Biomedical subjects
Publications and source records attributed to B Zaltzman.
We consider a modified Bouchaud-Cates-Ravi Prakash-Edwards model for pile surface dynamics, and show that in the long-scale limit this model converges to a quasistationary model of pile growth in the form of an evolutionary variational inequality.
The purpose of this paper is to show through a systematic asymptotic analysis that fluctuations, accounted for as a diffusional perturbation in the Lifshitz-Slyozov-Wagner (LSW) model of Ostwald ripening, provides, as conjectured previously by Meerson [Phys. Rev. E 60, 3072 (1999)], a "strong" selection of the limiting solution, out of a one-parameter family of similarity solutions with a finite support, as the sole attractor of time evolution. Throughout the latter, the previously described weak selection of other similarity solutions of that family, by the initial conditions with finite supports, occurs as intermediate time asymptotics. The respective mechanism is traced first for a simple instance of the LSW model with linear characteristic equations (integer power in the particle growth rate law equals -1), beginning with the analysis of steady states in the perturbed problem in similarity variables and weak selection in the unperturbed problem, followed by a detailed asymptotic analysis of the time-dependent perturbed problem, and generalized next for an arbitrary integer power in the range [-1,2]. The approximate asymptotic solutions obtained are compared with the exact numerical ones.
The paper is concerned with convection at an ion exchange electrodialysis membrane induced by nonequilibrium electro-osmosis in the course of concentration polarization under the passage of electric current through the membrane. Derivation of nonequilibrium electro-osmotic slip condition is recapitulated along with the linear stability analysis of quiescent electrodiffusion through a flat ion exchange membrane. Results of numerical calculation for nonlinear steady state convection, developing from the respective instability, are reported along with those for a slightly wavy membrane. Besides these results, we report those of time dependent calculations for periodic and chaotic oscillations, resulting from instability of the respective steady state flows, and also the results of recent experiments with modified membranes. These latter rule in favor of electro-osmotic versus bulk electroconvective origin of overlimiting conductance through ion exchange membranes.
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