Extreme Thouless effect in a minimal model of dynamic social networks.

In common descriptions of phase transitions, first-order transitions are characterized by discontinuous jumps in the order parameter and normal fluctuations, while second-order transitions are associated with no jumps and anomalous fluctuations. Outside this paradigm are systems exhibiting "mixed-order" transitions displaying a mixture of these characteristics. When the jump is maximal and the fluctuations range over the entire range of allowed values, the behavior has been coined an "extreme Thouless effect.

Epidemic spreading on preferred degree adaptive networks.

We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree κ. Using very simple rules for forming such preferred degree networks, we find some unusual statistical properties not found in familiar Erdös-Rényi or scale free networks. By letting κ depend on the fraction of infected individuals, we model the behavioral changes in response to how the extent of the epidemic is perceived.

Opinion formation on adaptive networks with intensive average degree.

We study the evolution of binary opinions on a simple adaptive network of N nodes. At each time step, a randomly selected node updates its state ("opinion") according to the majority opinion of the nodes that it is linked to; subsequently, all links are reassigned with probability p̃ (q̃) if they connect nodes with equal (opposite) opinions. In contrast to earlier work, we ensure that the average connectivity ("degree") of each node is independent of the system size ("intensive"), by choosing p̃ and q̃ to be of O(1/N).

Competition between multiple totally asymmetric simple exclusion processes for a finite pool of resources.

Using Monte Carlo simulations and a domain-wall theory, we discuss the effect of coupling several totally asymmetric simple exclusion processes (TASEPs) to a finite reservoir of particles. This simple model mimics directed biological transport processes in the presence of finite resources such as protein synthesis limited by a finite pool of ribosomes. If all TASEPs have equal length, we find behavior which is analogous to a single TASEP coupled to a finite pool.

Opinion dynamics on an adaptive random network.

We revisit the classical model for voter dynamics in a two-party system with two basic modifications. In contrast to the original voter model studied in regular lattices, we implement the opinion formation process in a random network of agents in which interactions are no longer restricted by geographical distance. In addition, we incorporate the rapidly changing nature of the interpersonal relations in the model.

Inhomogeneous exclusion processes with extended objects: the effect of defect locations.

We study the effects of local inhomogeneities, i.e., slow sites of hopping rate q<1, in a totally asymmetric simple exclusion process for particles of size l>or=1 (in units of the lattice spacing).

Power spectra of the total occupancy in the totally asymmetric simple exclusion process.

As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of nonequilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensional open lattice and its power spectrum. Using both Monte Carlo simulations and analytic methods, we explore its behavior in different characteristic regimes.

Coarsening of "clouds" and dynamic scaling in a far-from-equilibrium model system.

A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams (''clouds''), as the system approaches a nonequilibrium steady state from a disordered initial state. We monitor the dynamic structure factor S(k{x},k{y};t) and find that the k{x}=0 component exhibits dynamic scaling, of the form S(0,k{y};t)=t;{beta}S[over](k{y}t;{alpha}) .

Strongly anisotropic roughness in surfaces driven by an oblique particle flux.

Using field theoretic renormalization, an MBE-type growth process with an obliquely incident influx of atoms is examined. The projection of the beam on the substrate plane selects a "parallel" direction, with rotational invariance restricted to the transverse directions. Depending on the behavior of an effective anisotropic surface tension, a line of second-order transitions is identified, as well as a line of potentially first-order transitions, joined by a multicritical point.

Steady states of a nonequilibrium lattice gas.

We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force.

Exact dynamics of a reaction-diffusion model with spatially alternating rates.

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative "temperatures" have a perfectly natural interpretation.

Anomalous nucleation far from equilibrium.

We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a 2xL lattice. To resolve a stark discrepancy between earlier simulation data and an analytic conjecture, we argue that the presence of a single macroscopic cluster is an intermediate stage of a complex nucleation process: in smaller systems, this cluster is destabilized while larger systems form multiple clusters. Both limits lead to exponential cluster size distributions, controlled by very different length scales.

Driven diffusive systems: how steady states depend on dynamics.

In contrast to equilibrium systems, nonequilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber, and heat bath rates, we illustrate this expectation for an Ising lattice gas, driven far from equilibrium by an "electric" field. While heat bath and Glauber rates generate essentially identical data for structure factors and two-point correlations, Metropolis rates give noticeably weaker correlations, as if the "effective" temperature were higher in the latter case.

Stationary correlations for a far-from-equilibrium spin chain.

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature T(e) (T(o)). Detailed balance is violated so that the spin chain settles into a nonequilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state.

Microscopic kinetics and time-dependent structure factors.

The time evolution of structure factors (SF) in the disordering process of an initially phase-separated lattice depends crucially on the microscopic disordering mechanism, such as Kawasaki dynamics (KD) or vacancy-mediated disordering (VMD). Monte Carlo simulations show unexpected "dips" in the SFs. A phenomenological model is introduced to explain the dips in the odd SFs, and an analytical solution of KD is derived, in excellent agreement with simulations.

Field-induced vacancy localization in a driven lattice gas: scaling of steady states.

With the help of Monte Carlo simulations and a mean-field theory, we investigate the ordered steady-state structures resulting from the motion of a single vacancy on a periodic lattice which is filled with two species of oppositely "charged" particles. An external field biases particle-vacancy exchanges according to the particle's charge, subject to an excluded volume constraint. The steady state exhibits charge segregation, and the vacancy is localized at one of the two characteristic interfaces.

Viability of competing field theories for the driven lattice gas.

It has recently been suggested that the driven lattice gas should be described by an alternate field theory in the limit of infinite drive. We review the original and the alternate field theory, invoking several well-documented key features of the microscopics. Since the alternate field theory fails to reproduce these characteristics, we argue that it cannot serve as a viable description of the driven lattice gas.