טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentYair Shokef
SubjectThermodynamic Analogies in Granular Materials
DepartmentDepartment of Physics
Supervisor Full Professor Levine Dov


Abstract

We investigate possible statistical mechanics descriptions of granular materials. We identify two characteristics of granular materials, which prevent them from being in thermodynamic equilibrium. Since thermal energy is irrelevant for the translational motion of macroscopic grains, granular systems tend to jam in a limited set of states and do not explore their possible states effectively. This limit on ergodicity is even stronger in densely packed systems, where global rearrangements are required for single particles to move. The second property preventing even dilute granular systems from being in thermodynamic equilibrium is dissipation, or energy loss in the inelastic grain collisions. Dissipation breaks the dynamics' symmetry to time reversal and prohibits detailed-balance. We distinguish between these factors by considering two extreme systems: of dense and static packings of grains, where jamming is prominent, and of dilute and dynamic granular gases, where dissipation dominates.


For strongly jammed systems, we investigate the role of friction on compaction and segregation in static granular packings. We construct a mechanical model incorporating the effect of friction on the local volume and entropy of the packing, and together with original mean field geometrical calculations, combine it with Edwards' thermodynamic hypothesis on the statistical mechanics of static granular packings. Our model predicts that larger friction causes less efficient compaction and that mixtures segregate due to frictional differences between grains. A phase diagram for segregation versus friction coefficients of the two species is generated. Finally, the resulting segregation is related directly to the volume fraction without the explicit use of the yet unclear notion of compactivity.


Inspired by granular gases, we investigate the statistical mechanics of driven dissipative systems by introducing a minimal stochastic model for their dynamics. The model incorporates the essential features of dissipative interactions with maximal randomness. Upon an interaction between two particles, the non-dissipated energy is randomly redistributed between them. We demonstrate various aspects of the non-equilibrium behavior of driven dissipative systems on our model: The energy distribution differs from the equilibrium Boltzmann distribution, however we find that its high energy tail is proportional to the Boltzmann distribution; Time dependent fluctuation-dissipation relations are generally violated, however we show that they asymptotically hold for long waiting times, and exactly hold for simple measurements; Effective temperatures defined by different means on the same system generally differ, however their numerical values are ordered and in some cases we were able to show that effective temperatures exactly coincide.