J. Marro

Dynamical scaling of structure function in quenched binary alloys

Abstract We study the structure functions S(k, t) obtained from computer simulations of the time evolution of a segregating binary alloy following quenching into the miscibility gap. They are shown to have a simple scaling behavior, S(k, t) ∼ K−3(t) F(k/K(t)). The shape of the function F(x) depends somewhat on the part of the coexistence region into which the quench is made. Comparison with some recent experiments on quenched alloys is quite satisfactory. The time evolution of K−3(t) appears to be linear for late times, consistent with the Lifshitz-Slyozov theory.

Entropic Origin of Disassortativity in Complex Networks

Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated? To answer this long-standing question, we define the ensemble of correlated networks and obtain the associated Shannon entropy. Maximum entropy can correspond to either assortative (correlated) or disassortative (anticorrelated) configurations, but in the case of highly heterogeneous, scale-free networks a certain disassortativity is predicted--offering a parsimonious explanation for the question above. Our approach provides a neutral model from which, in the absence of further knowledge regarding network evolution, one can obtain the expected value of correlations. When empirical observations deviate from the neutral predictions--as happens for social networks--one can then infer that there are specific correlating mechanisms at work.

Influence of topology on the performance of a neural network

Abstract We studied the computational properties of an attractor neural network (ANN) with different network topologies. Though fully connected neural networks exhibit, in general, a good performance, they are biologically unrealistic, as it is unlikely that natural evolution leads to such a large connectivity. We demonstrate that, at finite temperature, the capacity to store and retrieve binary patterns is higher for ANN with scale-free (SF) topology than for highly random-diluted Hopfield networks with the same number of synapses. We also show that, at zero temperature, the relative performance of the SF network increases with increasing values of the distribution power-law exponent. Some consequences and possible applications of our findings are discussed.

THE INTERPRETATION OF STRUCTURE FUNCTIONS IN QUENCHED BINARY ALLOYS

Abstract We study the segregation process in quenched binary alloys by analyzing and comparing the time evolution of the structure function and of the grain distribution obtained from computer simulations on a model system. We find good agreement between cluster sizes and densities determined directly on the computer sample and ones obtained by the Guinier method from the structure function. We then describe a graphical method for determining the scaling behaviour of the structure function S(k, t) which gives good statistics because the whole curve S(k, t) vs k is used. This yields very good agreement between the scaling function (scaled with the Guinier radius) obtained from the computer simulations and from a variety of real experiments. This function shows a universal behaviour independent of the alloy composition, the temperature and even the substance investigated. Our results are also not consistent with the more recent theoretical work (Binder et al., Furukawa et al.) which give alternate derivations and extensions of the Guinier formulas.

Monte Carlo studies of percolation phenomena for a simple cubic lattice

The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates forpc (0.3115±0.0005),β (0.41±0.01),γ (1.6±0.1), andν(0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average “surface area” for clusters of sizek is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizesk is found to have an exponential tail for large values ofk forP pc there is too much scatter in the data to draw firm conclusions about the size distribution.

Competition Between Synaptic Depression and Facilitation in Attractor Neural Networks

We study the effect of competition between short-term synaptic depression and facilitation on the dynamic properties of attractor neural networks, using Monte Carlo simulation and a mean-field analysis. Depending on the balance of depression, facilitation, and the underlying noise, the network displays different behaviors, including associative memory and switching of activity between different attractors. We conclude that synaptic facilitation enhances the attractor instability in a way that (1) intensifies the system adaptability to external stimuli, which is in agreement with experiments, and (2) favors the retrieval of information with less error during short time intervals.

Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59Tc, whereTc is the critical temperature, and the concentration of minority atoms wasρ=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc1≈(1-ρ)3w(t),c1≈ (1−ρ)4Qlw(t)l(2≤l≤10); wherecl is the concentration of clusters of sizel;Q2,...,Q10 are known constants, the “cluster partition functions”;t is the time; andw(t)=0.015(1+7.17t−1/3). The distribution of large clusters (l≥20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,cl,(t)=−(d/dl)ψ[lnt+pϕ(l/t)], whereϕ is a function given by those authors andψ is defined byψ(x)=Coe−x-C1e−4x/3-C2e−5x/3;C0,C1,C2 are constants determined by considering how the total number of particles in large clusters changes with time.

Nonequilibrium second-order phase transitions in stochastic lattice systems: A finite-size scaling analysis in two dimensions

Two-dimensional lattice-gas models with attractive interactions and particleconserving happing dynamics under the influence of a very large external electric field along a principal axis are studied in the case of a critical density. A finite-size scaling analysis allows the evaluation of critical indexes for the infinite system asβ=0.230±0.003,v=0.55±0.2, and α 0. We also describe some qualitative features of the system evolution and the existence of certain anisotropic order even well above the critical temperature in the case of finite lattices.

Effects of Fast Presynaptic Noise in Attractor Neural Networks

We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short timescale compared to that for the neuron dynamics and it produces short-time synaptic depression. This is inspired in recent neurobiological findings that show that synaptic strength may either increase or decrease on a short timescale depending on presynaptic activity. We thus describe a mechanism by which fast presynaptic noise enhances the neural network sensitivity to an external stimulus. The reason is that, in general, presynaptic noise induces nonequilibrium behavior and, consequently, the space of fixed points is qualitatively modified in such a way that the system can easily escape from the attractor. As a result, the model shows, in addition to pattern recognition, class identification and categorization, which may be relevant to the understanding of some of the brain complex tasks.

Nonequilibrium phase transition in stochastic lattice gases: Simulation of a three-dimensional system

We report results of computer simulations of a three-dimensional lattice gas of interacting particles subject to a uniform external fieldE. The dynamics of the system is given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction ofE. As for the two-dimensional system we find that here too there exists a critical temperature,Tc(E) such that forT < Tc(E) the systems orders in a very anisotropic phase with striplike typical configurations parallel to the field.Tc(E) increases withE but substantially less strongly than in two dimensions. There is a break in the slope of the saturation current atTc(E). Our data are consistent with the critical exponentβ being mean field.