Abstract:
We investigate the application of matrix product states to the Hubbard model in one spatial dimension with both of open and periodic boundary conditions. We develop the variatinal method that the optimization of the variational parameters is carried out locally and sequentially in the framework of matrix product operators (MPO) by including the sign, due to the anti-commutation relation of fermion operators, in the matrix element of MPO. The numerical accuracy of the ground state energy is examined.

Abstract:
Pyrolysis gas jets out from the surface of a solid fuel particle when heated. This study experimentally observes the occurrence of gas jets？from heated solid fuel particles. Results reveal a local gas jet occurs from the particle’s surface when its temperature reaches the point at which a pyrolysis reaction occurs. To investigate the influence of the gas jet on particle motion, a numerical simulation of the uniform flow around a spherical particle with a nonuniform outflow or high surface temperature is conducted, and the drag force acting on the spherical particle is estimated. In the numerical study, the magnitude of the outflow velocity, direction of outflow, and Rayleigh number,？i.e., particle surface temperature, are altered, and outflow velocities and the Rayleigh number are set based on the experiment. The drag coefficient is found to decrease when an outflow occurs in the direction against the mainstream; this drag coefficient at a higher Rayleigh number is slightly higher than that at a Rayleigh number of zero.

Abstract:
We have developed a simulation code with the techniques which enhance both spatial and time resolution of the PM method for which the spatial resolution is restricted by the spacing of structured mesh. The adaptive mesh refinement (AMR) technique subdivides the cells which satisfy the refinement criterion recursively. The hierarchical meshes are maintained by the special data structure and are modified in accordance with the change of particle distribution. In general, as the resolution of the simulation increases, its time step must be shortened and more computational time is required to complete the simulation. Since the AMR enhances the spatial resolution locally, we reduce the time step locally also, instead of shortening it globally. For this purpose we used a technique of hierarchical time steps (HTS) which changes the time step, from particle to particle, depending on the size of the cell in which particles reside. Some test calculations show that our implementation of AMR and HTS is successful. We have performed cosmological simulation runs based on our code and found that many of halo objects have density profiles which are well fitted to the universal profile proposed by Navarro, Frenk, & White (1996) over the entire range of their radius.

Abstract:
Using a simple mixed oligopoly model, this paper examines the
relationship between market-openings to foreign capital and privatization of a
domestic public firm. Two types of market-openings are considered. First
is that, given the number of the firms, the restriction on the share of foreign
capital in each corporate joint venture is relaxed. Second is that, given the
share of foreign capital in each corporate joint venture, the restriction on
the number of the firms is relaxed. The analysis shows that the optimal level
of privatization critically depends on the types of market openings to foreign
capital. The optimal level of privatization declines as the share of foreign capital
in each corporate joint venture increases. By contrast, the optimal level of
privatization rises with an increase in the number of the firms operating in
the market. The two different strategies for market-openings result in the opposite impacts on the welfare-maximizing
government’s incentive for privatization.

Abstract:
Detailed account is given of the chirality scenario of experimental spin-glass transitions. In this scenario, the spin glass order of weakly anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses are essentially chirality driven. Recent numerical and experimental results are discussed in conjunction with this scenario.

Abstract:
Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether there is a thermodynamic transition in zero field, what are the associated critical properties, what is the nature of the ordered state, particularly of a possible replica-symmetry breaking, and whether there is a thermodynamic transition in applied fields. The properties of the two models are contrasted, and possible relation to experiments is discussed.

Abstract:
The stability and the critical properties of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated in the unscreened limit based on a lattice {\it XY} model with a uniform field. By performing equilibrium Monte Carlo simulations for the system with periodic boundary conditions, the existence of a stable vortex-glass order is established in the unscreened limit. Estimated critical exponents are compared with those of the gauge-glass model.

Abstract:
Fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. Numerically determined FD ratio exhibits a ``one-step-ike''behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, $T_{{\rm eff}}\simeq 2T_g$, irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Herisson and Ocio, and with the chirality scenario of spin-glass transition.

Abstract:
We discuss the recent experimental data on various frustrated quasi-two-dimensional Heisenberg antiferromagnets from the viewpoint of the Z2-vortex order, which include S=3/2 triangular-lattice antiferromagnet NaCrO2, S=1 triangular-lattice antiferromagnet NiGa2S4, S=1/2 organic triangular-lattice antiferromagnets \kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, and S=1/2 kagome-lattice antiferromagnet volborthite Cu3V2O7(OH)22H2O, etc.

Abstract:
Ordering properties of XY-like spin-glass magnets with an easy-plane magnetic anisotropy are studied based on a symmetry consideration and the results of recent numerical simulations on the pure Heisenberg and XY spin-glass models. The effects of an easy-plane-type uniaxial anisotropy, a random magnetic anisotropy and an applied magnetic field are investigated. In the XY regime in zero field, the "spin-chirality decoupling" persists even under the random magnetic anisotropy, escaping the "spin-chirality recoupling" phenomenon which inevitably occurs in the Heisenberg regime. Contrast between the scalar chiral order and the vector chiral order is emphasized. Implications to experiments are discussed.