Nonequilibrium identities and response theory for dissipative particles

We derive some nonequilibrium identities such as the integral fluctuation theorem and the Jarzynski equality starting from a nonequilibrium state for dissipative classical systems. Thanks to the existence of the integral fluctuation theorem we can naturally introduce an entropy-like quantity for dissipative classical systems in far from equilibrium states. We also derive the generalized Green-Kubo formula as a nonlinear response theory for a steady dynamics around a nonequilibrium state. We numerically verify the validity of the derived formulas for sheared frictionless granular particles.Comment: 10 pages, 5 figures, to be published in Phys. Rev.

Rheology of sheared granular particles near jamming transition

We investigate the rheology of sheared granular materials near the jamming transition point. We numerically determine the values of the critical fraction and the exponents for the jamming transition using a finite size scaling and the nonlinear minimization method known as the Levenberg-Marquardt algorithm. The exponents are close to our previous theoretical prediction, but there is a small discrepancy, if the critical point is independently determined.Comment: 10 pages, 4 figure

Mode-coupling theory of sheared dense granular liquids

Mode-coupling theory (MCT) of sheared dense granular liquids %in the vicinity of jamming transition is formulated. Starting from the Liouville equation of granular particles, the generalized Langevin equation is derived with the aid of the projection operator technique. The MCT equation for the density correlation function obtained from the generalized Langevin equation is almost equivalent to MCT equation for elastic particles under the shear. It is found that there should be the plateau in the density correlation function.Comment: 22 pages, 2 figure. to be published in Progress of Theoretical Physics. to be published in Progress of Theoretical Physic

Behavior of pressure and viscosity at high densities for two-dimensional hard and soft granular materials

The pressure and the viscosity in two-dimensional sheared granular assemblies are investigated numerically. The behavior of both pressure and viscosity is smoothly changing qualitatively when starting from a mono-disperse hard-disk system without dissipation and moving towards a system of (i) poly-disperse, (ii) soft particles with (iii) considerable dissipation. In the rigid, elastic limit of mono-disperse systems, the viscosity is approximately inverse proportional to the area fraction difference from $\phi_{\eta} \simeq 0.7$, but the pressure is still finite at $\phi_{\eta}$. In moderately soft, dissipative and poly-disperse systems, on the other hand, we confirm the recent theoretical prediction that both scaled pressure (divided by the kinetic temperature $T$) and scaled viscosity (divided by $\sqrt{T}$) diverge at the same density, i.e., the jamming transition point $\phi_J > \phi_\eta$, with the exponents -2 and -3, respectively. Furthermore, we observe that the critical region of the jamming transition becomes invisible as the restitution coefficient approaches unity, i.e. for vanishing dissipation. In order to understand the conflict between these two different predictions on the divergence of the pressure and the viscosity, the transition from soft to hard particles is studied in detail and the dimensionless control parameters are defined as ratios of various time-scales. We introduce a dimensionless number, i.e. the ratio of dissipation rate and shear rate, that can identify the crossover from the scaling of very hard, i.e. rigid disks to the scaling in the soft, jamming regime.Comment: 23 pages, 20 figures, to appear in Progress of Theoretical Physics Supplemen

Representation of the nonequilibrium steady-state distribution function for sheared granular systems

We derive the representation of the nonequilibrium steady-state distribution function which is expressed in terms of the excess free energy production. This representation resembles the one derived recently by Komatsu and Nakagawa [Phys. Rev. Lett. 100 (2008), 030601] resting on the use of microscopic time-reversal symmetry, but our representation applies also to sheared granular systems in which such a symmetry is broken.Comment: 16 pages, to appear in Progress of Theoretical Physics Supplemen

Nonequilibrium liquid theory for sheared granular liquids

A noneqilibrium liquid theory for uniformly sheared granular liquids is developed starting from the SLLOD Liouville equation. We derive a generalized Green-Kubo formula and also demonstrate that the formulation is essentially independent of the choice of initial condition.Comment: 12 pages, 2 figure