An expression for stationary distribution in nonequilibrium steady state

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths and/or driven by an external force. Starting from the detailed fluctuation theorem we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate $\eta$ is proportional to $\exp[{\Phi}(\eta)]$ where ${\Phi}(\eta)=-\sum_k\beta_k\mathcal{E}_k(\eta)$ is the excess entropy change. Here $\mathcal{E}_k(\eta)$ is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the $k$-th heat bath whose inverse temperature is $\beta_k$. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.Comment: 4 pages, 2 figure

Properties of Color-Coulomb String Tension

We study the properties of the color-Coulomb string tension obtained from the instantaneous part of gluon propagators in Coulomb gauge using quenched SU(3) lattice simulation. In the confinement phase, the dependence of the color-Coulomb string tension on the QCD coupling constant is smaller than that of the Wilson loop string tension. On the other hand, in the deconfinement phase, the color-Coulomb string tension does not vanish even for $T/T_c = 1 \sim 5$, the temperature dependence of which is comparable with the magnetic scaling, dominating the high temperature QCD. Thus, the color-Coulomb string tension is not an order parameter of QGP phase transition.Comment: 17 pages, 5 figures; one new figure added, typos corrected, version to appear in PR

Roundabout relaxation: collective excitation requires a detour to equilibrium

Relaxation to equilibrium after strong and collective excitation is studied, by using a Hamiltonian dynamical system of one dimensional XY model. After an excitation of a domain of $K$ elements, the excitation is concentrated to fewer elements, which are made farther away from equilibrium, and the excitation intensity increases logarithmically with $K$. Equilibrium is reached only after taking this ``roundabout'' route, with the time for relaxation diverging asymptotically as $K^\gamma$ with $\gamma \approx 4.2$.Comment: 4 pages, 5 figure

The S shape of a granular pile in a rotating drum

The shape of a granular pile in a rotating drum is investigated. Using Discrete Elements Method (DEM) simulations we show that the "S shape" obtained for high rotation speed can be accounted for by the friction on the end plates. A theoretical model which accounts for the effect of the end plates is presented and the equation of the shape of the free surface is derived. The model reveals a dimensionless number which quantifies the influence of the end plates on the shape of the pile. Finally, the scaling laws of the system are discussed and numerical results support our conclusions

Dust Size Growth and Settling in a Protoplanetary Disk

We have studied dust evolution in a quiescent or turbulent protoplanetary disk by numerically solving coagulation equation for settling dust particles, using the minimum mass solar nebular model. As a result, if we assume an ideally quiescent disk, the dust particles settle toward the disk midplane to form a gravitationally unstable layer within 2x10^3 - 4x10^4 yr at 1 - 30 AU, which is in good agreement with an analytic calculation by Nakagawa, Sekiya, & Hayashi (1986) although they did not take into account the particle size distribution explicitly. In an opposite extreme case of a globally turbulent disk, on the other hand, the dust particles fluctuate owing to turbulent motion of the gas and most particles become large enough to move inward very rapidly within 70 - 3x10^4 yr at 1 - 30 AU, depending on the strength of turbulence. Our result suggests that global turbulent motion should cease for the planetesimal formation in protoplanetary disks.Comment: 27 pages, 8 figures, accepted for publication in the Ap