Wave optics analysis by phase-shifting real-time holographic interferometry

The purpose of this work is to study the potentialities in the phase-shifting real-time holographic interferometry using photorefractive crystals as the recording medium for wave-optics analysis in optical elements and non-linear optical materials. This technique was used for obtaining quantitative measurements from the phase distributions of the wave front of lens and lens systems along the propagation direction with in situ visualization, monitoring and analysis in real time. (C) 2008 Elsevier GmbH. All rights reserved.

Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor

We present a solitary solution of the three-wave nonlinear partial differential equation (PDE) model - governing resonant space-time stimulated Brillouin or Raman backscattering - in the presence of a cw pump and dissipative material and Stokes waves. The study is motivated by pulse formation in optical fiber experiments. As a result of the instability any initial bounded Stokes signal is amplified and evolves to a subluminous backscattered Stokes pulse whose shape and velocity are uniquely determined by the damping coefficients and the cw-pump level. This asymptotically stable solitary three-wave structure is an attractor for any initial conditions in a compact support, in contrast to the known superluminous dissipative soliton solution which calls for an unbounded support. The linear asymptotic theory based on the Kolmogorov-Petrovskii-Piskunov assertion allows us to determine analytically the wave-front slope and the subluminous velocity, which are in remarkable agreement with the numerical computation of the nonlinear PDE model when the dynamics attains the asymptotic steady regime. © 1997 The American Physical Society.

Magnetic resonance imaging of the manipulation of a chemical wave using an inhomogeneous magnetic field

The effects of applied magnetic fields on the traveling wave formed by the reaction of (ethylenediaminetetraacetato)cobalt(II) (Co(II)EDTA2-) and hydrogen peroxide have been studied using magnetic resonance imaging (MRI). It was found that the wave could be manipulated by applying pulsed magnetic field gradients to a sample contained in a vertical cylindrical tube in the 7.0 T magnetic field of the spectrometer. Transverse field gradients decelerated the propagation of the wave down the high-field side of the tube and accelerated it down the low-field side. This control of the wave propagation eventually promoted the formation of a finger on the low-field side of the tube and allowed the wave to be maneuvered within the sample tube. The origin of these effects is rationalized by considering the Maxwell stress arising from the combined homogeneous and inhomogeneous magnetic fields and the magnetic susceptibility gradient across the wave front.

Comparing methods for modelling spreading cell fronts

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performace of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made.

Pressure shocks in relativistic viscous heat-conducting fluids

In this paper we have studied the propagation of pressure shocks in viscous, heat-conducting, relativistic fluids. Velocities of wave fronts and growth equations for the strength of the waves are obtained in the case of low and high temperatures with variable transport coefficients. On the basis of numerical integrations the growth equation results have been discussed. In the case of constant transport coefficients and for all admissible values of ratio of specific heats of the fluid, an analytical solution for the velocity of the wave as a function of distance along the normal trajectory to the wave front, has been obtained.

Finite-amplitude love-waves on an isotropic layered half-space

A pair of semi-linear hyperbolic partial differential equations governing the slow variations in amplitude and phase of a quasi-monochromatic finite-amplitude Love-wave on an isotropic layered half-space is derived using the method of multiple-scales. The analysis of the exact solution of these equations for a signalling problem reveals that the amplitude of the wave remains constant along its characteristic and that the phase of the wave increases linearly behind the wave-front.

An appendix to the paper "approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic"

The theory of Varley and Cumberbatch [l] giving the intensity of discontinuities in the normal derivatives of the dependent variables at a wave front can be deduced from the more general results of Prasad which give the complete history of a disturbance not only at the wave front but also within a short distance behind the wave front. In what follows we omit the index M in Eq. (2.25) of Prasad [2].

Trapped waves in the neighborhood of a sonic-type singularity

A model equation is derived to study trapped nonlinear waves with a turning effect, occurring in disturbances induced on a two-dimensional steady flow. Only unimodal disturbances under the short wave assumption are considered, when the wave front of the induced disturbance is plane. In the neighbourhood of certain special points of sonic-type singularity, the disturbances are governed by a single first-order partial differential equation in two independent variables. The equation depends on the steady flow through three parameters, which are determined by the variations of velocity and depth, for example (in the case of long surface water waves), along and perpendicular to the wave front. These parameters help us to examine various relative effects. The presence of shocks in a continuously accelerating or decelerating flow has been studied in detail.

Polarization studies in electromagnetic scattering by small Solar-system particles

In remote-sensing studies, particles that are comparable to the wavelength exhibit characteristic features in electromagnetic scattering, especially in the degree of linear polarization. These features vary with the physical properties of the particles, such as shape, size, refractive index, and orientation. In the thesis, the direct problem of computing the unknown scattered quantities using the known properties of the particles and the incident radiation is solved at both optical and radar spectral regions in a unique way. The internal electromagnetic fields of wavelength-scale particles are analyzed by using both novel and established methods to show how the internal fields are related to the scattered fields in the far zone. This is achieved by using the tools and methods that were developed specifically to reveal the internal field structure of particles and to study the mechanisms that relate the structure to the scattering characteristics of those particles. It is shown that, for spherical particles, the internal field is a combination of a forward propagating wave with the apparent wavelength determined by the refractive index of the particle, and a standing wave pattern with the apparent wavelength the same as for the incident wave. Due to the surface curvature and dielectric nature of the particle, the incident wave front undergoes a phase shift, and the resulting internal wave is focused mostly at the forward part of the particle similar to an optical lens. This focusing is also seen for irregular particles. It is concluded that, for both spherical and nonspherical particles, the interference at the far field between the partial waves that originate from these concentrated areas in the particle interior, is responsible for the specific polarization features that are common for wavelength-scale particles, such as negative values and local extrema in the degree of linear polarization, asymmetry of the phase function, and enhancement of intensity near the backscattering direction. The papers presented in this thesis solve the direct problem for particles with both simple and irregular shapes to demonstrate that these interference mechanisms are common for all dielectric wavelength-scale particles. Furthermore, it is shown that these mechanisms can be applied to both regolith particles in the optical wavelengths and hydrometeors at microwave frequencies. An advantage from this kind of study is that it does not matter whether the observation is active (e.g., polarimetric radar) or passive (e.g., optical telescope). In both cases, the internal field is computed for two mutually perpendicular incident polarizations, so that the polarization characteristics can then be analyzed according to the relation between these fields and the scattered far field.

A Macroscopic Model for First Return Stroke of Lightning

A lightning return stroke model for a downward flash is proposed. The model includes underlying physical phenomena governing return stroke evolution, namely, electric field due to charge distributed along the leader and cloud, transient enhancement of series channel conductance at the bridging regime, and the nonlinear variation of channel conductance, which supports the return stroke current evolution. Thermal effects of free burning arc at the stroke wave front and its impact on channel conductance are studied. A first-order arc model for determining the dynamic channel conductance along with a field-dependent conductivity for corona sheath is used in the model. The model predicts consistent current propagation along the channel with regard to current amplitude and return stroke velocity. The model is also capable of predicting the remote electromagnetic fields that are consistent with the experimental observations.

Numerical simulation of an adaptive optics system with laser propagation in the atmosphere

A comprehensive model of laser propagation in the atmosphere with a complete adaptive optics (AO) system for phase compensation is presented, and a corresponding computer program is compiled. A direct wave-front gradient control method is used to reconstruct the wave-front phase. With the long-exposure Strehl ratio as the evaluation parameter, a numerical simulation of an AO system in a stationary state with the atmospheric propagation of a laser beam was conducted. It was found that for certain conditions the phase screen that describes turbulence in the atmosphere might not be isotropic. Numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree well with those computed by means of an integration method. However, the computer time required for the FFT method is 1 order of magnitude less than that of the integration method. Phase tailoring of the calculated phase is presented as a means to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time to our knowledge that for a constant delay time of an AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. This finding indicates that the better compensation capability of an AO system does not mean better correction effectiveness. (C) 2000 Optical Society of America.

Building the perfect 3D hologram

A new liquid crystal device structure has been developed using a vertically grown Multi-Wall Carbon NanoTube (MWCNT) as a 3D electrode structure, which allows complicated phase only hologram to be displayed using conventional liquid crystal materials. The nanotubes act as an individual electrode sites that generate an electric field profile, dictating the refractive index profile with the liquid crystal cell. Changing the electric field applied makes it possible to tune the properties to modulate the light in an ideal kinoform. A perfect 3D image can be generated by a computer generated hologram by using the diffraction of the light from the hologram pixels to create an optical wave front that appears to come from 3D object. A multilevel phase modulating device based on nematic LC's is also under progress, which will be used with the LC/CNT devices on an LCOS backplane to project a full 3D image from the kinoform.

Cellular Cell Bifurcation Of Cylindrical Detonations

Cellular cell pattern evolution of cylindrically-diverging detonations is numerically simulated successfully by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. From the simulation, three cell bifurcation modes are observed during the evolution and referred to as concave front focusing, kinked and wrinkled wave front instability, and self-merging of cellular cells. Numerical research demonstrates that the wave front expansion resulted from detonation front diverging plays a major role in the cellular cell bifurcation, which can disturb the nonlinearly self-sustained mechanism of detonations and finally lead to cell bifurcations.

在激波波面中氧分子的非平衡离解

对强激波作用下双原子分子振动与离解耦合的非平衡离解过程进行了理论计算.本工作的特点是将计算起点建立在分子基本参数上,采用主方程理论处理振动与离解的耦合,振动跃迁几率用SSH理论计算,在离解限附近考虑多量子数跃迁并计及原子复合的影响.对O2-Ar体系,计算给出了在正激波后O2分子振动能级分布、振动弛豫时间、离解孕育时间、离解产物浓度、离解速率系数等物理量随时间的演化.计算结果分别与Camac和Wray的实验相符.计算显示,在激波作用的后期,有准稳态的振动能级布居分布.计算结果显示,Park模型低估了非平衡离解速率系数,Hansen模型则高估了非平衡离解速率系数.

Investigation on mechanism of critical cavitating flow in liquid jet pumps under operating limits

The critical cavitating flow in liquid jet pumps under operating limits is investigated in this paper. Measurements on the axial pressure distribution along the wall of jet pumps indicate that two-phase critical flow occurs in the throat pipe under operating limits. The entrained flow rate and the distribution of the wall pressure upstream lowest pressure section does not change when the outlet pressure is lower than a critical value. A liquid-vapor mixing shockwave is also observed under operating limits. The wave front moves back and forth in low frequency around the position of the lowest pressure. With the measured axial wall pressures, the Mach number of the two-phase cavitating flow is calculated. It's found that the maximum Mach number is very close to I under operating limits. Further analysis infers a cross-section where Mach number approaches to I near the wave front. Thus, the liquid-vapor mixture velocity should reach the local sound velocity and resulting in the occurrence of operating limits.