27 research outputs found
Bulk-mediated diffusion on a planar surface: full solution
We consider the effective surface motion of a particle that intermittently
unbinds from a planar surface and performs bulk excursions. Based on a random
walk approach we derive the diffusion equations for surface and bulk diffusion
including the surface-bulk coupling. From these exact dynamic equations we
analytically obtain the propagator of the effective surface motion. This
approach allows us to deduce a superdiffusive, Cauchy-type behavior on the
surface, together with exact cutoffs limiting the Cauchy form. Moreover we
study the long-time dynamics for the surface motion.Comment: 12 pages, 1 figur
Effective surface motion on a reactive cylinder of particles that perform intermittent bulk diffusion
In many biological and small scale technological applications particles may
transiently bind to a cylindrical surface. In between two binding events the
particles diffuse in the bulk, thus producing an effective translation on the
cylinder surface. We here derive the effective motion on the surface, allowing
for additional diffusion on the cylinder surface itself. We find explicit
solutions for the number of adsorbed particles at one given instant, the
effective surface displacement, as well as the surface propagator. In
particular sub- and superdiffusive regimes are found, as well as an effective
stalling of diffusion visible as a plateau in the mean squared displacement. We
also investigate the corresponding first passage and first return problems.Comment: 26 pages, 5 figure
Bulk-mediated surface diffusion on a cylinder: propagators and crossovers
We consider the effective surface motion of a particle that freely diffuses
in the bulk and intermittently binds to that surface. From an exact approach we
derive various regimes of the effective surface motion characterized by
physical rates for binding/unbinding and the bulk diffusivity. We obtain a
transient regime of superdiffusion and, in particular, a saturation regime
characteristic for the cylindrical geometry. This saturation, however, in a
finite system is not terminal but eventually turns over to normal surface
diffusion. The first passage behavior of particles to the cylinder surface is
derived. Consequences for actual systems are discussed.Comment: 4 pages REVTeX4, 2 figure
Continuous time random walk with correlated waiting times
Based on the Langevin description of the Continuous Time Random Walk (CTRW),
we consider a generalization of CTRW in which the waiting times between the
subsequent jumps are correlated. We discuss the cases of exponential and slowly
decaying persistent power-law correlations between the waiting times as two
generic examples and obtain the corresponding mean squared displacements as
functions of time. In the case of exponential-type correlations the
(sub)diffusion at short times is slower than in the absence of correlations. At
long times the behavior of the mean squared displacement is the same as in
uncorrelated CTRW. For power-law correlations we find subdiffusion
characterized by the same exponent at all times, which appears to be smaller
than the one in uncorrelated CTRW. Interestingly, in the limiting case of an
extremely long power-law correlations, the (sub)diffusion exponent does not
tend to zero, but is bounded from below by the subdiffusion exponent
corresponding to a short time behavior in the case of exponential correlations
Kramers escape driven by fractional Brownian motion
We investigate the Kramers escape from a potential well of a test particle
driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical
analysis we demonstrate the exponential distribution of escape times from the
well and analyze in detail the dependence of the mean escape time as function
of H and the particle diffusivity D. We observe different behavior for the
subdiffusive (antipersistent) and superdiffusive (persistent) domains. In
particular we find that the escape becomes increasingly faster for decreasing
values of H, consistent with previous findings on the first passage behavior.
Approximate analytical calculations are shown to support the numerically
observed dependencies.Comment: 14 pages, 16 figures, RevTeX
First passage and arrival time densities for L\'evy flights and the failure of the method of images
We discuss the first passage time problem in the semi-infinite interval, for
homogeneous stochastic Markov processes with L{\'e}vy stable jump length
distributions (),
namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the method
of images leads to a result, which violates a theorem due to Sparre Andersen,
according to which an arbitrary continuous and symmetric jump length
distribution produces a first passage time density (FPTD) governed by the
universal long-time decay . Conversely, we show that for LFs the
direct definition known from Gaussian processes in fact defines the probability
density of first arrival, which for LFs differs from the FPTD. Our findings are
corroborated by numerical results.Comment: 8 pages, 3 figures, iopart.cls style, accepted to J. Phys. A (Lett
Oxygen sensors based on gallium oxide thin films with addition of chromium
This article reveals the gas-sensitive properties of polycrystalline gallium oxide thin films with chromium additives. Incorporation of the Cr2O3 phase into the β-phase gallium oxide film structure leads to the Ga2O3 grain size decrease. The oxygen-sensitivity of the gallium oxide films appears at 300 C. The oxygen increases reversibly the sensor resistance due to an increase in the height of the energy band bending at the Ga2O3 grain boundary with the chemisorption of atomic O. The chromium oxide formed in the Ga2O3 films stimulated dissociative adsorption of the oxygen due to its high catalytic activity via a spill-over mechanism. The temperature range of 500–700 C appears to be the most efficient for the oxygen detection in the concentration range from 9 to 100 vol%. The response time of the sensor was 20 s at 700 C in an initial nitrogen- containing atmosphere at О2 exposure to 21 vol% and the recovery time comprised 52 s. Meantime, the sensors did not practically react to a gas reducing and high humidity