Statistical mechanics of nonequilibrium processes

非平衡过程的统计力学

• 批准号: 6424-2009
• 负责人: Shizgal, Bernard
• 金额: $ 3.42万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=420248
• 关键词: Statistical; mechanics; nonequilibrium; processes

My research expertise is in the kinetic theory and hydrodynamics of systems far from thermal equilibrium. The theoretical models are based on transport equations for the velocity distribution functions of different species and/or the hydrodynamic equations for the lower order moments of the distribution function namely the density, mean flow and temperature. The physical systems considered include the energization of ions in gases by external electromagnetic fields, the relaxation of energetic particles created in the laboratory or that occur in the atmosphere, the escape of planetary atmospheres, the kinetic theory of granular materials and reaction-diffusion models for excitable systems directed towards the study cardiac arrhythmias. The nonequilibrium neutral and ionized systems are modeled with kinetic theory based on the Boltzmann and/or Fokker-Planck equations. Fundamental aspects of these relaxation processes are considered as well as the interpretation of laboratory experiments such as Doppler spectroscopy. Pseudospectral methods are generally the method of choice for the solution of the appropriate model equations and the further development of these numerical methods is an ongoing research activity. I am planning to apply these methods to two-dimensional problems such as reactive systems governed by a Kramers equation and the calculation of the vibrational states in some triatomic molecules The Kramers equation models a reactive system coupled to an equilibrium background characterized by a viscosity or a collision frequency. The problem is thus analogous to a similar problem in rarefied gas dynamics for which solutions are sought for all degrees of rarefaction, that is, for all collision frequencies. Occasionally, Monte Carlo methods are used in the simulation of the systems described above. I am also proposing further work on the resolution of the Gibb's phenomenon and the analysis of images in applied science and tomography. Many aspects of the research described here have practical applications to medicine and industry.

我的研究专长是远离热平衡的系统的动力学理论和流体力学。理论模型是基于传输方程的速度分布函数的不同物种和/或流体动力学方程的低阶矩的分布函数，即密度，平均流量和温度。考虑的物理系统包括气体中的离子通过外部电磁场，在实验室中创建或发生在大气中的高能粒子的弛豫，行星大气的逃逸，颗粒材料的动力学理论和针对研究心律失常的可激发系统的反应扩散模型。非平衡中性和电离系统的动力学理论的基础上玻尔兹曼和/或福克-普朗克方程建模。这些松弛过程的基本方面被认为是以及实验室实验，如多普勒光谱的解释。伪谱方法通常是用于求解适当的模型方程的选择方法，并且这些数值方法的进一步发展是正在进行的研究活动。我计划将这些方法应用于二维问题，例如由Kramers方程控制的反应系统和某些三原子分子振动态的计算Kramers方程模拟了与平衡背景耦合的反应系统，其特征在于粘度或碰撞频率。 因此，该问题类似于稀薄气体动力学中的类似问题，其中针对所有稀薄度，即针对所有碰撞频率，寻求解决方案。有时，蒙特卡罗方法用于上述系统的模拟。 我还建议进一步研究吉布现象的解决方案以及应用科学和断层摄影术中的图像分析。这里描述的研究的许多方面在医学和工业上都有实际应用。