Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect

We present a stochastic theory for the nonequilibriurn dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action, which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle’s worldline around its semiclassical trajectory. We point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations, and discuss how, in the framework that we have developed, an array of phenomena, from classical radiation and radiation reaction to the Unruh effect, are interrelated to each other as manifestations at the classical, stochastic and quantum levels. Using this method we give a derivation of the Unruh effect for the spacetime worldline coordinates of an accelerating charge. Our stochastic particle-field model, which was inspired by earlier work in cosmological backreaction, can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon.     

Dynamics of DNA replication in yeast

We present a mathematical model for the spatial dynamics of DNA replication. Using this model we determine the probability distribution for the time at which each chromosomal position is replicated. From this we show, contrary to previous reports, that mean replication time curves cannot be used to directly determine origin parameters. We demonstrate that the stochastic nature of replication dynamics leaves a clear signature in experimentally measured population average data, and we show that the width of the activation time probability distribution can be inferred from this data. Our results compare favorably with experimental measurements in Saccharomyces cerevisae.     

Stochastic matching problem

The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the deterministic case can be solved in polynomial time, stochastic variants are worst-case intractable. We propose an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method. We test it on random bipartite graphs, for which we analyze the phase diagram and compare the results with exact bounds. Our approach is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods. Finally we discuss how the method can be generalized to other problems of optimization under uncertainty.     

Stochastic cellular automata modeling of excitable systems

A stochastic cellular automaton is developed for modeling waves in excitable media. A scale of key features of excitation waves can be reproduced in the presented framework such as the shape, the propagation velocity, the curvature effect and spontaneous appearance of target patterns. Some well-understood phenomena such as waves originating from a point source, double spiral waves and waves around some obstacles of various geometries are simulated. We point out that unlike the deterministic approaches, the present model captures the curvature effect and the presence of target patterns without permanent excitation. Spontaneous appearance of patterns, which have been observed in a new experimental system and a chemical lens effect, which has been reported recently can also be easily reproduced. In all cases, the presented model results in a fast computer simulation.      

Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise

We discuss how the effective parameters characterising averaged motion in nonlinear systems are affected by noise (random fluctuations). In this approach to stochastic dynamics, the stochastic system is replaced by its deterministic equivalent but with noise-dependent parameters. We show that it can help to resolve certain paradoxes and that it has a utility extending far beyond its usual application in passing from the microscopic equations of motion to the macroscopic ones. As illustrative examples, we consider the diode-capacitor circuit, a Brownian ratchet, and a generic stochastic resonance system. In the latter two cases we calculate for the first time their effective parameters of averaged motion as functions of noise intensity. We speculate that many other stochastic problems can be treated in a similar way. PACS: 05.10.Gg, 05.40.-a, 05.40.Jc     

Analysis of weak signal detection based on tri-stable system under Levy noise

Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.     

Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays

In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen-Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.     

Asymmetric delay feedback stochastic resonance detection method based on prior knowledge particle swarm optimization

For the adjustable parameters stochastic resonance system, the selection of the structural parameters plays a decisive role in the performance of the detection method. The vibration signal of rotating machinery is non-linear and unstable, and its weak fault characteristics are easily concealed by noise. Under strong background noise interference, the detection of fault features is particularly challenging. Therefore, a type of weak fault feature extraction method, named knowledge-based particle swarm optimization algorithm for asymptotic delayed feedback stochastic resonance (abbreviated as KPSO-ADFSR) is proposed. Through deduction under adiabatic approximation, we observe that both the asymmetric parameters, the length of delay and the feedback strength, impact the potential function. After adjusting the asymmetric parameters of the system, the output signal-to-noise ratio (SNR) is used as the fitness function, and the setting of the relationship between the noise intensity and barrier height is used as the prior knowledge of the particle swarm algorithm. Through this algorithm, the delay length and the feedback strength are optimized. This method achieves global optimization of system parameters in a short time; it overcomes the shortcomings of the traditional stochastic resonance method, which has a long convergence time and tends to easily fall into local optimization. It can effectively improve the detection of weak fault features. In the bearing rolling body pitting corrosion failure experiment and steel field engineering experiment, the proposed method could extract the characteristics of a weak fault more effectively than the traditional stochastic resonance method based on the standard particle swarm algorithm.     

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.     

Self-consistent Shaw optimized model potential: Application to the determination of structural and atomic transport properties of liquid alkali metals by molecular dynamics simulations

The ‘first-principles’ fully non-local and energy-dependent optimized model potential (OMP) derived by Shaw is developed further. In contrast to Shaw's original paper, OMP parameters are derived in a self-consistent manner that does not rely on knowledge of experimental values of the ionization and cohesive energies. To our knowledge, this is the first time that this method has been used for effective potential calculations. In an application to liquid Li, Na, and K alkali metals, we used OMP pseudopotential-based interactions between ions to carry out standard molecular dynamics simulations. In the calculations, the ionic structure for the liquid state was first checked at a temperature near the melting point. Similar accurate calculations, but for atomic transport properties, predict the temperature dependence of the self-diffusion coefficients. The theoretical results obtained are in overall agreement with available experimental measurements. Thus, one can have some confidence in the ability of the optimized model potential to give a good representation of the physical properties of these alkali ions in the liquid environment.     

Control of stochastic resonance in bistable system by using periodic signal

<正>According to the characteristic structure of double wells in bistable systems,this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal.Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization.By adding a bistable system with a controllable periodic signal,fluctuations in the single potential well can be effectively controlled,thus affecting the probability transitions between the two potential wells.In this way,an effective control can be achieved which allows one to either enhance or realize stochastic resonance.     

Ratchets, power strokes, and molecular motors

We present a method for determining the effective driving potential for a molecular motor from measurements of its stochastic position versus time. In developing the method we can make precise the previously vague notions of ‘Brownian ratchet’ and ‘power stroke’, and suggest means to experimentally distinguish between the two. In particular, we distinguish between two kinds of ratchets: ratchets that rectify large fluctuations and ratchets that bias small fluctuations. Received: 24 October 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Focusing of acoustic fields in a randomly inhomogeneous waveguide by using the time reversal method

We perform theoretical analysis of the method of field focusing in a randomly inhomogeneous waveguide using reradiation of the received signal with time reversal. The simplest case where point sources and receivers are used for emission and reception is considered. As an example, the waveguide is chosen which simulates an underwater sound channel with refractive-index fluctuations caused by random internal waves. In underwater acoustics, the considered method of field focusing is usually applied at relatively short distances that are shorter than or about 10 km. This work deals with much longer paths, along which sound waves propagate under conditions of well-developed ray and wave chaos. Main attention is given to studying the width of the focal spot and the field amplitude at its center. It is shown that the amplitude distribution in the vertical section of the focal spot and the peak amplitude value at its center can be estimated analytically using the stochastic ray theory.     

自适应光学中SPGD算法关键参数实时调节方法

介绍了随机并行梯度下降（SPGD）算法及其在相干合成中的应用,针对实验中算法关键参数难以调节的难点,提出采用软硬件结合的新方式,实现对实验数据的在线采集和分析以及对SPGD算法关键参数的自动实时调节。开展了4路光纤激光相干合成实验,对不同调节方法进行对比。实验中采用新方式有效调节了SPGD算法中增益系数和随机扰动幅度的取值,合成效果显著。     

Levy噪声激励下的幂函数型单稳随机共振特性分析

将Levy噪声与幂函数型单稳随机共振系统相结合, 为确保实验数据的可靠性, 以平均信噪比增益为衡量指标, 针对Levy噪声激励下的随机共振现象进行了研究. 详细介绍了单稳系统势函数形式及Levy噪声的产生原理, 深入探究了不同特征指数α 和不同对称参数β 取值条件下, 单稳系统参数a和b、Levy噪声强度放大系数D对幂函数型单稳系统共振输出的作用规律. 研究结果表明, 在任意Levy噪声分布条件下, 通过对系统参数a和b的适当调整均能诱导随机共振, 完成微弱信号检测, 且有多个随机共振区间与之对应, 同时这些区间不随α 或β 的改变而改变; 此外, 在研究噪声诱导的随机共振时也发现了同样的规律, 通过调节噪声强度放大系数D也能产生随机共振, 且随机共振区间也不随α 或β 的改变而改变; 最后, 在研究系统参数a和b之间的相互作用关系时发现, 一个系统参数的随机共振取值区间会随着另一个系统参数的改变而改变. 所获得的研究结果有效解决了Levy噪声激励下幂函数型单稳随机共振系统的系统参数、噪声强度放大系数的选择问题, 为其应用于工程实践提供了可靠的理论依据.     

Electric Nusselt number characterization of electroconvection in nematic liquid crystals

We develop a characterization method of electroconvection structures in a planar nematic liquid crystal layer by a study of the electric current transport. Because the applied potential difference has a sinusoidal time dependence, we define two electric Nusselt numbers corresponding to the in-phase and out-of-phase components of the current. These Nusselt numbers are predicted theoretically using a weakly nonlinear analysis of the standard model. Our measurements of the electric current confirm that both numbers vary linearly with the distance from onset until the occurence of secondary transitions. A systematic comparison between our theoretical and experimental results, using no adjusted parameters, demonstrates moderate agreement, but discrepancies remain. Electric transport measurements during electroconvection represent a quantitative test of the standard model completely independent from optical probes. Thus, the technique described here can be a useful complement to traditional structural measurements. Received 21 January 2001 and Received in final form 1st February 2002     

The influence of exciton motion on spin-resonance absorption

We use a stochastic model for the exciton motion which comprises both the coherent and the incoherent motion. The incoherent part is taken care of by a stochastic process which allows the local excitation energy and the transition matrix element to fluctuate by means of a Markovian process. The interaction between the spins and their surroundings is described by the usual spin-Hamiltonian which is, however, simplified to a spin 1/2 particle (instead of the triplet state). In the present paper we solve exactly the two limiting cases of completely coherent and incoherent motion (for two molecules). In the incoherent case the influence of the exchange interaction integral is taken into account by perturbation theory. We find expressions which are immediately comparable with ESR-experimental data. This comparison and additional information derived from optical absorption measurements allow us to determine all free parameters of our model uniquely. In particular, the fluctuations of the exchange interaction integral (with strength γ₁) play an important role. From these parameters we may furthermore calculate the correlation time of the proton spin resonance in agreement with experimental data. The results show clearly that at room temperature in anthracene crystals the exciton undergoes a hopping process.     

基于相位差混合处理方法的高分辨力成像技术

为了提高成像系统的分辨能力, 并尽量减小系统的复杂度, 本文将相位差波前探测技术和相位差图像恢复技术结合起来构成相位差混合处理方法, 给出了点目标和扩展目标情况下混合处理方法的数值仿真结果, 并针对点目标情况进行了实验验证. 实验表明, 在像差较大的情况下, 直接用事后处理方法无法得到满意的结果. 在三种湍流强度下, 经混合方法处理后得到光斑的半高宽分别由自适应光学系统校正后的5.1, 5.1和5.0个像素减小到3.3, 3.2和3.0个像素. 可以看出, 利用相位差混合处理方法得到的图像明显优于单独的事后图像处理方法和自适应光学校正, 相位差混合处理方法在高分辨力成像领域有着巨大的应用潜力.