Defect Formation in a Dynamic Transition

When a system that undergoes a continuous phase transition is swept through its critical point the initial symmetry is broken and domains are formed. Because of critical slowing down it is not possible to sweep adiabatically; the number of domains therefore depends on the rate of increase of the critical parameter. We give a summary of recent theoretical results for the number of defects produced as a function of how rapidly the transition point is passed. They are obtained from a simplified model, using a stochastic partial differential equation that is also solved numerically.     

Nonlinearity in cooperative systems-dynamical Bethe-Ising model

The dynamics of the short-range order as well as the long-range order in the nonlinear cooperative system is investigated specifically for a kinetic Ising model in the Bethe approximation. The phenomena of critical slowing down near the transition temperatureT _c and anomalous fluctuation belowT _c are directly related to the instability of the long-range order. The dynamics of the short-range order is essentially a fast mode and is noncritical. However, through the nonlinear coupling the short-range order is also influenced by the critical behavior of the long-range order.     

Equilibration and relaxation times at the chiral phase transition including reheating

We investigate the relaxational dynamics of the order parameter of chiral symmetry breaking, the sigma mean-field, with a heat bath consisting of quarks and antiquarks. A semiclassical stochastic Langevin equation of motion is obtained from the linear sigma model with constituent quarks. The equilibration of the system is studied for a first order phase transition and a critical point, where a different behavior is found. At the first order phase transition we observe the phase coexistence and at a critical point the phenomenon of critical slowing down with large relaxation times. We go beyond existing Langevin studies and include reheating of the heat bath by determining the energy dissipation during the relaxational process. The energy of the entire system is conserved. In a critical point scenario we again observe critical slowing down.     

Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions

We study the slowing down of a particle beam passing through the dusty plasma with power‐law κ‐distributions. Three plasma components, electrons, ions, and dust particles, can have a different κ‐parameter. By using Fokker‐Planck theory, the deceleration factor and slowing down time are derived and expressed by a hyper‐geometric κ‐function. Numerically, we study the slowing down property of an electron beam in the κ‐distributed dusty plasma. We show that the slowing down in the plasma depends strongly on the κ‐parameters of plasma components, and dust particles play a dominant role in the deceleration effects. We also show dependence of the slowing down on mass and charge of a dust particle in the kappa‐distributed plasma.     

Critical acceleration of lattice gauge simulations

We present a stochastic cluster algorithm that drastically reduces critical slowing down forZ ₂ lattice gauge theory in three dimensions. The dynamical exponentz is reduced fromz>2 (standard Metropolis algorithm) tozO.73. The Monte Carlo pseudodynamics acts on the gauge-invariant flux tubes that are known to be the relevant large-scale low-energy excitations. A comparison of our results with known results for the 3D Ising model and ⁴ model supports the conjecture of universality classes for stochastic cluster algorithms.     

Critical dynamics of the random spherical model

The spherical model with random infinite-range interactions which shows a spin-glass property is investigated rigorously by the kinetic model. The uniform magnetization as well as the order parameter shows a critical slowing down. The static nonlinear susceptibility is found to diverge at the freezing temperature.     

三维随机点阵Ising模型的集团Monte Carlo方法模拟

为了解决Monte Carlo模拟中的临界慢化问题,应用S-W方法,对一维随机点阵的模型进行了研究。找到该系统的相变点为β_c=0.075±0.001,与此同时,在相变点附近研究了SW方法的动力学性质,计算得动力学临界指数z=0.74±0.03,结果表明,SW方法对克服三维随机点阵Ising模型的临界慢化是非常有效的。 关键词：     

混合型非线性Fabry-Perot标准具的光学双稳特性

本文描述了一种用光电反馈改变Fabry-Perot(以下简称F-P)标准具腔长的办法来实现光学双稳工作的装置,我们从动态方程出发,得到了表述双稳行为的平衡态解析解;讨论并观察了光学双稳特性和线性调制特性;分析了系统的稳定性和瞬态过程中的“临界延迟”效应,同时给出与理论相一致的实验结果。 关键词：     

Self organization of interacting polya urns

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations - stochastic, quenched and deterministic - are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous stationary state, the presence of a non-stationary critical phase and non-trivial exponents even in mean field. We discuss simple interpretations in term of biological evolution and earthquake dynamics and we report on extensive numerical simulations in dimensions d=1,2 as well as in the random neighbors limit. Received: 18 February 1998 / Revised: 20 March 1998 / Accepted: 29 March 1998     

A study of the early warning signals of abrupt change in the Pacific decadal oscillation

In recent years, the phenomenon of a critical slowing down has demonstrated its major potential in discovering whether a complex dynamic system tends to abruptly change at critical points. This research on the Pacific decadal oscillation(PDO) index has been made on the basis of the critical slowing down principle in order to analyze its early warning signal of abrupt change. The chaotic characteristics of the PDO index sequence at different times are determined by using the largest Lyapunov exponent(LLE). The relationship between the regional sea surface temperature(SST) background field and the early warning signal of the PDO abrupt change is further studied through calculating the variance of the SST in the PDO region and the spatial distribution of the autocorrelation coefficient, thereby providing the experimental foundation for the extensive application of the method of the critical slowing down phenomenon. Our results show that the phenomenon of critical slowing down, such as the increase of the variance and autocorrelation coefficient, will continue for six years before the abrupt change of the PDO index. This phenomenon of the critical slowing down can be regarded as one of the early warning signals of an abrupt change. Through calculating the LLE of the PDO index during different times, it is also found that the strongest chaotic characteristics of the system occurred between 1971 and 1975 in the early stages of an abrupt change(1976), and the system was at the stage of a critical slowing down, which proves the reliability of the early warning signal of abrupt change discovered in 1970 from the mechanism. In addition, the variance of the SST,along with the spatial distribution of the autocorrelation coefficient in the corresponding PDO region, also demonstrates the corresponding relationship between the change of the background field of the SST and the change of the PDO.     

Does the onset of epileptic seizure start from a bifurcation point?

Detection of epileptic seizures is a major challenge of these days. There are lots of papers which pay their attention to this subject. Recently, some dynamical disease with attacks such as epilepsy are considered as a system in which critical slowing down can be seen before their attacks (seizure). Although there are not many researches on the prediction of seizures using this phenomenon. Recently [P. Milanowski, P. Suffczynski, Int. J. Neural Syst. 26, 1650053 (2016)] have investigated the application of critical slowing down indicators and surprisingly they found that only in 8% of nearby 300 epileptic patients have the evidence of critical slowing down before seizures. The main goal of this paper is finding the answer of the important question “can we trust that epileptic seizures are bifurcations in the neural system”. In order to find the answer, different studies on the prediction of seizure are investigated and we prove that features which are used in those papers are critical slowing down indicators although they are not aware of it. So we present some reasons for the occurrence of critical slowing down before the seizure. We hope that this study will be a motivation of future studies on the application of critical slowing down indicators for predicting epileptic seizures.     

The influences of the ionic channel conductances and kinetics on the phase-locking behaviors of modeled sinoatrial node cells and tissue

Sinoatrial node (SAN) is the leading pacemaker of the heart, whose pathologies are closely associated to certain kinds of arrhythmias. Phase-locking is a characteristic behavior of the self-oscillatory SAN system, which is relevant to the heart rate modulation. It is known that the SAN phase-locking properties are influenced by the stimulating magnitude, the stimulated site in the tissue, the intercellular coupling strength and even the couplings from the atrial cells. Besides the above knowledge, a practical problem remains undiscussed, i.e., the influences of the channel conductances and kinetics on the phase-locking property. In the present paper a detailed electrophysiological SAN model is investigated. The effects of several major parameters modulating the channels' conductances and the time constants are illustrated. We find that the phase-locking ranges depend on the automaticity of the system. Any parameter variation slowing down the intrinsic oscillating rate may increase the phase-locking ranges, while that speeding up the rate may shrink them. The well known phase resetting property is applied to explain the phenomena, founding on which the analytical formulas for estimating the phase-locking ranges are derived.     

The magnetic phase transition in amorphous ferromagnets and in spin glasses

The magnetic phase transition in materials with exchange disorder (amorphous ferromagnets, spin glasses) is discussed. In the critical temperature range the behavior of amorphous ferromagnetic transition metal-metalloid glasses is found to be similar to the one derived for a three-dimensional homogeneous Heisenberg ferromagnet. The most prominent difference between disordered and homogeneous materials is manifested in a large temperature range of deviations from the mean field behavior beyond the critical region, as observed experimentally for the temperature dependence of the linear susceptibility of amorphous ferromagnets and of the nonlinear susceptibility of spin glasses. A molecular field theory with correlations in space and time is developed, which relates the deviations from the mean field behavior to the interplay between the temperature dependent thermal correlations in the spin system and the spatial fluctuations of the material. Application to dynamical processes (kinetic critical slowing down) is discussed.     

Scaling behaviour of the fictitious time correlation function in stochastic quantization and its implications in Langevin simulation

The scaling behaviour of the fictitious time correlation length in stochastic quantization is investigated. Its implications in the numerical Langevin simulation are studied by the use of the two-dimensional 0(3) non-linear σ-model. It is discussed in connection with the measurement of the mass gap. Possible relations between the scaling behavior and higher order algorithms or the critical slowing down are also suggested.     

试用临界慢化原理探讨气候突变

近年来, 临界慢化现象在揭示复杂动力系统是否趋向于临界性灾变方面展示了重要潜力. 本文基于临界慢化的理念, 着重研究不同噪声影响下, 气候突变前兆信号出现的时间; 对含有不同噪声的气温观测资料、太平洋年代际振荡指数以及阿留申低压强度资料进行处理, 研究突变的前兆信号. 以20世纪70年代末80年代初这次气候突变为例, 分别计算了表征临界慢化现象的方差和自相关系数. 结果表明, 临界慢化现象出现在具有不同信噪比的资料中, 这表明临界慢化现象可能是气候突变发生前的一个前兆信号, 并且噪声对气候突变前兆信号的检测结果影响较小, 从而论证了临界慢化现象检测突变前兆信号的可靠性, 为该方法在实际观测资料中的广泛应用提供了实验基础.     

Optimal multigrid algorithms for calculating thermodynamic limits

Beyond eliminating the critical slowing down, multigrid algorithms can also eliminate the need to produce many independent fine-grid configurations for averaging out their statistical deviations, by averaging over the many samples produced in coarse grids during the multigrid cycle. Thermodynamic limits can be calculated to accuracy in justO(^-2) computer operations. Examples described in detail and with results of numerical tests are the calculation of the susceptibility, the -susceptibility, and the average energy in Gaussian models, and also the determination of the susceptibility and the critical temperature in a two-dimensional Ising spin model. Extension to more advanced models is outlined.     

Relaxation Property and Stability Analysis of the Quasispecies Models

The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and second-largest eigenvalues locates the error threshold at whichcritical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error (mutation) threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition isfurther confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Eigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.     

Monte Carlo computer experiments on critical phenomena and metastable states

Ising and Heisenberg models are studied by the Monte Carlo method. Several hundred up to 60 000 spins located at two- and three-dimensional lattices are treated and various boundary conditions used to elucidate various aspects of phase transitions. Using free boundaries the finite size scaling theory is tested and surface properties are derived, while the periodic boundary condition or the effective field-like ‘self-consistent’ boundary condition are used to derive bulk critical properties. Since Monte Carlo averages can be interpreted as time averages of a stochastic model, ‘critical slowing down of convergence’ occurs. The critical dynamics is investigated in the case of the single spin-flip kinetic Ising model. Also non-equilibrium relaxation processes are treated, e.g. switching on small negative fields the magnetization reversal and nucleation processes are studied. The metastable states found can be understood in terms of a scaling theory and the droplet model. Using a spin exchange model the phase separation kinetics of a binary alloy is simulated.     

光学双稳态和混沌运动中的临界现象

本文以具有反馈时间延迟的非线性系统弛豫方程为出发点,讨论了双稳态临界点的临界现象。发现双稳区边沿的临界慢化与混沌运动中切分叉点附近阵发混沌时间间隔发散具有一致性,临界指数为1/2。在双稳区(尖顶突变模型)的尖顶处,与双稳区边沿临界点不同,它与混沌运动中倍周期分叉点及劈分叉点的临界慢化具有一致性,临界指数为1。上述结果具有普适性。以液晶混合光学双稳系统为例,进行了计算机实验,其结果与分析相一致。 关键词：