Percolation model of fire dynamic

A percolation model for fire dynamic is proposed, with two parameters, related to the combustibility and the ignitability of the medium. The expression of the critical line and of the rate of spread are given in function of that of bond percolation (BP). Finally, the relevance of the model is discussed in the light of results of experiments taken from literature: this simple model catches both the dynamical and static qualitative properties of fire propagation.     

Criticality of Parasitic Disease Transmission in a Diffusive Population

Through using the methods of finite-size effect and short time dynamic scaling, we study the critical behavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment. Through comprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. We determine the critical population density, above which the system reaches an epidemic spreading stationary state. We also perform a scaling analysis to determine the order parameter and critical relaxation exponents. The results show that the model does not belong to the usual directed percolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields.     

逾渗分立时间量子行走的传输及纠缠特性

在一维分立时间量子行走中,通过静态和动态两种方式随机地断开连接边引入无序效应,研究了静态逾渗和动态逾渗对量子行走传输特性以及位置自由度和硬币自由之间纠缠的影响.随着演化时间的增加,静态逾渗会使得量子行走从弹道传输转变为安德森局域化,而动态逾渗则会使之转变为经典扩散.理想情况下,量子纠缠在较短的时间内就达到一个常数值E_0.静态逾渗量子行走的纠缠减小,并随着时间做无规振荡,而动态逾渗量子行走的纠缠则会随着时间光滑地增加,并在某一时间超过理想情况下的常数值,表现出动态逾渗增强量子纠缠的特性.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

Non-linear behaviour of electron acoustic wave dynamics in a magnetized plasma with non-thermal hot electrons

Non-linear dynamical behaviour of electron acoustic waves (EAWs) is studied in a magnetized non-thermal plasma (containing inertial cold electrons, inertialess hot electrons following non-thermal distribution function, and static ions) via a fluid dynamical approach. A linear dispersion relation is derived and the propagation of two possible modes and their evolution are studied through the different plasma configuration parameters, such as non-thermality and external magnetic field strength. In a non-linear perturbation regime, a reductive perturbation technique is employed to derive the non-linear evolution equation and the analysis is executed for travelling plane waves in terms of a non-linear dynamical system to enlighten the numerous aspects of the phase space dynamics. The results of numerical simulation predict the existence of a wide class of non-linear structures, namely solitonic, periodic, quasiperiodic, and chaotic depending upon different controlling plasma parameters. Also, Poincaré return map analysis confirms these non-linear structures of the EAWs.     

Scaling behaviour in the fracture of fibrous materials

We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation. Received 24 June 1999     

Random walk on topologically biased anisotropic percolation clusters and transport properties

Unbiased random walks are performed on topologically biased anisotropic percolation clusters (APC). Topologically biased APCs are generated using suitable anisotropic percolation models. New walk dimensions are found to characterize the anisotropic behaviour of the unbiased random walk on the biased topology. Critical properties of electro and magneto conductivities are characterized estimating respective dynamical critical exponents. A dynamical scaling theory relating dynamical and static critical exponents has been developed. The dynamical critical exponents satisfy the scaling relations within error bar.     

Dynamic percolation in water in oil microemulsions revisited

Microemulsions (dispersions of water droplets, typical radius about 10 nm, in oil) show a particular percolation pattern, a so-called dynamical percolation. Predictions of scaling theory and Monte Carlo simulations were compared with experimental static and frequency dependent conductivity data. The latter gives evidence of two different time scales of charge transport.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Phase and vortex dynamics in Josephson junction arrays with percolative disorder

The AC conductance G of site-diluted Josephson junction arrays close to the percolation threshold was studied over a broad frequency range. As a function of frequency, G exhibits a crossover from a low-frequency Euclidean to a high-frequency fractal regime. At low-frequency the response is dominated by vortices and its temperature dependence is well-described by dynamical extensions of the Kosterlitz–Thouless theory for two-dimensional systems.     

Asymmetrically coupled directed percolation systems

We introduce a dynamical model of coupled directed percolation systems with two particle species. The two species A and B are coupled asymmetrically in that A particles branch B particles, whereas B particles prey on A particles. This model may describe epidemic spreading controlled by reactive immunization agents. We study nonequilibrium phase transitions with attention focused on the multicritical point where both species undergo the absorbing phase transition simultaneously. In one dimension, we find that the inhibitory coupling from B to A is irrelevant and the model belongs to the unidirectionally coupled directed percolation class. On the contrary, a mean-field analysis predicts that the inhibitory coupling is relevant and a new universality appears with a variable dynamic exponent. Numerical simulations on small-world networks confirm our predictions.     

The strange man in random networks of automata

We have performed computer simulations of Kauffman’s automata on several graphs, such as the regular square lattice and invasion percolation clusters, in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent) and propagation speeds of the damage when one adds a damaging agent, nicknamed “strange man”. Despite the increase in the damaging efficiency, we have not observed any appreciable change of the transition threshold to chaos neither for the short-range nor for the small-world case on the square lattices when the strange man is added, in comparison to when small initial damages are inserted in the system. Particularly, we have checked the damage spreading when some connections are removed on the square lattice and when one considers special invasion percolation clusters (high boundary-saturation clusters). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution on the square lattice and to the degree of saturation on invasion percolation clusters.     

Critical behavior of a one-dimensional contact process with time-uncorrelated disorder

In this work, the critical behavior of the one-dimensional contact process with time-uncorrelated disorder is investigated. We develop simulations on finite chains and explore the finite size scaling hypothesis to obtain estimates for the relevant parameters associated with static and dynamical critical quantities. We use an auto-adaptative technique that has been recently shown to provide reliable results for the standard contact process transition. We compare the main results with those derived from the usual short-time dynamics scaling. We found that, contrary to the behavior of the contact-process with quenched disorder which displays an infinite randomness critical point with activated scaling, the contact process with time-uncorrelated disorder belongs to the usual universality class of directed percolation.     

Multiplicity of Phase Transitions and Mean-Field Criticality on Highly Non-Amenable Graphs

We consider independent percolation, Ising and Potts models, and the contact process, on infinite, locally finite, connected graphs. It is shown that on graphs with edge-isoperimetric Cheeger constant sufficiently large, in terms of the degrees of the vertices of the graph, each of the models exhibits more than one critical point, separating qualitatively distinct regimes. For unimodular transitive graphs of this type, the critical behaviour in independent percolation, the Ising model and the contact process are shown to be mean-field type. For Potts models on unimodular transitive graphs, we prove the monotonicity in the temperature of the property that the free Gibbs measure is extremal in the set of automorphism invariant Gibbs measures, and show that the corresponding critical temperature is positive if and only if the threshold for uniqueness of the infinite cluster in independent bond percolation on the graph is less than 1. We establish conditions which imply the finite-island property for independent percolation at large densities, and use those to show that for a large class of graphs the q-state Potts model has a low temperature regime in which the free Gibbs measure decomposes as the uniform mixture of the q ordered phases. In the case of non-amenable transitive planar graphs with one end, we show that the q-state Potts model has a critical point separating a regime of high temperatures in which the free Gibbs measure is extremal in the set of automorphism-invariant Gibbs measures from a regime of low temperatures in which the free Gibbs measure decomposes as the uniform mixture of the q ordered phases. Received: 27 March 2000 / Accepted: 7 December 2000     

On the continuity of the critical value for long range percolation in the exponential case

We show that for a long range percolation model with exponentially decaying connections, the limit of critical values of any sequence of long range percolation models approaching the original model from below is the critical value for the original long range percolation model. As an interesting corollary, this implies that if a long range percolation model with exponential connections is supercritical, then it still percolates even if all long bonds are removed. We also show that the percolation probability is continuous (in a certain sense) in the supercritical regime for long range percolation models with exponential connections.Research supported by a grant from the Swedish National Science Foundation.     

Self-consistent current relaxation theory for the electron localization problem

The self-consistent current relaxation theory for the Anderson transition is generalized to include quantum interference effects. The influence of long-ranged potential fluctuations as opposed to short-ranged ones is discussed and for dimensionalityd>2 a crossover for the dynamical conductivity from a regime with Wegner scaling to one with the scaling laws for classical percolation is found. Ford=2 an abrupt transition from strong to extremely weak localization is obtained.     

A phenomenology of boundary lubrication: the lumped junction model

We propose a phenomenological model of boundary lubricated junctions consisting of a few layers of small molecules which describes the rheological properties of these sytems both in the static, frozen, and sliding, molten, states as well as the dynamical transition between them. Two dynamical regimes can be distinguished, according to the level of internal damping of the junction, which depends on its thickness and on the normal load. In the overdamped regime, under driving at constant velocity v through an external spring, the motion evolves continuously from “atomic stick-slip” to modulated sliding. Underdamped systems exhibit, under given external stress, a range of dynamic bistability where the sheared static state coexists with a steadily sliding one. The frictional dynamics under shear driving is analyzed in detail, it provides a complete account of the qualitative dynamical scenarios observed by Israelashvili et al., and yields semiquantitative agreement with experimental data. A few complementary experimental tests of the model are suggested. Received: 18 December 1997 / Received in final form and accepted: 26 March 1998     

Propagation and ghosts in the classical kagome antiferromagnet

We investigate the classical spin dynamics of the kagome antiferromagnet by combining Monte Carlo and spin dynamics simulations. We show that this model has two distinct low temperature dynamical regimes, both sustaining propagative modes. The expected gauge invariance type of the low energy, low temperature, out-of-plane excitations is also evidenced in the nonlinear regime. A detailed analysis of the excitations allows us to identify ghosts in the dynamical structure factor, i.e., propagating excitations with a strongly reduced spectral weight. We argue that these dynamical extinction rules are of geometrical origin.     

Transitional Channel Flow: A Minimal Stochastic Model

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.