Statistical Mechanics of Granular Systems

From a first principles theory for the behavior of smooth grarular systems, we derive the form for the instantaneous dissipative force acting between two grains. The present model, which is based on the classical harmonic crystal, reproduces the dependence of the kinetic energy dissipation on the grain deformation obtained by models that assume a viscoelastic behavior (without permanent plastic deformations) during the collision. We then derive kinetic equations for the rarified granular gas from the FokkerPlanck equation that describes the time evolution of the reduced distribution function for the translational granular degrees of freedom. We obtain the inelastic dissipation rate term and calculate the time evolution of the granular temperature for the homogeneous granular gas. We also derive kinetic equations for the non-homogeneous, rarified granular gas and obtain hydrodynamic equations for the system. Thesis Supervisor: Irwin Oppenheim Title: Professor of Chemistry Statistical Mechanics of Granular Systems First and foremost, I would like to thank my supervisor Prof. Irwin Oppenheim for the help and guidance throughout my graduate studies. His patience and able advice were of invali... le imnortance for me. his friendly character always made scientific research a fun thing to do. I would like to thank all the members of my thesis committee, and in particular Profs. A. Nihat Berker and Mehran Kardar for their kindness and help, and also for being great teachers. I always felt inspired by their excellent classes and by the amazing amount of knowledge I gained from them. In the same breath, I would like to thank Prof. Tom Greytak for making being a TA something of a great learning experience. I would like to recognize the fundamental importance that CAPES (brazilian funding agency) and the Department of Physics had in making possible my graduate studies. It was always a great pleasure to work, grade and teach under the guidance of Profs. George Benedek, Jacqueline Hewitt, Daniel Kleppner, David Pritchard, George Stephans and Claude Williamson. I am indebted to all my friends and to all people who helped me in one way or another during this journey. I will name but a few, but all of them who are not here are not forgotten. I would like to thank in special my brazilian and non-brazilian friends: Frank Brown, Rodrigo Capaz, Claudio Chamon, James Chen, Shanhui Fan, Mari Ferreira, Robert Ferrell, Francisco Justo, Cliff Liu, Luis Pedrosa, David Reichman, Joan Shea, Flavia Vidal, Sophia Yaliraki. And to my family goes my last and most important thank you of all. Acknowledgments