ORBITAL INSTABILITY OF STANDING WAVES FOR THE COUPLED NONLINEAR KLEIN-GORDON EQUATIONS

This paper deals with a type of standing waves for the coupled nonlinear Klein-Gordon equations in three space dimensions. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational argument. Then we prove the orbital instability of the standing waves by defining invariant sets and applying some priori estimates.     

Optical Digital Logic Operations by Self-pumped Phase Conjugation in Photorefractive Crystal

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The applications of unsteady, multi-dimensional studies of detonation waves to ram accelerators

Since much of the early work on the concepts on which ram accelerators are based dates back to the 1960s, although many of these are still being actively pursued, it is difficult to formulate a completely logical approach. This situation is compounded by the use of presently unacceptable treatments of unidimensional detonations in the early work and unfortunately extended to some of the more modern treatments. My approach has been to start by dealing with the early work and recent work impinging upon it, then to re-emphasise recent work on detonations, particularly that dealing with the influence of changes in confinement on quenching and re-initiation of detonations. However, some knowledge of this is inferred in suggestions made in Part 2 for possible improvements in the techniques. Latter sections cover the development of the ram accelerator, the use of various types of projectiles, developments in experimental techniques and finally on areas in space flight where the results from ram accelerators might be utilised. Received 14 January 1999 / Accepted 16 June 1999     

Lamb wave sensors array for nonviscous liquid sensing

The interdigital transducer (IDT) can excite Lamb wave in a piezoelectric plate loading with a liquid layer, and the phase velocity of Lamb wave is associated with the properties of the liquid layer. In this paper, the concept of effective permittivity is introduced to study the Lamb wave’s potential application in liquid sensing. Considering the measuring of ideal nonviscous liquid, the sensors array is designed to sense the density and the dielectric constant of the liquid layer simultaneously. Using LiNbO₃ as piezoelectric material, in order to improve the sensors array sensitivity and the electro-mechanical coupling coefficient, the optimized results including plate thicknesses and cut orientations are presented by numerical simulation. These studies show that the Lamb wave sensors array can be potential in liquid sensing.     

Velocity variation of internal shock waves in gamma ray bursts: Observational properties

The work uses the data in the TTS mode of BATSE to analyze the time lags and pulse widths of GRB960113 and GRB960722 in high as well as low energy bands. The results show that their time lags increase monotonously. This phenomenon can reasonably be interpreted with the model of internal shock waves of γ-ray bursts (GRB). Perhaps we obtain the direct observational evidence for the fireball model of GRBs for the first time.     

Micron-sized particle separation with standing surface acoustic wave—Experimental and numerical approaches

Traditional cell/particle isolation methods are time-consuming and expensive and can lead to morphology disruptions due to high induced shear stress. To address these problems, novel lab-on-a-chip-based purification methods have been employed. Among various methods introduced for the separation and purification of cells and synthetics particles, acoustofluidics has been one of the most effective methods. Unlike traditional separation techniques carried out in clinical laboratories based on chemical properties, the acoustofluidic process relies on the physical properties of the sample. Using acoustofluidics, manipulating cells and particles can be achieved in a label-free, contact-free, and highly biocompatible manner. To optimize the functionality of the platform, the numerical study should be taken into account before conducting experimental tests to save time and reduce fabrication expenses. Most current numerical studies have only considered one-dimensional harmonic standing waves to simulate the acoustic pressure distribution. However, one-dimensional simulations cannot calculate the actual acoustic pressure distribution inside the microchannel due to its limitation in considering longitudinal waves. To address this limitation, a two-dimensional numerical simulation was conducted in this study. Our numerical simulation investigates the effects of the platform geometrical and operational conditions on the separation efficiency. Next, the optimal values are tested in an experimental setting to validate these optimal parameters and conditions. This work provides a guideline for future acoustofluidic chip designs with a high degree of reproducibility and efficiency.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).     

Analysis of natural frequency for imaging interface in liquid lens

Transmission beam can be modulated at the liquid–liquid interface inside an electrowetting liquid lens. The fluctuation characteristics of the interface has a decisive effect on the beam modulation. A closed cylinder in capillary constant scale is analyzed and the natural frequencies of a flat interface are obtained using capillary wave hydrodynamics. Results in modes0 and 1 are in good agreement with previous experiments in the literature. The influences of the radius, the height ratio and the height-to-diameter ratio of a liquid lens on the interface eigenfrequencies are analyzed.     

Two model equations with a second degree logarithmic nonlinearity and their Gaussian solutions

In the paper, we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions. We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity. And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept. Our mathematical tool is the logarithmic trial equation method.