Cascade of Random Rotation and Scaling in a Shell Model Intermittent Turbulence

The time behaviors of intermittent turbulence in Gledzer-Ohkitani-Yamada model are investigated. Two kinds of orbits of each shell which is in the inertial range are discussed by portrait analysis in phase space. We find intermittent orbit parts wandering randomly and the directions of unstable quasi-periodic orbit parts of different shells form rotational, reversal and locked cascade of period three with shell number. We calculate the critical scaling of intermittent turbulence and the extended self-similarity of the two parts of orbit and point out that nonlinear scaling in inertial-range is decided by intermittent orbit parts.     

Scaling Behavior of an Aggregation-Migration Model

We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates K_A(i;j)=K'_A(i;j) ∝ij^v₁ and K_B(i;j)=K'_B(i;j) ∝ij^v₂, we find that the evolution behavior of the system depends crucially on the values of the indexes v₁ and v₂. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.     

Dynamics of aggregation－annihilation process with cluster removals

We have studied the kinetic behaviours of irreversible aggregation－annihilation models with cluster removals. In the models, an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible annihilation reaction occurs simultaneously between two different species; meanwhile, the clusters of large size are gradually removed from the system. In a mean-field limit, we obtain the general solutions of the cluster-mass distributions for the cases with an arbitrary removal probability. We found that the cluster-mass distribution of either species satisfies a generalized or modified scaling form. The results also indicate that the evolution behaviours of the systems depend strongly on the details of the reaction events.     

谐和与有界噪声联合参激作用下的Visco-Elastic系统

研究了带visco-elastic项的非线性系统,在谐和与有界噪声联合参激作用下的响应和稳定性问题。用多尺度法分离了系统的快变项,并求出了系统的最大Liapunov指数和稳态概率密度函数,根据最大Liapunov指数可得系统解稳定的充分必要条件。讨论了系统的visco-elastic项对系统阻尼项和刚度项的贡献,给出了随机项和确定性参激强度等参数对系统响应影响的讨论。数值模拟表明该方法是有效的。     

Scaling Equation for Invariant Measure

An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.     

EFFECTS OF POISSON’S RATIO ON SCALING LAW IN HERTZIAN FRACTURE

In this paper the Auerbach＇s scaling law of Hertzian fracture induced by a spherical indenter pressing on a brittle solid is studied. In the analysis, the singular integral equation method is used to analyze the fracture behavior of the Hertzian contact problem. The results show that the Auerbach＇s constant sensitively depends on the Poisson＇s ratio, and the effective Auerbach＇s domain is also determined for a given value of the Poisson＇s ratio.     

两点边值问题的小波配点法

根据多分辨分析,提出用任意连续的尺度函数构造区间上的插值基函数,形成以尺度函数为基础的求解两点边值问题的小波配点法.该方法中,尺度函数不受紧支撑、插值等性质的限制,计算复杂度小,数值解收敛性由多分辨分析理论保证.同时,给出边值条件的积分处理方法,能够方便地处理任意边界条件,当尺度函数不具有高阶导数时,该方法也能有效使用.数值算例表明,该方法是一个高效、高精度的算法.     

基于排队理论的最优生产线设计

本研究了在工厂生产线的设计过程中,如何安排生产线上的机器、工人、甚至物料运输设备,以提高生产率的水平,降低生产过程中的原料和半成品存量的最优化问题,用排队论方法建立了该问题的数学模型,并解出了结果和进行经济评价。     

湍流的分形特征

综述了湍流分维测量的最新成果,涉及湍流分维测量的传统证据、分维测量方法以及湍流分维测量成果,重点详细介绍了湍流分维测量的各种方法及其优缺点,讨论了各家的测量成果,指出了具有广泛影响的 Ｓｒｅｅｎｉｖａｓａｎ等人使用的分维测量方法存在的问题,介绍了作者最新的成果．最后,综述了Ｎ－Ｓ方程与分形、标度律、湍流的理论分形模型等与湍流分维应用相关的领域的最新进展．对湍流分形研究进行了讨论和展望