5,166 research outputs found
Comment on "Anomalous heat conduction and anomalous diffusion in one-dimensional systems"
We comment on a recent paper by Li and Wang [Phys. Rev. Lett. 91, 044301
(2003)], and argue that their results violate the non-existence of a
characteristic time scale in subdiffusive systems.Comment: 1 page, REVTeX, accepted to Phys. Rev. Let
L\'{e}vy flights as subordination process: first passage times
We obtain the first passage time density for a L\'{e}vy flight random process
from a subordination scheme. By this method, we infer the asymptotic behavior
directly from the Brownian solution and the Sparre Andersen theorem, avoiding
explicit reference to the fractional diffusion equation. Our results
corroborate recent findings for Markovian L\'{e}vy flights and generalize to
broad waiting times.Comment: 4 pages, RevTe
On solutions of a class of non-Markovian Fokker-Planck equations
We show that a formal solution of a rather general non-Markovian
Fokker-Planck equation can be represented in a form of an integral
decomposition and thus can be expressed through the solution of the Markovian
equation with the same Fokker-Planck operator. This allows us to classify
memory kernels into safe ones, for which the solution is always a probability
density, and dangerous ones, when this is not guaranteed. The first situation
describes random processes subordinated to a Wiener process, while the second
one typically corresponds to random processes showing a strong ballistic
component. In this case the non-Markovian Fokker-Planck equation is only valid
in a restricted range of parameters, initial and boundary conditions.Comment: A new ref.12 is added and discusse
Towards deterministic equations for Levy walks: the fractional material derivative
Levy walks are random processes with an underlying spatiotemporal coupling.
This coupling penalizes long jumps, and therefore Levy walks give a proper
stochastic description for a particle's motion with broad jump length
distribution. We derive a generalized dynamical formulation for Levy walks in
which the fractional equivalent of the material derivative occurs. Our approach
will be useful for the dynamical formulation of Levy walks in an external force
field or in phase space for which the description in terms of the continuous
time random walk or its corresponding generalized master equation are less well
suited
Study of Spectral/Radiometric Characteristics of the Thematic Mapper for Land Use Applications
An investigation conducted in support of the LANDSAT 4/5 Image Data Quality Analysis (LIDQA) Program is discussed. Results of engineering analyses of radiometric, spatial, spectral, and geometric properties of the Thematic Mapper systems are summarized; major emphasis is placed on the radiometric analysis. Details of the analyses are presented in appendices, which contain three of the eight technical papers produced during this investigation; these three, together, describe the major activities and results of the investigation
Thermodynamics and Fractional Fokker-Planck Equations
The relaxation to equilibrium in many systems which show strange kinetics is
described by fractional Fokker-Planck equations (FFPEs). These can be
considered as phenomenological equations of linear nonequilibrium theory. We
show that the FFPEs describe the system whose noise in equilibrium funfills the
Nyquist theorem. Moreover, we show that for subdiffusive dynamics the solutions
of the corresponding FFPEs are probability densities for all cases where the
solutions of normal Fokker-Planck equation (with the same Fokker-Planck
operator and with the same initial and boundary conditions) exist. The
solutions of the FFPEs for superdiffusive dynamics are not always probability
densities. This fact means only that the corresponding kinetic coefficients are
incompatible with each other and with the initial conditions
Monte Carlo evaluation of FADE approach to anomalous kinetics
In this paper we propose a comparison between the CTRW (Monte Carlo) and
Fractional Derivative approaches to the modelling of anomalous diffusion
phenomena in the presence of an advection field. Galilei variant and invariant
schemes are revised.Comment: 13 pages, 6 figure
Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
A growing number of biological, soft, and active matter systems are observed
to exhibit normal diffusive dynamics with a linear growth of the mean squared
displacement, yet with a non-Gaussian distribution of increments. Based on the
Chubinsky-Slater idea of a diffusing diffusivity we here establish and analyze
a minimal model framework of diffusion processes with fluctuating diffusivity.
In particular, we demonstrate the equivalence of the diffusing diffusivity
process with a superstatistical approach with a distribution of diffusivities,
at times shorter than the diffusivity correlation time. At longer times a
crossover to a Gaussian distribution with an effective diffusivity emerges.
Specifically, we establish a subordination picture of Brownian but non-Gaussian
diffusion processes, that can be used for a wide class of diffusivity
fluctuation statistics. Our results are shown to be in excellent agreement with
simulations and numerical evaluations.Comment: 19 pages, 6 figures, RevTeX. Physical Review X, at pres
Accelerating random walks by disorder
We investigate the dynamic impact of heterogeneous environments on
superdiffusive random walks known as L\'evy flights. We devote particular
attention to the relative weight of source and target locations on the rates
for spatial displacements of the random walk. Unlike ordinary random walks
which are slowed down for all values of the relative weight of source and
target, non-local superdiffusive processes show distinct regimes of attenuation
and acceleration for increased source and target weight, respectively.
Consequently, spatial inhomogeneities can facilitate the spread of
superdiffusive processes, in contrast to common belief that external disorder
generally slows down stochastic processes. Our results are based on a novel
type of fractional Fokker-Planck equation which we investigate numerically and
by perturbation theory for weak disorder.Comment: 8 pages, 5 figure
Development, implementation and evaluation of satellite-aided agricultural monitoring systems
Research supporting the use of remote sensing for inventory and assessment of agricultural commodities is summarized. Three task areas are described: (1) corn and soybean crop spectral/temporal signature characterization; (2) efficient area estimation technology development; and (3) advanced satellite and sensor system definition. Studies include an assessment of alternative green measures from MSS variables; the evaluation of alternative methods for identifying, labeling or classification targets in an automobile procedural context; a comparison of MSS, the advanced very high resolution radiometer and the coastal zone color scanner, as well as a critical assessment of thematic mapper dimensionally and spectral structure
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