Self-sustained oscillations of turbulent pipe flow terminated by an axisymmetric cavity

Turbulent flow through a long pipe terminated by an axisymmetric cavity can give rise to self-sustained oscillations exhibiting a very strong coherence, as evidenced by the narrow-band character of corresponding amplitude spectra. These oscillations, associated with the turbulent axisymmetric jet passing through the cavity, are strongly influenced by the acoustic modes of the pipe. The frequencies of oscillation lie within or near the range of most “unstable” frequencies of the turbulent jet previously predicted by using concepts of inviscid hydrodynamic stability theory; consequently, these experiments show truly self-excited and strongly coherent “instability” of a fully turbulent, low Mach number (～10^?2), axisymmetric flow undergoing separation, corroborating previous experiments involving the external forcing of free turbulent jets. As flow velocity or cavity length is varied, both upward and downward jumps in oscillation frequency are observed; the sign (up or down) of these jumps tends to systematically alternate with increase of velocity or length. The role of these frequency jumps is, in effect, to allow the oscillation of the flow to remain “locked-on” to a pipe mode over a wide range of impingement length or flow velocity. Moreover, these jumps exhibit two types of behavior: for the first kind, the predominant frequency makes a relatively continuous transition between stages and the frequency of the neighboring stage appears as a secondary component; for the second kind, there is a dead zone (where no oscillation occurs) between stages. The consequence of externally exciting the system is strongly dependent on whether the self-sustaining oscillation is relatively near, or well away from, a frequency jump. During excitation, the amplitudes of pressure fluctuations in the cavity substantially exceed the corresponding no-flow values only in regions away from the frequency jumps; at locations of jumps, there can be significant attenuation of the no-flow excitation amplitude. For the type of frequency jump involving a “dead zone”, enhancement of a given mode of oscillation can be achieved by externally exciting not only the given mode, but also neighboring modes. For the other type of jump, involving a relatively continuous transition from one stage to the next, the predominant mode of oscillation following the jump is that mode giving maximum amplitude response to excitation before the jump.     

Mechanisms behind spheroidal oscillations and electrostatic instability of a charged drop

Mechanisms behind the oscillations of a charged spheroidal drop deformed at the zero time and the sequence of oscillation modes are investigated. It is shown that two modes adjacent to those governing the initial deformation are also excited on either side due to interaction between the spheroidal deformation and oscillation modes. If the charge of the drop is so close to a value critical for electrostatic instability that the finite-amplitude virtual initial deformation makes the fundamental mode unstable, its amplitude, as well as the amplitude of the nearest neighbor coupled to the fundamental mode through deformation, starts to exponentially grow with time. If the charge is equal to, or slightly exceeds the critical value, the amplitudes of the fundamental mode and all modes deformation-coupled with it lose stability almost simultaneously. This qualitatively changes the conditions under which the charged drop becomes unstable against the self-charge. The superposition of higher oscillation modes at the vertices of the spheroidal drop generates dynamic (i.e., time-oscillating) hillocks emitting an excessive charge.     

Oscillation modes of supersonic multijets exhausting from very adjacent multiple nozzles.

The oscillation modes of a supersonic circular twin jet and multijet with square configuration where the center-to-center spacing of nozzles was fixed to 1.4 times the nozzle diameter were investigated experimentally. It is found that the twin jet oscillates simultaneously in three different oscillation modes for the pressure ratios of about 4.1. From the acoustical observation, these oscillation modes are identified as one lateral oscillation mode perpendicular to a plane composed of the twin jet axes and two lateral oscillation modes parallel to this plane. For a multijet with a square configuration, only one lateral oscillation mode was observed. In this case, it is observed that when the spacing between two facing sides of the square formed by four jets is stretched, the spacing between the other two sides shrinks and vice versa.     

Self oscillations of a bistable element in two coupled hybrid ring resonators

A CdS crystal showing thermally induced optical bistability is incorporated into two coupled hybrid ring resonators with different delay times. Both delay times are much longer than the relaxation time of the nonlinearity. The resulting self-oscillations are investigated both experimentally and theoretically. We find two different types of oscillation modes. If the crystal is on the lower branch of the bistability during the longer delay time, step like oscillations similar to the case of a single resonator occur. If the crystal is in the lower state onlh for the shorter delay time (also the shorter of the two delay times is much longer than the relaxation time) we find more complicated modes with plateaus and stairs because the long resonator acts as a memory for the system state before the switching process. We find complex mode locking structures exhibiting Farey-tree like transitions between different oscillation modes as well as mode coexistence. Based on an adiabatic theory we compute the regions of extstence of the different oscillation modes and compare them with experimental results.     

Rijke管热声振荡的稳定性切换行为研究

采用数值方法模拟了强弱两种阻尼条件下传热迟滞时间对一维Rijke管热声系统稳定性的影响,发现Rijke管系统存在稳定性切换现象.在推导了无量纲形式的管内声波动量方程和能量方程之后,利用Galerkin方法对控制方程进行展开并在时间域内数值求解.分析了强阻尼和弱阻尼条件下,给定热源的Rijke管热声振荡的稳定性与传热迟滞时间的关系.结果显示:在两类阻尼条件下,持续增大传热与速度的迟滞时间,系统均呈现出稳定性切换现象,即系统在稳定和不稳定两个状态间持续转变;但弱阻尼系统的不稳定区域宽于强阻尼系统的不稳定区域,系统最大振幅相对增大,且系统热声振荡的主模态在不同模态之间发生转换.最后,通过求解系统各阶模态极限环幅值随传热迟滞时间的变化,发现Rijke管热声振荡稳定性切换现象与迟滞时间存在近似周期性关系.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Chaos dynamics in semiconductor lasers with polarization-rotated optical feedback

By using polarization-rotated optical feedback from the transverse-electric (TE) mode to the transverse-magnetic (TM) mode, chaotic oscillations for both polarization modes are excited in a semiconductor laser. We find different correlations between these chaotic oscillations than those found in previous studies. In this study, the dynamics are strongly dependent on their radio-frequency (RF) components and they are divided into three RF regions. For low-pass filtered signals lower than the laser relaxation oscillation, there is an antiphase correlation between the two polarization modes. On the other hand, the two polarization modes have an in-phase correlation for the RF components of the high-pass filtered signals, which are higher than the relaxation oscillation. However, no correlations were observed between the two modes for the intermediate RF components that include the relaxation oscillation frequency. We also perform numerical calculations for the model and obtain good agreement between the theoretical and experimental results.     

A two-frequency acoustic technique for bubble resonant oscillation studies

A two-frequency acoustic apparatus has been developed to study the dynamics of a single gas or vapor bubble in water. An advantage of the apparatus is its capability of trapping a bubble by an ultrasonic standing wave while independently driving it into oscillations by a second lower frequency acoustic wave. For a preliminary application, the apparatus is used to study resonant oscillations. First, near-resonant coupling between the volume and the n = 3 shape oscillation modes of air bubbles at room temperature is studied, where n is the mode number. The stability boundary, amplitude versus frequency, of the volume oscillation forms a wedge centered at the resonant frequency, which qualitatively agrees with a theoretical prediction based on a phase-space analysis. Next, the resonant volume oscillations of vapor bubbles are studied. The resonant radius of vapor bubbles at 80 degrees C driven at 1682 Hz is determined to be 0.7 mm, in agreement with a prediction obtained by numerical simulation.     

Bloch oscillations and Wannier-Stark ladder in the coupled LC circuits

We present a new scheme for realizing Bloch oscillations and Wannier-Stark ladder based on a lattice of coupled LC circuits. By converting the second order dynamical ODEs of the system into a first order Schrödinger-like equation, we propose an equivalent tight binding Hamiltonian to describe the circuit. We show that a synthesized electric field is produced by introducing a frequency mismatch into the resonant frequency of the adjacent LC resonators. The Wannier-Stark modes are the normal modes of the circuit and the Bloch oscillations can be observed in a coupled LC lattice. By addition of coupling capacitors between nodes of the circuit, we study the Bloch oscillation in the presence of long-range couplings. We also show that the circuit converts to a transmission line simulating synthetic electric fields in the continuum limit. The coupled LC circuit is, in some sense, amongst the simplest physical systems exhibiting Bloch oscillation and Wannier-Stark Ladder.     

Instability of a spherical drop in the field of an electrical dipole

Analytical calculations show that, as a field in which an initially spherical charged conducting incompressible drop is placed becomes more and more nonuniform, coupling between the drop’s oscillation modes grows and the threshold of stability against the electrical field pressure declines. When an electrostatic parameter characterizing the electric field pressure exceeds a value that is critical for a certain mode to be unstable, the amplitude of this mode exponentially grows in an aperiodic manner and the amplitudes of modes coupled with this mode build up in an oscillatory manner, each mode having its own instability growth rate. In all cases, there exists a threshold value of the dimensionless electric parameter above which all oscillation modes are unstable.     

磁声参量振荡的理论

在本文中,我们从磁-弹性耦合的宏观表达式,通过经典场论的方法,求得弹性振动和磁振璗的耦合方程,用来分析了伴随波长约等于铁氧体样品的线度的声振动而存在的磁振璗(磁声模)。文中指出,Spencer和LeCraw所发现的磁声效应是磁声模和静磁模在注入场的激发下产生的参量振璗现象(也可以说是热声子的电磁讯号的放大)。我们引用Berk等人在讨论一种半静磁操作放大器的文章中给出的公式,算出Spencer-LeCraw实验所需要的功率,其结果与记录的数据相接近。我们提出了使任一静磁模配合磁声模产生振璗的调谐条件以及降低激发功率和观测几十到几百兆赫的声频的办法。通过磁声模和静磁模的交变场向量的空间对称性的分析,我们推导出磁声参量振璗的选择定则:对于球体三个主要弹性振动模(旋转模、向径模和椭球模),(1)静磁模(n,m,r)的Walker指标n是偶数者不产生磁声效应;(2)指标m是奇数者不与旋转模产生磁声效应,m是偶数者不与向径模或椭球模产生磁声效应。我们也举出第一类本征振动中有只可能和n是偶数、m是奇数的静磁模产生参量振璗的例子。Spencer-LeCraw局限于使静磁场调谐在(110)模上,所观察到的现象仅仅是本文所给出理论预见的一个特殊情况。他们发现了椭球模和向径模的频率显著地出现,但并无旋转模的频率,这是上述的选择定则的具体验证。最后,我们指出,热声子的参量放大可形成铁氧体微波放大器的噪声的来源。     

Manipulating atomic coherence and interference in a coupled atom-cavity system

Collective coupling of multiple atoms with a cavity mode produces two normal modes that are separated in energy by Vacuum Rabi splitting. We show that quantum coherence and interference can be produced by a control laser that couples the atoms confined in the cavity mode from free space, which leads to suppression of the normal mode excitation, or polariton excitation of the cavity-atom system. The control laser splits the normal mode of the cavity-atoms system and opens two excitation channels. The destructive quantum interference between the two channels renders the cavity-atoms system opaque to the light coupled into the cavity mode. We demonstrate suppression of the normal mode (polariton) excitation by the destructive quantum interference in an experiment with cold Rb atoms confined in an optical cavity.     

Ferromagnetic resonance in interacting magnetic microstrips

The results of the micromagnetic simulation of forced oscillations of the magnetization in a system of two interacting microstrips located at an angle to each other have been presented. The ferromagnetic resonance spectra and the mode composition of resonant oscillations of the system have been investigated under the conditions of magnetostatic and exchange interactions between the microstrips. It has been shown that the magnetostatic interaction leads to the possibility of the excitation of in-phase and out-of-phase coupled oscillations of the magnetization of the microstrips. In the systems of exchange-coupled microstrips, there are intense resonances due to oscillations of the domain walls. The transformation of the ferromagnetic resonance spectrum and the change in the mode composition of resonant oscillations in different equilibrium configurations of the magnetization of the system have been discussed, as well as the conditions for the excitation of oscillations of different types depending on the direction of the microwave magnetic field.     

Polar modes with elastic restoring forces, “bose condensation” and the possibility of a metastable “ferroelectric” state

The system consists of an electric polarisation field coupled on the one hand to an elastic field and on the other to a thermal reservoir. When the polarisation modes are pumped, Bose condensation in the lowest mode occurs, for energy inflow above a certain critical amount. It is shown that elastic forces, called into play to stabilise the excitation of the polar modes, lowers the threshold for Bose condensation. With further increase in the pumping rate the possibility exists for the softening of the polarisation oscillations leading, in the presence of quartic self-interaction of the polarisation field (inserted for stability), to a metastable ferroelectric state. The work represents an attempt to develop a microscopic approach to the Fröhlich model for the dynamics of macromolecules (such as proteins and enzymes) of biological significance.     

Optical absorption and magnetotransport in quantum wires in a perpendicular magnetic field

A periodic array of δ function potentials are used to simulate the potential barriers between quantum wires in the presence or absence of lattice site dislocation. The exact eigenenergies and eigenfunctions are found by employing a numerical diagonalization procedure. Based on these results, a self-consistent field theory is derived for the mid-infrared absorption coefficient of the system. The crossover from a cyclotron mode to two tunneling coupled modes and finally to edge and 1D lattice magnetoplasmon modes with increasing modulation strength is investigated. The magnetic field enhanced and suppressed electron tunneling, associated with the evolution to cyclotron modes at strong magnetic fields passing through the formation of tunneling coupled modes, is observed. The edge mode excitation energy oscillates as a function of the electron density. These oscillations correspond to a soft or hard potential wall for which the electron states are extended or localized, respectively. The displacement of the 1D lattice magnetoplasmon modes under strong modulation is found to be periodic and corresponds to the evolution from a complex unit cell which is composed of one narrow and one wide quantum wire to a simple unit cell containing only one quantum wire. The magnetoresistivities and the associated conductivities are also calculated for the lateral surface superlattice. At strong potential modulation there is a giant peak in the Hall conductivity and many peaks in its resistivity in the quantum regime. With strong modulation, the suppression of the transverse conductivity along with oscillations in its resistivity are obtained.     

Complex dynamics and chaos in the parametric coupling of counter-propagating waves

We study the dynamics of a distributed self-oscillating system of three parametrically coupled waves, one of which is propagating counter to the other two. We show that an infinite number of natural modes are self-excited as the bifurcation parameter, which has the meaning of the pump amplitude, increases without bound. Exact solutions describing steady-state oscillation regimes are found. We present the results of computer simulation, which show that for moderate pump amplitudes the transient process terminates when a stationary state corresponding to the fundamental mode sets in. As supercriticality increases, the oscillations become chaotic, with the transition to chaos being rapid. We note an analogy that exists between the dynamics of such a system and the dynamics of a Lorentz system. Zh. éksp. Teor. Fiz. 116, 1871–1881 (November 1999)     

Quantum dynamic behaviour in a coupled cavities system

The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated.The exact dynamic solutions in the general condition are obtained via Laplace transform.The simple analytical solutions are obtained in several particular cases,which demonstrate the clear and simple physical picture for the quantum state transition of the system.In the large detuning or hoppling case,the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode.In the large coupling case,the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities.In the case of λ≈△>> g,the quantum states transition of qubits is accompanied by the excitation of the cavity,and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.     

On the dynamics of pulsating detonations

To understand the circumstances in which a pulsatingdetonation wave may prefer a low-frequency mode ofoscillation, and the implications this has formathematical modelling, the dynamics of a detonation waveare studied when the underlying linear stability spectrumconsists of at most two unstable modes. One mode α₁ has a period much larger than the time-scaleof particle passage through the half-reaction length inthe steady one-dimensional detonation; the second α₂ has a smaller period than α₁. Thequestion addressed in this paper concerns the long-timebehaviour of the pulsating detonation in the presence ofthe unstable modes α₁ and α₂. Westudy two general scenarios related to a crossing of theneutral stability boundaries traced out by α₁ and α₂. In all cases where the mode α₁ is unstable, the pulsating detonation emerges with alow-frequency, large-amplitude oscillation, regardlessof the relative growth rates of α₁ and α₂. Only in one case, where thehigher-frequency mode α₂ is alone unstable, isthe long-time nonlinear pulsation of high frequency. Inthis case, the amplitude of the oscillation issignificantly smaller than that observed in thelow-frequency oscillations. In all cases, the finalperiod of the nonlinear oscillation is closely related tothat of the relevant underlying linear mode.     

Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity

The theoretical work of Braginsky predicted that radiation pressure can couple the mechanical, mirror eigenmodes of a Fabry-Pérot resonator to its optical modes, leading to a parametric oscillation instability. This regime is characterized by regenerative mechanical oscillation of the mechanical mirror eigenmodes. We have recently observed the excitation of mechanical modes in an ultrahigh Q optical microcavity. Here, we present a detailed experimental analysis of this effect and demonstrate that radiation pressure is the excitation mechanism of the observed mechanical oscillations.     

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes, the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop.