Investigation of Galilean invariance of multi-phase lattice Boltzmann methods

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is a major source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to two orders of magnitude for large velocities. We found that this is true in particular for methods in which the interactions are incorporated through a forcing term. Methods in which interactions are incorporated through a non-ideal pressure tensor only benefit for large velocities.     

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system’s chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.     

The Properties and Applications of Invariable Function for Markov Chains in Random Environments

In this paper, various concepts of recurrence and transience are introduced into the research field of Markov chains in random environments, and the concepts and properties of invariant function for Markov chains in random environments are investigated. By using those properties, we obtain a criterion for the state to be recurrent or transient.     

一类具有欧拉形式的中立型微分方程的振动性

研究具有欧拉形式的无界时滞中立型微分方程解的振动性，给出了方程振动的几个充分条件。     

离散椭球分布下两阶段WCVaR风险利润优化模型及应用

本文研究随机变量非完全分布下的两阶段风险-利润优化问题。采用最坏情况下条件风险(Worst-case Conditional Value-at-Risk:WCVaR) 度量指标,在离散椭球分布下建立了两阶段WCVaR 约束下利润期望最大优化模型,运用优化对偶方法将复杂的Max-Min 结构化简,理论上证明了简化模型和原模型的同解性,以发电商电能分配组合优化为数值实例,验证了模型和计算方法的有效性。     

“化学反应速率”有关实验的优化与改进研究

利用体温、室温和冰温控制碱性葡萄糖溶液与蓝色亚甲基蓝溶液反应的温度,利用自制装置观察不同浓度稀盐酸与锌反应生成氢气的速率,利用EDTA钠盐调控催化剂催化过氧化氢分解,对中学化学"化学反应速率"一节学生实验进行巧妙改进和适当拓展。使实验过程更为生动、科学和形象地揭示了温度、浓度和催化剂对化学反应速率的影响。     

Global analysis of smooth solutions to a hyperbolic-parabolic coupled system

We investigate a model arising from biology, which is a hyperbolic- parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the Hs ∩ Ll-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L2 decay rate of the solution and the almost optimal L2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods.     

二维射影线性群与区传递4-(q+1,5,λ)设计

在组合设计的研究领域中,如何构造具有给定参数的t-设计是一个重要而且困难的问题.利用设计的自同构群来构造t-设计是这一问题有效的解决方法之一.在本文中,设D=(X,B)是一个4-(q+1,5,λ)设计,G≤Aut(D)区传递地作用在D上且X=GF(q)∪{∞},这里GF(q)是q元有限域.设PSL(2,q)(?)G≤PTL(2,q).利用Kramer和Mesner的关于构造区组设计的一个结果和二维射影线性群作用在X的5-子集的集合上的轨道,得到了如下结果:(1)G=PGL(2,17)并且D是一个4-(18,5,4)设计;或(2)G=PSL(2,32)并且D是一个4-(33,5,4)设计;或(3)G=PTL(2,32)并且D是4-(33,5,5)和4-(33,5,20)设计之一.