Statistical mechanics of nonequilibrium processes

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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.