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.

Luz e cores: relato de atividade educacional usando uma abordagem dialógica problematizadora

Anais do II Seminário Seminário Estadual PIBID do Paraná: tecendo saberes / organizado por Dulcyene Maria Ribeiro e Catarina Costa Fernandes — Foz do Iguaçu: Unioeste; Unila, 2014O Programa Institucional de Bolsa de Iniciação à Docência (PIBID) oportuniza aos bolsistas uma aproximação do espaço escolar, permitindo que estes futuros professores estejam mais bem preparados para a tarefa docente. Dentro do ensino de física, a utilização de práticas experimentais ou demonstrativas pode ser uma forma muito eficaz de substituir o uso do Método Bancário, uma vez que os alunos têm a oportunidade de observar e chegar às suas conclusões, e não apenas aceitar aquilo que o professor diz. Infelizmente, a realidade do ensino público muitas vezes impede essas práticas, devido à falta de laboratórios e/ou aparatos experimentais. Nesse trabalho é apresentada uma atividade educacional abordando o tema luz e cores, executada como ação do PIBID, que utiliza um experimento simples e de baixo custo

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

Non-equilibrium thermodynamic description of junctions in semiconductor devices

The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of transport processes in semiconductor junctions. A complete phenomenological model for drift-diffusion processes in a junction has been derived, which includes, from first principles, both surface equations and boundary conditions, together with the usual drift-diffusion equations for the bulks. In this way a self-consistent characterisation of the whole system, bulks and interface, has been obtained in a common framework. The completeness of the model has been shown and a simple application to metal-semiconductor junctions developed.Comment: 12 pages, RevTex. Submitted to Phys. Rev. B minor LaTex errors correcte

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

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

Theoretical Principles of Single-Molecule Electronics: A Chemical and Mesoscopic View

Exploring the use of individual molecules as active components in electronic devices has been at the forefront of nanoelectronics research in recent years. Compared to semiconductor microelectronics, modeling transport in single-molecule devices is much more difficult due to the necessity of including the effects of the device electronic structure and the interface to the external contacts at the microscopic level. Theoretical formulation of the problem therefore requires integrating the knowledge base in surface science, electronic structure theory, quantum transport and device modeling into a single unified framework starting from the first-principles. In this paper, we introduce the theoretical framework for modeling single-molecule electronics and present a simple conceptual picture for interpreting the results of numerical computation. We model the device using a self-consistent matrix Green's function method that combines Non-Equilibrium Green's function theory of quantum transport with atomic-scale description of the device electronic structure. We view the single-molecule device as "heterostructures" composed of chemically well-defined atomic groups, and analyze the device characteristics in terms of the charge and potential response of these atomic groups to perturbation induced by the metal-molecule coupling and the applied bias voltage. We demonstrate the power of this approach using as examples devices formed by attaching benzene-based molecules of different size and internal structure to the gold electrodes through sulfur end atoms.Comment: To appear in International Journal of Quantum Chemistry, Special Issue in memory of J.A. Pople. 13 pages, 9 figure