软物质动力学系统阻尼效应的保结构分析方法研究

Different from the traditional dynamic system, dissipation and stochastic perturbation in the soft matter dynamic system determine some important dynamical behaviors. Thus, focusing on the inherent geometic properties, the dissipation effect and the stochastic perturbation effect of the soft matter dynamic system, a structure-preserving method is proposed to study the damping effects of the linear polymer soft matter dynamic system and reveal the inherent mechanism of the nonlinear dynamical properties in this project. Considering the nonlinear viscoelastic constitutive relation and the time-variant viscosity depending on the flow velocity gradient, firstly the macroscopic model and mesoscopic model of the soft matter dynamic system under the Lagrange framework are established. Then, based on the Hamilton variation principle, the infinite-dimensional Hamilton canonical systems are proposed. Subsequently, according to the symplectic dimensionality reduction method and multi-symplectic order reduction method, the coupled generalized symplectic sub-systems as well as the generalized multi-symplectic sub-systems are derived from the canonical systems, which preserve all of the inherent geometic properties of the original system theoretically. Finally, the generalized symplectic algorithm and the generalized multi-symplectic algorithm are constructed to study the global damping effects as well as the local damping effects of the soft matter dynamic system. From the numerical results of the structure-preserving damping effects analysis, the physical-mechanical mechanism of the nonlinear dynamical properties for soft matter system is explored. Studying the damping effects of the soft matter dynamic system by structure-preserving method and revealing the physical-mechanical mechanism of the nonlinear dynamical properties for soft matter system will not only advance the structure-preserving numerical methodology, but also give some advices for the controllable preparation of some new soft matter materials.

软物质动力学系统阻尼效应的保结构分析是揭示其诸如自组织等特性物理力学机理的前提条件。考虑线形高分子软物质材料粘弹性本构关系和阻尼- - 应变速率非线性关系，建立软物质动力学问题的宏观和介观Lagrange随机动力学控制方程；基于Hamilton变分原理，将控制方程导入耗散无限维Hamilton正则系统；借助辛降维和多辛降阶方法，分别构造其低维一阶耦合广义辛子系统和广义多辛子系统，该子系统保持了原系统的一切固有几何特性；采用广义辛算法研究宏观软物质动力学系统的整体阻尼效应；并采用广义多辛算法研究软物质动力学系统的宏观和介观局部阻尼效应，实现保持系统守恒型几何性质同时精确提取阻尼效应和随机微扰效应；基于阻尼效应分析结果，探索软物质特殊性质的介观机理。 建立软物质动力学问题的保结构分析方法用于研究其阻尼效应，探索软物质特性的物理力学机理，完善保结构算法理论体系，同时为软物质材料的可控制备提供参考。

软物质系统存在独特的微观结构，在外界温度及浓度等因素发生变化/扰动时，其力学本构关系将随之改变，而本构关系的变化将直接影响软物质动力学体系的动力学行为，因此，软物质动力学系统阻尼效应的保结构分析是揭示其诸如自组织等特性物理力学机理的前提条件。.本项目主要开展了如下三个方面的研究工作：保守Hamilton动力学系统的保结构分析方法研究；非保守动力学系统的保结构分析方法研究；软物质动力学系统的保结构分析研究。在保守动力学系统保结构分析方法研究方面，发展了多辛分析方法用于研究诸如尖波碰撞、孤子共振等无限维动力学系统局部动力学特性。在非保守动力学系统的保结构分析方法方面，发展了广义多辛分析方法，重现了无限维动力学系统的非保守性质。在软物质动力学系统保结构分析方法研究方面，应用广义多辛分析方法揭示了软物质体系的温度效应和阻尼效应的动力学机理。.本项目建立软物质动力学问题的保结构分析方法用于研究其阻尼效应，探索软物质特性的物理力学机理，完善保结构算法理论体系，同时为软物质材料的可控制备提供参考。