Nonconservative earthquake model of self-organized criticality on a random graph

We numerically investigate the Olami-Feder-Christensen model on a quenched random graph. Contrary to the case of annealed random neighbors, we find that the quenched model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents. In addition, a power law relation between the size and the duration of an avalanche exists. We propose that this may represent the correct mean-field limit of the model rather than the annealed random neighbor version.     

Diffusion modeling of the Rayleigh piston

A Markov jump process in which a massive labeled particle undergoes random elastic collisions with a thermal bath is investigated. It is found that the behavior of the labeled particle can be divided into three distinct regimes depending on whether its velocity is (1) much less than, (2) on the order of, or (3) much greater than the mean speed of a bath particle. In each regime the jump process can be approximated by a particular continuous-path diffusion process. The first case corresponds to the Ornstein-Uhlenbeck process, while each of the latter can be modeled by a deterministic process with a nonlinear Langevin equation. In addition, in cases (2) and (3), the scaled deviation from the mean velocity can be modeled by a nonstationary diffusion. By scaling the time and letting the mass of the labeled particle become large, a continuous-path diffusion is constructed which approximates the jump process in each regime. Analytic solutions for the transition probability density are provided in each case, and numerical comparisons are made between the mean and variance of the diffusions and the original jump process.     

Azimuthal pion fluctuation in ultra relativistic nuclear collisions and centrality dependence—a study with chaos based complex network analysis

Various works on multiplicity fluctuation have investigated the dynamics of particle production process and eventually have tried to reveal a signature of phase transition in ultra-relativistic nuclear collisions. Analysis of fluctuations of spatial patterns has been conducted in terms of conventional approach. However, analysis with fractal dynamics on the scaling behavior of the void has not been explored yet. In this work we have attempted to analyze pion fluctuation in terms of the scaling behavior of the void probability distribution in azimuthal space in ultra-relativistic nuclear collisions in the light of complex networks. A radically different and rigorous method viz. Visibility Graph was applied on the data of ³²S-Ag/Br interaction at an incident energy of 200 GeV per nucleon. The analysis reveals strong scaling behavior of void probability distributions in azimuthal space and a strong centrality dependence.     

Universal order statistics of random walks

We study analytically the order statistics of a time series generated by the positions of a symmetric random walk of n steps with step lengths of finite variance σ(2). We show that the statistics of the gap d(k,n) = M(k,n)-M(k+1,n) between the kth and the (k+1)th maximum of the time series becomes stationary, i.e., independent of n as n → ∞ and exhibits a rich, universal behavior. The mean stationary gap exhibits a universal algebraic decay for large k, ~d(k,∞)-/σ 1/sqrt[2πk], independent of the details of the jump distribution. Moreover, the probability density (pdf) of the stationary gap exhibits scaling, Pr(d(k,∞) = δ) ~/= (sqrt[k]/σ)P(δsqrt[k]/σ), in the regime δ~ (d(k,∞)). The scaling function P(x) is universal and has an unexpected power law tail, P(x) ~ x(-4) for large x. For δ> (d(k,∞)) the scaling breaks down and the pdf gets cut off in a nonuniversal way. Consequently, the moments of the gap exhibit an unusual multiscaling behavior.     

The Arctic Curve of the Domain-Wall Six-Vertex Model

The problem of the form of the ‘arctic’ curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed. It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve. To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder. We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value. In explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle-point equations. The arctic curve is obtained in parametric form and appears to be a non-algebraic curve in general; it turns into an algebraic one in the so-called root-of-unity cases. The arctic curve is also discussed in application to the limit shape of q-enumerated (with 0<q ≤4) large alternating sign matrices. In particular, as q→0 the limit shape tends to a nontrivial limiting curve, given by a relatively simple equation.     

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative: the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our model with the model introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 (2002) 228301], it is proved that they are not in the same universality class.     

Adsorption of a flexible self-avoiding polymer chain: Exact results on fractal lattices

The large-scale behavior of surface-interacting self-avoiding polymer chains placed on finitely ramified fractal lattices is studied using exact recursion relations. It is shown how to obtain surface susceptibility critical indices and how to modify a scaling relation for these indices in the case of fractal lattices. We present the exact results for critical exponents at the point of adsorption transition for polymer chains situated on a class of Sierpinski gasket-type fractals. We provide numerical evidence for a critical behavior of the type found recently in the case of bulk self-avoiding random walks at the fractal to Euclidean crossover.     

Fractals and dynamical chaos in a random 2D Lorentz gas with sinks

Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the asymptotic decay of the survival probability is exponential and characterized by an escape rate γ, which can be related to the average positive Lyapunov exponent and to the dimension of the fractal repeller of the system. For infinite systems, the survival probability obeys a stretched exponential law of the form P(c,t)∼exp(−Ct^1/2). The transition between the two regimes is studied and we show that, for a given trap density, the non-integer dimension of the fractal repeller increases with the system size to finally reach the integer dimension of the phase space. Nevertheless, the repeller remains fractal. We determine the special scaling properties of this fractal.     

Space use by foragers consuming renewable resources

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: (i) the high-order moments, ?x(t) ^q ? for q > 2 and the probability density of the process exhibit multiscaling; (ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; (iii) positive order moments satisfying standard scaling does not imply an exact scaling property of the probability density.     

Annealed Scaling for a Charged Polymer

This paper studies an undirected polymer chain living on the one-dimensional integer lattice and carrying i.i.d. random charges. Each self-intersection of the polymer chain contributes to the interaction Hamiltonian an energy that is equal to the product of the charges of the two monomers that meet. The joint probability distribution for the polymer chain and the charges is given by the Gibbs distribution associated with the interaction Hamiltonian. The focus is on the annealed free energy per monomer in the limit as the length of the polymer chain tends to infinity. We derive a spectral representation for the free energy and use this to prove that there is a critical curve in the parameter plane of charge bias versus inverse temperature separating a ballistic phase from a subballistic phase. We show that the phase transition is first order. We prove large deviation principles for the laws of the empirical speed and the empirical charge, and derive a spectral representation for the associated rate functions. Interestingly, in both phases both rate functions exhibit flat pieces, which correspond to an inhomogeneous strategy for the polymer to realise a large deviation. The large deviation principles in turn lead to laws of large numbers and central limit theorems. We identify the scaling behaviour of the critical curve for small and for large charge bias. In addition, we identify the scaling behaviour of the free energy for small charge bias and small inverse temperature. Both are linked to an associated Sturm-Liouville eigenvalue problem. A key tool in our analysis is the Ray-Knight formula for the local times of the one-dimensional simple random walk. This formula is exploited to derive a closed form expression for the generating function of the annealed partition function, and for several related quantities. This expression in turn serves as the starting point for the derivation of the spectral representation for the free energy, and for the scaling theorems. What happens for the quenched free energy per monomer remains open. We state two modest results and raise a few questions.     

Scaling of waves in the bak-tang-wiesenfeld sandpile model

We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>/=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk and boundary waves by means of their correspondence to spanning trees, and by extensive numerical simulations. While the scaling behavior of avalanches is complex and usually not governed by simple scaling laws, we show that the probability distributions for waves display clear power-law asymptotic behavior in perfect agreement with the analytical predictions. Critical exponents are obtained for the distributions of radius, area, and duration of bulk and boundary waves. Relations between them and fractal dimensions of waves are derived. We confirm that the upper critical dimension D(u) of the model is 4, and calculate logarithmic corrections to the scaling behavior of waves in D=4. In addition, we present analytical estimates for bulk avalanches in dimensions D>/=4 and simulation data for avalanches in D相似文献   

Mean first passage time for a class of non-Markovian processes

We determine the probability distribution of the first passage time for a class of non-Markovian processes. This class contains, amongst others, the well-known continuous time random walk (CTRW), which is able to account for many properties of anomalous diffusion processes. In particular, we obtain the mean first passage time for CTRW processes with truncated power-law transition time distribution. Our treatment is based on the fact that the solutions of the non-Markovian master equation can be obtained via an integral transform from a Markovian Langevin process.     

Delocalization transition of a rough adsorption-reaction interface

We introduce a kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-affine interface with Kardar-Parisi-Zhang-like scaling behavior undergoes a delocalization transition with critical exponents that fall into a different universality class. As the critical point is approached, the interface becomes a multivalued, multiply connected self-similar fractal set. The scaling behavior and critical exponents of the relevant correlation functions are determined from Monte Carlo simulations and scaling arguments.     

Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure function under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is z=1 rather than the KPZ exponent z=3/2 which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case.     

Fractal behavior in trapping and reaction: A random walk study

We investigate the trapping of a random walker in fractal structures (Sierpinski gaskets) with randomly distributed traps. The survival probability is determined from the number of distinct sites visited in the trap-free fractals. We show that the short-time behavior and the long-time tails of the survival probability are governed by the spectral dimensiond. We interpolate between these two limits by introducing a scaling law. An extension of the theory, which includes a continuous-time random walk on fractals, is discussed as well as the case of direct trapping. The latter case is shown to be governed by the fractal dimensiond.     

Multilayer Cooperative Sequential Adsorption

Cooperative sequential adsorption is here extended to multilayer coverages. We discuss two different growth rules with cooperativity either restricted to only the first layer of coverage or applied in all layers. The unrestricted variant is considered in the case where lateral growth dominates over the nucleation of terraces. The limit of completely suppressed nucleation corresponds to a morphological transition to a flat interface from one governed by the Kardar–Parisi–Zhang equation. With the restricted growth rule we find interesting behavior resulting from a competition between lateral growth at the first layer and growth on the top of nucleated islands. There is an intermediate regime between random deposition at the submonolayer coverage and asymptotic random deposition behavior. In this regime the kinetic roughening can be studied by applying sequential adsorption rate equations for cluster lengths in the first layer, with an additional geometric argument.     

模拟退火算法在化学自由能模型中的应用

对化学自由能模型进行系统性的研究，着重分析化学反应动态平衡条件下粒子组分的求解方案，提出应用模拟退火算法寻找自由能密度函数极小值点的求解方案.该方案同时解决了两个难题：1）在一级相变区化学势平衡方程组可能遇到多个解而无法甄别其物理意义.通过模拟退火算法定位到自由能密度函数曲面的最低点，因而可从多个解中甄别出稳定的热力学平衡态.2）模拟退火算法用随机的"热涨落"消除初值敏感性，因而可采用同一套初值计算不同的温度密度点，为实现宽区域上大量温度密度点的连续快速计算奠定基础.作为该平衡态求解方案的应用，计算氦流体在"等离子相变"区的物态方程，揭示了丰富的"等离子相变"现象，并与第一性原理计算揭示的氢流体"液液相变"现象进行类比.     

Lyapunov exponent, generalized entropies and fractal dimensions of hot drops

We calculate the maximal Lyapunov exponent, the generalized entropies, the asymptotic distance between nearby trajectories and the fractal dimensions for a finite two-dimensional system at different initial excitation energies. We show that these quantities have a maximum at about the same excitation energy. The presence of this maximum indicates the transition from a chaotic regime to a more regular one. In the chaotic regime the system is composed mainly of a liquid drop while the regular one corresponds to almost freely flowing particles and small clusters. At the transitional excitation energy the fractal dimensions are similar to those estimated from the Fisher model for a liquid-gas phase transition at the critical point. Received: 16 March 2001 / Accepted: 12 July 2001     

Replacing energy by von Neumann entropy in quantum phase transitions

We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.     

Universality class of nonequilibrium phase transitions with infinitely many absorbing states

We consider systems whose steady states exhibit a nonequilibrium phase transition from an active state to one-among an infinite number-absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks, and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper-critical dimension below which anomalous fluctuation driven scaling appears is d(c)=6, in contrast to a widespread belief. We provide the exponents governing the critical behavior close to or at the transition point to first order in an epsilon =6-d expansion.