430 research outputs found
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
Nonlinear preferential rewiring in fixed-size networks as a diffusion process
We present an evolving network model in which the total numbers of nodes and
edges are conserved, but in which edges are continuously rewired according to
nonlinear preferential detachment and reattachment. Assuming power-law kernels
with exponents alpha and beta, the stationary states the degree distributions
evolve towards exhibit a second order phase transition - from relatively
homogeneous to highly heterogeneous (with the emergence of starlike structures)
at alpha = beta. Temporal evolution of the distribution in this critical regime
is shown to follow a nonlinear diffusion equation, arriving at either pure or
mixed power-laws, of exponents -alpha and 1-alpha
Is the particle current a relevant feature in driven lattice gases?
By performing extensive MonteCarlo simulations we show that the infinitely
fast driven lattice gas (IDLG) shares its critical properties with the randomly
driven lattice gas (RDLG).
All the measured exponents, scaling functions and amplitudes are the same in
both cases. This strongly supports the idea that the main relevant
non-equilibrium effect in driven lattice gases is the anisotropy (present in
both IDLG and RDLG) and not the particle current (present only in the IDLG).
This result, at odds with the predictions from the standard theory for the
IDLG, supports a recently proposed alternative theory. The case of finite
driving fields is also briefly discussed.Comment: 4 pages. Slightly improved version. Journal Reference: To appear in
Phys. Rev. Let
Nonuniversal exponents in sandpiles with stochastic particle number transfer
We study fixed density sandpiles in which the number of particles transferred
to a neighbor on relaxing an active site is determined stochastically by a
parameter . Using an argument, the critical density at which an
active-absorbing transition occurs is found exactly. We study the critical
behavior numerically and find that the exponents associated with both static
and time-dependent quantities vary continuously with .Comment: Some parts rewritten, results unchanged. To appear in Europhys. Let
A simple sandpile model of active-absorbing state transitions
We study a simple sandpile model of active-absorbing state transitions in
which a particle can hop out of a site only if the number of particles at that
site is above a certain threshold. We show that the active phase has product
measure whereas nontrivial correlations are found numerically in the absorbing
phase. It is argued that the system relaxes to the latter phase slower than
exponentially. The critical behavior of this model is found to be different
from that of the other known universality classes.Comment: Revised version. To appear in Phys. Rev.
Conservation laws for the voter model in complex networks
We consider the voter model dynamics in random networks with an arbitrary
distribution of the degree of the nodes. We find that for the usual node-update
dynamics the average magnetization is not conserved, while an average
magnetization weighted by the degree of the node is conserved. However, for a
link-update dynamics the average magnetization is still conserved. For the
particular case of a Barabasi-Albert scale-free network the voter model
dynamics leads to a partially ordered metastable state with a finite size
survival time. This characteristic time scales linearly with system size only
when the updating rule respects the conservation law of the average
magnetization. This scaling identifies a universal or generic property of the
voter model dynamics associated with the conservation law of the magnetization.Comment: 5 pages, 4 figures; for related material please visit
http://www.imedea.uib.e
Active Absorbing State Phase Transition Beyond Directed Percolation : A Class of Exactly Solvable Models
We introduce and solve a model of hardcore particles on a one dimensional
periodic lattice which undergoes an active-absorbing state phase transition at
finite density. In this model an occupied site is defined to be active if its
left neighbour is occupied and the right neighbour is vacant. Particles from
such active sites hop stochastically to their right. We show that, both the
density of active sites and the survival probability vanish as the particle
density is decreased below half. The critical exponents and spatial
correlations of the model are calculated exactly using the matrix product
ansatz. Exact analytical study of several variations of the model reveals that
these non-equilibrium phase transitions belong to a new universality class
different from the generic active-absorbing-state phase transition, namely
directed percolation.Comment: 5 pages, revtex4, 1 eps fi
Dynamic range of hypercubic stochastic excitable media
We study the response properties of d-dimensional hypercubic excitable
networks to a stochastic stimulus. Each site, modelled either by a three-state
stochastic susceptible-infected-recovered-susceptible system or by the
probabilistic Greenberg-Hastings cellular automaton, is continuously and
independently stimulated by an external Poisson rate h. The response function
(mean density of active sites rho versus h) is obtained via simulations (for
d=1, 2, 3, 4) and mean field approximations at the single-site and pair levels
(for all d). In any dimension, the dynamic range of the response function is
maximized precisely at the nonequilibrium phase transition to self-sustained
activity, in agreement with a reasoning recently proposed. Moreover, the
maximum dynamic range attained at a given dimension d is a decreasing function
of d.Comment: 7 pages, 4 figure
Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers
We study the microscopic structure and the stationary propagation velocity of
(1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model,
which are driven far from equilibrium by an applied force, such as a magnetic
field or a difference in (electro)chemical potential. We use an analytic
nonlinear-response approximation [P.A. Rikvold and M. Kolesik, J. Stat. Phys.
100, 377 (2000)] together with kinetic Monte Carlo simulations. Here we
consider interfaces that move under Arrhenius dynamics, which include a
microscopic energy barrier between the allowed Ising/lattice-gas states. Two
different dynamics are studied: the standard one-step dynamic (OSD) [H.C. Kang
and W. Weinberg, J. Chem. Phys. 90, 2824 (1992)] and the two-step
transition-dynamics approximation (TDA) [T. Ala-Nissila, J. Kjoll, and S.C.
Ying, Phys. Rev. B 46, 846 (1992)]. In the OSD the effects of the applied force
and the interaction energies in the model factorize in the transition rates (a
soft dynamic), while in the TDA such factorization is not possible (a hard
dynamic). In full agreement with previous general theoretical results we find
that the local interface width under the TDA increases dramatically with the
applied force. In contrast, the interface structure with the OSD is only weakly
influenced by the force, in qualitative agreement with the theoretical
expectations. Results are also obtained for the force-dependence and anisotropy
of the interface velocity, which also show differences in good agreement with
the theoretical expectations for the differences between soft and hard
dynamics. Our results confirm that different stochastic interface dynamics that
all obey detailed balance and the same conservation laws nevertheless can lead
to radically different interface responses to an applied force.Comment: 18 pages RevTex. Minor revisions. Phys. Rev. B, in pres
spl(2,1) dynamical supersymmetry and suppression of ferromagnetism in flat band double-exchange models
The low energy spectrum of the ferromagnetic Kondo lattice model on a N-site
complete graph extended with on-site repulsion is obtained from the underlying
spl(2,1) algebra properties in the strong coupling limit. The ferromagnetic
ground state is realized for 1 and N+1 electrons only. We identify the large
density of states to be responsible for the suppression of the ferromagnetic
state and argue that a similar situation is encountered in the Kagome,
pyrochlore, and other lattices with flat bands in their one-particle density of
states.Comment: 7 pages, 1 figur
- …