A differential geometrical consideration on a “nonlocal” field

In this paper, the concept of “nonlocality”, which is carried by the internal variable (ω) ascribed to each point (x), is first investigated generally in connection with the concept of “unified” gauge field. Next, as a typical example, a Finslerian “nonlocal” field is considered, which is obtained by taking for ω a vector (ξ), and two examples are proposed: one is a unified field with Randers metric and the other is a micro-gravitational field endowed with space-time fluctuation.     

Effect of controlling optical wavelength by spectacle lenses on visual quality

Optical Review - In this study, the effects of selectively yellow-cut lenses on contrast sensitivity were investigated in healthy young and middle-aged individuals and elderly patients with...     

From optical spectroscopy to a concentration quenching model and a theoretical approach to laser optimization for Yb3+-doped YLiF4 crystals

A spectroscopic characterization was carried out to identify crystal-field levels for magnetic-dipole transitions of Yb³⁺ ions located in the Y³⁺ dodecahedral S₄ crystallographic site in YLiF₄ (YLF) crystals which were grown either by the Czochralski technique or by the laser heated pedestal growth (LHPG) technique. The concentration dependence of the measured decay time of the ²F_5/2 excited level of Yb³⁺ was analysed in order to understand relevant concentration quenching mechanisms. Under Yb³⁺ ion infrared pumping, self-trapping and up-conversion non-radiative energy transfer to trace rare-earth impurities (Er³⁺, Tm³⁺) has been observed over the visible region and interpreted by a limited-diffusion process within the Yb³⁺ doping ion subsystem to the impurities. The principal parameters useful for a theoretical approach for potential laser applications of Yb³⁺-doped YLiF₄ crystals have also been given.     

Semiconductor diamond heater in the Kawai multianvil apparatus: an innovation to generate the lower mantle geotherm

Semiconductor diamond is considered the best heater material to generate ultra-high temperatures in a Kawai cell. In two pioneering studies, a mixture of graphite and amorphous boron (or boron carbide, B₄C) was converted to semiconductor diamond in the diamond stability field and was confirmed to generate 2000°C and 3500°C, respectively. Following these works, we synthesized a homemade boron-doped graphite block with fine machinability. With this technical breakthrough, we developed a semiconductor diamond heater in a smaller Kawai-type cell assembly. Here, we report the procedure for making machinable boron-doped graphite, and the performance of the material as a heater in a Kawai cell at 15?GPa using tungsten carbide anvils and at ～50?GPa using sintered diamond anvils. Furthermore, we present a finite element simulation of the temperature distribution generated by a semiconductor diamond heater, which is much more homogeneous than that generated by a metal heater.     

Systematics of Mössbauer parameters in Fe57-doped titanate and germanate ilmenites

The Mössbauer spectra of ilmenite (FeTiO₃), Fe²⁺-doped ilmenites, MTiO₃ (M = Cd, Mn, Zn, Co, Mg and Ni) and MGeO₃ (M = Mn, Zn and Mg), have been studied from 4.2 K to room temperature. Systematic variations in the isomer shift and quadrupole splitting at room temperature are correlated with the change in ionic radii of the host M ions and the c/a ratio of the host crystal, respectively. The quadrupole splittings show a remarkable temperature variation; the magnetic ilmenites show either a sudden increase or a sudden decrease of quadrupole splittings below the Néel temperature, depending on the orientation of the spin axis with respect to the c axis.     

Size distribution of fractured areas in one-dimensional systems

We study a one-dimensional model for fracture, identifying fractured areas with intervals on which a stress field exceeds a threshold value. When is a diffusion process, the cumulative numberN(l) of fractured areas whose length is greater thanl obeys a power lawCl ^–p asl0 with probability one. The exponentp and the constantC are determined. The exponentp agrees with the Hausdorff dimension of the end points of fractured areas, i.e., ^–1(). Even if is self-similar with parameterH>0, i.e.,(cx)– is equivalent toc ^H {(x)–} for anyc>0, the exponentp does not depend solely onH;p=H, where(0, 1/H) is another parameter characterizing. Non-diffusion processes are given whereN(l) does not follow a power law.     

Canonical linear transformation on fock space with an indefinite metric

We first construct a Fock space with an indefinite metric ,=( , ), where is a unitary and Hermitian operator. We define a -selfadjoint (Segal's) field (f) which obeys the canonical commutation relations (CCR) with an indefinite metric. We consider a transformation 349-2 (T = real linear) which leaves the CCR invariant. We investigate the implementability of T by an operator on the Fock space.     

Determination of average ion energy in turbulently heated plasmas by secondary emission detector

An average energy of a high temperature part of ions in turbulently heated plasmas was measured by use of a secondary emission detector, and availability of this simple method for a determination of an average ion energy was discussed.     

Remarks on the relation between the Lee-Yang circle theorem and the correlation inequalities

We investigate the relation between the Lee-Yang circle theorem and the correlation inequalities. These results are general and independent of models. General properties of the partition functions which belong to the Lee-Yang class are given.