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

Divergent Time Scale in Axelrod Model Dynamics

We study the evolution of the Axelrod model for cultural diversity. We consider a simple version of the model in which each individual is characterized by two features, each of which can assume q possibilities. Within a mean-field description, we find a transition at a critical value q_c between an active state of diversity and a frozen state. For q just below q_c, the density of active links between interaction partners is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma

Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions

We investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language $X$ or language $Y$, while the second model incorporates a third state XY, representing individuals that use both languages (bilinguals). We analyze the models on complex networks and two-dimensional square lattices by analytical and numerical methods, and show that they exhibit a transition from one-language dominance to language coexistence. We find that the coexistence of languages is more difficult to maintain in the Bilinguals model, where the presence of bilinguals in use facilitates the ultimate dominance of one of the two languages. A stability analysis reveals that the coexistence is more unlikely to happen in poorly-connected than in fully connected networks, and that the dominance of only one language is enhanced as the connectivity decreases. This dominance effect is even stronger in a two-dimensional space, where domain coarsening tends to drive the system towards language consensus.Comment: 30 pages, 11 figure

Phase Separation in a Simple Model with Dynamical Asymmetry

We perform computer simulations of a Cahn-Hilliard model of phase separation which has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function which is order parameter dependent. Simulations of this model reveal morphological features similar to those observed in viscoelastic phase separation. In the early stages, the minority phase domains form a percolating structure which shrinks with time eventually leading to the formation of disconnected domains. The domains grow as L(t) ~ t^{1/3} in the very late stages. Although dynamical scaling is violated in the area shrinking regime, it is restored at late times. However, the form of the scaling function is found to depend on the extent of dynamical asymmetry.Comment: 16 pages in LaTeX format and 6 Postscript figure

Molecular Dynamics Simulation of Spinodal Decomposition in Three-Dimensional Binary Fluids

Using large-scale molecular dynamics simulations of a two-component Lennard-Jones model in three dimensions, we show that the late-time dynamics of spinodal decomposition in concentrated binary fluids reaches a viscous scaling regime with a growth exponent $n=1$, in agreement with experiments and a theoretical analysis for viscous growth.Comment: 4 pages, 3 figure

Molecular dynamics simulations of phase separation in the presence of surfactants

The dynamics of phase separation in two-dimensional binary mixtures diluted by surfactants is studied by means of molecular dynamics simulations. In contrast to pure binary systems, characterized by an algebraic time dependence of the average domain size, we find that systems containing surfactants exhibit nonalgebraic, slow dynamics. The average domain size eventually saturates at a value inversely proportional to the surfactant concentration. We also find that phase separation in systems with different surfactant concentrations follow a crossover scaling form. Finally, although these systems do not fully phase separate, we observe a dynamical scaling which is independent of the surfactant concentration. The results of these simulations are in general in agreement with previous Langevin simulations [Laradji, Guo, Grant, and Zuckermann, J. Phys. A 44, L629 (1991)] and a theory of Ostwald ripening [Yao and Laradji, Phys. Rev. E 47, 2695 (1993)]. © 1994 The American Physical Society

Analytical and numerical studies of multiplicative noises

We consider stochastic differential equations for a variable q with multiplicative white and nonwhite ("colored") noise appropriate for the description of nonequilibrium systems which experience fluctuations which are not "self-originating." We discuss a numerical algorithm for the simulation of these equations, as well as an alternative analytical treatment. In particular, we derive approximate Fokker-Planck equations for the probability density of the process by an analysis of an expansion in powers of the correlation time τ of the noise. We also discuss the stationary solution of these equations. We have applied our numerical and analytical methods to the "Stratonovich model" often used in the literature to study nonequilibrium systems. The numerical analysis corroborates the analytical predictions for the time-independent properties. We show that for large noise intensity D the stationary distribution develops a peak for increasing τ that becomes dominant in the large- τ limit. The correlation time of the process in the steady state has been analyzed numerically. We find a "slowing down" in the sense that the correlation time increases as a function of both D and τ .. This result shows the incorrectness of an earlier analysis of Stratonovich