul University, 243 South Wabash, Chicago, Illinois 60604-2301, USA and Beckman Institute, Caltech, Pasadena, California 91125, USA.
authors.forename: John J
authors.initials: JJ
authors.lastname: Kozak
authors.affiliation: Department of Chemistry and Seaver Chemistry Laboratory, Pomona College, Claremont, California 60604-2301, USA.
authors.forename: Roberto A
authors.initials: RA
authors.lastname: Garza-López
authors.affiliation: Departamento de Física Aplicada, Centro Universitario de Mérida, Universidad de Extremadura, E-06800 Mérida, Spain.
authors.forename: Enrique
authors.initials: E
authors.lastname: Abad
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D017709:Fractals; D008956:Models, Chemical; D015233:Models, Statistical