Abstract:
We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows that the behavior of the model is very robust and universal.

Abstract:
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset distribution. We show that our model is very robust against various variations. Next, we explain theoretically why our model reproduces Zipf's law. By considering the time-evolution equation of our model, we see that the essence of Zipf's law is an asymmetric random walk in a logarithmic scale. Finally, we extend our model by introducing an additional asymmetry. We show that the extended model reproduces various power-law exponents. By extending the theoretical argument for Zipf's law, we find a simple equation of the power-law exponent.

Abstract:
We investigate the spatial distribution of temperature induced by a dc current in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential phi and the temperature T in a 2DEG enclosed in a square area surrounded by insulated-adiabatic (top and bottom) and isopotential-isothermal (left and right) boundaries (with phi_{left} < phi_{right} and T_{left} =T_{right}), using a pair of nonlinear Poisson equations (for phi and T) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the vicinity of the left-bottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.

Abstract:
The removal of Cr(III) from aqueous Cr(III) using Arthrobacter nicotianae cells was examined. Cr(III) removal was strongly affected by the pH of the solution and the amounts of Cr(III) removed increased as the pH (1 - 5) of the solution increased. The removal of Cr(III) using the cells was also strongly affected by the Cr(III) concentration of the solution, and obeyed the Langmuir isotherm. The percentage of Cr increased as the cell quantity increased, whereas the amount of Cr (μmol/g dry wt. cells) decreased. The removal of Cr(III) using the cells was very fast, and reached an equilibrium within 6 h from the supply of Cr(III) in the solution. A small amount of Cr(III) absorbed by immobilized cells was desorbed at 30^{o}C; however, most was desorbed at reflux temperature using diluted HCl. Cr(III) adsorption-desorption cycles can be repeated 5 times using immobilized cells. These results have practical implications for industrial wastewater management.

Abstract:
This study herein was investigated the removal of chromium(VI) from an aqueous solution using persimmon tannin gel and its subsequent recovery as chromium(III). At pH 2, Cr(VI) was effectively adsorbed (~80% adsorption) and
<20% of this Cr(VI) was reduced to Cr(III) in the solution. More specifically, all adsorbed Cr(VI) from a 50ppm solution was reduced to Cr(III) on the persimmon gel within 10 min. Although
desorption of the Cr(III) species was challenging at 30°, it was increased upon increasing the temperature and was quantitatively desorbed in the presence of 1 M hydrochloric acid under reflux. In addition, although the quantity of retained Cr(VI) on the tannin gel increased upon increasing the chromium concentration of the original aqueous solution, all the desorbed chromium was successfully reduced to Cr(III). Finally, Cr(VI) removal and recovery as Cr(III) was repeated effectively 8 times using the same persimmon tannin gel sample, thus demonstrating the recyclability of this system.

Abstract:
We first show that quantum resonant states observe particle number conservation and hence are consistent with the probabilistic interpretation of quantum mechanics. We then present for a class of quantum open systems, a resonant-state expansion of the sum of the retarded and advanced Green's functions. The expansion is given purely in terms of all discrete eigenstates and does not contain any background integrals. Using the expansion, we argue that the Fano asymmetry of resonance peaks is interpreted as interference between discrete eigenstates. We microscopically derive the Fano parameters for several cases.

Abstract:
We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dot\gamma$ is realized. The system behaves as a power-law fluid and the relevant exponents are estimated; e.g., the shear stress is proportional to $\dot\gamma^{1/\delta_S}$, where $1/\delta_S=0.64(2)$. It is also found that the relaxation time $\tau$ and the correlation length $\xi$ of the velocity increase obeying power laws: $\tau\sim\dot\gamma^{-\beta}$ and $\xi\sim\dot\gamma^{-\alpha}$, where $\beta=0.27(3)$ and $\alpha=0.23(3)$.

Abstract:
We investigate the nature of friction in granular layers by means of numerical simulation focusing on the critical slip distance, over which the system relaxes to a new stationary state. Analyzing a transient process in which the sliding velocity is instantaneously changed, we find that the critical slip distance is proportional to the sliding velocity. We thus define the relaxation time, which is independent of the sliding velocity. It is found that the relaxation time is proportional to the layer thickness and inversely proportional to the square root of the pressure. An evolution law for the relaxation process is proposed, which does not contain any length constants describing the surface geometry but the relaxation time of the bulk granular matter. As a result, the critical slip distance is scaled with a typical length scale of a system. It is proportional to the layer thickness in an instantaneous velocity change experiment, whereas it is scaled with the total slip distance in a spring-block system on granular layers.