254 research outputs found
Self-gravitating systems in a three-dimensional expanding Universe
The non-linear evolution of one-dimensional perturbations in a
three-dimensional expanding Universe is considered. A general Lagrangian scheme
is derived, and compared to two previously introduced approximate models. These
models are simulated with heap-based event-driven numerical procedure, that
allows for the study of large systems, averaged over many realizations of
random initial conditions. One of the models is shown to be qualitatively, and,
in some respects, concerning mass aggregation, quantitatively similar to the
adhesion model.Comment: 11 figures, simulations of Q model include
Emergence of a collective crystal in a classical system with long-range interactions
A one-dimensional long-range model of classical rotators with an extended
degree of complexity, as compared to paradigmatic long-range systems, is
introduced and studied. Working at constant density, in the thermodynamic limit
one can prove the statistical equivalence with the Hamiltonian Mean Field model
(HMF) and -HMF: a second order phase transition is indeed observed at
the critical energy threshold . Conversely, when the
thermodynamic limit is performed at infinite density (while keeping the length
of the hosting interval constant), the critical energy is
modulated as a function of . At low energy, a self-organized collective
crystal phase is reported to emerge, which converges to a perfect crystal in
the limit . To analyze the phenomenon, the equilibrium
one particle density function is analytically computed by maximizing the
entropy. The transition and the associated critical energy between the gaseous
and the crystal phase is computed. Molecular dynamics show that the crystal
phase is apparently split into two distinct regimes, depending on the the
energy per particle . For small , particles are
exactly located on the lattice sites; above an energy threshold
, particles can travel from one site to another. However,
does not signal a phase transition but reflects the finite
time of observation: the perfect crystal observed for
corresponds to a long lasting dynamical transient, whose life time increases
when the approaches zero.Comment: 6 pages, 4 figure
Persistent random walk with exclusion
Modelling the propagation of a pulse in a dense {\em milieu} poses
fundamental challenges at the theoretical and applied levels. To this aim, in
this paper we generalize the telegraph equation to non-ideal conditions by
extending the concept of persistent random walk to account for spatial
exclusion effects. This is achieved by introducing an explicit constraint in
the hopping rates, that weights the occupancy of the target sites. We derive
the mean-field equations, which display nonlinear terms that are important at
high density. We compute the evolution of the mean square displacement (MSD)
for pulses belonging to a specific class of spatially symmetric initial
conditions. The MSD still displays a transition from ballistic to diffusive
behaviour. We derive an analytical formula for the effective velocity of the
ballistic stage, which is shown to depend in a nontrivial fashion upon both the
density (area) and the shape of the initial pulse. After a density-dependent
crossover time, nonlinear terms become negligible and normal diffusive
behaviour is recovered at long times.Comment: Revised version accepted for publication in Europ. Phys. J.
Reactive explorers to unravel network topology
A procedure is developed and tested to recover the distribution of
connectivity of an a priori unknown network, by sampling the dynamics of an
ensemble made of reactive walkers. The relative weight between reaction and
relocation is gauged by a scalar control parameter, which can be adjusted at
will. Different equilibria are attained by the system, following the externally
imposed modulation, and reflecting the interplay between reaction and diffusion
terms. The information gathered on the observation node is used to predict the
stationary density as displayed by the system, via a direct implementation of
the celebrated Heterogeneous Mean Field (HMF) approximation. This knowledge
translates into a linear problem which can be solved to return the entries of
the sought distribution. A variant of the model is then considered which
consists in assuming a localized source where the reactive constituents are
injected, at a rate that can be adjusted as a stepwise function of time. The
linear problem obtained when operating in this setting allows one to recover a
fair estimate of the underlying system size. Numerical experiments are carried
so as to challenge the predictive ability of the theory
Delay induced Turing-like waves for one species reaction-diffusion model on a network
A one species time-delay reaction-diffusion system defined on a complex
networks is studied. Travelling waves are predicted to occur as follows a
symmetry breaking instability of an homogenous stationary stable solution,
subject to an external non homogenous perturbation. These are generalized
Turing-like waves that materialize in a single species populations dynamics
model, as the unexpected byproduct of the imposed delay in the diffusion part.
Sufficient conditions for the onset of the instability are mathematically
provided by performing a linear stability analysis adapted to time delayed
differential equation. The method here developed exploits the properties of the
Lambert W-function. The prediction of the theory are confirmed by direct
numerical simulation carried out for a modified version of the classical Fisher
model, defined on a Watts-Strogatz networks and with the inclusion of the
delay
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