197 research outputs found
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 . 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
. Using this reaction rate we find that the width of the reaction front
grows as in one dimension and as 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
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