Abstract:
We first construct a genus zero positive allowable Lefschetz fibration over the disk (a genus zero PALF for short) on the Akbulut cork and describe the monodromy as a positive factorization in the mapping class group of a surface of genus zero with five boundary components. We then construct genus zero PALFs on infinitely many exotic pairs of compact Stein surfaces such that one is a cork twist of the other along an Akbulut cork. The difference of smooth structures on each of exotic pairs of compact Stein surface is interpreted as the difference of the corresponding positive factorizations in the mapping class group of a common surface of genus zero.

Abstract:
Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.

Abstract:
A numerical simulation scheme is proposed to analyze domain tessellation and pattern formation on a spherical surface using the phase-field method. A multi-phase-field model is adopted to represent domain growth, and the finite-difference method (FDM) is used for numerical integration. The lattice points for the FDM are distributed regularly on a spherical surface so that a mostly regular triangular domain division is realized. First, a conventional diffusion process is simulated using this lattice to confirm its validity. The multi-phase-field equation is then applied, and pattern formation processes under various initial conditions are simulated. Unlike pattern formation on a flat plane, where the regular hexagonal domains are always stable, certain different patterns are generated. Specifically, characteristic stable patterns are obtained when the number of domains, n, is 6, 8, or 12; for instance, a regular pentagonal domain division pattern is generated for n = 12, which corresponds to a regular dodecahedron.

Abstract:
Grain refinement in a polycrystalline material resulting from severe compressive deformation was simulated using molecular dynamics. A simplified model with four square grains surrounded by periodic boundaries was prepared, and compressive deformation was imposed by shortening the length in the y direction. The model first deformed elastically, and the compressive stress increased monotonically. Inelastic deformation was then initiated, and the stress decreased drastically. At that moment, dislocation or slip was initiated at the grain boundaries or triple junction and then spread within the grains. New grain boundaries were then generated in some of the grains, and sub-grains appeared. Finally, a microstructure with refined grains was obtained. This process was simulated using two types of grain arrangements and three different combinations of crystal orientations. Grain refinement generally proceeded in a similar fashion in each scenario, whereas the detailed inelastic deformation and grain refinement behavior depended on the initial microstructure.

Abstract:
A numerical method for simulating the stability of particle-packing structures is presented. The packing structures were modeled on the basis of face-centered cubic (fcc) and body-centered cubic (bcc) structures, and the stability of these structures was investigated using the distinct element method. The interaction between the particles was simplified by considering repulsive, adhesive, and damping forces, and the stability against the gravitational force was simulated. The results under a certain set of parameters showed characteristic deformation when the particles were arranged in an fcc array. Focusing on the local structure, the resulting model was divided into several domains: The bottom base, four top corners, and intermediate domains. The bottom base notably became a body-centered tetragonal (bct) structure, which corresponds to a uniaxially compressed bcc structure. Conversely, the models based on the bcc arrangement were structurally stable, as no specific deformation was observed, and a monotonously compressed bct structure was obtained. Consequently, the bcc arrangement is concluded to be more stable against uniaxial compression, such as the gravitational force, in a particle-packing system.

Abstract:
This
paper compares ad-valorem and specific taxation in models where a
representative consumer with an exogenous income has both a quality and a
quantity choice under perfect competition. In the setting, while ad-valorem tax
causes income effect only, specific tax causes both income effect and
substitution effect. Therefore, ad-valorem tax decreases consumer demand for
both quality and quantity; on the other hand, specific tax decreases consumer demand
for quantity. However, the sign of consumer demand for quality is ambiguous and
is determined by the curvature of marginal utility on quantity. Additionally,
using a constant elasticity of substitution (CES) utility function and a linear
price function, we show that ad-valorem tax is superior to specific tax except
for the Leontief preference under which the two forms of commodity taxes
generate the same tax revenue. The substitution effect caused by specific tax
disappears if the elasticity of substitution converges to zero.

Abstract:
Rhodium oxides, including a misfitlayered structure with alternate stacking of a rock salttype layer and a hexagonal RhO_{2} layer, are expected to have good thermoelectric properties. Among them, the thermoelectric properties (electrical conductivity (σ), Seebeck coefficient (S), Figure of merit (ZT) and calculated thermal conductivity (κ) by S, σ, ZT, and absolute temperature (T)) of bismuth-based rhodium oxides ((Bi_{1-x},Pb_{x}) _{2}Sr_{2}Rh_{2}O_{y}, x = 0 and 0.02, hereafter BSR and BPSR, respectively) were investigated. In comparison with Bi_{2}Sr_{2}Co_{2}O_{y} (BSC) at 700°C, S and κ enhanced (increased S, 110 (BSR) and 105 μV K^{-1} (BPSR) from 85 μV K^{-1} (BSC) and decreased κ, 0.32 (BSR) and 0.50 W m^{-1} K^{-1} (BPSR) from 1.75 W m^{-1} K^{-1} (BSC)), whereas σ decreased (15 (BSR) and 31 S cm^{-1} (BPSR) from 70 S cm^{-1} (BSC)). BPSR reached the highest ZT value of 0.067 at 700°C, compared to those of 0.056 (BSR) and 0.027 (BSC).

Abstract:
The nonextensive entropy of Tsallis can be seen as a consequence of postulates on a self-information, i.e., the constant ratio of the first derivative of a self-information per unit probability to the curvature (second variation) of it. This constancy holds if we regard the probability distribution as the gradient of a self-information. Considering the form of the nth derivative of a self-information with keeping this constant ratio, we arrive at the general class of nonextensive entropies. Some properties on the series of entropies constructed by this picture are investigated.

Abstract:
An ensemble formulation for the Gompertz growth function within the framework of statistical mechanics is presented, where the two growth parameters are assumed to be statistically distributed. The growth can be viewed as a self-referential process, which enables us to use the Bose-Einstein statistics picture. The analytical entropy expression pertain to the law can be obtained in terms of the growth velocity distribution as well as the Gompertz function itself for the whole process.

Abstract:
As a possible generalization of Shannon's information theory, we review the formalism based on the non-logarithmic information content parametrized by a real number q, which exhibits nonadditivity of the associated uncertainty. Moreover it is shown that the establishment of the concept of the mutual information is of importance upon the generalization.