arXiv subjects
Publications and source records attributed to Hisao Hayakawa.
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.
Nanocluster impact on a free-standing graphene is performed by the molecular dynamics simulation, and the dynamical motion of the free-standing graphene is investigated. The graphene is bended by the incident nanocluster, and a transverse deflection wave isotropically propagated in the graphene is observed. We find that the time evolution of the deflection is semi-quantitatively described by the linear theory of elasticity. We also analyze the time evolution of the temperature profile of the graphene, and the analysis based on the least dissipation principle reproduces the result in the early stage of impact.
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.
Unified description on the long-time tail of velocity autocorrelation function and the long-range correlation for the equal-time spatial correlation functions is developed based on the generalized fluctuating hydrodynamics. The cross-over of the long-time tail from $t^{-3/2}$ to $t^{-5/2}$ is predicted independent of the density, and the equal-time spatial density correlation function and the equal-time spatial velocity correlation function respectively satisfy $r^{-11/3}$ and $r^{-5/3}$ for large $r$ limit.
The transport phenomena of Lennard-Jones molecules through a structural bottleneck driven by an external force are investigated by molecular dynamics simulations. We observe two distinct molecular flow regimes distinguished by a critical external force $F_{c}$ and find scaling behaviors between external forces and flow rates. Below the threshold $F_{c}$, molecules are essentially stuck in the bottleneck due to the attractive interaction between the molecules, while above $F_{c}$, molecules can smoothly move in the pipe. A critical flow rate $q_{c}$ corresponding to $F_{c}$ satisfies a simple relationship with angles and the value of $q_{c}$ can be estimated by a simple argument. We further clarify the role of the temperature dependence in the molecular flows through the bottleneck.
A generalized Green-Kubo formula is derived for a quantum dissipative system of driven Brownian particle, in which the coupling between the system and the environment is linear. The structure is essentially the same as that for the generalized Green-Kubo formula for driven granular particles. It is demonstrated that the correction to the conventional Green-Kubo formula is zero for a free Brownian particle.
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.
The long-time behaviors of the velocity autocorrelation function $C(t)$ for sheared fluids ^M are investigated theoretically and numerically. It is found the existence of the cross-overs of^M $C(t)$ from $t^{-d/2}$ to $t^{-d}$ ^M in sheared fluids of elastic particles without any thermostat, and from $t^{-d/2}$ to $t^{-(d+2)/2}$ ^M in both sheared fluids of elastic particles with a thermostat and sheared granular fluids,^M where $d$ is the spatial dimension. ^M The validity of the predictions has been confirmed by^M our numerical simulations.
Depositions of amorphous Lennard-Jones clusters on a crystalline surface are numerically investigated. From the results of the molecular dynamics simulation, we found that the deposited clusters exhibit a transition from multilayered adsorption to monolayered adsorption at a critical incident speed. Employing the energy conservation law, we can explain the behavior of the ratio of the number of atoms adsorbed on the substrate to the cluster size. The boundary shape of the deposited cluster depends strongly on the incident speed and some unstable modes grow during the spread of the deposited cluster on the substrate. We also discuss the wettability between different Lennard-Jones atoms.
Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa (Prog. Theor. Phys., 121, 647 (2009)). We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a phenomenology and the simulation.
We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem that apply to uniformly sheared granular systems in which microscopic time-reversal symmetry is broken. The former relation provides an exact representation of nonequilibrium steady-state properties as the integral of the time-correlation function describing transient dynamics from an initial quiescent towards a final sheared steady state. We also investigate implications of the integral fluctuation theorem on the approach towards the steady state and on the possible form of the steady-state distribution function in terms of the excess thermodynamic function.
Impact phenomena of nanoclusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions has a peak at a colliding speed due to the competition between the cohesive interaction and the repulsive interaction of colliding clusters. Some aspects of the collisions can be understood by the theory by Brilliantov {\it et al.} (Phys. Rev. E {\bf 76}, 051302 (2007)), but many new aspects are found from the simulation. In particular, we find that there are some anomalous rebounds in which the restitution coefficient is larger than unity. The phase diagrams of rebound processes against impact speed and the cohesive parameter can be understood by a simple phenomenology.
The existence of universal scaling in the vicinity of the jamming transition of sheared granular materials is predicted by a phenomenology. The critical exponents are explicitly determined, which are independent of the spatial dimension. The validity of the theory is verified by the molecular dynamics simulation.
Spatial correlations for sheared isothermal elastic liquids and granular liquids are theoretically investigated. Using the generalized fluctuating hydrodynamics, correlation functions for both the microscopic scale and the macroscopic scale are obtained. The existence of the long-range correlation functions obeying power laws has been confirmed. The validity of our theoretical predictions have been verified from the molecular dynamics simulation.
A field theoretical method for the fluctuating hydrodynamics with preserving fluctuation-dissipation relations (FDR) is reformulated. It is shown that the long time behavior within the first-loop order perturbation under the assumption that the correlations include the momentum decay fast enough, is equivalent to that for the standard mode-coupling theory.
The spatial correlation function of the momentum density in the three-dimensional dilute sheared granular fluids is theoretically investigated. The existence of the long-range correlation is verified through both the analytic calculation and the numerical simulation.
Impact processes of nanoclusters subject to thermal fluctuations are investigated, theoretically. In the former half of the paper, we discuss the basis of quasi-static theory. In the latter part, we carry out the molecular dynamics simulation of collisions between two identical nanoclusters, and report some statistical properties of impacts of nanoclusters.
Impact phenomena of small clusters subject to thermal fluctuations are numerically investigated. From the molecular dynamics simulation for colliding two identical clusters, it is found that the restitution coefficient for head-on collisions can exceed unity when the colliding speed is smaller than the thermal velocity of one ``atom'' of the clusters. The averaged behavior can be understood by the quasi-static theory of impact phenomena. It is also confirmed that our result is governed by the fluctuation theorem.