New Solutions of the 2+12+1 Dimensional Einstein Gravity Coupled to Maxwell Power type Non Linear Electric field with Dilaton field

New solutions are derived in the $2+1$ gravity which is coupled to $|{\cal F}|^k$ type non-linear electric field in Maxwell Power theory with dilaton field. We obtain consistent solutions in general $k$ case. We also investigate the behavior of the metric function with the space-time singularity. Then, we found some black hole solutions when the space-time has a singular point at $r=0$. Addition, we derive the Brown-York mass when the space-time represents black hole.Comment: 6 pages, 3 figure

Weakly nonlinear analysis of two dimensional sheared granular flow

Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg-Landau (TDGL) equation of a disturbance amplitude starting from a set of granular hydrodynamic equations and discuss the bifurcation of the steady amplitude in the hydrodynamic limit.Comment: 24 pages, 6 figures. Section 3, 4 and 5 are changed. Figures 2-6 are update

A microscopic theory for discontinuous shear thickening of frictional granular materials

We extend a recent theory for the rheology of frictionless granular materials [K. Suzuki and H. Hayakawa, Phys. Rev. Lett. 2015, 115, 098001] to the case of frictional disks in two dimensions. Employing a frictional contact model for molecular dynamics simulations, we derive difference equations of the shear stress, the granular temperature, and the spin temperature from the generalized Green-Kubo formula, where all the terms are given by microscopic expressions. The numerical solutions of the difference equations not only describe the flow curve, but also reproduce the hysteresis of shear stress, which can be the signature of discontinuous shear thickening of frictional disks.Comment: 4 pages, 1 figure, the conference proceedings for Powders & Grains 201

Quantitative test of the time dependent Gintzburg-Landau equation for sheared granular flow in two dimension

We examine the validity of the time-dependent Ginzburg-Landau equation of granular fluids for a plane shear flow under the Lees-Edwards boundary condition derived from a weakly nonlinear analysis through the comparison with the result of discrete element method. We verify quantitative agreements in the time evolutions of the area fraction and the velocity fields, and also find qualitative agreement in the granular temperature.Comment: 10 pages, 4 figures. This paper is one of contributed papers to the proceedings of IUTAM symposium on "MOBILE PARTICULATE SYSTEMS: Kinematics, Rheology and Complex Phenomena" held at Bangalore in January 23-27, 201

Kinetic theory for dilute cohesive granular gases with a square well potential

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the validity of our theory by performing the direct simulation Monte Carlo.Comment: 22 pages, 11 figure

A Master equation for force distributions in polydisperse frictional particles

An incremental evolution equation, i.e. a Master equation in statistical mechanics, is introduced for force distributions in polydisperse frictional particle packings. As basic ingredients of the Master equation, the conditional probability distributions of particle overlaps are determined by molecular dynamics simulations. Interestingly, tails of the distributions become much narrower in the case of frictional particles than frictionless particles, implying that correlations of overlaps are strongly reduced by microscopic friction. Comparing different size distributions, we find that the tails are wider for the wider distribution.Comment: 12 pages, 7 figures. Conference proceedings for PARTICLES 2015, 28-30 September, 2015, Barcelona, Spai