Decay Process for Three - Species Reaction - Diffusion System

We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The particle density and the global reaction rate are also shown analytically and numerically on a two-dimensional square lattice with the periodic boundary conditions. Especially, the crossover of the global reaction rate is discussed in both early-time and long-time regimes.Comment: 6 pages, 3 figures, Late

Reaction-diffusion fronts with inhomogeneous initial conditions

Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time-evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.Comment: 11 pages, 3 figures, submitted to J. Phys.

Porous silicon formation and electropolishing

Electrochemical etching of silicon in hydrofluoride containing electrolytes leads to pore formation for low and to electropolishing for high applied current. The transition between pore formation and polishing is accompanied by a change of the valence of the electrochemical dissolution reaction. The local etching rate at the interface between the semiconductor and the electrolyte is determined by the local current density. We model the transport of reactants and reaction products and thus the current density in both, the semiconductor and the electrolyte. Basic features of the chemical reaction at the interface are summarized in law of mass action type boundary conditions for the transport equations at the interface. We investigate the linear stability of a planar and flat interface. Upon increasing the current density the stability flips either through a change of the valence of the dissolution reaction or by a nonlinear boundary conditions at the interface.Comment: 18 pages, 8 figure

Diffusion-Limited Annihilation with Initially Separated Reactants

A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$. Using this reaction rate we find that the width of the reaction front grows as $t^{1/4}$ in one dimension and as $t^{1/6}(\ln t)^{1/3}$ in two dimensions.Comment: 9 pages, Plain Te

Formation of Liesegang patterns: A spinodal decomposition scenario

Spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of Liesegang bands. This mechanism yields a sequence of band positions x_n that obeys the spacing law x_n~Q(1+p)^n. The dependence of the parameters p and Q on the initial concentration of the reagents is determined and we find that the functional form of p is in agreement with the experimentally observed Matalon-Packter law.Comment: RevTex, 4 pages, 4 eps figure

Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure

Scaling analysis of electron transport through metal-semiconducting carbon nanotube interfaces: Evolution from the molecular limit to the bulk limit

We present a scaling analysis of electronic and transport properties of metal-semiconducting carbon nanotube interfaces as a function of the nanotube length within the coherent transport regime, which takes fully into account atomic-scale electronic structure and three-dimensional electrostatics of the metal-nanotube interface using a real-space Green's function based self-consistent tight-binding theory. As the first example, we examine devices formed by attaching finite-size single-wall carbon nanotubes (SWNT) to both high- and low- work function metallic electrodes through the dangling bonds at the end. We analyze the nature of Schottky barrier formation at the metal-nanotube interface by examining the electrostatics, the band lineup and the conductance of the metal-SWNT molecule-metal junction as a function of the SWNT molecule length and metal-SWNT coupling strength. We show that the confined cylindrical geometry and the atomistic nature of electronic processes across the metal-SWNT interface leads to a different physical picture of band alignment from that of the planar metal-semiconductor interface. We analyze the temperature and length dependence of the conductance of the SWNT junctions, which shows a transition from tunneling- to thermal activation-dominated transport with increasing nanotube length. The temperature dependence of the conductance is much weaker than that of the planar metal-semiconductor interface due to the finite number of conduction channels within the SWNT junctions. We find that the current-voltage characteristics of the metal-SWNT molecule-metal junctions are sensitive to models of the potential response to the applied source/drain bias voltages.Comment: Minor revision to appear in Phys. Rev. B. Color figures available in the online PRB version or upon request to: [email protected]

The Origins of Concentric Demyelination: Self-Organization in the Human Brain

Baló's concentric sclerosis is a rare atypical form of multiple sclerosis characterized by striking concentric demyelination patterns. We propose a robust mathematical model for Baló's sclerosis, sharing common molecular and cellular mechanisms with multiple sclerosis. A reconsideration of the analogies between Baló's sclerosis and the Liesegang periodic precipitation phenomenon led us to propose a chemotactic cellular model for this disease. Rings of demyelination appear as a result of self-organization processes, and closely mimic Baló lesions. According to our results, homogeneous and concentric demyelinations may be two different macroscopic outcomes of a single fundamental immune disorder. Furthermore, in chemotactic models, cellular aggressivity appears to play a central role in pattern formation