A Difference Hamiltonian Operator and a Hierarchy of Generalized Toda Lattice Equations

A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constants in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulations a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy.     

Squeeze flow of a second-order fluid between two parallel disks or two spheres

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds‘ lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neelected.     

离散元与有限元结合的多尺度方法及其应用

在深入研究复杂结构和非均质材料冲击响应和破坏机理的过程中,往往遇到多尺度计算问题.提出并建立起离散元与有限元结合的多尺度方法,该方法采用离散元对感兴趣的局部进行细观尺度的模拟,利用有限元进行宏观的模拟,从而节约了计算时间.采用一种特殊的过渡层衔接离散元区和有限元区.将这一方法应用于激光辐照下预应力铝板的破坏响应,并将得到的模拟结果与实验进行了比较.     

激光辐照受拉铝板破坏行为的时空多尺度数值模拟

推导耦合过渡区内参变量信息交换的元/网格动量传递多尺度算法,建立离散元与有限元耦合时空多尺度计算模型,并应用于激光辐照下受拉铝板破坏行为的数值模拟中.通过对比有限元计算模型、空间多尺度计算模型与时空多尺度计算模型在激光辐照下受拉铝板破坏算例的模拟结果,验证离散元与有限元耦合时空多尺度计算模型的准确性和数值计算高效率优势.使用该多尺度计算模型从宏观和细观尺度对铝板破坏行为进行数值模拟,模拟结果与实验结果基本一致.     

功能梯度材料平面问题的辛弹性力学解法

将辛弹性力学解法推广用于功能梯度材料平面问题的分析,考虑沿长度方向弹性模量为指数函数变化而泊松比为常数的矩形域平面弹性问题,给出了具体的求解步骤. 提出了移位Hamilton矩阵的新概念,建立起相应的辛共轭正交关系;导出了对应特殊本征值的本征解,发现材料的非均匀特性使特殊本征解的形式发生明显的变化.      

夹层梁低速冲击下的接触定律与结构响应

在考虑面板面内拉伸刚度等非线性因素的基础上,将夹层梁上面板视为弹塑性地基上的梁,由其平衡方程推导准静态压入接触定律. 进而研究了底面固定于刚性平面的夹层梁的低速冲击响应,验证了所推导的准静态压入接触定律在低速冲击下依然足够精确. 最后,用能量守恒模型,离散模型和连续模型分析了两端简支夹层梁的低速冲击响应以及接触持续时间.同时讨论了冲头与夹层梁质量比和初速度对结构响应以及分析模型适用性的影响. 理论分析结果与数值模拟结果比较表明:推导的接触定律是准确有效的. 给定初速度,质量比很小时,只有连续模型有效,而当质量比较大时3种模型均有效;给定质量,初速度较大时只有连续模型比较有效. 连续模型预测的接触持续时间与初速度无关.      

关闭—启动型Geom／G／1离散排队及其在ATM网络中的应用

研究带有关闭延迟和启动时间的Geom/G/1离散时间排队,导出了稳态队长、等待时间的分布及其随机分解结果,该模型可用于ATM网络的虚通道分析,给出响应时间、启动率,闲置率等指标公式。     

Noncommutative Differential Calculus Approach to Discrete Symplectic Schemes on Regular Lattice

By means of a noncommutative differential calculus on function space of discrete Abelian groups and that of the regular lattice with equal spacing as well as the discrete symplectic geometry and a kind of classical mechanical systems with separable Hamiltonian of the type H(p, q) = T(p) + V(q) on regular lattice, we introduce the discrete symplectic algorithm, i.e., the phase-space discrete counterpart of the symplectic algorithm including original symplectic schemes and the jet-symplectic schemes in terms of the discrete time jet bundle formalism, on the regular lattice. We show some numerical calculation examples and compare the results of different schemes.     

Photo-controlled alignment and helical organization in main-chain liquid crystalline alternating polymers

Materials with highly ordered nanoscale structures can translate molecular processes to macroscopic function. Here we report on the photo-controlled organization of achiral alternating copolymers composed of discrete length blocks showing well-defined sub-10 nm morphologies. These alternating copolymers consist of main-chain azobenzene building blocks alternating with discrete oDMS blocks of various precise lengths. Remarkably, we demonstrate the imprinting of a stable helical molecular arrangement in spin-casted thin films by irradiation with circularly polarized light, without chiral dopant or plasticizer required. By following the out-of-equilibrium photo-switching process over irradiation time, the mechanism of molecular reorganization is unraveled and rationalized with the nature of the morphology. Linear photo-organization is preferentially reached with flexible and symmetric cylindrical structures while helical photo-organization is most easily obtained with robust but rotatable lamella structures. These findings suggest that precision in the synthesis and assembly of alternating copolymers can lead to complete control over molecular organization and main-chain motion.     

Experiment Driven Ann-GA Based Technique for Optimal Distribution of Discrete Heat Sources Under Mixed Convection

This article reports the results of mixed convection heat transfer studies from five heat sources (aluminum) mounted at different positions on a substrate board (Bakelite). The goal is to determine the optimal arrangement, such that, the maximum temperature excess is minimum among all the possible configurations. For accomplishing this, a completely experimental driven hybrid optimization strategy, that combines Artificial neural network (ANN) with Genetic algorithm (GA) is used. Initial optimization studies are carried out by employing a heuristic non-dimensional geometric parameter λ, which is identified to be the key parameter to decide the maximum temperature in the system.