325 research outputs found
Transport properties of a modified Lorentz gas
We present a detailed study of the first simple mechanical system that shows
fully realistic transport behavior while still being exactly solvable at the
level of equilibrium statistical mechanics. The system under consideration is a
Lorentz gas with fixed freely-rotating circular scatterers interacting with
point particles via perfectly rough collisions. Upon imposing a temperature
and/or a chemical potential gradient, a stationary state is attained for which
local thermal equilibrium holds for low values of the imposed gradients.
Transport in this system is normal, in the sense that the transport
coefficients which characterize the flow of heat and matter are finite in the
thermodynamic limit. Moreover, the two flows are non-trivially coupled,
satisfying Onsager's reciprocity relations to within numerical accuracy as well
as the Green-Kubo relations . We further show numerically that an applied
electric field causes the same currents as the corresponding chemical potential
gradient in first order of the applied field. Puzzling discrepancies in higher
order effects (Joule heating) are also observed. Finally, the role of entropy
production in this purely Hamiltonian system is shortly discussed.Comment: 16 pages, 16 figures, submitted to J. Stat. Phy
Phase transitions in systems of self-propelled agents and related network models
An important characteristic of flocks of birds, school of fish, and many
similar assemblies of self-propelled particles is the emergence of states of
collective order in which the particles move in the same direction. When noise
is added into the system, the onset of such collective order occurs through a
dynamical phase transition controlled by the noise intensity. While originally
thought to be continuous, the phase transition has been claimed to be
discontinuous on the basis of recently reported numerical evidence. We address
this issue by analyzing two representative network models closely related to
systems of self-propelled particles. We present analytical as well as numerical
results showing that the nature of the phase transition depends crucially on
the way in which noise is introduced into the system.Comment: Four pages, four figures. Submitted to PR
Metastability in Markov processes
We present a formalism to describe slowly decaying systems in the context of
finite Markov chains obeying detailed balance. We show that phase space can be
partitioned into approximately decoupled regions, in which one may introduce
restricted Markov chains which are close to the original process but do not
leave these regions. Within this context, we identify the conditions under
which the decaying system can be considered to be in a metastable state.
Furthermore, we show that such metastable states can be described in
thermodynamic terms and define their free energy. This is accomplished showing
that the probability distribution describing the metastable state is indeed
proportional to the equilibrium distribution, as is commonly assumed. We test
the formalism numerically in the case of the two-dimensional kinetic Ising
model, using the Wang--Landau algorithm to show this proportionality
explicitly, and confirm that the proportionality constant is as derived in the
theory. Finally, we extend the formalism to situations in which a system can
have several metastable states.Comment: 30 pages, 5 figures; version with one higher quality figure available
at http://www.fis.unam.mx/~dsanders
Transport Properties of the Diluted Lorentz Slab
We study the behavior of a point particle incident from the left on a slab of
a randomly diluted triangular array of circular scatterers. Various scattering
properties, such as the reflection and transmission probabilities and the
scattering time are studied as a function of thickness and dilution. We show
that a diffusion model satisfactorily describes the mentioned scattering
properties. We also show how some of these quantities can be evaluated exactly
and their agreement with numerical experiments. Our results exhibit the
dependence of these scattering data on the mean free path. This dependence
again shows excellent agreement with the predictions of a Brownian motion
model.Comment: 14 pages of text in LaTeX, 7 figures in Postscrip
How rare are diffusive rare events?
We study the time until first occurrence, the first-passage time, of rare
density fluctuations in diffusive systems. We approach the problem using a
model consisting of many independent random walkers on a lattice. The existence
of spatial correlations makes this problem analytically intractable. However,
for a mean-field approximation in which the walkers can jump anywhere in the
system, we obtain a simple asymptotic form for the mean first-passage time to
have a given number k of particles at a distinguished site. We show
numerically, and argue heuristically, that for large enough k, the mean-field
results give a good approximation for first-passage times for systems with
nearest-neighbour dynamics, especially for two and higher spatial dimensions.
Finally, we show how the results change when density fluctuations anywhere in
the system, rather than at a specific distinguished site, are considered.Comment: 6 pages, 5 figures. Accepted for publication in Europhysics Letters
(http://www.iop.org/EJ/journal/EPL
Rotor interaction in the annulus billiard
Introducing the rotor interaction in the integrable system of the annulus
billiard produces a variety of dynamical phenomena, from integrability to
ergodicity
Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems
We consider nonequilibrium transport in a simple chain of identical
mechanical cells in which particles move around. In each cell, there is a
rotating disc, with which these particles interact, and this is the only
interaction in the model. It was shown in \cite{eckmann-young} that when the
cells are weakly coupled, to a good approximation, the jump rates of particles
and the energy-exchange rates from cell to cell follow linear profiles. Here,
we refine that study by analyzing higher-order effects which are induced by the
presence of external gradients for situations in which memory effects, typical
of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a
set of balance equations for the particle number and energy in terms of the
reflection probabilities of the cell and solve it phenomenologically. Using
this approximate theory we explain how these asymmetries affect various aspects
of heat and particle transport in systems of the general type described above
and obtain in the infinite volume limit the deviation from the theory in
\cite{eckmann-young} to first-order. We verify our assumptions with extensive
numerical simulations.Comment: Several change
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
Diffusion-Limited Annihilation with Initially Separated Reactants
A diffusion-limited annihilation process, A+B->0, with species initially
separated in space is investigated. A heuristic argument suggests the form of
the reaction rate in dimensions less or equal to the upper critical dimension
. Using this reaction rate we find that the width of the reaction front
grows as in one dimension and as in two
dimensions.Comment: 9 pages, Plain Te
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