One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Optical wave turbulence and wave condensation in a nonlinear optical experiment

We present theory, numerical simulations and experimental observations of a 1D optical wave system. We show that this system is of a dual cascade type, namely, the energy cascading directly to small scales, and the photons or wave action cascading to large scales. In the optical context the inverse cascade is particularly interesting because it means the condensation of photons. We show that the cascades are induced by a six-wave resonant interaction process described by weak turbulence theory. We show that by starting with weakly nonlinear randomized waves as an initial condition, there exists an inverse cascade of photons towards the lowest wavenumbers. During the cascade nonlinearity becomes strong at low wavenumbers and, due to the focusing nature of the nonlinearity, it leads to modulational instability resulting in the formation of solitons. Further interaction of the solitons among themselves and with incoherent waves leads to the final condensate state dominated by a single strong soliton. In addition, we show the existence of the direct energy cascade numerically and that it agrees with the wave turbulence prediction.

Design and construction of a two dimensional duct equipped with a wave generator and a variable coastal slope and an ocean wave energy conversion system (OWC)

The aims of this thesis were evaluation the type of wave channel, wave current, and effect of some parameters on them and identification and comparison between types of wave maker in laboratory situations. In this study, designing and making of two dimension channels (flume) and wave maker for experiment son the marine buoy, marine building and energy conversion systems were also investigated. In current research, the physical relation between pump and pumpage and the designing of current making in flume were evaluated. The related calculation for steel building, channels beside glasses and also equations of wave maker plate movement, power of motor and absorb wave(co astal slope) were calculated. In continue of this study, the servo motor was designed and applied for moving of wave maker’s plate. One Ball Screw Leaner was used for having better movement mechanisms of equipment and convert of the around movement to linear movement. The Programmable Logic Controller (PLC) was also used for control of wave maker system. The studies were explained type of ocean energies and energy conversion systems. In another part of this research, the systems of energy resistance in special way of Oscillating Water Column (OWC) were explained and one sample model was designed and applied in hydrolic channel at the Sheikh Bahaii building in Azad University, Science and Research Branch. The dimensions of designed flume was considered at 16 1.98 0. 57 m which had ability to provide regular waves as well as irregular waves with little changing on the control system. The ability of making waves was evaluated in our designed channel and the results were showed that all of the calculation in designed flume was correct. The mean of error between our results and theory calculation was conducted 7%, which was showed the well result in this situation. With evaluating of designed OWC model and considering of changes in the some part of system, one bigger sample of this model can be used for designing the energy conversion system model. The obtained results showed that the best form for chamber in exit position of system, were zero degree (0) in angle for moving below part, forty and five (45) degree in front wall of system and the moving forward of front wall keep in two times of height of wave.

Normal-mode sound propagation in an ocean with sinusoidal surface waves

The normal-mode solution to the problem of acoustic wave propagation in an isovelocity ocean with a wavy surface is considered. The surface wave amplitude is assumed to be small compared to the acoustic wavelength, and the method of multiple scales is employed to study the interaction between normal-mode acoustic waves and the surface waves. A nonresonant interaction causes small fluctuations of the amplitude and phase of the acoustic wave at a rate dependent on the frequency of the surface wave. Backscatter occurs if the wavenumber of the surface wave is larger than that of the acoustic wave. The interaction becomes resonant if appropriate phase-matching conditions are satisfied. In this case, two acoustic normal modes get coupled, resulting in a large-scale periodic exchange of energy from one mode to another.

The effect of radiation on the electron pairing in a multiband system

The possible occurrence of a generalized (1-wave) nonequilibrium superconducting state in a multiband system under certain conditions is studied. In the model the radiation field causes interband mixing, and phonons of an appropriate mode (branch) are involved in the interband scattering of electrons of two conduction bands of the system. The strength of the generalized 1-wave pairing interaction between quasiparticles belonging to new radiation admixed states depends on the density (n o/V) of quanta in the system. The coupling constant has the form Xl= AiB(n o/V)/[C + B(no/V)], where A1, B, and C are parameters. For C > B(n0/V), the transition temperature T1* increases with (no/V) in the initial stages. It levels off with higher power. With further increase of power, the transition temperature is expected to drop sharply due to heating effects which cause pair breaking. Estimates show that p-wave (triplet state) pairing may be possible under radiation-induced nonequilibrium situations in appropriate systems. Estimates for lifetimes of various processes quasiparticle, phonon, pair relaxation, and photon-induced mixing) show that the coherence required for the mixing and pairing effects will be maintained for the temperature range and photon density considered.

Investigation of the characteristics of an SF6 rotating arc by a mathematical model

A mathematical model has been developed for predicting the performance of rotating arcs in SF6 gas by considering the energy balance and force balance equations. The finite difference technique has been adopted for the computer simulation of the arc characteristics. This method helps in considering the spatial variation of the transport and radiative properties of the arc. All the three heat loss mechanisms-conduction, convection, and radiation-have been considered. Results obtained over a 10 ms (half cycle of 50 Hz wave) current flow period for 1.4 kA (peak) and 4.2 kA (peak), show that the proposed arc model gives the expected behavior of the arc over the range of currents studied.

Shocked Flows Induced by Supersonic Projectiles Moving in Tubes

A numerical study on shocked flows induced by a supersonic projectile moving in tubes is described in this paper. The dispersion-controlled scheme was adopted to solve the Euler equations implemented with moving boundary conditions. Four test cases were carried out in the present study: the first two cases are for validation of numerical algorithms and verification of moving boundary conditions, and the last two cases are for investigation into wave dynamic processes induced by the projectile moving at Mach numbers of M-p = 2.0 and 2.4, respectively, in a short time duration after the projectile was released from a shock tube into a big chamber. It was found that complex shock phenomena exist in the shocked flow, resulting from shock-wave/projectile interaction, shock-wave focusing, shock-wave reflection and shock-wave/contact-surface interactions, from which turbulence and vortices may be generated. This is a fundamental study on complex shock phenomena, and is also a useful investigation for understanding on shocked flows in the ram accelerator that may provide a highly efficient facility for launching hypersonic projectiles.

Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability-vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000-10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e. f(t)/f(s) similar to Re-0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza's prediction and some early experimental results f(t)/f(s) similar to Re-0.5 given by Bloor et nl. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f(t), f(s)) leading to spectra broadening to form the coupling mf(s) +/- nf(t) are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the three-dimensional evolution is provided.

波浪和风生浪流作用下的近岸海底泥沙运移模型的推广和应用

本文利用数值计算和经验公式相结合的方法，获得了在波浪和风生流和波浪共同作用下海底泥沙输移的二维模型．在此基础上，讨论了海底泥沙输移在风速、风向和泥沙粒径不同等三种情况下的变化特征；指出了经验公式对泥沙输移规律的适用范围以及风速、风向对于近岸处泥沙输移重要性．这一研究结果对近岸结构物的选址设计具有实际应用价值．

Influence of Wind and Grain Size on Migration of Asymmetric Sand Waves

Large parts of shallow seas are covered by regular seabed patterns and sand wave is one kind of these patterns. The instability of the sedimentary structures may hazard pipelines and the foundations of offshore structures. In the last decade or so, it's a focus for engineers to investigate the movement mechanism of sand waves. Previous theoretical studies of the subject have developed a general model to predict the growth and migration of sand waves, which is based on the two-dimensional vertical shallow water equations and the bed-form deformation equations. Although the relation between wave-current flow and sand bed deformation has been established, the topographic influence has not been considered in the model. In this paper some special patterns, which are asymmetric and close to the reality, are represent as the perturbed seabed and the evolution of sand waves is calculated. The combination of a steady flow induced by wind and a sinusoidal tidal flow is considered as the basic flow. Finally the relations of some parameters (grain size, etc.) and sand waves' growth and migration are discussed, and the growth rate and migration speeds of asymmetric sand waves are carried out.

Two-dimensional Vortex-induced Vibrations of Submerged Floating Tunnel Tethers

A vortex-induced vibration (VIV) model is presented for predicting the nonlinear dynamic response of submerged floating tunnel (SFT) tethers which are subjected to wave, current and tunnel oscillatory displacements at their upper end in horizontal and vertical directions. A nonlinear fluid force formula is introduced in this model, and the effect of the nonlinearity of tether is investigated. First, the tunnel is stationary and the tether vibrates due to the vortices shedding. The calculated results show that the cross-flow amplitude of VIV decreases compared with the linear model. However the in-line amplitude of VIV increases. Next, the periodical oscillation of tunnel is considered. The oscillation caused by wave forces plays the roles of parametric exciter and forcing exciter to the VIV of tether. The time history of displacement of the tether mid-span is obtained by the proposed model. It is shown that the in-line amplitude increases obviously and the corresponding frequency is changed. The cross-flow amplitude exhibits a periodic behavior.

Quantum Electromechanics with Two Tone Drive

In the field of mechanics, it is a long standing goal to measure quantum behavior in ever larger and more massive objects. It may now seem like an obvious conclusion, but until recently it was not clear whether a macroscopic mechanical resonator -- built up from nearly 10¹³ atoms -- could be fully described as an ideal quantum harmonic oscillator. With recent advances in the fields of opto- and electro-mechanics, such systems offer a unique advantage in probing the quantum noise properties of macroscopic electrical and mechanical devices, properties that ultimately stem from Heisenberg's uncertainty relations. Given the rapid progress in device capabilities, landmark results of quantum optics are now being extended into the regime of macroscopic mechanics.

The purpose of this dissertation is to describe three experiments -- motional sideband asymmetry, back-action evasion (BAE) detection, and mechanical squeezing -- that are directly related to the topic of measuring quantum noise with mechanical detection. These measurements all share three pertinent features: they explore quantum noise properties in a macroscopic electromechanical device driven by a minimum of two microwave drive tones, hence the title of this work: "Quantum electromechanics with two tone drive".

In the following, we will first introduce a quantum input-output framework that we use to model the electromechanical interaction and capture subtleties related to interpreting different microwave noise detection techniques. Next, we will discuss the fabrication and measurement details that we use to cool and probe these devices with coherent and incoherent microwave drive signals. Having developed our tools for signal modeling and detection, we explore the three-wave mixing interaction between the microwave and mechanical modes, whereby mechanical motion generates motional sidebands corresponding to up-down frequency conversions of microwave photons. Because of quantum vacuum noise, the rates of these processes are expected to be unequal. We will discuss the measurement and interpretation of this asymmetric motional noise in a electromechanical device cooled near the ground state of motion.

Next, we consider an overlapped two tone pump configuration that produces a time-modulated electromechanical interaction. By careful control of this drive field, we report a quantum non-demolition (QND) measurement of a single motional quadrature. Incorporating a second pair of drive tones, we directly measure the measurement back-action associated with both classical and quantum noise of the microwave cavity. Lastly, we slightly modify our drive scheme to generate quantum squeezing in a macroscopic mechanical resonator. Here, we will focus on data analysis techniques that we use to estimate the quadrature occupations. We incorporate Bayesian spectrum fitting and parameter estimation that serve as powerful tools for incorporating many known sources of measurement and fit error that are unavoidable in such work.

实际波流场中水动力系数的反演

根据实测载荷与波浪相关数据,在频域里利用自谱法对频率取矩的方法计算了西江平台一桩腿测力段的拖曳力系数与惯性力系数,计算结果与前人实验结果所得结论和变化趋势相符。

三维波流数值水槽的构建方法

为了模拟波浪与水流的联合作用,基于Reynolds平均的Navier-Stokes方法,构建了一个三维波流数值水槽. 使用该模型对不同出流边界条件进行了对比分析. 结果表明:引入合理的入流和出流边界条件,可以保证在计算稳定后,水槽平均水面基本保持不变. 垂向时均流速分布的计算结果与实验数据吻合良好. 这表明:该波流数值水槽具有较好的波流特性,可用于计算波浪与水流、以及与三维固定结构之间相互作用.

Hybrid simulation of ion cyclotron resonance in the solar wind: evolution of velocity distribution functions

Li, Xing; Habbal, S.R., (2005) 'Hybrid simulation of ion cyclotron resonance in the solar wind: evolution of velocity distribution functions', Journal of Geophysical Research 110(A10) pp.A10109 RAE2008