Hiizu Nakanishi

Soliton Lattice Modulation of Incommensurate Spin Density Wave in Two Dimensional Hubbard Model : A Mean Field Study

Spatially modulated magnetic phases are investigated within the mean field theory for an itinerant electron model, i.e. the Hubbard model on a two-dimensional square lattice. By numerically diagonalizing the Hamiltonian for finite-size systems under a periodic boundary condition, we examine relative stability and physical properties of several possible magnetic states. When the electron fillings are nearly half-full, the diagonally or vertically modulated spin density wave (SDW) state is stabilized over the uniform antiferromagnetic state and a crossover from the vertical to the diagonal states appears. The diagonal or vertical stripe state is characterized by the presence of the midgap band due to the soliton lattice formation inside the main SDW gap, being an insulator. The wave length λ SDW is linearly proportional to the excess carrier concentration. Excess carriers are accommodated in the form of the soliton lattice, forming a charge density wave whose wave length is λ SDW /2.

Collisional granular flow as a micropolar fluid.

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.

Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow

We investigate the bulk rheology of dense granular flow down a rough slope, where the density profile has been found to show a plateau except for the boundary layers in simulations [Silbert et al., Phys. Rev. E 64, 051302 (2001)]. It is demonstrated that both the Bagnold scaling and the framework of kinetic theory are applicable in the bulk, which allows us to extract the constitutive relations from simulation data. The detailed comparison of our data with the kinetic theory shows quantitative agreement for the normal and shear stresses, but there exists a slight discrepancy in the energy dissipation, which causes a rather large disagreement in the kinetic theory analysis of the flow.

Spatiotemporal structure of traffic flow in a system with an open boundary

The spatiotemporal structure of a traffic flow pattern is investigated under the open boundary condition using the optimal velocity model. The parameter region where the uniform solution is convectively unstable is determined. It is found that a localized perturbation triggers a linearly unstable oscillatory solution out of the linearly unstable uniform state, and it is shown that the oscillatory solution is also convectively stabilized. It is demonstrated that the observed traffic pattern near an on-ramp can be interpreted as the noise sustained structure in the open flow system.

Velocity correlations in dense granular shear flows: effects on energy dissipation and normal stress.

We study the effect of precollisional velocity correlations on granular shear flow by molecular dynamics simulations of an inelastic hard sphere system. Comparison of the simulations with kinetic theory reveals that the theory overestimates both the energy dissipation rate and the normal stress in the dense flow region. We find that the relative normal velocity of colliding particles is smaller than that expected from random collisions, and the discrepancies in the dissipation and the normal stress can be adjusted by introducing the idea of the collisional temperature, from which we conclude that the velocity correlation neglected in the kinetic theory is responsible for the discrepancies. Our analysis of the distributions of the precollisional velocity suggests that the correlation grows through multiple inelastic collisions during the time scale of the inverse of the shear rate. As for the shear stress, the discrepancy is also found in the dense region, but it depends strongly on the particle inelasticity.

On the Stability of Topologically Non-Trivial Point Defects

We demonstrate that a topologically non-trivial point defect can be energetically unstable against expanding into a ring defect by taking nematic liquid crystal as an example.

Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition

We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter region where the uniform solution is stable against a localized perturbation. We also found an oscillatory solution in the linearly unstable region and its period is not commensurate with the periodicity of the car index space. The oscillatory solution has some features in common with the synchronized flow observed in real traffic.

Hard-sphere limit of soft-sphere model for granular materials: Stiffness dependence of steady granular flow

Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard-sphere limit of the soft-sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard-sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard-sphere limit, although the contact time fraction for the binary collisions tends to zero.

Topological classification of unknotted ring defects

Unknotted ring defects in ordered media are classified in terms of the homotopy theory. It is also investigated what type of point defects will appear when a radius of the ring defect tends to zero.

Possible phase change between itinerant ferromagnetism and superconductivity

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 .