A criterion for the stability of a charged sphere in general relativity

A criterion for stability of a charged sphere is obtained by use of two different methods. The result is applied to a charged dust in order to investigate its stability.     

Nonlinear acoustic response through minute surface cracks: FEM simulation and experimentation

The second harmonic of a Rayleigh wave passing through a minute surface crack has been numerically analyzed by semi-explicit FEM including special elements which account for a nonlinear stress-strain relation at crack surfaces. Minute cracks perpendicular to a free, flat surface close under compressive stress when width of the crack opening is less than the longitudinal amplitude of the Rayleigh wave. Thereafter, compressive and shear stresses are partially transmitted through the closed cracks, whereas tensile and shear stresses are not transmitted through cracks that remain open. This leads to marked nonlinear ultrasonic response. Calculation was performed for an aluminum block having a surface crack. The transverse component of the Rayleigh wave propagating through the cracks shows distorted waveforms, making the second harmonic amplitude clearly noticeable. In an experiment, the second harmonic component of the leaky Rayleigh wave was detected for a simple crack model consisting of two aluminum blocks, by use of a PVDF line-focused transducer. The results of the experiment show that the second harmonic amplitude is a second-order function of the fundamental wave amplitude, and is more pronounced for low compressive stress applied to close the crack surfaces.     

Chaotic on off keying for secure communications

We experimentally demonstrate a chaotic on-off keying method for secure communications by using chaos synchronization in two microchip lasers. The output of the microchip laser in the transmitter is externally modulated with an acousto-optic modulator at ~4 MHz . One encodes a digital message in the chaotic carrier by turning the modulation on and off at 100 kHz. Because the accuracy of synchronization for the slave laser in the receiver tends to be degraded in the presence of external modulation in the injection laser signal, one can distinguish two binary states. The digital message can be recovered as an envelope of the chaotic oscillation when the difference between the two laser outputs of the transmitter and the receiver is calculated.     

A time dependent density functional method for the interaction site model

A new method is developed to study nonlinear dynamics of molecular liquids. It is a time dependent density functional method for the interaction site model. The nonlinear Langevin theory provides the formulation of the method. An approximation is introduced to calculate the reversible term.     

The synthesis and properties of 2-substituted dihydropyrimidines

Various 2-substituted 1,4-dihydro-4,4,6-trimethyl-1-phenylpyrimidines and 1,6-dihydro-4,6,6-trimethylpyrimidines were synthesized independently. For these dihydropyrimidines, the physical data such as the uv, ir, and nmr spectra and the oxidation potential were compared. 2-Dimethylamino substituted dihydropyrimidine showed the lowest oxidation potential, which expected the similar reducing ability as dihydropyridines.     

Investigation of manganese(III) fluoride for coulometric titration

A study has been made of the use of electrogenerated manganese(III), in an electrolyte containing fluoride, for coulometric titration. The addition of fluoride prevented the deposition of manganese dioxide on the anode, and was responsible for increase of the current efficiency and for extension of the feasible range of current density, owing to complex formation between manganese(III) and fluoride. The bonding ratio, the apparent stability constant and the redox potential of the complex were also estimated from the Nernst equation and the current-potential curves.     

Renormalization using the background-field method

Renormalization using the background-field method is examined in detail. The subtraction mechanism of subdivergences is described with reference to multi-loop diagrams and one- and two-loop counter-term formulae are explicitly given. The original one-loop counter-term formula of 't Hooft is thereby improved. The present method of renormalization is far easier to manage than the usual one owing to the fact that only gauge-invariant quantities are to be considered when worked in an appropriate gauge. Gravity and Yang-Mills theories are studied as examples.     

Simple synthesis of β-trifluoromethylstyrenes using (E)-trimethyl-(3,3,3-trifluoroprop-1-enyl)silane

(E)-trimethyl-(3,3,3-trifluoroprop-1-enyl)silane (1) was synthesized as a reagent for use in Hiyama cross-coupling reactions for the production of β-trifluoromethylstyrene derivatives. Cross-coupling of 1 with electronically diverse aryl iodides was achieved by treatment with CsF in the presence of catalytic amounts of palladium to afford the desired products in moderate to good yields.