title: Diffusion in the presence of scale-free absorbing boundaries.
abstract: Scale-free surfaces, such as cones, remain unchanged under a simultaneous expansion of all coordinates by the same factor. Probability density of a particle diffusing near such absorbing surface at large time approaches a simple form that incorporates power-law dependencies on time and distance from a special point, such as apex of the cone, which are characterized by a single exponent η. The same exponent is used to describe the number of spatial conformations of long ideal polymer attached to the special point of a repulsive surface of the same geometry and can be used in calculation of entropic forces between such polymers and surfaces. We use the solution of diffusion equation near such surfaces to find the numerical values of η, as well as to provide some insight into the behavior of ideal polymers near such surfaces.
authors.affiliation: Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.|Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Nir
authors.initials: N
authors.lastname: Alfasi
authors.affiliation: Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.
authors.forename: Yacov
authors.initials: Y
authors.lastname: Kantor
mesh_terms: D004058:Diffusion; D019277:Entropy; D008956:Models, Chemical; D011108:Polymers / Q000737:chemistry*; D012503:Saponins; D013499:Surface Properties; D014315:Triterpenes
chemical_list: D011108:Polymers; D012503:Saponins; D014315:Triterpenes; C104472:proacaciaside-I