Analysis of a Kind of Stochastic Dynamics Model with Nonlinear Function

In this paper, we establish stochastic differential equations on the basis of a nonlinear deterministic model and study the global dynamics. For the deterministic model, we show that the basic reproduction number $\Re _0$ determines whether there is an endemic outbreak or not: if $\Re _0< 1$, the disease dies out; while if $\Re _0> 1$, the disease persists. For the stochastic model, we provide analytic results regarding the stochastic boundedness, perturbation, permanence and extinction. Finally, some numerical examples are carried out to confirm the analytical results. One of the most interesting findings is that stochastic fluctuations introduced in our stochastic model can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.     

A segmentation method for noisy photoelectric image

In order to improve the ability of noisy photoelectric image segmentation and satisfy the requirement of human visual apperception, a noisy photoelectric image segmentation method is proposed in this paper. Firstly, the basic principle of FCM algorithm is analyzed in detail. Secondly, on the basis of PCM algorithm, only such pixels affected by noise lesser that centralized in the diagonal area of two-dimensional histogram is actualized image processing, and the probability of the pixel that lie in such area is obtained. Thirdly, objective function, membership matrix and cluster centers are renovated on the basis of PCM algorithm. Finally, experiment contrast between our method and other methods is executed, the results of experiment indicate that our method has relatively better segmentation quality and faster segmentation speed.     

高斯型耦合Tavis-Cummings模型中原子的熵压缩

利用全量子理论研究了高斯型耦合Tavis-Cummings模型中一个原子的熵压缩,运用数值计算方法讨论了原子垂直于腔轴的运动速度、光场强度以及两原子的初态对单个原子熵压缩的影响.结果表明,原子的熵压缩时间由原子的运动速度决定,压缩程度由光场强度决定,压缩时间和压缩程度还决定于原子的初始状态.     

Mn42Al50-xFe8+x合金的磁性和磁热效应

研究了Mn₄₂Al_50-xFe_8+x合金的结构、磁性和磁热效应. 通过成分调节, 居里温度T_C在室温附近一宽温区连续可调, 分别为270 K (Mn₄₂Al₄₂Fe₁₆), 341 K (Mn₄₂Al₄₀Fe₁₈)和370 K(Mn₄₂Al₃₈Fe₂₀). 磁化强度在相变温度处发生一陡降, 热磁曲线和等温磁化曲线均未观察到热和磁的滞后, 表明发生一可逆的二级相变. 在各自居里温度附近, 0-5 T的外磁场变化下磁熵变峰值分别为2.48, 2.52和2.40 J·kg^-1·K^-1. Mn_50-xAl_50-yFe_x+y合金的磁熵变峰值虽然与许多优良的磁制冷材料相比并不大, 但是制备该化合物的原材料价格非常低廉, 制备工艺简单, 加工成型也较容易, 化合物本身耐腐蚀性、延展性较好, 且在居里温度附近发生的是可逆的二级相变, 无晶格或结构的变化, 有利于制冷剂的多次循环使用. 关键词： 磁性 磁热效应 二级相变     

Control of multi-node mobile communications networks with time-varying channels via stability methods

Consider a communications network consisting of mobiles and random external data processes, each destined to a particular destination. Each mobile can serve as a node in the multi-hop path from source to destination. At each mobile the data is queued according to the source destination pair. The quality of the connecting channels are randomly varying. Time is divided into small scheduling intervals. At the beginning of each interval, the channels are estimated and this information is used for the decisions concerning allocation of transmission power and/or time, bandwidth, and perhaps antennas, in a queue and channel-state dependent way. Under a natural (and “almost” necessary) “average flow” condition, stochastic stability methods are used to develop scheduling policies that assure stability. The policies are readily implementable and allow a range of tradeoffs between current rates and queue lengths, under very weak conditions. Because of the non-Markovian nature of the problem, we use the perturbed Stochastic Liapunov function method. The choice of Liapunov function allows a choice of the effective performance criteria. All essential factors are incorporated into a “mean rate” function, so that the results cover many different systems. Extensions concerning acknowledgments, multicasting, non-unique routes, and others are given to illustrate the versatility of the method, and a useful method for getting the a priori routes is discussed.     

Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.     

Renormalization of branching models of triggered seismicity from total to observable seismicity

Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold m_d) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to investigate how the statistical properties of observable earthquakes differ from the statistics of all events. The ETAS (epidemic-type aftershock sequence) model assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. The triggering efficiency of earthquakes is assumed to vanish below a lower magnitude limit m₀, in order to ensure the convergence of the theory and may reflect the physics of state-and-velocity frictional rupture. We show that, to a good approximation, the statistical distribution of seismic rates of events with magnitudes above m_d generated by an ETAS model with branching ratio n is the same as that of events generated by another ETAS model with effective parameter n(m_d). Our present analysis thus confirms, for the full statistical (time-independent or large time-window approximation) properties, the results obtained previously by one of us and Werner, based solely on the average seismic rates (the first-order moment of the statistics). Our analysis also demonstrates that this correspondence is not exact, as there are small corrections which can be systematically calculated, in terms of additional contributions that can be mapped onto a different branching model. We also show that this approximate correspondence of the ETAS model onto itself obtained by changing m₀ into m_d, and n into n(m_d) holds only with respect to its statistical properties and not for all its space-time properties.     

Calorimetry

Methods for determining the heat content E ^*/A of hot nuclei formed in energetic nuclear reactions are discussed. The primary factors involved in converting raw data into thermal physics distributions include: 1) design of the detector array, 2) constraints imposed by the physics of the reaction mechanism, and 3) assumptions involved in converting the filtered data into E ^*/A. The two primary sources of uncertainty in the calorimetry are the elimination of nonequilibrium emissions from the event components and accounting for the contribution of neutron emission to the excitation energy sum.