非线性阻尼驱动的莱维飞行动力学性质

基于动力学连续时间无规行走方法,对受非线性阻尼驱动的莱维飞行在自由势场以及周期势场中的扩散行为进行了研究.非线性阻尼取代斯托克斯阻尼,通过动力学连续时间无规行走方法体现在莱维随机行走粒子的每一步跳跃中.结果显示,非线性阻尼的强阻尼耗散作用导致莱维飞行的超扩散行为衰减为正常扩散,粒子速度定态分布呈现双峰与单峰的相互转化.周期势场的束缚作用会导致粒子扩散达到一个稳定态,而莱维粒子自身性质会使粒子存在极小概率跃出周期势阱的跳跃行为,表现为方均位移随时间的演化出现跃迁现象.     

强束缚势中Lévy飞行的非Gibbs-Boltzmann统计

解析和数值研究了强束缚势中Lévy飞行粒子的稳态分布.结果表明:当势从单稳态变化到双稳态时,粒子的稳态分布呈现单模到双模或双模到三模的转换;特别在势的鞍点处,坐标分布密度函数出现了一个峰,这违背了Gibbs-Boltzmann统计.     

周期场中非各态历经布朗运动

将自由状态下呈弹道扩散的非各态历经系统置于周期场中,进而将非各态历经布朗运动分为两类.第一类是阻尼核的Laplace变换的低频为零的系统,当温度远大于势垒高度时,系统平均能量的动能部分依赖粒子的初始速度分布;随温度降低,系统的各态历经性得到恢复.然后将第一类系统的稳定速度变量作为一个内部噪声,再去驱动一个自由布朗粒子,则阻尼核的Laplace变换在零频时为无穷大.结果发现,粒子扩散系数随温度的增加而趋于零,显示一种经典局域化特征,系统的渐进分布依赖于初始坐标分布.这是第二类非各态历经性运动,不能通过外加势而恢复. 关键词： 非各态历经 非Markov布朗运动 扩散系数 噪声谱     

双频驱动下分数阶过阻尼马达在空间对称势中的定向输运

从阻尼对历史加速度记忆的角度出发,对阶数p∈(0,2)的分数阶阻尼物理意义给出了统一的合理解释,具体分析了不同阶数下的阻尼记忆特性,在此基础上研究了空间对称势中分数阶单分子马达在无偏置双频简谐激励下的输运问题,通过数值方法分析了输运速度与模型各参数的关系以及分数阶阻尼对输运现象的影响机理.研究表明,在不同阶数下历史加速度对当前时刻阻尼力的贡献与距当前时刻的时间长度呈单增或单减关系;在适当参数下输运速度随空间势深和外力频率的增大均会出现广义共振现象,特别地,在存在输运且阻尼阶数较大的情况下输运速度随势深增大出现阶梯状变化而与外力频率呈正比例关系;输运速度及方向对外力波形十分敏感,在不同外力下阻尼力的记忆性会分别促进或阻碍粒子跃迁,甚至引发与整数阶方向相反的定向流.     

晶体摆动场辐射系统的全局分叉与混沌行为

引入正弦平方势,在经典力学框架内和偶极近似下,考虑到运动阻尼和非线性影响,把粒子在晶体摆动场中的运动方程化为具有阻尼项和受迫项的广义摆方程.利用Jacob椭圆函数和椭圆积分分析了无扰动系统的相平面特征,并解析地给出了系统的解和粒子振动周期; 进一步利用Melnikov方法分析相平面上三类轨道的分叉性质和进入Smale马蹄意义下的混沌行为,找到系统的全局分叉与系统进入混沌的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免、抑制分叉或混沌的出现. 关键词： 晶体摆动场辐射 Melnikov方法 分叉 混沌     

晶体摆动场辐射系统的全局分叉与混沌行为

引入正弦平方势,在经典力学框架内和偶极近似下,考虑到运动阻尼和非线性影响,把粒子在晶体摆动场中的运动方程化为具有阻尼项和受迫项的广义摆方程.利用Jacob椭圆函数和椭圆积分分析了无扰动系统的相平面特征,并解析地给出了系统的解和粒子振动周期; 进一步利用Melnikov方法分析相平面上三类轨道的分叉性质和进入Smale马蹄意义下的混沌行为,找到系统的全局分叉与系统进入混沌的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免、抑制分叉或混沌的出现.     

外力作用下反馈耦合布朗棘轮的定向输运

本文研究了处于外力作用下双阱棘轮势中两个反馈耦合布朗粒子的定向输运性能. 通过对过阻尼朗之万方程的数值求解, 详细讨论了外力、热噪声与势阱的不对称参数等对耦合布朗粒子的平均速度、 有效扩散系数及Pe数的影响. 研究发现, 平均速度随外力呈周期性的变化规律. 同时耦合系统存在最优噪声强度会使定向输运达到最强. 值得指出的是棘轮系统可通过改变双阱势的结构来获得较强的定向流. 关键词： 耦合布朗棘轮 外力 双阱棘轮势 平均速度     

Berry联络与吴–杨单极势

通过研究一半整数自旋值的中性粒子在球对称磁场中的Born-Oppenheimer方程,发现在自旋空间Berry联络呈非阿贝尔形式.在绝热近似下,Berry联络相当于阿贝尔形式的吴-杨单极场.由于拓扑的非平庸性,利用纤维丛中截面的概念研究了位形空间的动力学,发现中心势场中粒子的角动量和能量均取量子化值,但数值发生移动,这是纯几何起源的现象.     

基于莱维飞行的鸟群优化算法

针对鸟群优化算法(BSA)在求解高维多极值优化问题时容易陷入局部最优解和出现早熟收敛的情况,在原始鸟群算法的基础上,在模拟鸟群飞行行为的过程中引入莱维飞行,提出了一种基于莱维飞行的改进算法——莱维-鸟群算法(LBSA)。这种算法替换了原算法中随机的飞行位置跳变,而采用莱维飞行更新鸟群飞行后的位置,大幅提高了鸟群的位置变化活力,提高了算法的有效性。仿真结果表明,在求解高维多极值优化问题时,该算法性能优于原始鸟群算法。     

一维均匀势场中含时薛定谔方程的求解

本文详细讨论了一维均匀势场中含时薛定谔方程的求解.求解的思想是以均匀势场中经典粒子的运动作为参考，从经典粒子的运动轨迹出发，构建出量子情形下描述粒子运动的高斯波包形式的演化波函数，进而借助含时薛定谔方程确定波函数的具体形式.在上述思想指导下，推导得出了坐标表象和动量表象下均匀势场内一维粒子的传播子函数.同时，作为比较，狄拉克态矢量符号提供了另一种得到上述传播子函数的途径.     

A speculative study of 23-order fractional Laplacian modeling of turbulence: some thoughts and conjectures

This study makes the first attempt to use the 23-order fractional Laplacian modeling of Kolmogorov -53 scaling of fully developed turbulence and enhanced diffusing movements of random turbulent particles. Nonlinear inertial interactions and molecular Brownian diffusivity are considered to be the bifractal mechanism behind multifractal scaling of moderate Reynolds number turbulence. Accordingly, a stochastic equation is proposed to describe turbulence intermittency. The 23-order fractional Laplacian representation is also used to model nonlinear interactions of fluctuating velocity components, and then we conjecture a fractional Reynolds equation, underlying fractal spacetime structures of Levy 23 stable distribution and the Kolmogorov scaling at inertial scales. The new perspective of this study is that the fractional calculus is an effective approach to modeling the chaotic fractal phenomena induced by nonlinear interactions.     

Using bimodal probability distributions in the problems of Brownian diffusion

When analyzing nonlinear stochastic systems, we deal with the chains of differential equations for the moments or cumulants of dynamic variables. To disconnect such chains, the well-known cumulant approach, which is adequate to the quasi-Gaussian expansion of the higher-order moments is used. However, this method is inefficient in the problems of Brownian diffusion in bimodal potential profiles, and the disconnection problem should be solved on the basis of bimodal probability distributions. To this end, we propose to construct bimodal model distributions, in particular, the bi-Gaussian distribution. Cumulants and the expansions of the higher-order moments for symmetric and nonsymmetric bi-Gaussian models. On this basis, we consider relaxation of probability characteristics of one-dimensional Brownian motion in the bimodal potential profile. The dependences of relaxation of the mean value and variance of particle coordinate on the potential barrier “power,” the noise intensity, and the initial distribution of particles are analyzed numerically. In particular, it is shown that relaxation proceeds by stages with different temporal scales in the case of a powerful barrier. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 8, pp. 718–729, August 2006.     

Stochastic resonance characteristic analysis of new potential function under Levy noise and bearing fault detection

Based on the output saturation of classcial bistable stochastic resonance (CBSR), a new type of piecewise nonlinear bistable stochastic resonance (PNBSR) system is constructed. The mean signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon. The laws for the resonant output of piecewise nonlinear bistable system governed by l, c, a, b and D of Levy noise are explored under different characteristic index α and symmetry parameter β of Levy noise. The results show that the output of PNBSR system has increased 4?dB by comparing with the output signal-to-noise ratio of CBSR system. And the stochastic resonance phenomenon can be induced by adjusting the piecewise nonlinear system's parameters under any α or β of Levy noise. The interval of the parameters of system which induces good stochastic resonance is roughly the same. And the output signal waveform of resonance is very similar to the input signal waveform, which has some reference value for the signal recovery. Moreover, we can find the good stochastic resonance interval of the system parameters do not change with D of Levy noise under the different noise intensity D of Levy noise. On the basis of this, adjusting the intensity amplification factor D of Levy noise, which induces good stochastic resonance, and the interval does not change with α or β. At last, the piecewise nonlinear bistable system is applied to detect bearing fault signals, which achieves better performance compared with the classical bistable system.     

基于自回归模型的超细颗粒动态光散射模拟

为了获取超细颗粒动态散射光模拟信号, 在分析超细颗粒动态散射光信号特性的基础上, 通过建立动态光散射随机过程的自回归(AR)模型, 利用Levison-Durbin递推算法确定模型参数, 并给出了单峰、双峰分布颗粒信号模拟的模型阶数确定方法, 从而提出了一种基于AR模型的态光散射信号模拟方法。分别对50 nm, 300 nm, 1000 nm, 50 nm与1000 nm, 100 nm与500 nm, 300 nm与1000 nm的单峰、双峰分布颗粒在模型阶数分别为1, 1, 1, 57, 28, 40时进行了模拟, 得到的模拟信号的光强自相关函数与理论值吻合, 用累积法对单峰分布颗粒反演和双指数法对双峰分布颗粒反演, 相对误差分别小于0.58%和3.7%, 因此, 单峰分布颗粒信号模拟需一阶模型, 双峰分布颗粒信号模拟粒径不同所需阶数不同。     

Levy Stability Analysis of Random Cascade Model

The Levy stable analysis for random cascade model is performed. The Levy stable index μ ofa-model is obtained by both Monte-Carlo simulation and analytical calculation. It is foundthat μ is increasing when the fluctuation becomes weaker, and vice versa, just as expected.It is shown that the Levy stable index of α-model depends mainly upon the model parameter α. Its weak dependence on the number λ of branches in each elementary splitting is due tothe normalization of probability in each step. The possible reason of the Levy stable indexgreater than 2 found experimentally is briefly discussed.     

Viscosity minimum in bimodal concentrated suspensions under shear

We study a model of concentrated suspensions under shear in two dimensions. Interactions between suspended particles are dominated by direct-contact viscoelastic forces and the particles are neutrally bouyant. The bimodal suspensions consist of a variable proportion between large and small droplets, with a fixed global suspended fraction. Going beyond the assumptions of the classical theory of Farris (R.J. Farris, Trans. Soc. Rheol. 12, 281 (1968)), we discuss a shear viscosity minimum, as a function of the small-to-large-particle ratio, in shear geometries imposed by external body forces and boundaries. Within a linear-response scheme, we find the dependence of the viscosity minimum on the imposed shear and the microscopic drop friction parameters. We also discuss the viscosity minimum under dynamically imposed shear applied by boundaries. We find a reduction of macroscopic viscosity with the increase of the microscopic friction parameters that is understood using a simple two-drop model. Our simulation results are qualitatively consistent with recent experiments in concentrated bimodal emulsions with a highly viscous or rigid suspended component. Received 28 June 2002 RID="a" ID="a"e-mail: ernesto@pion.ivic.ve     

Symmetric and Anti-Symmetric Solitons of the Fractional Second-and Third-Order Nonlinear Schr?dinger Equation

The fractional second-and third-order nonlinear Schr?dinger equation is studied,symmetric and antisymmetric soliton solutions are derived,and the influence of the Levy index on different solitons is analyzed.The stability and stability interval of solitons are discussed.The anti-interference ability of stable solitons to the small disturbance shows a good robustness.     

双峰分布颗粒体系的多角度动态光散射数据反演

采用多角度动态光散射和加权正则化反演方法,对4组模拟的双峰分布颗粒体系(100/600 nm,200/600 nm,300/600 nm和350/600 nm)分别选取1、3、6和10个散射角进行测量.粒度反演结果表明,采用加权正则化方法反演双峰颗粒体系的多角度动态光散射测量数据,可获得峰值位置比小于2∶1且含有大粒径(＞350 nm)颗粒的双峰颗粒粒度分布.采用标准聚苯乙烯乳胶颗粒进行实测的结果验证了这一结论.得到含大粒径颗粒的双峰粒度分布反演结果的原因在于,多角度动态光散射能提供更多的大粒径颗粒的粒度信息,加权正则化反演方法能减少测量数据中的噪声,因而多角度动态光散射测量数据的加权反演能实现峰值位置比小于2∶1且含有大粒径颗粒的双峰颗粒体系的测量.     

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.     

Levy scaling in random walks with fluctuating variance

Truncated Levy flights with correlated fluctuations of the variance (heteroskedasticity) are considered. A stylized model is introduced, in which the variance fluctuates between two possible values following a Markov chain process. Analogously to conventional truncated Levy flights with fixed variance, the central part of the probability distribution function of the increments at short time scales is found to be close to a Levy distribution. What makes these processes interesting is the fact that the crossover to the Gaussian regime may occur for times considerably larger than for uncorrelated (or no) variance fluctuations. Processes of this type may find direct application in the modeling of some economic time series, in which Levy scaling and heteroskedasticity are known to coexist.