Multiscale Coupling in Complex Mechanical Systems

Multiscale coupling attracts broad interests from mechanics, physics and chemistry to biology. The diversity and coupling of physics at different scales are two essential features of multiscale problems in far-from-equilibrium systems. The two features present fundamental difficulties and are great challenges to multiscale modeling and simulation. The theory of dynamical system and statistical mechanics provide fundamental tools for the multiscale coupling problems. The paper presents some closed multiscale formulations, e.g., the mapping closure approximation, multiscale large-eddy simulation and statistical mesoscopic damage mechanics, for two typical multiscale coupling problems in mechanics, that is, turbulence in fluids and failure in solids. It is pointed that developing a tractable, closed nonequilibrium statistical theory may be an effective approach to deal with the multiscale coupling problems. Some common characteristics of the statistical theory are discussed.

基于代理模型的水下滑翔机机翼设计优化方法

在复杂工程系统的概念设计优化中,高精度数值分析方法得到广泛应用,将高精度数值分析与优化方法有机结合,对设计空间展开全面搜索与寻优,已经成为现代设计优化方法的重要发展方向。以水下滑翔机的概念设计为研究对象,引入代理模型,控制高精度分析试验的数量,有效地化解精度与效率之间的矛盾。将参数化几何建模、网格划分以及流体数值模拟分析集成为自动分析流程,并以此为基础采用试验设计理论,构建代理模型,解决水下滑翔机机翼的多目标设计优化问题。给出基于代理模型的设计优化过程,并系统地比较几种试验设计方法的适应性,重点讨论多项式响应面和径向基函数代理模型,所得代理模型相对误差小于2%。采用梯度寻优方法与遗传算法在给定设计空间内进行全面搜索,获得机翼的最佳平面构形,水下滑翔机的升阻比提高6.76%,俯仰力矩的绝对值由0.2760N•m降低为0.0015N•m,提高水下滑翔机的运动性能。

大型复杂工程系统研究开发中的方法论问题

本文通过大量事例说明了方法论对完成大型工程项目的重要意义,总结了工程技术中方法论的一般原理,并以此为指导,提出了大型自动化系统开发中的新思路。

Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. (c) 2007 American Institute of Physics.