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William Greenberg - Statistical mechanics, first developed in the 19th century by Maxwell, Boltzmann and Gibbs, among others, attempts to explain the macroscopic properties of matter in terms of the microscopic properties of its large ensemble of constituent particles. Equilibrium statistical mechanics is concerned with states of matter that appear macroscopically at rest, and presents many interesting problems to the mathematical physicist, including the study of lattice spin systems and the existence of thermodynamic variables. Non-equilibrium statistical mechanics is concerned with systems in motion, for example, with the equations which describe the transport of matter. This class of so-called transport equations has been extended to include the transport of radiation, momentum, energy, information, or any transportable quantity. Much of my own research has concentrated on determining under what conditions solutions exist for the equations of neutron transport, of gas kinetics, of radiative transfer and of plasma theory, and, when solutions exist, what some of their mathematical properties might be. Some of these existence results have been open questions for more than 130 years.Click here and look under the heading Research for more information.