485 research outputs found
Systematic Series Expansions for Processes on Networks
We use series expansions to study dynamics of equilibrium and non-equilibrium
systems on networks. This analytical method enables us to include detailed
non-universal effects of the network structure. We show that even low order
calculations produce results which compare accurately to numerical simulation,
while the results can be systematically improved. We show that certain commonly
accepted analytical results for the critical point on networks with a broad
degree distribution need to be modified in certain cases due to
disassortativity; the present method is able to take into account the
assortativity at sufficiently high order, while previous results correspond to
leading and second order approximations in this method. Finally, we apply this
method to real-world data.Comment: 4 pages, 3 figure
Exact solution of the one-dimensional deterministic Fixed-Energy Sandpile
In reason of the strongly non-ergodic dynamical behavior, universality
properties of deterministic Fixed-Energy Sandpiles are still an open and
debated issue. We investigate the one-dimensional model, whose microscopical
dynamics can be solved exactly, and provide a deeper understanding of the
origin of the non-ergodicity. By means of exact arguments, we prove the
occurrence of orbits of well-defined periods and their dependence on the
conserved energy density. Further statistical estimates of the size of the
attraction's basins of the different periodic orbits lead to a complete
characterization of the activity vs. energy density phase diagram in the limit
of large system's size.Comment: 4 pages, accepted for publication in Phys. Rev. Let
Reentrant Behavior of the Spinodal Curve in a Nonequilibrium Ferromagnet
The metastable behavior of a kinetic Ising--like ferromagnetic model system
in which a generic type of microscopic disorder induces nonequilibrium steady
states is studied by computer simulation and a mean--field approach. We pay
attention, in particular, to the spinodal curve or intrinsic coercive field
that separates the metastable region from the unstable one. We find that, under
strong nonequilibrium conditions, this exhibits reentrant behavior as a
function of temperature. That is, metastability does not happen in this regime
for both low and high temperatures, but instead emerges for intermediate
temperature, as a consequence of the non-linear interplay between thermal and
nonequilibrium fluctuations. We argue that this behavior, which is in contrast
with equilibrium phenomenology and could occur in actual impure specimens,
might be related to the presence of an effective multiplicative noise in the
system.Comment: 7 pages, 4 figures; Final version to appear in Phys. Rev. E; Section
V has been revise
Theoretical Characterization of the Interface in a Nonequilibrium Lattice System
The influence of nonequilibrium bulk conditions on the properties of the
interfaces exhibited by a kinetic Ising--like model system with nonequilibrium
steady states is studied. The system is maintained out of equilibrium by
perturbing the familiar spin--flip dynamics at temperature T with
completely--random flips; one may interpret these as ideally simulating some
(dynamic) impurities. We find evidence that, in the present case, the
nonequilibrium mechanism adds to the basic thermal one resulting on a
renormalization of microscopic parameters such as the probability of
interfacial broken bonds. On this assumption, we develop theory for the
nonequilibrium "surface tension", which happens to show a non--monotonous
behavior with a maximum at some finite T. It ensues, in full agreement with
Monte Carlo simulations, that interface fluctuations differ qualitatively from
the equilibrium case, e.g., the interface remains rough at zero--T. We discuss
on some consequences of these facts for nucleation theory, and make some
explicit predictions concerning the nonequilibrium droplet structure.Comment: 10 pages, 7 figures, submitted to Phys. Re
Non-equilibrium Anisotropic Phases, Nucleation and Critical Behavior in a Driven Lennard-Jones Fluid
We describe short-time kinetic and steady-state properties of the
non--equilibrium phases, namely, solid, liquid and gas anisotropic phases in a
driven Lennard-Jones fluid. This is a computationally-convenient
two-dimensional model which exhibits a net current and striped structures at
low temperature, thus resembling many situations in nature. We here focus on
both critical behavior and details of the nucleation process. In spite of the
anisotropy of the late--time spinodal decomposition process, earlier nucleation
seems to proceed by Smoluchowski coagulation and Ostwald ripening, which are
known to account for nucleation in equilibrium, isotropic lattice systems and
actual fluids. On the other hand, a detailed analysis of the system critical
behavior rises some intriguing questions on the role of symmetries; this
concerns the computer and field-theoretical modeling of non-equilibrium fluids.Comment: 7 pages, 9 ps figures, to appear in PR
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