基于量子粒子群算法的自适应随机共振方法研究

为提升随机共振理论在微弱信号检测领域中的实用性,以随机共振系统参数为研究对象,提出了基于量子粒子群算法的自适应随机共振方法.首先将自适应随机共振问题转化为多参数并行寻优问题,然后分别在Langevin系统和Duffing振子系统下进行仿真实验.在Langevin系统中,将量子粒子群算法和描点法进行了寻优结果对比;在Duffing振子系统中,Duffing振子系统的寻优结果则直接与Langevin系统的寻优结果进行了对比.实验结果表明:在寻优结果和寻优效率上,基于量子粒子群算法的自适应随机共振方法要明显高于描点法;在相同条件下,Duffing振子系统的寻优结果要优于Langevin系统的寻优结果;在两种系统下,输入信号信噪比越低就越能体现出量子粒子群算法的优越性.最后还对随机共振系统参数的寻优结果进行了规律性总结.     

Diffusion in a Weakly Random Hamiltonian Flow

We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves undergoes a spatial diffusion.     

The stochastic quantum mechanics approach to the unification of relativity and quantum theory

The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR paradox, etc., are discussed.Supported in part by NSERC Grant A5208.     

Equilibrium of a mesoscopic system with conformation dependent damping: An alternative approach

We look at the dynamics of a Brownian particle with internal degrees of freedom and conformation dependent damping. Inhomogeneous damping apparently makes the problem a stochastic process with multiplicative noise. We derive the equilibrium distribution of such a system on the basis of a single postulate that the stochastic forces on the system produces no drift. Based on this postulate, we generalize the expression of the stochastic force for the equilibrium of such systems. The equilibrium probability distribution obtained deviates from the exact canonical form, although, the equipartition of energy remains intact when the internal degrees of freedom are integrated out. We also show a crucial local balance of the rate of average energy inflow and outflow as a consequence of the equilibrium probability distribution.     

Browninan motion in a fluctuating periodic potential

A classical Brownian particle is considered in a periodic potential field with a rapidly oscillating phase. The concept of effective potential is used for describing a slow averaged motion of a particle. It is shown that there exists a certain region in which a particle performs a stationary random motion without appreciable drift. By analogy with the ideal case, this region can be called an effective locking region. The situation described is valid for stationary fluctuations of the phase of a potential function, provided that they have a sufficiently small but finite correlation time. The study of the problem is reduced to the analysis of a stochastic system with external noise whose spectral density is zero at zero frequency (“green” noise [1]). The analysis of the first-and second-approximation equations of the averaging method exhibits the high stability of the locking phenomenon. This result has been verified by the numerical solution of appropriate stochastic equations. In this case, a predictor-corrector algorithm was used that allowed one to carry out a numerical simulation to a sufficiently high degree of accuracy. The result of the simulation is in good agreement with the theoretical results. The effective locking bandwidth calculated analytically by the averaging method actually coincides with the value obtained by the simulation.     

Channeling and percolation in two-dimensional chaotic dynamics

The Hamiltonian dynamics of a particle moving in a nearly periodic two-dimensional (2-D) potential of square symmetry is analyzed. The particle undergoes two types of unbounded stochastic or random walks in such a system: a quasi-1-D motion (a "stochastic channeling") and a 2-D motion which results from a sort of stochastic percolation. A scenario for the onset of this stochastic percolation is analyzed. The threshold energy for percolation is found as a function of the perturbation parameter. Each type of random walk has the property of intermittency. The particle transport is anomalous in certain energy intervals.     

Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle....     

Improved particle filters for multi-target tracking

We present a novel approach for improving particle filters for multi-target tracking. The suggested approach is based on drift homotopy for stochastic differential equations. Drift homotopy is used to design a Markov Chain Monte Carlo step which is appended to the particle filter and aims to bring the particle filter samples closer to the observations while at the same time respecting the target dynamics. We have used the proposed approach on the problem of multi-target tracking with a nonlinear observation model. The numerical results show that the suggested approach can improve significantly the performance of a particle filter.     

An exactly soluble relaxation problem

The problem of a particle moving in a two-valued random potential occurred in a recent paper by Pomeau. The exact time-dependent solution is here obtained for a quadratic potential by two different methods. The first method treats the problem as a stochastic differential equation and leads to the characteristic function of the probability distribution of the particle coordinate. In the second method the equation for the joint probability density of particle and potential is solved, which leads to the temporal Laplace transform of the distribution. The spectral properties of the evolution operator are examined.     

Particle tracking simulation in the CSRe stochastic cooling system

A stochastic cooling system is under design and construction at HIRFL-CSRe(Heavy Ion Research Facility in Lanzhou- experimental Cooling Storage Ring), with the aim of cooling secondary particles produced at HIRFL-RIBLL2(2nd Radioactive Ion Beam Line in Lanzhou).The optical layout of CSRe has been optimized to meet the requirements of a stochastic cooling system.In this paper, a particle tracking method is used to investigate both transverse and longitudinal cooling on the basis of the modified optical layout, demonstrating how it can be used to optimize stochastic cooling parameters.Simulation results indicate that the particle tracking method is an innovative and reasonable method to study stochastic cooling.It also has the advantage of discovering the influence of Twiss parameters at the pickups and kickers, which will be explored in further studies.     

Stochastic motion of the untrapped particle in electrostatic mode

The stochastic energy diffusion of the untrapped particle in the electrostatic mode is investigated analytically.We find that the equilibrium electrostatic field of periodical structure plays the same role as the usual focusing magnetic field to lead the test particle to stochastic motion.The resonance overlapping criterion for the random state is given,and also the Fokker-Planck-Kolmogorov approach to diffusion is considered for our system.     

Stochastic motion of the untrapped particle in electrostatic mode

The stochastic energy diffusion of the untrapped particle in the electrostatic mode is investigated analytically. We find that the equilibrium electrostatic field of periodical structure plays the same role as the usual focusing magnetic field to lead the test particle to stochastic motion. The resonance overlapping criterion for the random state is given, and also the Fokker-Planek-Kohnogorov approach to diffusion is considered for our system.     

随机参数Duffing系统中的随机混沌及其延迟反馈控制

研究了谐和激励下含有界随机参数Duffing系统(简称随机Duffing系统)中的随机混沌及其延迟反馈控制问题.借助Gegenbauer多项式逼近理论，将随机Duffing系统转化为与其等效的确定性非线性系统.这样，随机Duffing系统在谐和激励下的混沌响应及其控制问题就可借等效的确定性非线性系统来研究.分析阐明了随机混沌的主要特点，并采用Wolf算法计算等效确定性非线性系统的最大Lyapunov指数，以判别随机Duffing系统的动力学行为.数值计算表明，恰当选取不同的反馈强度和延迟时间，可分别达到抑制或诱发系统混沌的目的，说明延迟反馈技术对随机混沌控制也是十分有效的. 关键词： 随机Duffing系统 延迟反馈控制 随机混沌 Gegenbauer多项式     

Dynamics of particles in the steady flows of an inviscid fluid

Advection of small particles with inertia in two-dimensional ideal flows is studied both numerically and analytically. It is assumed that the flow disturbance around the particle corresponds to a potential dipole, so that the motion is driven by pressure gradient, inertial, and added-mass forces. It is found that in general the motion is nonintegrable, but particular exact solutions can be obtained. The problem is then studied for the cases of axisymmetric flow, when the motion proves to be completely integrable, and of a cellular flow, for which both regular and stochastic (bounded and unbounded) trajectories are calculated. In the latter case, the unbounded stochastic motion is of Brownian-like character, and the results derived show that the particle dispersion process is generally anomalous.     

Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method

We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems.This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy.Experiments are conducted on the Lorenz system and the Chen system.The proposed algorithm is used to estimate the parameters for these two systems.Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained.     

Stochastic global optimization as a filtering problem

We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be optimized. Similarly, we may not be able to evaluate exactly the functions involved in iterative optimization algorithms. For example, we may only have access to noisy measurements of the functions or statistical estimates provided through Monte Carlo sampling. This makes iterative optimization algorithms behave like stochastic maps. Naive global optimization amounts to evolving a collection of realizations of this stochastic map and picking the realization with the best properties. This motivates the use of filtering techniques to allow focusing on realizations that are more promising than others. In particular, we present a filtering reformulation of global optimization in terms of a special case of sequential importance sampling methods called particle filters. The increasing popularity of particle filters is based on the simplicity of their implementation and their flexibility. We utilize the flexibility of particle filters to construct a stochastic global optimization algorithm which can converge to the optimal solution appreciably faster than naive global optimization. Several examples of parametric exponential density estimation are provided to demonstrate the efficiency of the approach.     

Modelling nanoparticle dynamics: coagulation,sintering, particle inception and surface growth

In this paper we investigated a stochastic particle method (SPM) for solving an extension to the sintering–coagulation equation and modelled two particle systems: the production of SiO₂ and TiO₂. A new mass-flow stochastic algorithm to find numerical solutions to the particle model is stated. The stochastic method calculates fully the evolution of the bivariate particle size distribution (PSD) and is computationally very efficient in comparison to traditional finite element methods. The SPM was compared to a bivariate sectional method for a system with coagulation and sintering as the only mechanisms. The results obtained agree closely to those in the literature and were obtained in a small fraction of the time. An extended model with particle inception and surface growth was then used to model the TiCl₄ → TiO₂ system under various conditions. At low precursor concentration the effect of varying temperature was investigated, whilst at high precursor concentration the effect of surface growth on the system was explored. The results agree well with the conclusions reached previously in the literature.     

Stochastic processes for indirectly interacting particles and stochastic quantum mechanics

This work has two objectives. The first is to begin a mathematical formalism appropriate to treating particles which only interact with each otherindirectly due to hypothesized memory effects in a stochastic medium. More specifically we treat a situation in which a sequence of particles consecutively passes through a region (e.g., a measuring apparatus) in such a way that one particle leaves the region before the next one enters. We want to study a situation in which a particle may interact with other particles that previously passed through the system via disturbances made in the region by these previous particles.Second, we apply the type of stochastic process appearing in this context to the stochastic interpretation of quantum mechanics to obtain a modified version of this interpretation. This version is free of many of the criticisms made against the stochastic interpretation of quantum mechanics.     

A survey of numerical methods for nonlinear filtering problems

The main goal of filtering is to obtain, recursively in time, good estimates of the state of a stochastic dynamical system based on noisy partial observations of the same. In settings where the signal/observation dynamics are significantly nonlinear or the noise intensities are high, an extended Kalman filter (EKF), which is essentially a first order approximation to an infinite dimensional problem, can perform quite poorly: it may require very frequent re-initializations and in some situations may even diverge. The theory of nonlinear filtering addresses these difficulties by considering the evolution of the conditional distribution of the state of the system given all the available observations, in the space of probability measures. We survey a variety of numerical schemes that have been developed in the literature for approximating the conditional distribution described by such stochastic evolution equations; with a special emphasis on an important family of schemes known as the particle filters. A numerical study is presented to illustrate that in settings where the signal/observation dynamics are non linear a suitably chosen nonlinear scheme can drastically outperform the extended Kalman filter.