Statistical Mechanics of Almost One-dimensional Systems

Statistical mechanics of relativistic one-dimensional self-gravitating systems.

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of N particles coupled to lineal gravity and can be considered as a model of N relativistically interacting sheets of uniform mass. The partition function and one-particle distribution functions are computed to leading order in 1/c where c is the speed of light; as c --> ...

Probability Densities for Some One-Dimensional Problems in Statistical Mechanics

Statistical mechanics of complex neural systems and high dimensional data

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? And second...

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...

Statistical Mechanics of Lattice Systems

We study the thermodynamic limit for a classical system of particles on a lattice and prove the existence of infinite volume correlation functions for a "large" set of potentials and temperatures. §