Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

Models of Meson-Baryon Reactions in the Nucleon Resonance Region

It is shown that most of the models for analyzing meson-baryon reactions in the nucleon resonance region can be derived from a Hamiltonian formulation of the problem. An extension of the coupled-channel approach to include $\pi\pi N$ channel is briefly described and some preliminary results for the $N^*(1535)$ excitation are presented.Comment: Latex 13 pages; to appear in the Proceedings of Workshop on the Physics of excited nucleons (NSTAR2004), Grenoble (France), March 24-27, 200

Canonical Theory of 2+1 Gravity

Recently 2+1 dimensional gravity theory, especially ${\rm AdS_3}$ has been studied extensively. It was shown to be equivalent to the 2+1 Chern-Simon theory and has been investigated to understand the black hole thermodynamics, i.e. Hawking temperature and others. The purpose of this report is to investigate the canonical formalism of the original 2+1 Einstein gravity theory instead of the Chern-Simon theory. For the spherically symmetric space-time, local conserved quantities(local mass and angular momentum) are introduced and using them canonical quantum theory is defined. Constraints are imposed on state vectors and solved analytically. The strategy to obtain the solution is followed by our previous work.Comment: 6 pages, talk given at LLWI-2000: From Particles to Universe, Alberta, 20-26 February 200

Self-similar dynamics of bacterial chemotaxis

Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in bacterial colony is investigated theoretically through a continuum model that considers chemotaxis. In the case of the gradient sensed by the bacterium is nearly uniform, the bacterial colony patterns are self-similar, which they look the same at every scale. The scaling law of the bacterial colony growth has been revealed explicitly. Chemotaxis biases the movement of bacterial population in colony trend toward the chemical attractant. Moreover, the bacterial colonies evolve long time as the traveling wave with sharp front.Comment: 4 pages, 3 figures, accepted by Phys. Rev. E (Brief Report

Magnetic and Electronic Phase Diagram and Superconductivity in the Organic Superconductors k-(BEDT-TTF)2X

The magnetic susceptibility of the organic superconductors $\kappa$-(h8 or d8-ET)$_{2}$$X$, $X =$ Cu(NCS)$_{2}$ and Cu[N(CN)$_{2}$]Br has been studied. A metallic phase below $T^{*} =$ 37 $\sim$ 38 K for $X =$ Cu[N(CN)$_{2}$]Br and 46 $\sim$ 50 K for $X =$ Cu(NCS)$_{2}$ has an anisotropic temperature dependence of the susceptibility and the charge transport. Partial charge-density-wave or charge fluctuation is expected to coexist with the metallic phase instead of the large antiferromagnetic fluctuation above $T^{*}$. The phase diagram and the superconductivity of $\kappa$-(ET)$_{2}$$X$ are discussed in connection with this phase.Comment: 5 pages, 4figures, REVTeX, references are corrected, accepted for pubication in Phys. Rev.

Effects of Fe2O3 addition on the nitridation of silicon powder

The reaction of silicon powder and nitrogen was studied in the range of 1300-1400 C. When an addition of Fe2O3 was more than 0.8wt%, the reaction was linear and compared to samples with no Fe2O3, the reaction velocity increased 5 to 10 times. The reactions were mediated by the process of peeling and cracking in a thin layer of Si2N4 formed on the silicon particles or on the surface of the Fe-Si melts. As the addition of Fe2O3 increased, the reaction activation energy for highly pure samples decreased. Fe2O3 which exceeded the Si3N4 solubility limits was finally converted to d-Fe

Weak localization and spin splitting in inversion layers on p-type InAs

We report on the magnetoconductivity of quasi two-dimensional electron systems in inversion layers on p-type InAs single crystals. In low magnetic fields pronounced features of weak localization and antilocalization are observed. They are almost perfectly described by the theory of Iordanskii, Lyanda-Geller and Pikus. This allows us to determine the spin splitting and the Rashba parameter of the ground electric subband as a function of the electron density.Comment: Accepted for publication in Phys. Rev. B, 4 page