Nonequilibrium energy transport phenomena are studied using molecular dynamics simulation. The system is made of hard-core particles which contact with the heat baths at the both ends: hot at left end, and cold at right end. In case of fluid, normal (Fourier-type) heat conduction is reproduced in threedimensional system, but it is not observed in lower-dimensional systems. In solid-fluid coexisting state, the property of energy transport is different between each phase. Fourier-type heat conduction is reproduced, but the solid phase has larger thermal conductivity than the fluid phase. When hydrodynamic shear is induced at hot end, temperature profile of fluid phase is parabolic form but that of solid phase is straight one. These results suggest that continuum description can be applicable to much shorter length scales (for example, micrometer-or nanometer-scale technology) and in contrast, molecular dynamics approach in such scale systems can be used to study nonequilibrium macroscopic phenomena.

Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-onedimensional system of the size of Lx × Ly × Lz(Lz ≫ Lx, Ly) is simulated. Heat baths are put in both end: one has higher temperature than the other. In the crystal case, the interaction potential V has fourth-order non-linear term in addition to the harmonic term, and Nose-Hoover method is used for the heat baths. In the fluid case, stochastic boundary condition is charged, which works as the heat baths. Fourier-type heat conduction is reproduced both in crystal and fluid models in three-dimensional system, but it is not observed in lower dimensional system. Autocorrelation function of heat flux is also observed and long-time tails of the form of ∼ t −d/2 , where d denotes the dimensionality of the system, are confirmed. The normal heat conduction, which is described by the Fourier heat lawwhere J and T denote the heat flux and the temperature respectively, is one of the most fundamental nonequilibrium phenomena. However the microscopic origin of it has not been clarified completely. Unlike the Debye's theory for the specific heat in equilibrium solids, this phenomena cannot be modeled by the harmonic chain [1]. In the harmonic chain, global internal temperature gradient is not formed, so that the thermal conductivity diverges. Disorder of mass of particles in the system does not give the saturated thermal conductivity in the thermodynamic limit [2]. This behavior attributes to the lack of scattering process between modes in the system. On the other hand, some chaotic systems realize the Fourier heat law [3][4][5]. Thus the nonintegrability of the system which causes scattering between modes is one of crucial elements for the Fourier heat law. It is worth stressing that all these chaotic models and the Lorentz-gas model, which is used as the model of the heat conduction in metals or diluted gas [6,7] are characterized by the nature that the total momentum is not conserved in the bulk. Recent studies for total momentum conserving system by Lepri et al. shed a light on another crucial aspect, that is, dimensionality [8]. They first study the thermodynamic behavior of energy transport in the onedimensional Fermi-Pasta-Ulam (FPU) β lattice numerically and analytically investigated the dimensionalitydependence. In the numerical investigation for the onedimensional case, they found numerically that the thermal conductivity diverges as N α where N is the number of oscillators and α is estimated roughly to be 1/2. They also calculated the power spectrum S(ω) of the global heat flux in the equilibrium and found its power-law divergence as ω −0.37 in the low-frequency region. It corresponds to a slow decay of autocorrelation function of globally averaged heat flux C j (t) as t −0.63 . This powerlow decay of the autocorrelation function implies the divergence of the thermal conductivity as κ ∼ N α≈0.37 by applying the Green-Kubo formula [9,10] because ...

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Flow simulation with a particle dynamics method is studied. The fluid is made of hard particles which obey the Newtonian equations of motion and the collisions between particles are elastic, that is, energy and momentum are conserved. The viscosity appears autonomously together with the local equilibrium state. When a particle collides with a nonslip boundary, a new velocity is given randomly from the thermal distribution if the wall is isothermal, or a random reflection angle is selected if the wall is adiabatic. Shear viscosity is estimated from simulations of plane Poiseuille flow together with the confirmation that the system obeys the Navier–Stokes equation. Flows past a cylinder are also simulated. Depending on the Reynolds number up to 106, flow patterns are properly reproduced, and Kármán vortex shedding is observed. The estimated values of drag coefficient show quantitative agreement with experiments.

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