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Energy transport phenomena in Lennard-Jones particle systems are studied using nonequilibrium simulation with molecular dynamics method. Thermal conductivity in finite size system κ(L) converges with a simple 1/√L in gas, liquid and solid phases. Lennard-Jones particle system reproduced normal thermal conduction which is described by Fourier's heat law. The κ(L) decreases by 10 % from the macroscopic thermal conductivity at L ∼1100 in gas phase, L ∼80 in liquid phase, and L ∼150 in solid phase. To describe and understand the microscopic origin of the nonequilibrium thermal conduction, we study the microscopic energy flux carried by a single particle j and its distribution. When steady heat flux flows in the system, the distribution of j is distorted along the direction of the energy flux. The nonequilibrium distribution is described by the equilibrium distributions with different two temperatures. When the system is in nonlinear response region, the distribution has a form different from the one of linear response region even though the global temperature profile reproduces a linear form.

Computer performance is now reaching to realize 1 mol operations, that is, 6 ×1023 arithmetic operations. Such Avogadro-scale computer will open a new era of sciences and technologies via renovations of fields in material sciences, which had been assuming that the Avogadro number be a synonym of infinity. Since the first milestone was placed by B. J. Alder half-a-century ago, a road to thermal equilibrium properties was well paved and linear transport phenomena have also been tamed with nonequilibrium simulations. Now the front lines confront nonlinear nonequilibrium problems. As an example, molecular-dynamics simulation of a shock tube which is an analogue of volcanic eruption is given.

We study the distribution of the microscopic energy flux j which is carried by a single particle. It is observed in Lennard-Jones particle system that the distribution of the norm of the energy flux Pn(j) has a broad peak in small j regime and a stretched-exponential decay for large j. The broad peak originates in the potential advection and energy transfer between particles. The stretched exponential tail is from the momentum energy advection.In nonlinear-lattice systems, all the flux components jK, jU, and jF show stretched exponential decay.

We have proposed a new traffic flow simulation model, Coupled Map traffic flow model based on Optimal Velocity functions (CMOV model). The model is improved to treat two-lane roads with entranceways. The lanusage characteristics and the flow correlations between lanes are observed.

We present a modified Optimal Velocity model which has the asymmetry of the sensitivity between the acceleration and deceleration process. This is very realistic modification and we search the possibility for correction toward more realistic behavior of a car in traffic flow.

Nonequilibrium distribution of the microscopic thermal current is investigated by direct molecular dynamics simulations. The microscopic thermal current in this study is defined by a flow of kinetic energy carried by a single particle. Asymptotic parallel and antiparallel tails of the nonequilibrium distribution to an average thermal current are identical to ones of equilibrium distribution with different temperatures. These temperatures characterizing the tails are dependent on a characteristic length in which a memory of dynamics is completely erased by several particle collisions. This property of the tails of nonequilibrium distribution is confirmed in other thermal transport systems. In addition, statistical properties of a particle trapped by a harmonic potential in a steady thermal conducting state are also studied. This particle feels a finite force parallel to the average thermal current as a consequence of the skewness of the distribution of the current. This force is interpreted as the microscopic origin of thermophoresis.