27 research outputs found
Single Stranded DNA Translocation Through A Nanopore: A Master Equation Approach
We study voltage driven translocation of a single stranded (ss) DNA through a
membrane channel. Our model, based on a master equation (ME) approach,
investigates the probability density function (pdf) of the translocation times,
and shows that it can be either double or mono-peaked, depending on the system
parameters. We show that the most probable translocation time is proportional
to the polymer length, and inversely proportional to the first or second power
of the voltage, depending on the initial conditions. The model recovers
experimental observations on hetro-polymers when using their properties inside
the pore, such as stiffness and polymer-pore interaction.Comment: 7 pages submitted to PR
Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation
A pointlike particle of finite mass m, moving in a one-dimensional viscous
environment and biased by a spatially dependent force, is considered. We
present a rigorous mapping of the Fokker-Planck equation, which determines
evolution of the particle density in phase space, onto the spatial coordinate
x. The result is the Smoluchowski equation, valid in the overdamped limit,
m->0, with a series of corrections expanded in powers of m. They are determined
unambiguously within the recurrence mapping procedure. The method and the
results are interpreted on the simplest model with no field and on the damped
harmonic oscillator.Comment: 13 pages, 1 figur
Pascal Principle for Diffusion-Controlled Trapping Reactions
"All misfortune of man comes from the fact that he does not stay peacefully
in his room", has once asserted Blaise Pascal. In the present paper we evoke
this statement as the "Pascal principle" in regard to the problem of survival
of an "A" particle, which performs a lattice random walk in presence of a
concentration of randomly moving traps "B", and gets annihilated upon
encounters with any of them. We prove here that at sufficiently large times for
both perfect and imperfect trapping reactions, for arbitrary spatial dimension
"d" and for a rather general class of random walks, the "A" particle survival
probability is less than or equal to the survival probability of an immobile
target in the presence of randomly moving traps.Comment: 4 pages, RevTex, appearing in PR
Survival and residence times in disordered chains with bias
We present a unified framework for first-passage time and residence time of
random walks in finite one-dimensional disordered biased systems. The
derivation is based on exact expansion of the backward master equation in
cumulants. The dependence on initial condition, system size, and bias strength
is explicitly studied for models with weak and strong disorder. Application to
thermally activated processes is also developed.Comment: 13 pages with 2 figures, RevTeX4; v2:minor grammatical changes, typos
correcte
A continuous time random walk model for financial distributions
We apply the formalism of the continuous time random walk to the study of
financial data. The entire distribution of prices can be obtained once two
auxiliary densities are known. These are the probability densities for the
pausing time between successive jumps and the corresponding probability density
for the magnitude of a jump. We have applied the formalism to data on the US
dollar/Deutsche Mark future exchange, finding good agreement between theory and
the observed data.Comment: 14 pages, 5 figures, revtex4, submitted for publicatio
Diffusion Time-Scale Invariance, Markovization Processes and Memory Effects in Lennard-Jones Liquids
We report the results of calculation of diffusion coefficients for
Lennard-Jones liquids, based on the idea of time-scale invariance of relaxation
processes in liquids. The results were compared with the molecular dynamics
data for Lennard-Jones system and a good agreement of our theory with these
data over a wide range of densities and temperatures was obtained. By
calculations of the non-Markovity parameter we have estimated numerically
statistical memory effects of diffusion in detail.Comment: 10 pages, 3 figure
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
Kinetics of active surface-mediated diffusion in spherically symmetric domains
We present an exact calculation of the mean first-passage time to a target on
the surface of a 2D or 3D spherical domain, for a molecule alternating phases
of surface diffusion on the domain boundary and phases of bulk diffusion. We
generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a
biased diffusion in a general annulus with an arbitrary number of regularly
spaced targets on a partially reflecting surface. The presented approach is
based on an integral equation which can be solved analytically. Numerically
validated approximation schemes, which provide more tractable expressions of
the mean first-passage time are also proposed. In the framework of this minimal
model of surface-mediated reactions, we show analytically that the mean
reaction time can be minimized as a function of the desorption rate from the
surface.Comment: Published online in J. Stat. Phy
On the applicability of entropy potentials in transport problems
Transport in confined structures of varying geometry has become the subject of growing attention in recent years since such structures are ubiquitous in biology and technology. In analyzing transport in systems of this type, the notion of entropy potentials is widely used. Entropy potentials naturally arise in one-dimensional description of equilibrium distributions in multidimensional confined structures. However, their application to transport problems requires some caution. In this article we discuss such applications and summarize the results of recent studies exploring the limits of applicability. We also consider an example of a transport problem in a system of varying geometry, where the conventional approach is inapplicable since the geometry changes abruptly. In addition, we demonstrate how the entropy potential can be used to analyze optimal transport through a three-dimensional cosine-shaped channel