【作者】 袁常青；

【导师】 赵同军；

【作者基本信息】 河北工业大学 ， 理论物理， 2005， 硕士

【摘要】 研究有限多自由度耦合系统能量耗散过程中不同自由度的动力学行为不仅是统计物理学的基本问题,也是核物理、生物物理等领域的重要问题。本文借鉴已有的理论依据和数值模拟,采用非线性动力学分析手段研究有限多自由度耦合哈密顿系统能量耗散过程的动力学特征,对深入理解与能量耗散有关的不同自由度的动力学过程有一定的意义。 本文研究了与有关自由度运动的动量p(t)相对应的功率谱随时间以及环境中无关自由度数的变化,同时研究了与无关自由度运动的动量p(t)相对应的功率谱,在子系统之间耦合作用开启前后两种不同情况的对比,以及在无关自由度数取不同有限值时,与无关自由度运动相对应的功率谱的变化。结果发现在有关系统的能量耗散过程中,有关自由度运动的频率成分向高频和低频方向都有明显展宽,随着无关系统自由度增多,展宽明显增加,低频成分比较稳定,高频成分随着时间的演变逐渐减少,最终有关自由度的运动在一个混沌的环境影响下也达到混沌;这一过程中,环境中各自由度运动的混沌特征比耦合作用开启之前更加明显:就整个系统来说,有关自由度与无关自由度之间的耦合作用开启之后的很短一段时间内,系统部分具有准周期运动的特征,部分具有混沌特征。另外,根据各自由度运动的坐标q(t)的方差在子系统之间耦合作用开启之后短期内的变化,发现有关自由度和无关自由度运动的轨迹所能分布的区域在这一时间内有短促的收缩—膨胀现象。 论文一共分五章。 第一章简要介绍多自由度耦合体系动力学问题的研究背景和发展状况,并对本工作进行简要概括。第二章和第三章分别介绍非线性动力学分析手段和用投影算符推导耦合主方程的理论。第四章从合理的数值模拟结果出发分析有关自由度及无关自由度运动的动力学特征。第五章总结本工作得出的结论。更多还原

【Abstract】 It’s a fundamental problem in statistical physics to study the dynamical behavior of different degree of freedom (DOF) in the energy dissipative process of finite coupled multi-DOF system. This is also an important topic in some fields such as nuclear physics, biophysics etc.. With some widely admitted theories and numerical simulation consulted, dynamical features of the energy dissipative process in finite coupled multi-DOF Hamiltonian system is explored in this dissertation by nonlinear dynamical analyzing methods. There are certain meanings in mis work for thoroughly understanding the nonlinear dynamical course of different DOFs related to energy dissipation.It is studied that how the power spectrum of moment pit) in the motion of relevant DOF changes with time and the number of irrelevant DOFs. The work discusses the comparison between the power spectrum of moment p(t) in the motion of irrelevant DOFs before the coupling interaction between subsystems activated and that after the coupling interaction activated, as well as the difference between the power spectrum of moment pit) in the motion of irrelevant DOFs and that with different number of irrelevant DOFs. It is found that in energy dissipative process, the distribution of spectral density about the motion of relevant DOF remarkably extends to either lower or higher frequency. The more irrelevant DOFs are, the much broader the distribution expands. In the power spectrum about relevant DOF, higher frequency components are weakened as time evolves but there are no remarkable changes for lowercomponents. Finally, the motion of relevant DOF runs to chaos with the effects from a chaotic environment. With the interaction from relevant system, the chaotic feature in the motion of all DOFs contained in irrelevant system is accordingly enhanced after the coupling interaction activated. As far as the whole system concerned, feature of quasi-periodic motion as well as feature of chaos is partially kept during an interval shortly after the coupling interaction between subsystems activated. In addition, by the variance of q(i) related to different DOF, an acute contracting-expanding behavior in the probable distribution area of the track about different DOF is observed during the interval shortly after the coupling interaction activatedThe dissertation consists of 5 sections.The background and progress for study on the problems about finite multi-DOF coupled system are introduced in Section 1, which ends with a brief summary of this work. Section 2 quotes some useful nonlinear dynamical analyzing methods. The theory of coupled-master equation derived by time-dependent projection operator is recapitulated in Section 3. With a reliable numerical simulation consulted, the dynamical features in the motion of relevant or irrelevant DOF are discussed. The last section gives a summary of the conclusions from this work.更多还原