基于Lorenz映射的混沌系统分支变换预报规律研究

尽管Lorenz系统具有混沌和非周期性质, 但其分支变换是可预报的.本文以强迫Lorenz系统为数学模型, 基于Lorenz映射, 研究了混沌系统分支变换的预报规律, 将原有关于分支开始变换条件和新分支持续时间的两条一般规律扩展到了3条, 并首次分析了系统当前状态达到变换条件所需时间的预报规律, 从而为预报混沌系统非周期演变提供了另一途径.结果表明: 映射尖点位置为分支变换的临界值, 当变量z超过相应临界值时, 系统在当前分支的运动即将结束, 下一循环将跳跃到另一分支运动; 系统在同一分支循环的次数随极值z_max单调减小, z_max 越小, 达到变换条件需循环的次数越多; 系统在新分支持续的时间是先前分支最大极值z_M 的单调增加函数, z_M越大, 持续时间增加的幅度也越大.此外, 外强迫影响着混沌系统分支变换的预报规律, 其不但使正负分支的变换条件出现差异, 且与新分支持续时间的增加速率和达到变换条件所需时间的递减速率密切相关. 关键词： Lorenz映射 分支变换 外强迫 预报规律     

雷电电磁场峰值的概率分布

获得雷电电磁场的随机特性,是研究雷电电磁场对电子系统有害耦合效应评估的基础。基于雷电流的统计特性,在具有一般性的概率框架下讨论雷电电磁场,导出电磁场峰值的概率分布函数及密度函数,采用多重积分法计算出不同位置处电场强度和磁场强度峰值的概率分布图和累积概率分布图,计算结果与蒙特卡洛模拟结果吻合。     

Numerical simulation of back discharge: Influence of pinhole geometry on the regime transitions

This paper presents numerical simulation of back discharge activity that is modelled at a pinhole in a dielectric layer on plane anode. First, for a given pinhole geometry, the transitions between back discharge regimes have been depicted as a mode diagram. Then, we have studied the influence of the dielectric layer thickness on the regime transitions. We have shown that increase in the layer thickness (within range of 0.02–0.2 mm) promotes the back discharge development. Finally, we have studied the influence of ‘crater configuration’. We have shown that ‘crater shape’ favours the back discharge ignition, whereas limits the resulting discharge development.     

Method of invariant grid for model reduction of hydrogen combustion

The Method of Invariant Grid (MIG) is a model reduction technique based on the concept of slow invariant manifold (SIM). The MIG approximates the SIM by a set of nodes in the concentration space (invariant grid). In the present work, the MIG is applied to a realistic combustion system: an adiabatic constant volume reactor with H₂-air at stoichiometric proportions. By considering the thermodynamic Lyapunov function of the detailed kinetic system, the notion of the quasi-equilibrium manifold (QEM) is adopted as an initial approximation to the SIM. One- and two-dimensional discrete approximations of the QEM (quasi-equilibrium grids) are constructed and refined via MIG to obtain the corresponding invariant grids. The invariant grids are tabulated and used to integrate the reduced system. Excellent agreement between the reduced and detailed kinetics is demonstrated.     

Theory of the successive phase transitions in KNbO3

The microscopic mechanism of the successive cubic-tetragonal-orthorhombic-rhombohedral phase transitions in KNbO₃ is discussed quantitatively from the microscopic free energy based upon the mean field approximation where the Nb ions are displaced to create spontaneous deformations. From the calculation of the microscopic free energy, it is shown that the order of the phase transitions and the experimental values of the transition entropy in KNbO₃ are well explained by this model.     

外强迫对Lorenz系统初值可预报性的影响

利用强迫Lorenz模型, 研究了外强迫对Lorenz系统混沌性质、 映射结构及初值可预报性的影响, 并以海表温度为大气运动的外强迫, 用实际大气海洋资料分析了外强迫对大气可预报性的影响. 结果发现, 系统混沌现象的出现与外强迫有关, 外强迫改变了Lorenz系统的运动规律, 使围绕两奇怪吸引子运动的随机性减少. 考虑外强迫后, 系统运动轨迹的概率密度函数呈不对称的双峰结构, 且Lorenz映射由无外强迫时的一个尖点分离为两个尖点, 尖点的偏离方向和偏离位置分别与外强迫的正负和大小有关. 外强迫可减小Lorenz系统对初值的敏感性, 提高系统的初值可预报性, 尤其是外强迫越大, 可预报性提高的幅度也越大. 这些结果在不同强度海表温度强迫下的实际大气可预报性分析中得到了证实, 即海温异常越大, 实际大气变量的可预报性也越大.     

On the p,q-binomial distribution and the Ising model

We employ p, q-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case p = q. We apply our investigation to the simple d-dimensional lattices for d = 1, 2, 3, 4, 5 and fit p, q-binomial distributions to our data, some of which are exact but most are sampled. For d = 1 and d = 5, the magnetisation distributions are remarkably well-fitted by p,q-binomial distributions. For d = 4 we are only slightly less successful, while for d = 2, 3 we see some deviations (with exceptions!) between the p, q-binomial and the Ising distribution. However, at certain temperatures near T _c the statistical moments of the fitted distribution agree with the moments of the sampled data within the precision of sampling. We begin the paper by giving results of the behaviour of the p, q-distribution and its moment growth exponents given a certain parameterisation of p, q. Since the moment exponents are known for the Ising model (or at least approximately for d = 3) we can predict how p, q should behave and compare this to our measured p, q. The results speak in favour of the p, q-binomial distribution's correctness regarding its general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution, however, is not settled.     

Local field distribution revisited in the light of percolation model of spin glass transition

The existence of a ‘hole’ in the local field distributionP(H) in canonical spin glasses is proved in the framework of Mookerjee and Chowdhury’s percolation model of spin glass transition.     

几率分布指数律与间歇现象

本文举例指出,落入快度区间的概率本身具有某种分布,并不一定能导致阶乘矩随区间长度变化的指数律,因此,不是导致Intermittency行为的充分条件.     

Evolution of the Probability Measure for the Majda Model: New Invariant Measures and Breathing PDFs

In 1993, Majda proposed a simple, random shear model from which scalar intermittency was rigorously predicted for the invariant probability measure of passive tracers. In this work, we present an integral formulation for the tracer measure, which leads to a new, comprehensive study on its temporal evolution based on Monte Carlo simulation and direct numerical integration. An interesting, non-monotonic “breathing” phenomenon is discovered from these results and carefully defined, with a solid example for special initial data to predict such phenomenon. The signature of this phenomenon may persist at long time, characterized by the approach of the PDF core to its infinite time, invariant value. We find that this approach may be strongly dependent on the non-dimensional Péclet number, of which the invariant measure itself is independent. Further, the “breathing” PDF is recovered as a new invariant measure in a distinguished time scale in the diffusionless limit. Rigorous asymptotic analysis is also performed to identify the Gaussian core of the invariant measures, and the critical rate at which the heavy, stretched exponential regime propagates towards the tail as a function of time is calculated.     

The distribution of clusters for the Ising model

We rigorously prove that the probabilityP _n for the origin to belong to a cluster of exactlyn positive spins in thev-dimensional Ising model behaves as exp(–n^{(v – 1)/v}) in various regions, including in particular the low-temperature positive and negative phases in zero magnetic field.     

Probability distribution of normalized structure factor magnitudes for a centrosymmetric crystal with planar molecules in the unit cell

The reasons and conditions for applicability of the Cauchy distribution law for crystal structure factor components are discussed. It is shown that the standardized structure factors of centrosymmetric crystals are quite prone to be Cauchy distributed for crystals having planar molecules in their unit cells.     

Evolutionary model of the personal income distribution

The aim of this work is to develop a qualitative picture of the personal income distribution. Treating an economy as a self-organized system the key idea of the model is that the income distribution contains competitive and non-competitive contributions. The presented model distinguishes between three main income classes. 1. Capital income from private firms is shown to be the result of an evolutionary competition between products. A direct consequence of this competition is Gibrat’s law suggesting a lognormal income distribution for small private firms. Taking into account an additional preferential attachment mechanism for large private firms the income distribution is supplemented by a power law (Pareto) tail. 2. Due to the division of labor a diversified labor market is seen as a non-competitive market. In this case wage income exhibits an exponential distribution. 3. Also included is income from a social insurance system. It can be approximated by a Gaussian peak. A consequence of this theory is that for short time intervals a fixed ratio of total labor (total capital) to net income exists (Cobb–Douglas relation). A comparison with empirical high resolution income data confirms this pattern of the total income distribution. The theory suggests that competition is the ultimate origin of the uneven income distribution.     

Probability distribution of the ratio of consecutive level spacings in interacting particle systems

We study the probability distribution of the ratio of consecutive level spacings for embedded one- plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between the numerical results and the recently derived analytic form for the distribution and other related quantities is found to be close. This establishes that the statistics of quotients of successive spacings, which do not depend on unfolding, is useful tool in the analysis of local level fluctuations in many-particle systems.     

一个描述合作网络顶点度分布的模型

讨论一类社会合作网络以及一些与其拓扑结构相似的技术网络的度分布.建议一个最简化模型，通过解析的方法说明这些网络演化的共同动力学机理，而且说明顶点的度分布和项目度分布之间具有密切的一致关系，而项目所含的顶点数分布对度分布的影响较小；对模型的更一般情况进行数值模拟，说明上述结论具有一定的普遍性.这个模型显示这类广义的合作网络一般具有处于幂函数和指数函数这两种极端情况之间的度分布.简要介绍对一些实际合作网络做统计研究的结果，说明本模型的合理性. 关键词： 合作网络 度分布 项目度分布 项目含顶点数     

最概然分布、微观状态数及其相关问题

通过对一个简单模型的研究可知,最概然分布包含的微观状态数和全部可能微观状态数的比值在热力学极限下为零.当一个热力学体系处于平衡态时,最概然分布及其附近相对于实验可以达到的精度来说的极其狭窄的区域内的分布包括了体系几乎全部可能的微观状态数.     

Nonlinear-map model for the control of an airplane schedule

We study the dynamics and control of an airplane in air transportation between two airports. The dynamic models are presented for the airplane schedule. The dynamics of an airplane is described by the piecewise map and delayed map models. The characteristics of the nonlinear maps are studied analytically and numerically. The airplane displays the complex motion in the unstable region. The motion of the airplane depends on the quantity of goods, the control method, and the delay. It is shown that the control delay has an important effect on the motion.     

Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

ˮ�����ģ��ֲ�ģ������������ֵģ��

用JAEA水冷包层(WCSB)模块侧壁的流量分配实验验证了SST湍流模型,建立了水冷包层模块第一壁的数值分析模型,研究了第一壁各冷却管中的流量分配情况。分析结果发现,第一壁模型入口集管中存在复杂的流动行为,冷却剂可以明显的区分为主流和逆流两大部分,其中主流进入冷却管的位置是影响流量分配的主要因素,逆流区形成了一系列次级涡流和沿管壁的环向流动。分析结果表明,在第一壁模型中,在所以条件下,各冷却剂通道中存在流量分配不均匀现象,流速最大值与最小值偏差均小于2%。