17,208 research outputs found
Analysis of a heterogeneous kinetic model for traffic flow
In this work we extend a recent kinetic traffic model to the case of more
than one class of vehicles, each of which is characterized by few different
microscopic features. We consider a Boltzmann-like framework with only binary
interactions, which take place among vehicles belonging to the various classes.
Our approach differs from the multi-population kinetic model based on a lattice
of speeds because here we assume continuous velocity spaces and we introduce a
parameter describing the physical velocity jump performed by a vehicle that
increases its speed after an interaction. The model is discretized in order to
investigate numerically the structure of the resulting fundamental diagrams and
the system of equations is analyzed by studying well posedness. Moreover, we
compute the equilibria of the discretized model and we show that the exact
asymptotic kinetic distributions can be obtained with a small number of
velocities in the grid. Finally, we introduce a new probability law in order to
attenuate the sharp capacity drop occurring in the diagrams of traffic.Comment: 31 page
Many-body theory of excitation dynamics in an ultracold Rydberg gas
We develop a theoretical approach for the dynamics of Rydberg excitations in
ultracold gases, with a realistically large number of atoms. We rely on the
reduction of the single-atom Bloch equations to rate equations, which is
possible under various experimentally relevant conditions. Here, we explicitly
refer to a two-step excitation-scheme. We discuss the conditions under which
our approach is valid by comparing the results with the solution of the exact
quantum master equation for two interacting atoms. Concerning the emergence of
an excitation blockade in a Rydberg gas, our results are in qualitative
agreement with experiment. Possible sources of quantitative discrepancy are
carefully examined. Based on the two-step excitation scheme, we predict the
occurrence of an antiblockade effect and propose possible ways to detect this
excitation enhancement experimentally in an optical lattice as well as in the
gas phase.Comment: 12 pages, 8 figure
Patchiness and Demographic Noise in Three Ecological Examples
Understanding the causes and effects of spatial aggregation is one of the
most fundamental problems in ecology. Aggregation is an emergent phenomenon
arising from the interactions between the individuals of the population, able
to sense only -at most- local densities of their cohorts. Thus, taking into
account the individual-level interactions and fluctuations is essential to
reach a correct description of the population. Classic deterministic equations
are suitable to describe some aspects of the population, but leave out features
related to the stochasticity inherent to the discreteness of the individuals.
Stochastic equations for the population do account for these
fluctuation-generated effects by means of demographic noise terms but, owing to
their complexity, they can be difficult (or, at times, impossible) to deal
with. Even when they can be written in a simple form, they are still difficult
to numerically integrate due to the presence of the "square-root" intrinsic
noise. In this paper, we discuss a simple way to add the effect of demographic
stochasticity to three classic, deterministic ecological examples where
aggregation plays an important role. We study the resulting equations using a
recently-introduced integration scheme especially devised to integrate
numerically stochastic equations with demographic noise. Aimed at scrutinizing
the ability of these stochastic examples to show aggregation, we find that the
three systems not only show patchy configurations, but also undergo a phase
transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy
Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems
The approach to the theory of many-particle interacting systems from a
unified standpoint, based on the variational principle for free energy is
reviewed. A systematic discussion is given of the approximate free energies of
complex statistical systems. The analysis is centered around the variational
principle of N. N. Bogoliubov for free energy in the context of its
applications to various problems of statistical mechanics and condensed matter
physics. The review presents a terse discussion of selected works carried out
over the past few decades on the theory of many-particle interacting systems in
terms of the variational inequalities. It is the purpose of this paper to
discuss some of the general principles which form the mathematical background
to this approach, and to establish a connection of the variational technique
with other methods, such as the method of the mean (or self-consistent) field
in the many-body problem, in which the effect of all the other particles on any
given particle is approximated by a single averaged effect, thus reducing a
many-body problem to a single-body problem. The method is illustrated by
applying it to various systems of many-particle interacting systems, such as
Ising and Heisenberg models, superconducting and superfluid systems, strongly
correlated systems, etc. It seems likely that these technical advances in the
many-body problem will be useful in suggesting new methods for treating and
understanding many-particle interacting systems. This work proposes a new,
general and pedagogical presentation, intended both for those who are
interested in basic aspects, and for those who are interested in concrete
applications.Comment: 60 pages, Refs.25
A structural comparison of models of colloid-polymer mixtures
We study the structure of colloidal fluids with reference to colloid-polymer
mixtures. We compare the one component description of the Asakura-Oosawa (AO)
idealisation of colloid-polymer mixtures with the full two-component model. We
also consider the Morse potential, a variable range interaction, for which the
ground state clusters are known. Mapping the state points between these
systems, we find that the pair structure of the full AO model is equally well
described by the Morse potential or the one component AO approach. We employ a
recently developed method to identify in the bulk fluid the ground state
clusters relevant to the Morse potential. Surprisingly, when we measure the
cluster populations, we find that the Morse fluid is significantly closer the
full AO fluid than the one component AO description.Comment: 13 pages, accepted by J. Phys. Condens: Matter special issue for
CECAM meeting 'New Trends in Simulating Colloids: from Models to
Applications
A hybrid model for Rydberg gases including exact two-body correlations
A model for the simulation of ensembles of laser-driven Rydberg-Rydberg
interacting multi-level atoms is discussed. Our hybrid approach combines an
exact two-body treatment of nearby atom pairs with an effective approximate
treatment for spatially separated pairs. We propose an optimized evolution
equation based only on the system steady state, and a time-independent Monte
Carlo technique is used to efficiently determine this steady state. The hybrid
model predicts features in the pair correlation function arising from
multi-atom processes which existing models can only partially reproduce. Our
interpretation of these features shows that higher-order correlations are
relevant already at low densities. Finally, we analyze the performance of our
model in the high-density case.Comment: significantly expanded and revised version (more observables,
high-density regime); 9 pages, 8 figure
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