Complexity and hierarchical game of life

Hierarchical structure is an essential part of complexity, important notion relevant for a wide range of applications ranging from biological population dynamics through robotics to social sciences. In this paper we propose a simple cellular-automata tool for study of hierarchical population dynamics

Waiting time phenomena forced by critical boundary conditions in classical diffusion problems

This paper revisits some very classical initial-boundary value problems for parabolic equations, providing simple examples in which the occurrence of flux discontinuities at the boundary when the unknown function reaches some critical value may give rise to a waiting time phenomenon. A physical interpretation could be a modification of the surface of the considered body taking place at the mentioned critical value, affecting the way the body interacts with the surroundings. The waiting time, whose length (finite or infinite) is a priori unknown allows the system to evolve gradually through the critical state. Some numerical simulations are also presented

Overlimiting Current and Shock Electrodialysis in Porous Media

Most electrochemical processes, such as electrodialysis, are limited by diffusion, but in porous media, surface conduction and electro-osmotic flow also contribute to ionic fluxes. In this paper, we report experimental evidence for surface-driven over-limiting current (faster than diffusion) and deionization shocks (propagating salt removal) in a porous medium. The apparatus consists of a silica glass frit (1 mm thick with 500 nm mean pore size) in an aqueous electrolyte (CuSO$_4$ or AgNO$_3$) passing ionic current from a reservoir to a cation-selective membrane (Nafion). The current-voltage relation of the whole system is consistent with a proposed theory based on the electro-osmotic flow mechanism over a broad range of reservoir salt concentrations (0.1 mM - 1.0 M), after accounting for (Cu) electrode polarization and pH-regulated silica charge. Above the limiting current, deionized water ($\approx 10 \mu$ $M$) can be continuously extracted from the frit, which implies the existence of a stable shock propagating against the flow, bordering a depleted region that extends more than 0.5mm across the outlet. The results suggest the feasibility of "shock electrodialysis" as a new approach to water desalination and other electrochemical separations.Comment: 39 pages, 9 fig

Effect of concentration polarization on permselectivity

In this paper, the variation of permselectivity in the course of concentration polarization is systematically analyzed for a three-layer membrane system consisting of a nonperfectly permselective ion exchange membrane, homogeneous or heterogeneous, flanked by two diffusion layers of a binary univalent electrolyte. For a heterogeneous membrane, an ionic transport model is proposed, which is amenable to analytical treatment. In this model, assuming a constant fixed charge in the membrane and disregarding water splitting, the entire transport problem is reduced to solution of a single algebraic equation for the counterion transport number. It is concluded that for both types of membrane the concentration polarization may significantly affect the permselectivity of the system through the effects of the induced nonuniformity of the coion diffusion flux in the membrane (convexity of the coion concentration profile) and varying membrane-solution interface concentration. While the former is significant for low membrane fixed charge density, for a heterogeneous membrane, the latter might be considerably affected by the flux focusing effect at the permeable membrane segments.United States-Israel Binational Science Foundation (Grant 2010199

On classical solutions of the two-phase steady-state Stefan problem in strips

Rodrigues, Jose-Francisco; Zaltzman, Boris. (1991). On classical solutions of the two-phase steady-state Stefan problem in strips. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1626

Waiting time phenomena forced by critical boundary conditions in classical diffusion problems

This paper revisits some very classical initial-boundary value problems for parabolic equations, providing simple examples in which the occurrence of flux discontinuities at the boundary when the unknown function reaches some critical value may give rise to a waiting time phenomenon. A physical interpretation could be a modification of the surface of the considered body taking place at the mentioned critical value, affecting the way the body interacts with the surroundings. The waiting time, whose length (finite or infinite) is a priori unknown allows the system to evolve gradually through the critical state. Some numerical simulations are also presented

Overlimiting Current in a Microchannel

We revisit the classical problem of diffusion-limited ion transport to a membrane (or electrode) by considering the effects of charged sidewalls. Using simple mathematical models and numerical simulations, we identify three basic mechanisms for overlimiting current in a microchannel: (i) surface conduction carried by excess counterions, which dominates for very thin channels, (ii) convection by electro-osmotic flow on the sidewalls, which dominates for thicker channels, and (iii) transitions to electro-osmotic instability on the membrane end in very thick channels. These intriguing electrokinetic phenomena may find applications in biological separations, water desalination, and electrochemical energy storage.Massachusetts Institute of Technology. Energy InitiativeIsrael Science Foundation (Grant No. 65/07

Effect of concentration polarization on permselectivity

In this paper, the variation of permselectivity in the course of concentration polarization is systematically analyzed for a three-layer membrane system consisting of a nonperfectly permselective ion exchange membrane, homogeneous or heterogeneous, flanked by two diffusion layers of a binary univalent electrolyte. For a heterogeneous membrane, an ionic transport model is proposed, which is amenable to analytical treatment. In this model, assuming a constant fixed charge in the membrane and disregarding water splitting, the entire transport problem is reduced to solution of a single algebraic equation for the counterion transport number. It is concluded that for both types of membrane the concentration polarization may significantly affect the permselectivity of the system through the effects of the induced nonuniformity of the coion diffusion flux in the membrane (convexity of the coion concentration profile) and varying membrane-solution interface concentration. While the former is significant for low membrane fixed charge density, for a heterogeneous membrane, the latter might be considerably affected by the flux focusing effect at the permeable membrane segments.United States-Israel Binational Science Foundation (Grant 2010199