221 research outputs found
Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents
A number of results for reactions involving subdiffusive species all with the
same anomalous exponent gamma have recently appeared in the literature and can
often be understood in terms of a subordination principle whereby time t in
ordinary diffusion is replaced by t^gamma. However, very few results are known
for reactions involving different species characterized by different anomalous
diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive
particle surrounded by a sea of (sub)diffusive traps in one dimension. We find
rigorous results for the asymptotic survival probability of the particle in
most cases, with the exception of the case of a particle that diffuses normally
while the anomalous diffusion exponent of the traps is smaller than 2/3.Comment: To appear in Phys. Rev.
Driven diffusion in a periodically compartmentalized tube: homogeneity versus intermittency of particle motion
We study the effect of a driving force F on drift and diffusion of a point Brownian particle in a tube formed by identical ylindrical compartments, which create periodic entropy barriers for the particle motion along the tube axis. The particle transport exhibits striking features: the effective mobility monotonically decreases with increasing F, and the effective diffusivity diverges as F → ∞, which indicates that the entropic effects in diffusive transport are enhanced by the driving force. Our consideration is based on two different scenarios of the particle motion at small and large F, homogeneous and intermittent, respectively. The scenarios are deduced from the careful analysis of statistics of the particle transition times between neighboring openings. From this qualitative picture, the limiting small-F and large-F behaviors of the effective mobility and diffusivity are derived analytically. Brownian dynamics simulations are used to find these quantities at intermediate values of the driving force for various compartment lengths and opening radii. This work shows that the driving force may lead to qualitatively different anomalous transport features, depending on the geometry design
Trapping of a random walk by diffusing traps
We present a systematic analytical approach to the trapping of a random walk
by a finite density rho of diffusing traps in arbitrary dimension d. We confirm
the phenomenologically predicted e^{-c_d rho t^{d/2}} time decay of the
survival probability, and compute the dimension dependent constant c_d to
leading order within an eps=2-d expansion.Comment: 16 pages, to appear in J. Phys.
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
Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories
In this paper we study the kinetics of diffusion-limited, pseudo-first-order
A + B -> B reactions in situations in which the particles' intrinsic
reactivities vary randomly in time. That is, we suppose that the particles are
bearing "gates" which interchange randomly and independently of each other
between two states - an active state, when the reaction may take place, and a
blocked state, when the reaction is completly inhibited. We consider four
different models, such that the A particle can be either mobile or immobile,
gated or ungated, as well as ungated or gated B particles can be fixed at
random positions or move randomly. All models are formulated on a
-dimensional regular lattice and we suppose that the mobile species perform
independent, homogeneous, discrete-time lattice random walks. The model
involving a single, immobile, ungated target A and a concentration of mobile,
gated B particles is solved exactly. For the remaining three models we
determine exactly, in form of rigorous lower and upper bounds, the large-N
asymptotical behavior of the A particle survival probability. We also realize
that for all four models studied here such a probalibity can be interpreted as
the moment generating function of some functionals of random walk trajectories,
such as, e.g., the number of self-intersections, the number of sites visited
exactly a given number of times, "residence time" on a random array of lattice
sites and etc. Our results thus apply to the asymptotical behavior of the
corresponding generating functions which has not been known as yet.Comment: Latex, 45 pages, 5 ps-figures, submitted to PR
Kinetics of Anchoring of Polymer Chains on Substrates with Chemically Active Sites
We consider dynamics of an isolated polymer chain with a chemically active
end-bead on a 2D solid substrate containing immobile, randomly placed
chemically active sites (traps). For a particular situation when the end-bead
can be irreversibly trapped by any of these sites, which results in a complete
anchoring of the whole chain, we calculate the time evolution of the
probability that the initially non-anchored chain remains mobile
until time . We find that for relatively short chains follows at
intermediate times a standard-form 2D Smoluchowski-type decay law , which crosses over at very large times to the
fluctuation-induced dependence , associated with
fluctuations in the spatial distribution of traps. We show next that for long
chains the kinetic behavior is quite different; here the intermediate-time
decay is of the form , which is the
Smoluchowski-type law associated with subdiffusive motion of the end-bead,
while the long-time fluctuation-induced decay is described by the dependence
, stemming out of the interplay between
fluctuations in traps distribution and internal relaxations of the chain.Comment: Latex file, 19 pages, one ps figure, to appear in PR
Universal fluctuations in the support of the random walk
A random walk starts from the origin of a d-dimensional lattice. The
occupation number n(x,t) equals unity if after t steps site x has been visited
by the walk, and zero otherwise. We study translationally invariant sums M(t)
of observables defined locally on the field of occupation numbers. Examples are
the number S(t) of visited sites; the area E(t) of the (appropriately defined)
surface of the set of visited sites; and, in dimension d=3, the Euler index of
this surface. In d > 3, the averages (t) all increase linearly with t as
t-->infinity. We show that in d=3, to leading order in an asymptotic expansion
in t, the deviations from average Delta M(t)= M(t)-(t) are, up to a
normalization, all identical to a single "universal" random variable. This
result resembles an earlier one in dimension d=2; we show that this
universality breaks down for d>3.Comment: 17 pages, LaTeX, 2 figures include
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
On the joint residence time of N independent two-dimensional Brownian motions
We study the behavior of several joint residence times of N independent
Brownian particles in a disc of radius in two dimensions. We consider: (i)
the time T_N(t) spent by all N particles simultaneously in the disc within the
time interval [0,t]; (ii) the time T_N^{(m)}(t) which at least m out of N
particles spend together in the disc within the time interval [0,t]; and (iii)
the time {\tilde T}_N^{(m)}(t) which exactly m out of N particles spend
together in the disc within the time interval [0,t]. We obtain very simple
exact expressions for the expectations of these three residence times in the
limit t\to\infty.Comment: 8 page
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