Statistical mechanics of nonequilibrium processes

我的研究专长是远离热平衡的系统的动力学理论和流体动力学。理论模型是基于不同种类的速度分布函数的输运方程和/或分布函数的低阶矩即密度、平均流量和温度的流体动力学方程。考虑的物理系统包括外部电磁场对气体中离子的充能，在实验室中产生的或在大气中发生的高能粒子的松弛，行星大气的逃逸，颗粒材料的动力学理论和用于研究心律失常的可激系统的反应扩散模型。非平衡中性和电离系统用基于玻尔兹曼和/或福克-普朗克方程的动力学理论建模。这些弛豫过程的基本方面，以及解释实验室实验，如多普勒光谱。伪谱法通常是求解适当模型方程的首选方法，这些数值方法的进一步发展是一项正在进行的研究活动。我计划将这些方法应用于二维问题，比如由Kramers方程控制的反应系统，以及一些三原子分子振动状态的计算。Kramers方程模拟了一个反应系统，它与一个以粘度或碰撞频率为特征的平衡背景相耦合。因此，这个问题类似于稀薄气体动力学中的一个类似问题，在稀薄气体动力学中寻求所有程度的解，即所有碰撞频率的解。有时，蒙特卡罗方法被用于上述系统的模拟。我还建议进一步研究吉布现象的解析度以及应用科学和断层扫描中的图像分析。这里描述的研究的许多方面对医学和工业有实际应用。

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.