Research Interests:
Research Interests:
Research Interests:
ABSTRACT
Research Interests:
We study the relaxational modes in the Glauber dynamics and their contribution to the spin auto‐correlation function by means of numerical diagonalization. Differences in the dynamics between the disordered and the ordered phase are... more
We study the relaxational modes in the Glauber dynamics and their contribution to the spin auto‐correlation function by means of numerical diagonalization. Differences in the dynamics between the disordered and the ordered phase are discussed.
Research Interests:
We show that a micropolar fluid model successfully describes granular flows on a slope. Micropolar fluid is the fluid with internal structures, and the coupling between the rotation of each particle and the macroscopic velocity field is... more
We show that a micropolar fluid model successfully describes granular flows on a slope. Micropolar fluid is the fluid with internal structures, and the coupling between the rotation of each particle and the macroscopic velocity field is taken into account; it is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. It is demonstrated that the model equations can quantitatively reproduce the velocity and angular velocity profiles obtained from the numerical simulation of the dilute surface flow using the parameters consistent with our simple estimate.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Recent progresses in understanding earthquake dynamics with the aid of a simple spring-block system is reviewed from a…
Research Interests:
An inhomogeneous superconducting state under a ferromagnetic molecular field is investigated theoretically. This problem is solved exactly within the mean field approximation for a one-dimensional electron band. It is found that the... more
An inhomogeneous superconducting state under a ferromagnetic molecular field is investigated theoretically. This problem is solved exactly within the mean field approximation for a one-dimensional electron band. It is found that the solution gives a spin modulated structure associated with a spatially inhomogeneous superconducting order parameter and a two-gap structure in the energy spectrum. Experiments on ErRh4B4 are interpreted by this solution.
Research Interests:
An analytical solution that represents a self-healing pulse of slip is presented for a dynamical model of fracture in a two-dimensional continuum medium. Even without the cohesive region, the solution does not show a singular behavior in... more
An analytical solution that represents a self-healing pulse of slip is presented for a dynamical model of fracture in a two-dimensional continuum medium. Even without the cohesive region, the solution does not show a singular behavior in the stress at the resticking point unlike at the breaking point, where the stress is diverging as 1/sqrt[r]. This means that the physical condition at the resticking point should depend on the microscopic processes of resticking while the condition at the breaking point is known to be described by the phenomenological fracture energy.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
ABSTRACT Granular flows on a rough slope in the collisional flow region are investigated by numerical simulations. It is demonstrated that the uniform flow is only metastable; it is maintained for a while, but fluctuations trigger... more
ABSTRACT Granular flows on a rough slope in the collisional flow region are investigated by numerical simulations. It is demonstrated that the uniform flow is only metastable; it is maintained for a while, but fluctuations trigger clustering of particles eventually. The micropolar fluid model is employed to analyze the properties of uniform flow. It is shown that the model can reproduce the deviation of angular velocity field from the rotation of velocity field.
Research Interests:
Research Interests:
We examine the linear stability of steady-state propagating fracture in two one-dimensional models. Both of these models include a cohesive force at the crack tip; they differ only in that the dissipative mechanism is a frictional force... more
We examine the linear stability of steady-state propagating fracture in two one-dimensional models. Both of these models include a cohesive force at the crack tip; they differ only in that the dissipative mechanism is a frictional force in the first model and a viscosity in the second. Our strategy is to compute the linear response of this system to a spatially periodic perturbation. As expected, we find no dynamical instabilities in these models. However, we do find some interesting analytic properties of the response coefficient that we expect to be relevant to the analysis of more realistic two-dimensional models.
Research Interests:
Research Interests:
Research Interests: Physics, Statistical Physics, Medicine, Mathematical Sciences, Ising Model, and 12 morePhysical sciences, FOkker Planck Equation, Autocorrelation, Physical, Eigenvalues, CHEMICAL SCIENCES, Spectrum analysis, Ferromagnetic Materials, Ferromagnetism, Eigenvalues and Eigenvectors, Autocorrelation Function, and Monte Carlo Method
We present a phenomenological fluid dynamics model for a dilatant fluid, i.e. a severe shear thickening fluid, by introducing a state variable. The Navier-Stokes equation is coupled with the state variable field, which evolves in response... more
We present a phenomenological fluid dynamics model for a dilatant fluid, i.e. a severe shear thickening fluid, by introducing a state variable. The Navier-Stokes equation is coupled with the state variable field, which evolves in response to the local shear stress as the fluid is sheared. The viscosity is assumed to depend upon the state variable and to diverge at a certain value due to jamming. We demonstrate that the coupling of the fluid dynamics with the shear thickening leads to an oscillatory instability in the shear flow. The model also shows a peculiar response of the fluid to a strong external impact. Comment: 4 pages, 6 figures
Research Interests:
When drinking a cup of coffee under the morning sunshine, you may notice white membranes of steam floating on the surface of the hot water. They stay notably close to the surface and appear to almost stick to it. Although the membranes... more
When drinking a cup of coffee under the morning sunshine, you may notice white membranes of steam floating on the surface of the hot water. They stay notably close to the surface and appear to almost stick to it. Although the membranes whiffle because of the air flow of rising steam, peculiarly fast splitting events occasionally occur. They resemble cracking to open slits approximately 1 mm wide in the membranes, and leave curious patterns. We studied this phenomenon using a microscope with a high-speed video camera and found intriguing details: i) the white membranes consist of fairly monodispersed small droplets of the order of 10 μm; ii) they levitate above the water surface by 10 ~ 100 μm; iii) the splitting events are a collective disappearance of the droplets, which propagates as a wave front of the surface wave with a speed of 1 ~ 2 m/s; and iv) these events are triggered by a surface disturbance, which results from the disappearance of a single droplet.
Research Interests:
The velocity distribution of inelastic granular gas is examined numerically on a two-dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state... more
The velocity distribution of inelastic granular gas is examined numerically on a two-dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after several inelastic collisions per particle, the system falls in the state that the Boltzmann's equation predicts with the stationary form of velocity distribution. It turns out, however, that due to the velocity correlation the form of the distribution function does not stay time independent, but gradually returns to the Maxwellian immediately after the initial transient till the clustering instability sets in. It shows that, even in the homogeneous cooling state (Haff state), where the energy decays exponentially as a function of collision number, the velocity correlation in the inelastic system invalidates the assumption of molecular chaos and the prediction of the Boltzmann's equation fails.
Research Interests:
ABSTRACT Granular media undergo so-called "the jamming transition" as the pack-ing fraction φ increases. The system jams above the jamming packing frac-tion φ J , which is close to the random closed packing in the case... more
ABSTRACT Granular media undergo so-called "the jamming transition" as the pack-ing fraction φ increases. The system jams above the jamming packing frac-tion φ J , which is close to the random closed packing in the case of frictionless spheres. At the jamming point, the system is in the isostatic state, and the particles start to overlap or deform as soon as the packing fraction φ exceeds φ J . Many of these features can, however, be sensitive to the thermal pertur-bations that allows the particles to rearrange to find other configurations. It is also possible that the effects of the perturbations on the jamming transition depend on the type of fluctuation and the system's history. In this paper, we investigate the effect of the thermal fluctuation on the jamming transition in a sheared system. In the granular shear flow without thermal noise, the system is still under the effect of the fluctuation, namely the grains' fluctuation energy (the granular "temperature" T) is determined by the balance between the dissipation and the energy influx from the shear. In a steady shear flow with a shear rate ˙ γ, this leads to T ∝ ˙ γ 2 and the Bagnold scaling S ∝ ˙ γ 2 in the unjammed regime, where S is the shear stress. It has also been shown that S, T and some other quantities as a function of the packing fraction φ and the shear rate ˙ γ obey critical scaling around the zero-temperature jamming point ˙ γ = 0 (hence T = 0) and φ = φ J [1, 2]. It is interesting to see how much of this critical behavior persists under the constant thermal fluctuation, which gives a finite fluctuation even at ˙ γ = 0. We simulate the shear flow of bidisperse grains in the three dimensions [1] with random forcing. We adopt the random force whose α-component on 1 the particle i at time t, R α i (t), satisfies α i (t) = 0, α i (t 1)R β j (t 2) = 2Bσ i δ α,β δ i,j δ(t 1 − t 2), where σ i is the diameter of the particle i. The simulation setups for B = 0 are the same as the linear spring model in ref. [1]. We study the steady shear flow with various values of the random force amplitude, B. Figure 1 shows a preliminary result of the shear stress S vs. the shear rate ˙ γ for B = 0 and 10 −2 . We can see that, in the unjammed regime (φ < 0.64), the Bagnold behavior S ∝ ˙ γ 2 at B = 0 is changed to the Newtonian behavior S ∝ ˙ γ at B = 10 −2 . This can be understood as a crossover between the regime where the shear is the dominant source of the kinetic energy and the regime thermal fluctuation becomes dominant. In our presentation, we analyze the B dependence of the system behaviors around the jamming transition point.
Research Interests:
ABSTRACT It is well known that just adding some liquid to dry granular materials changes their behaviors very much. Liquid forms bridges between grains, and the bridge induces cohesion between grains due to the surface tension. When the... more
ABSTRACT It is well known that just adding some liquid to dry granular materials changes their behaviors very much. Liquid forms bridges between grains, and the bridge induces cohesion between grains due to the surface tension. When the liquid content is small, the liquid forms a bridge at each contact point (the pendular state), which induces two-body cohesive force. As the liquid content increases, some liquid bridges merge, and more than two grains interact through a single liquid cluster (the funicular state). We propose a simple phenomenological model for wet granular media to take into account many particle interaction through a liquid cluster in the funicular state as well as two-body cohesive force by a liquid bridge in the pendular state. In our model, the cohesive force acts among the grains connected by a liquid-gas interface. As the liquid content is increased, the number of grains that interact through the liquid increase, but the liquid-gas interface may decrease when liquid clusters are formed. Due to this competition, the shear stress shows a maximum as a function of the liquid-content.
Research Interests:
We analyze the linear stability of a collisional granular flow on a slope under gravity using hydrodynamical equations based on kinetic theory of inelastic particles. It is shown that the steady, uniform flow is unstable against... more
We analyze the linear stability of a collisional granular flow on a slope under gravity using hydrodynamical equations based on kinetic theory of inelastic particles. It is shown that the steady, uniform flow is unstable against longitudinal long-wavelength perturbations in lower density region. The results are compared with the instabilities found in numerical simulations of granular flows.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests: Engineering, Mathematics, Algorithms, Chemistry, Kinetics, and 15 moreCollective Action, Biology, Medicine, Cytoskeleton, Numerical Simulation, Computer Simulation, Diffusion, CHEMICAL SCIENCES, Diffusion Coefficient, Cooperativity, Anomalous Diffusion, Hydrolysis, Molecular Motor, Adenosine Triphosphate, and Model simulation
Abstract We generally examine the analytic properties of the Ishida-Yonezawa approximation for the tight binding single s-band model. A sufficient condition is derived on which a solution satisfies the physical conditions; (1) sum rule,... more
Abstract We generally examine the analytic properties of the Ishida-Yonezawa approximation for the tight binding single s-band model. A sufficient condition is derived on which a solution satisfies the physical conditions; (1) sum rule, (2) reality, (3) definiteness, (4) analyticity, (5) boundary condition and (6) uniqueness.
Research Interests:
Abstract It is pointed out theoretically that a single electron band model is able to exhibit the interchange of two phases: itenerant band ferromagnetism and superconductivity. Our theory is based on the molecular field approximation... more
Abstract It is pointed out theoretically that a single electron band model is able to exhibit the interchange of two phases: itenerant band ferromagnetism and superconductivity. Our theory is based on the molecular field approximation applied for a simplified electron-electron interaction. Possible phase changes are discussed in connection with two phase transitions of ferromagnetism and superconductivity in the intermetallic compound Y 4 Co 3 .