arXiv subjects
Publications and source records attributed to Hisao Hayakawa.
We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation.
Hydrodynamic equations for granular gases driven by the Fokker-Planck operator are derived. Transport coefficients appeared in Navier-Stokes order change from the values of a free cooling state to those of a steady state.
We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $ω^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.
We have derived the effect of steady heat flux on the rate of chemical reaction based on the line-of-centers model using the explicit velocity distribution function of the steady-state Boltzmann equation for hard-sphere molecules to second order. It is found that the second-order velocity distribution function plays an essential role for the calculation of it. We have also compared our result with those from the steady-state Bhatnagar-Gross-Krook(BGK) equation and information theory, and found no qualitative differences among them.
The oblique collision between an elastic disk and an elastic wall is numerically studied. We investigate the dependency of the tangential coefficient of restitution on the incident angle of impact. From the results of simulation, our model reproduces experimental results and can be explained by a phenomenological theory of the oblique impact.
Hydrodynamic equations for an inelastic Maxwell model are derived from the inelastic Boltzmann equation based on a systematic Chapman-Enskog perturbative scheme. Transport coefficients appear in Navier-Stokes order have been determined as a function of the restitution coefficient $e$, which cannot be defined for small $e$ as a result of the high energy tail of the velocity distribution function obeying a power law. The dispersion relations for the linearized equation around a homogeneous cooling state have been obtained.
We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin 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. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.
The micropolar fluid mechanics and its transport coefficients are derived from the linearized Boltzmann equation of rotating particles. In the dilute limit, as expected, transport coefficients relating to microrotation are not important, but the results are useful for the description of collisional granular flow on an inclined slope. (This paper will be published in Traffic and Granular Flow 2001 edited by Y.Sugiyama and D. E. Wolf (Springer))
The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. This suggests that the elastic model cannot be used in the quasi-static limit. A new quasi-static theory of impacts is proposed, in which the effect of thermal diffusion is dominant. The abrupt decrease of COR has been found due to the plastic deformation of the disk, which is assisted by the initial internal motion. (This paper is to be published in Chemical Engineering Science.)
The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. The abrupt drop of COR is found due to the plastic deformation of the disk, which is assisted by the initial internal motion.(to be published in J. Phys. Soc. Jpn.)
The inelastic Lorentz gas in cooling states is studied. It is found that the inelastic Lorentz gas is localized and that the mean square displacement of the inelastic Lorentz gas obeys a power of a logarithmic function of time. It is also found that the scaled position distribution of the inelastic Lorentz gas has an exponential tail, while the distribution is close to the Gaussian near the peak. Using a random walk model, we derive an analytical expression of the mean square displacement as a function of time and the restitution coefficient, which well agrees with the data of our simulation. The exponential tail of the scaled position distribution function is also obtained by the method of steepest descent.
The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. The abrupt drop of COR has been found due to the plastic deformation of the disk, which is assisted by the initial internal motion. (to be published in Proceedings of 9 th Nisshin Engineering Particle Technology International Symposium on 'Solids Flow Mechanics and Their Applications' held at Kyoto, 7th-9th January, 2001
We formulate a phenomenological model for the segregation of binary mixtures of rough and smooth granular materials in a rotating drum. Our model successfully replicates a range of experimental behaviours, e.g., rapid radial segregation; slow axial segregation; and nonuniform radial structure of axial bands. We present some analytical results and detailed numerical results for our model.
Density waves of granular material (sand) flowing through a vertical pipe have been investigated. Clear density waves emerge when the cock attached to bottom end of the pipe is closed. The FFT power spectra were found to show a stable power-law form $ P(f) \sim f^{-α}. $ The value of the exponent was evaluated as $α\cong 4/3$. We also introduce a simple one-dimensional model which reproduces $α= 4/3$ from both simulation and theoretical analysis. (to be published in Phys.Rev.Lett.)
We review the current understanding on universal behaviors in granular flows through a vertical pipe and traffic flows. We carry out weakly nonlinear analysis of a model for traffic flows based on the technique of soliton perturbations, and determine the selected propagating velocity, the amplitude, the width of interfaces connecting between jam phase and non-jam phase. From the direct simulation of the model, we have confirmed the validity of our theoretical analysis. We also introduce a model for granular pipe flow supplemented by the white noise, which reproduces $P(f)\sim f^{-4/3}$, where $P(f)$ is the power spectrum in the frequency $f$.
Traffic jam in a fluid model of traffic flows proposed by Kerner and Konhäuser (B. S. Kerner and P. Konhäuser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the hetero-clinic bifurcation. The validity of the solution has been confirmed from the comparison with the simulation of the model.
Systematic simulations are carried out based on the model of fluidized beds proposed by the present authors [K.Ichiki and H.Hayakawa, Phys. Rev. E vol.52, 658 (1995)]. From our simulation, we confirm that fluidization is a continuous transition. We also confirm the existence of two types of fluidized phases, the channeling phase and the bubbling phase. We find the close relations between the averaged behaviors in fluidized beds and quasi equilibrium states in dense liquids. In fluidized beds, (i) the flow rate plays the role of the effective temperature, and (ii) the existence of a kind of the fluctuation-dissipation relation is suggested.
We present two continuum models A and B to study the convective instability of granular materials subjected to vibrations. We carry out the linear stability analysis for model A and uncover the instability mechanism as a supercritical bifurcation of a bouncing solution. We also explicitly determine the onset of convection as a function of control parameters. The results of simulations are in excellent agreement with the stability analysis. Additional feature of the model B is the inclusion of the relaxation term in the momentum equation, which appears to be crucial in capturing what is missing in model A, in particular, in reproducing experimental convection patterns for large aspect ratio, both vertically, in which case convective rolls move toward the surface, and horizontally, in which case convective rolls survive near the wall but are suppressed in the bulk region.