16 research outputs found
Front motion in an type reaction-diffusion process: Effects of an electric field
We study the effects of an external electric field on both the motion of the
reaction zone and the spatial distribution of the reaction product, , in an
irreversible reaction-diffusion process. The electrolytes
and are initially separated in space
and the ion-dynamics is described by reaction-diffusion equations obeying local
electroneutrality. Without an electric field, the reaction zone moves
diffusively leaving behind a constant concentration of -s. In the presence
of an electric field which drives the reagents towards the reaction zone, we
find that the reaction zone still moves diffusively but with a diffusion
coefficient which slightly decreases with increasing field. The important
electric field effect is that the concentration of -s is no longer constant
but increases linearly in the direction of the motion of the front. The case of
an electric field of reversed polarity is also discussed and it is found that
the motion of the front has a diffusive, as well as a drift component. The
concentration of -s decreases in the direction of the motion of the front,
up to the complete extinction of the reaction. Possible applications of the
above results to the understanding of the formation of Liesegang patterns in an
electric field is briefly outlined.Comment: 13 pages, 13 figures, submitted to J. Chem. Phy
Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model
We study the continuous limit of a multibox Erhenfest urn model proposed
before by the authors. The evolution of the resulting continuous system is
governed by a differential equation, which describes a diffusion process on a
circle with a nonzero drifting velocity. The short time behavior of this
diffusion process is obtained directly by solving the equation, while the long
time behavior is derived using the Poisson summation formula. They reproduce
the previous results in the large (number of boxes) limit. We also discuss
the connection between this diffusion equation and the Schrdinger
equation of some quantum mechanical problems.Comment: 4 pages prevtex4 file, 1 eps figur
Yang-Lee zeroes for an urn model for the separation of sand
We apply the Yang-Lee theory of phase transitions to an urn model of
separation of sand. The effective partition function of this nonequilibrium
system can be expressed as a polynomial of the size-dependent effective
fugacity . Numerical calculations show that in the thermodynamic limit, the
zeros of the effective partition function are located on the unit circle in the
complex -plane. In the complex plane of the actual control parameter certain
roots converge to the transition point of the model. Thus the Yang-Lee theory
can be applied to a wider class of nonequilibrium systems than those considered
previously.Comment: 4 pages, 3 eps figures include
Probabilistic ballistic annihilation with continuous velocity distributions
We investigate the problem of ballistically controlled reactions where
particles either annihilate upon collision with probability , or undergo an
elastic shock with probability . Restricting to homogeneous systems, we
provide in the scaling regime that emerges in the long time limit, analytical
expressions for the exponents describing the time decay of the density and the
root-mean-square velocity, as continuous functions of the probability and
of a parameter related to the dissipation of energy. We work at the level of
molecular chaos (non-linear Boltzmann equation), and using a systematic Sonine
polynomials expansion of the velocity distribution, we obtain in arbitrary
dimension the first non-Gaussian correction and the corresponding expressions
for the decay exponents. We implement Monte-Carlo simulations in two
dimensions, that are in excellent agreement with our analytical predictions.
For , numerical simulations lead to conjecture that unlike for pure
annihilation (), the velocity distribution becomes universal, i.e. does
not depend on the initial conditions.Comment: 10 pages, 9 eps figures include
Energy fluctuations in vibrated and driven granular gases
We investigate the behavior of energy fluctuations in several models of
granular gases maintained in a non-equilibrium steady state. In the case of a
gas heated from a boundary, the inhomogeneities of the system play a
predominant role. Interpreting the total kinetic energy as a sum of independent
but not identically distributed random variables, it is possible to compute the
probability density function (pdf) of the total energy. Neglecting correlations
and using the analytical expression for the inhomogeneous temperature profile
obtained from the granular hydrodynamic equations, we recover results which
have been previously observed numerically and which had been attributed to the
presence of correlations. In order to separate the effects of spatial
inhomogeneities from those ascribable to velocity correlations, we have also
considered two models of homogeneously thermostated gases: in this framework it
is possible to reveal the presence of non-trivial effects due to velocity
correlations between particles. Such correlations stem from the inelasticity of
collisions. Moreover, the observation that the pdf of the total energy tends to
a Gaussian in the large system limit, suggests that they are also due to the
finite size of the system.Comment: 13 pages, 10 figure
The second and third Sonine coefficients of a freely cooling granular gas revisited
In its simplest statistical-mechanical description, a granular fluid can be
modeled as composed of smooth inelastic hard spheres (with a constant
coefficient of normal restitution ) whose velocity distribution
function obeys the Enskog-Boltzmann equation. The basic state of a granular
fluid is the homogeneous cooling state, characterized by a homogeneous,
isotropic, and stationary distribution of scaled velocities, .
The behavior of in the domain of thermal velocities ()
can be characterized by the two first non-trivial coefficients ( and
) of an expansion in Sonine polynomials. The main goals of this paper are
to review some of the previous efforts made to estimate (and measure in
computer simulations) the -dependence of and , to report new
computer simulations results of and for two-dimensional systems,
and to investigate the possibility of proposing theoretical estimates of
and with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change
Lattice theory of trapping reactions with mobile species
We present a stochastic lattice theory describing the kinetic behavior of
trapping reactions , in which both the and particles
perform an independent stochastic motion on a regular hypercubic lattice. Upon
an encounter of an particle with any of the particles, is
annihilated with a finite probability; finite reaction rate is taken into
account by introducing a set of two-state random variables - "gates", imposed
on each particle, such that an open (closed) gate corresponds to a reactive
(passive) state. We evaluate here a formal expression describing the time
evolution of the particle survival probability, which generalizes our
previous results. We prove that for quite a general class of random motion of
the species involved in the reaction process, for infinite or finite number of
traps, and for any time , the particle survival probability is always
larger in case when stays immobile, than in situations when it moves.Comment: 12 pages, appearing in PR
Fluctuations in granular gases
A driven granular material, e.g. a vibrated box full of sand, is a stationary
system which may be very far from equilibrium. The standard equilibrium
statistical mechanics is therefore inadequate to describe fluctuations in such
a system. Here we present numerical and analytical results concerning energy
and injected power fluctuations. In the first part we explain how the study of
the probability density function (pdf) of the fluctuations of total energy is
related to the characterization of velocity correlations. Two different regimes
are addressed: the gas driven at the boundaries and the homogeneously driven
gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of
homogeneity in hydrodynamics profiles, even in the absence of velocity
correlations, the fluctuations of total energy are non-trivial and may lead to
erroneous conclusions about the role of correlations. In the second part of the
chapter we take into consideration the fluctuations of injected power in driven
granular gas models. Recently, real and numerical experiments have been
interpreted as evidence that the fluctuations of power injection seem to
satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an
alternative interpretation of such results which invalidates the
Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and
using techniques from large deviation theory, the general validity of a
Fluctuation Relation for power injection in driven granular gases is
questioned. Finally a functional is defined using the Lebowitz-Spohn approach
for Markov processes applied to the linear inelastic Boltzmann equation
relevant to describe the motion of a tracer particle. Such a functional results
to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure
Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
We review recent progress on the zero-range process, a model of interacting
particles which hop between the sites of a lattice with rates that depend on
the occupancy of the departure site. We discuss several applications which have
stimulated interest in the model such as shaken granular gases and network
dynamics, also we discuss how the model may be used as a coarse-grained
description of driven phase-separating systems. A useful property of the
zero-range process is that the steady state has a factorised form. We show how
this form enables one to analyse in detail condensation transitions, wherein a
finite fraction of particles accumulate at a single site. We review
condensation transitions in homogeneous and heterogeneous systems and also
summarise recent progress in understanding the dynamics of condensation. We
then turn to several generalisations which also, under certain specified
conditions, share the property of a factorised steady state. These include
several species of particles; hop rates which depend on both the departure and
the destination sites; continuous masses; parallel discrete-time updating;
non-conservation of particles and sites.Comment: 54 pages, 9 figures, review articl
Quantification of three macrolide antibiotics in pharmaceutical lots by HPLC: Development, validation and application to a simultaneous separation
A new validated high performance liquid chromatographic (HPLC) method with rapid analysis time and high efficiency, for the analysis of erythromycin, azithromycin and spiramycin, under isocratic conditions with ODB RP18 as a stationary phase is described. Using an eluent composed of acetonitrile –2-methyl-2-propanol –hydrogenphosphate buffer, pH 6.5, with 1.5% triethylamine (33:7: up to 100, v/v/v), delivered at a flow-rate of 1.0 mL min-1. Ultra Violet (UV) detection is performed at 210 nm. The selectivity is satisfactory enough and no problematic interfering peaks are observed. The procedure is quantitatively characterized and repeatability, linearity, detection and quantification limits are very satisfactory. The method is applied successfully for the assay of the studied drugs in pharmaceutical dosage forms as tablets and powder for oral suspension. Recovery experiments revealed recovery of 97.13–100.28%