259 research outputs found
Occurrence of normal and anomalous diffusion in polygonal billiard channels
From extensive numerical simulations, we find that periodic polygonal
billiard channels with angles which are irrational multiples of pi generically
exhibit normal diffusion (linear growth of the mean squared displacement) when
they have a finite horizon, i.e. when no particle can travel arbitrarily far
without colliding. For the infinite horizon case we present numerical tests
showing that the mean squared displacement instead grows asymptotically as t
log t. When the unit cell contains accessible parallel scatterers, however, we
always find anomalous super-diffusion, i.e. power-law growth with an exponent
larger than 1. This behavior cannot be accounted for quantitatively by a simple
continuous-time random walk model. Instead, we argue that anomalous diffusion
correlates with the existence of families of propagating periodic orbits.
Finally we show that when a configuration with parallel scatterers is
approached there is a crossover from normal to anomalous diffusion, with the
diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures,
additional comments. Some higher quality figures available at
http://www.fis.unam.mx/~dsander
L\'evy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments
Many studies on animal and human movement patterns report the existence of
scaling laws and power-law distributions. Whereas a number of random walk
models have been proposed to explain observations, in many situations
individuals actually rely on mental maps to explore strongly heterogeneous
environments. In this work we study a model of a deterministic walker, visiting
sites randomly distributed on the plane and with varying weight or
attractiveness. At each step, the walker minimizes a function that depends on
the distance to the next unvisited target (cost) and on the weight of that
target (gain). If the target weight distribution is a power-law, , in some range of the exponent , the foraging medium induces
movements that are similar to L\'evy flights and are characterized by
non-trivial exponents. We explore variations of the choice rule in order to
test the robustness of the model and argue that the addition of noise has a
limited impact on the dynamics in strongly disordered media.Comment: 15 pages, 7 figures. One section adde
Number of distinct sites visited by N random walkers on a Euclidean lattice
The evaluation of the average number S_N(t) of distinct sites visited up to
time t by N independent random walkers all starting from the same origin on an
Euclidean lattice is addressed. We find that, for the nontrivial time regime
and for large N, S_N(t) \approx \hat S_N(t) (1-\Delta), where \hat S_N(t) is
the volume of a hypersphere of radius (4Dt \ln N)^{1/2},
\Delta={1/2}\sum_{n=1}^\infty \ln^{-n} N \sum_{m=0}^n s_m^{(n)} \ln^{m} \ln N,
d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the
dimension and time. The first three terms of these series are calculated
explicitly and the resulting expressions are compared with other approximations
and with simulation results for dimensions 1, 2, and 3. Some implications of
these results on the geometry of the set of visited sites are discussed.Comment: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev.
Normal transport properties for a classical particle coupled to a non-Ohmic bath
We study the Hamiltonian motion of an ensemble of unconfined classical
particles driven by an external field F through a translationally-invariant,
thermal array of monochromatic Einstein oscillators. The system does not
sustain a stationary state, because the oscillators cannot effectively absorb
the energy of high speed particles. We nonetheless show that the system has at
all positive temperatures a well-defined low-field mobility over macroscopic
time scales of order exp(-c/F). The mobility is independent of F at low fields,
and related to the zero-field diffusion constant D through the Einstein
relation. The system therefore exhibits normal transport even though the bath
obviously has a discrete frequency spectrum (it is simply monochromatic) and is
therefore highly non-Ohmic. Such features are usually associated with anomalous
transport properties
Localisation Transition of A Dynamic Reaction Front
We study the reaction-diffusion process with injection of
each species at opposite boundaries of a one-dimensional lattice and bulk
driving of each species in opposing directions with a hardcore interaction. The
system shows the novel feature of phase transitions between localised and
delocalised reaction zones as the injection rate or reaction rate is varied. An
approximate analytical form for the phase diagram is derived by relating both
the domain of reactants and the domain of reactants to asymmetric
exclusion processes with open boundaries, a system for which the phase diagram
is known exactly, giving rise to three phases. The reaction zone width is
described by a finite size scaling form relating the early time growth,
relaxation time and saturation width exponents. In each phase the exponents are
distinct from the previously studied case where the reactants diffuse
isotropically.Comment: 13 pages, latex, uses eps
Immunodiagnosis of Neurocysticercosis: Ways to Focus on the Challenge
Neurocysticercosis (NCC) is a disease of the central nervous system that is considered a public health problem in endemic areas. The definitive diagnosis of this disease is made using a combination of tools that include imaging of the brain and immunodiagnostic tests, but the facilities for performing them are usually not available in endemic areas. The immunodiagnosis of NCC is a useful tool that can provide important information on whether a patient is infected or not, but it presents many drawbacks as not all infected patients can be detected. These tests rely on purified or semipurified antigens that are sometimes difficult to prepare. Recent efforts have focused on the production of recombinant or synthetic antigens for the immunodiagnosis of NCC and interesting studies propose the use of new elements as nanobodies for diagnostic purposes. However, an immunodiagnostic test that can be considered as “gold standard” has not been developed so far. The complex nature of cysticercotic disease and the simplicity of common immunological assumptions involved explain the low scores and reproducibility of immunotests in the diagnosis of NCC. Here, the most important efforts for developing an immunodiagnostic test of NCC are listed and discussed. A more punctilious strategy based on the design of panels of confirmed positive and negative samples, the use of blind tests, and a worldwide effort is proposed in order to develop an immunodiagnostic test that can provide comparable results. The identification of a set of specific and representative antigens of T. solium and a thorough compilation of the many forms of antibody response of humans to the many forms of T. solium disease are also stressed as necessary
The statistics of diffusive flux
We calculate the explicit probability distribution function for the flux
between sites in a simple discrete time diffusive system composed of
independent random walkers. We highlight some of the features of the
distribution and we discuss its relation to the local instantaneous entropy
production in the system. Our results are applicable both to equilibrium and
non-equilibrium steady states as well as for certain time dependent situations.Comment: 12 pages, 1 figur
Order statistics for d-dimensional diffusion processes
We present results for the ordered sequence of first passage times of arrival
of N random walkers at a boundary in Euclidean spaces of d dimensions
Low temperature shape relaxation of 2-d islands by edge diffusion
We present a precise microscopic description of the limiting step for low
temperature shape relaxation of two dimensional islands in which activated
diffusion of particles along the boundary is the only mechanism of transport
allowed. In particular, we are able to explain why the system is driven
irreversibly towards equilibrium. Based on this description, we present a
scheme for calculating the duration of the limiting step at each stage of the
relaxation process. Finally, we calculate numerically the total relaxation time
as predicted by our results and compare it with simulations of the relaxation
process.Comment: 11 pages, 5 figures, to appear in Phys. Rev.
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