A stochastic particle system modeling the Carleman equation

Two species of Brownian particles on the unit circle are considered; both have diffusion coefficient >0 but different velocities (drift), 1 for one species and –1 for the other. During the evolution the particles randomly change their velocity: if two particles have the same velocity and are at distance ( being a positive parameter), they both may simultaneously flip their velocity according to a Poisson process of a given intensity. The analogue of the Boltzmann-Grad limit is studied when goes to zero and the total number of particles increases like ^–1. In such a limit propagation of chaos and convergence to a limiting kinetic equation are proven globally in time, under suitable assumptions on the initial state. If, furthermore, depends on and suitably vanishes when goes to zero, then the limiting kinetic equation (for the density of the two species of particles) is the Carleman equation.Dedicated to the memory of Paola Calderoni.     

一阶线性系统的调参随机共振研究

分析了一阶线性系统在正弦和白噪声信号作用下的输出功率谱和信噪比.研究表明,加性噪声作用下的线性系统不存在传统意义上的随机共振,但却存在输出信噪比随系统参数非单调变化的调参广义随机共振现象.针对任意频率信号,分析了不同采样频率下的调参共振谱特性,得出适当增大采样频率有利于特征信号识别的结论.     

An algebra related to the fusion rules of Wess-Zumino-Witten models

We introduce a new family of examples of quantum groups. Its irreducible representations are indexed by level l dominant integral weights of affine Lie algebra s(n), and their branching rules with respect to the truncated tensor product is given by the fusion rules of SU(n) _l -Wess-Zumino-Witten model in conformal field theory.     

蒙特卡罗计算中颗粒型燃料的随机分布模型比较

高温气冷堆是新一代反应堆系统的热门候选堆型,已经受到国际上越来越多的关注。为设计和分析这种堆型,因其特有的包覆颗粒燃料引入了双重非均匀性,需要应用随机分布模型。对粗网格模型、细网格随机(FLS)模型、随机顺序添加(RSA)模型、子网格随机(Sub-FLS)模型和Metropolis模型等进行了研究,通过计算分析比较给出了各种模型的优缺点。结果表明：子网格随机模型和连续的RSA模型非常接近参考值,但是连续RSA模型的建模时间随着燃料体积份额的增加连续快速上升。 Key words: coated particle fuels; stochastic transport model; Monte Carlo; random distribution     

蒙特卡罗计算中颗粒型燃料的随机分布模型比较

高温气冷堆是新一代反应堆系统的热门候选堆型,已经受到国际上越来越多的关注。为设计和分析这种堆型,因其特有的包覆颗粒燃料引入了双重非均匀性,需要应用随机分布模型。对粗网格模型、细网格随机(FLS)模型、随机顺序添加(RSA)模型、子网格随机(Sub-FLS)模型和Metropolis模型等进行了研究,通过计算分析比较给出了各种模型的优缺点。结果表明:子网格随机模型和连续的RSA模型非常接近参考值,但是连续RSA模型的建模时间随着燃料体积份额的增加连续快速上升。 Key words: coated particle fuels; stochastic transport model; Monte Carlo; random distribution     

An analytical solution of the stochastic Navier-Stokes system

This paper, using the author's decomposition method and recent generalizations, presents algorithms for an analytic solution of the stochastic Navier-Stokes system without linearization, perturbation, discretization, or restrictive assumptions on the nature of stochasticity. The pressure, forces, velocities, and initial/boundary conditions can be stochastic processes and are not limited to white noise. Solutions obtained are physically realistic because of the avoidance of assumptions made purely for mathematical tractability by usual methods. Certain extensions and further generalizations of the decomposition method have provided the basis for the solution.     

An exactly solvable linear model giving indication of stochastic resonance

The linear stochastic equation dx _β /dt+[1+f _β (t)]x _β (t)=A sin (Ωt) is discussed. The functionƒ _β (t) is defined as a Poissonian noise dependent on a parameterβ>0,ƒ _β (t)=β Σ _j [δ(t − t _j ⁺ ) −δ (t − t _j ⁻ )]. The mean frequency of the delta-pulses is chosen asβ-dependent in the formλ(β)=2γ(β ⁻² + 1) exp(−β) whereγ is a constant from the interval (0, 0.974). With the stochastic functionƒ _β (t) defined in this way, attention is paid on the oscillational term of the averaged function 〈x(t)〉, 〈x(t)〉_osc=Āsin(Ωt − α). It is found that the dependenceĀ=Ā(β) exhibits one maximum and one minimum. The occurrence of these extrema seems to affirm the presence of stochastic resonance. This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97.     

A contribution to the systematics of stochastic volatility models

We systematically compare several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can also assume an algebraic decay, in the family of models which we call “GARCH” type. The intermediate regime is found in the exponential Ornstein-Uhlenbeck process. We also calculate the decay of the autocorrelation function of volatility.     

Probability density of a stochastic process at the output of a linear system

We propose and analyze a method of direct statistical analysis for linear first-order systems with deterministic parameters. We derive the one- and multi-dimensional (with arbitrary dimension n) probability density of a stochastic process at the output of a linear system. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 287–300, March 1999.     

Scattering theory relevant to the linear transport of particle swarms

The long-time behavior of the velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D.C. electric field is studied within the framework of scattering theory. We prove the existence of wave and scattering operators for a simplified one-dimensional model of the linearized Boltzmann equation. The theory is applied to the study of the long-term behavior of electrons and the occurrence of traveling waves in runaway processes.     

On the stochastic dynamics of Ising models

With the help of recent results in the mathematical theory of master equations, we present a rigorous derivation of the stochastic Glauber dynamics of Ising models from Hamiltonian quantum mechanics. A thermal bath is explicitly constructed and, as an illustration, the dynamics of the Ising-Weiss model is analyzed in the thermodynamic limit. We thus obtain an example of a nonequilibrium statistical mechanical system for which a link without mathematical gap can be established from microscopic quantum mechanics to a macroscopic irreversible thermodynamic process.     

Piecewise linear models for the quasiperiodic transition to chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode locking and the quasiperiodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic "sine-circle" map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction. (c) 1996 American Institute of Physics.     

Experiment and application of parameter-induced stochastic resonance in an over-damped random linear system

This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise.Non-monotonic dependence of signal-to-noise ratio on the system parameter is observed.Several potential applications of parameter-induced stochastic resonance are given in circuits.     

The stochastic models method applied to the critical behavior of Ising lattices

The stochastic models (SM) computer simulation method for treating manybody systems in thermodynamic equilibrium is investigated. The SM method, unlike the commonly used Metropolis Monte Carlo method, is not of a relaxation type. Thus an equilibrium configuration is constructed at once by adding particles to an initiallyempty volume with the help of a model stochastic process. The probability of the equilibrium configurations is known and this permits one to estimate the entropy directly. In the present work we greatly improve the accuracy of the SM method for the two and three-dimensional Ising lattices and extend its scope to calculate fluctuations, and hence specific heat and magnetic susceptibility, in addition to average thermodynamic quantities like energy, entropy, and magnetization. The method is found to be advantageous near the critical temperature. Of special interest are the results at the critical temperature itself, where the Metropolis method seems to be impractical. At this temperature, the average thermodynamic quantities agree well with theoretical values, for both the two and three-dimensional lattices. For the two-dimensional lattice the specific heat exhibits the expected logarithmic dependence on lattice size; the dependence of the susceptibility on lattice size is also satisfactory, leading to a ratio of critical exponents/=1.85 ±0.08. For the three-dimensional lattice the dependence of the specific heat, long-range order, and susceptibility on lattice size leads to similarly satisfactory exponents:=0.12 ±0.03,=0.30 ±0.03, and=1.32 ±0.05 (assuming =2/3).     

An active lateral suspension to a track/vehicle system using stochastic optimal control

An active suspension design to improve lateral ride quality and stability in a track/vehicle system subject to lateral track irregularity is presented. The measurement of the state variables is performed in a noisy environment, and unknown state variables of the system are estimated from the measurement data by using a Kalman filter. It is assumed that the lateral track irregularity and measurement noise are Gaussian random processes, respectively. The optimal control for the active suspension is determined by minimizing the quadratic performance index composed of the state variables and control efforts, and then the active suspension structure has a cascade feedback loop composed of the Kalman filter and the optimal controller. The numerical results indicate that the proposed active suspension provides much improved lateral ride quality and stability.     

Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises

Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system (CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system (PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time (MFPT), and output signal-to-noise ratio (SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency, and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.     

Power law behavior related to mutual synchronization of chemically coupled map neurons

The widely represented network motif, constituting an inhibitory pair of bursting neurons, is modeled by chaotic Rulkov maps, coupled chemically via symmetrical synapses. By means of phase plane analysis, that involves analytically obtaining the curves guiding the motion of the phase point, we show how the neuron dynamics can be explained in terms of switches between the noninteracting and interacting map. The developed approach provides an insight into the observed time series, highlighting the mechanisms behind the regimes of collective dynamics, including those concerning the emergent phenomena of partial and common oscillation death, hyperpolarization of membrane potential and the prolonged quiescence. The interdependence between the chaotic neuron series takes the form of intermittent synchronization, where the entrainment of membrane potential variables occurs within the sequences of finite duration. The contribution from the overlap of certain block sequences embedding emergent phenomena gives rise to the sudden increase of the parameter characterizing synchronization. We find its onset to follow a power law, that holds with respect to the coupling strength and the stimulation current. It is established how different types of synaptic threshold behavior, controlled by the gain parameter, influence the values of the scaling exponents.