具有记忆阻尼的随机系统的振动、扩散及信息熵演化研究

项目名称： 具有记忆阻尼的随机系统的振动、扩散及信息熵演化研究

项目编号： No.11302172

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 谢文贤

作者单位： 西北工业大学

项目金额： 25万元

中文摘要： 非线性随机动力学的研究是当前非线性科学领域中最活跃最受关注的研究课题之一。具有记忆阻尼的随机动力系统在现如今广泛应用于航空航天等各大领域的粘弹性功能材料方面；以及在湍流、渗透媒介、生物细胞等非均匀介质中粒子的反常扩散问题上都有着举足轻重的理论研究意义。鉴于此，本项目针对关联非高斯噪声激励下具有Maxwell型记忆阻尼的多自由度耦合系统，建立和发展对其随机响应及其二阶矩进行分析研究的有效理论方法和数值方法。明确Maxwell型记忆阻尼的多个延迟时间因子、耦合阻尼因子、噪声性质及关联性对随机振动、反常扩散问题以及信息熵演化规律的影响。从中确立关联简谐速度噪声的噪声频率与随机响应的瞬时演化概率密度的迁移和变化的关系。本项目的研究将丰富具有记忆阻尼的随机系统的研究理论和数值方法。进而以此为基础探索更多的非线性随机动力系统，为工程材料、物理、生物等学科相关问题的研究提供有效的理论分析手段和数值方法。

中文关键词： 反常扩散；随机共振；Maxwell型记忆阻尼；内噪声；信息熵

英文摘要： Study of nonlinear stochastic dynamics has become one of the most stirring and attention-getting problems in the field of the nonlinear science. The stochastic dynamical system with the memory damping is especially important in theoretical and application meanings, not only for the viscoelastic materials applied to the fields of Aeronautics, Astronautics and etc, but also for the anomalous diffusions of the particles in the dissymmetrical medium, such as turbulence, penetration medium, biological systems and etc. Therefore, some theoretical methods and numerical techniques are presented to analyze the stochastic responses and its second-order moments of the multiple degree-of-freedom systems with the Maxwell memory damping and two correlated non-Gaussian noises. We will illuminate the effects of the multiple relaxation times of the Maxwell memory damping, the coupling damping parameter, correlation and characteristic of noises on random vibration, anomalous diffusion and the time evolution of Shannon entropy.We will also illustrate the relationship between the frequency of harmonic-velocity noise and the transitions and changes of the instantaneous probability density. As a result, the obtained theoretical results and numerical methods will enrich the corresponding research of the stochastic dynamical systems w

英文关键词： anomalous diffusion；stochastic resonance；Maxwell memory damping；internal noise；information entropy