Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Charge transport study on single crystals of β-LiAl

Charge transport properties of β-LiAl were studied in the composition range of 48.0–50.2 at.% Li. Measurements were made on single crystal samples and down to the liquid He temperature. The resistivity changes linearly with temperature above 125 K, with a thermal coefficient of 72–95nΩ cm K^?1. The Matthiessen law was obeyed very well. A component dependent on temperature, which was described by the Grüneisen formula, is insensitive to a change of the chemical composition. On the other hand, the residual resistivity depends largely on the composition and contributes up to 58% of the total resistivity in Li_0.498. It is chiefly due to the substituted Li atoms on the Al sublattice.     

Investigation of the center intensity of first- and second-order Laguerre-Gaussian beams with linear and circular polarization

The vectorial Debye integral shows that tightly focused Laguerre-Gaussian (LG) beams have a residual intensity at the focal point for linear polarization, for a topological charge of m=1 and 2. We measured the shapes of linearly and circularly polarized LG beams and found that a central intensity appeared at m=1 and 2 for linear and right-handed circular polarization, however, it is completely canceled for left-handed circular polarization. In general, when the orbital angular momentum of the LG beam is parallel to the spin angular momentum of the photons, zero intensity is always achieved at the focus.     

Ferroelectric phase transitions in ultrathin films of BaTiO3

We present molecular dynamics simulations of a realistic model of an ultrathin film of BaTiO3 sandwiched between short-circuited electrodes to determine and understand effects of film thickness, epitaxial strain, and the nature of electrodes on its ferroelectric phase transitions as a function of temperature. We determine a full epitaxial strain-temperature phase diagram in the presence of perfect electrodes. Even with the vanishing depolarization field, we find that ferroelectric phase transitions to states with in-plane and out-of-plane components of polarization exhibit dependence on thickness; it arises from the interactions of local dipoles with their electrostatic images in the presence of electrodes. Secondly, in the presence of relatively bad metal electrodes which only partly compensate the surface charges and depolarization field, a qualitatively different phase with stripelike domains is stabilized at low temperature.     

Silicon-Based Integrated Optic Pressure Sensor Using Intermodal Interference between TM-Like and TE-Like Modes

In this paper, a silicon-based integrated optic pressure sensor using an intermodal interference between the fundamental TM-like and TE-like modes is described. The sensor consists of a micromachined rectangular diaphragm and a straight polystyrene optical waveguide passing over the diaphragm. Its sensitivity is theoretically known to be strongly dependent on the position of the waveguide over the diaphragm. To experimentally investigate such dependence, we fabricated a sensor with a 1.2 mm ×10 mm ×20 μm diaphragm, over which waveguides were placed at 50 μm intervals. The measured phase sensitivity was 98 mrad/kPa for the waveguide nearest to the diaphragm edge. The measurement was also carried out for the other waveguides. As theoretically expected, the largest sensitivity was obtained for the waveguide nearest to the edge.     

Ion-exchange resin decomposition in supercritical water

Abstract

Using supercritical water oxidation, the cation exchange resin was decomposed fast and completely to water, carbon dioxide and sulfuric acid. While the resin decomposition yield increased with the reaction time and the amount of hydrogen peroxide added as oxidizing agent, it was constant in the resin concentration from 0.14 to 1.9 dry resin weight percent to water. More than 99% of the cation exchange resin was decomposed with hydrogen peroxide added in the amount of 7 times the stoichiometric value at 673 K and 30MPa for 30 minutes of the reaction time. The cation exchange resin is decomposed through two main reaction pathways. One has a rate controlling intermediate such as acetic acid whose decomposition rate was very slow, and the other does not have stable intermediates. The decomposition of the acetic acid is a significant factor for the complete decomposition of the resin, although it does not dominate the whole resin decomposition. A simple kinetic model that estimates the resin decomposition yield was developed.     

Numerical and experimental investigations of dependence of photoacoustic signals from gold nanoparticles on the optical properties

Gold nanoparticles (AuNPs) are used as a contrast agent of the photoacoustic (PA) imaging. The efficiency of AuNPs has been discussed with the absorption cross section. However, the effects of the scattering of the light by AuNPs and surrounding medium on the PA signal from AuNPs have not been discussed. The PA signals from the aqueous solution of AuNPs were examined in the numerical simulation and the experiment. In the numerical simulation, the absorption and scattering cross sections of spherical and polyhedral AuNPs were calculated by Mie theory and discrete dipole approximation. Monte Carlo simulation calculated the absorbed light energy in the aqueous solution of AuNPs. Based on the PA wave equation, the PA signals were simulated. In the experiment, the PA signal from the aqueous solution of AuNP was measured by use of a piezoelectric film and a Q-switched Nd:YAG laser operated at 532 nm. The results of the numerical simulation and the experiment agreed well. In the numerical simulation and the experiment, a single Au nanocube with 50-nm edge generated the peak value of the PA signal significantly. It was approximately 350 times and twice as large as the peak values of the spherical AuNPs with 10- and 50-nm diameters, respectively. The peak value of the PA signal depended on both the absorption and scattering coefficients of the AuNPs and the surrounding medium. The peak value increased with the scattering coefficient in a quadratic manner. The character of the temporal profile of the PA signal such as full width at half maximum depended on the scattering coefficient of the AuNPs.     

Curved Ferroelectric Liquid Crystal Matrix Displays Driven by Field-Sequential-Color and Active-Matrix Techniques

This paper describes a curved field-sequential-color matrix display using fast-response ferroelectric liquid crystal. Black matrix and transparent electrode patterns were formed on a thin plastic substrate by a transfer method from a glass substrate. While a composite film of liquid crystal and micro-polymers of walls and fibers was formed between the flexible substrates by printing, laminating and curing processes of a solution of monomers and liquid crystal, the mechanical stability was enhanced by use of multi-functional monomers to form large display panels. The image pixels of the matrix panel were driven by an active matrix scheme using an external switch transistor array at a frequency of 180 Hz for intermittent three-primary-color backlight illumination. The flexible A4-paper-sized color display with 24 × 16 pixels and 60 Hz field frequency was demonstrated by illuminating it with sequential three-primary-color lights from light-emitting diodes of the backlight. Our display system is useful in various information displays because of its freedom of setting and location.     

WIDE RANGE DETECTOR USING PARABOLIC CYLINDRICAL MIRROR FOR THz APPLICATIONS

A new, wide-band, high-speed and high-sensitivity THz detector has been developed. The prototype detector consists of a parabolic cylindrical mirror, a long wire antenna and a Schottky barrier diode. Direct detection measurements have shown a stable sensitivity of 150 ± 50 V/W for 1–2 THz without any adjustments. The long wire antenna was fixed at the focus of parabolic cylindrical mirror then it has been realized less operation steps, easy coupling to the external THz signals and a dramatic enhancement in the practicality of this system. The optically polished mirror and frosted surface one showed comparable sensitivities, thus easy polishing and less cost mirror fabrication can be applied for this system. The radiation pattern showed a maximum radiation angle of approximately 23° with its dominant main lobe, which was attributed to the wire antenna character and confirmed good agreements with classical antenna theory.