Stability of travelling wave solutions to a semilinear hyperbolic system with relaxation

We study a semilinear hyperbolic system with relaxation and investigate the asymptotic stability of travelling wave solutions with shock profile. It is shown that the travelling wave solution is asymptotically stable, provided the initial disturbance is suitably small. Moreover, we show that the time convergence rate is polynomially (resp. exponentially) fast as t→∞ if the initial disturbance decays polynomially (resp. exponentially) for x→∞. Our proofs are based on the space–time weighted energy method. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal decay estimates of a regularity-loss type system with constraint condition

In the paper [14], the authors formulated a new structural condition which includes the Kawashima–Shizuta condition, and analyzed the weak dissipative structure called the regularity-loss type for general systems which contain the Timoshenko system and the Euler–Maxwell system. However, this new structural condition can not cover all of dissipative systems. Indeed we introduce a dissipative system which does not satisfy the new condition and analyze the weaker dissipative structure in this paper. Precisely we first derive the $L^2$ decay estimate of solutions and discuss the type of the corresponding regularity-loss structure. Moreover, in order to show the optimality of the decay estimate, we analyze the expansion for the corresponding eigenvalue of our problem and derive that the solution approaches the diffusion wave as time tends to infinity.     

Measurement of acoustic output power in a traveling wave engine

We built and tested a double-loop thermoacoustic cooler consisting of an engine-loop, a branch resonator, and a cooler-loop. The cooling power of 6.4 W was obtained at the cooling temperature of 0 degrees C, when the input heat power of 416 W was supplied to the engine-loop. We measured the acoustic power and found that the output power emitted from the engine-loop was 12 W, and that the input acoustic power entering the cooler-loop was 6 W.     

Beam polarization effects on top-pair production at the ILC

Full one-loop electroweak corrections for an \(e^-e^+\rightarrow t \bar{t}\) process associated with sequential \(t\rightarrow b \mu \nu _\mu \) decay are discussed. At the one-loop level, the spin-polarization effects of the initial electron and positron beams are included in the total and differential cross sections. A narrow-width approximation is used to treat the top-quark production and decay while including full spin correlations between them. We observed that the radiative corrections due to the weak interaction have a large polarization dependence on both the total and the differential cross sections. Therefore, experimental observables that depend on angular distributions such as the forward–backward asymmetry of the top-production angle must be treated carefully including radiative corrections. We also observed that the energy distribution of bottom quarks is largely affected by the radiative corrections.     

Fabrication of a quartz optical fiber tip for dental treatment with Nd:YAG laser—Proposal of a new process with TiO2 powder

In dental treatment with Nd:YAG laser beam, a quartz optical fiber is generally used to transmit the laser beam, which is irradiated to the hard and soft tissues for a caries treatment and a periodontal tissue excision. Since a normal optical fiber, which the laser beam comes out from the tip of the fiber, has difficulty irradiating to a narrow space and an inner root canal uniformly, it is effective to use a processed optical fiber tip from which is obtained a diffused and circumferential laser beam. In this paper, a new process to obtain these laser beams with TiO₂ powder is proposed, and the characteristics and the performances of the processed optical fiber were investigated. An experimental instrument was developed to measure the energy partition radiated from the processed fiber tip, and the ratio of a straight beam, a sideways beam and heat generated by the absorption of the laser beam was measured in each condition. As a result, the ratio of an energy partition was controllable by changing the incidence parameter to process the fiber tip, and the processed fiber tip corresponding to the clinical purpose could be obtained. The parameters which affected the processability of the fiber tip were processing time and incidence laser energy. The prepared cavity with processed fiber on the enamel was influenced by a straight beam, and the removal of enamel to the depth direction was controllable by using the processed fiber.     

Internal inelastic scattering satellite probed by molecular-frame photoelectron angular distributions from CO2

The molecular-frame photoelectron angular distribution (MFPAD) of the satellite accompanying the C 1s photoline of the CO2 molecule has been measured at the C 1s(2sigmag)-->4sigmau* shape resonance, using electron-ion multicoincidence momentum spectroscopy. The observed MFPAD indicates that the conjugate satellite is excited by internal inelastic scattering. In this scenario, a photoelectron is ejected from the C 1s(2sigmag) orbital along the molecular axis and collides with an O lone-pair electron in the highest occupied molecular orbital 1pig. Then one of the colliding electrons is trapped to the lowest unoccupied molecular orbital 2piu*, while the other is emitted as a satellite photoelectron of sigmag symmetry, losing the information of the original photoelectron emission direction and parity.     

New nonlinear-laser effects in YbVO4 crystal: Sesqui-octave stokes and anti-Stokes comb generation and the cascaded self-frequency “tripling” of χ(3)-Stokes components under a one-micron picosecond pumping

We report the experimental investigations of nonlinear-laser effects in vanadate YbVO₄ under a onemicron picosecond Nd³⁺:Y₃Al₅O₁₂ laser pumping. In this tetragonal host-crystal for Ln³⁺ lasants, for the first time, we excited more than one-and-a-half octave (≈11661 cm^?1) Raman-induced Stokes and anti-Stokes generation combs and observed a multistep cascaded parametric χ⁽³⁾ lasing in the deep-blue spectral region. All generation lines were identified and attributed to the SRS-promoting vibration mode of the crystal (ω_SRS ≈ 897 cm^?1). We classified the ytterbium vanadate as a promising material for Raman frequency converters, wideband χ⁽³⁾-nonlinear comb generators, and as a gain medium for solid-state lasers.     

Turbulence structure in an annuli with strongly heated inner cylinder

This structure of turbulent flow in an annulus with strong inner cylinder wall heating has been studied in terms of velocity and temperature with wall temperatures up to 707 °C and a Reynolds number of 48,000. With increase in wall heating, the turbulence very close to the wall was suppressed due to an increase in the kinematic viscosity. In the inner region, the intermittent mixing became intensive and the turbulent intensity increased whereas, in the outer region, the turbulence was suppressed since intermittent mixing was no longer effective. The results show that the thermal structure can be considered in terms of a passive scalar for wall temperatures less then around 200 °C, except in the leading region of the heated area. Received: 2 March 1998/Accepted: 2 November 1998     

Heat transfer and fluid dynamics of air–water two-phase flow in micro-channels

Heat transfer, pressure drop, and void fraction were simultaneously measured for upward heated air–water non-boiling two-phase flow in 0.51 mm ID tube to investigate thermo–hydro dynamic characteristics of two-phase flow in micro-channels. At low liquid superficial velocity j_l frictional pressure drop agreed with Mishima–Hibiki’s correlation, whereas agreed with Chisholm–Laird’s correlation at relatively high j_l. Void fraction was lower than the homogeneous model and conventional empirical correlations. To interpret the decrease of void fraction with decrease of tube diameter, a relation among the void fraction, pressure gradient and tube diameter was derived. Heat transfer coefficient fairly agreed with the data for 1.03 and 2.01 mm ID tubes when j_l was relatively high. But it became lower than that for larger diameter tubes when j_l was low. Analogy between heat transfer and frictional pressure drop was proved to hold roughly for the two-phase flow in micro-channel. But satisfactory relation was not obtained under the condition of low liquid superficial velocity.     

Improvement of a free piston driver for a high-enthalpy shock tunnel

In order to improve the operation of a high-enthalpy free piston shock tunnel its tuned operation was studied analytically and experimentally. First, the piston motion in the free piston driver tube was analytically solved by proposing a simple piston/gasdynamic model, and the tuned operation condition was formulated as an eigenvalue with which the piston has sufficiently high speed at the moment of diaphragm rupture, so as to maintain a constant driver gas pressure, and reduces its speed to come to rest when very closely approaching the end of the driver tube. Second, the result of this analysis was validated by its comparison with experiments which were conducted in the medium-sized free piston shock tunnel HEK installed at the NAL Kakuda Research Center. By observing the detail of piston landing at the end of the driver tube the present tuned operation was found to be successfully achieved with the operating condition given here. Its advantages in improving the pressure recovery factor and in enhancing the stagnation enthalpy were successfully demonstrated. Received 8 June 1997 / Accepted 1 October 1997