Steady state Behaviour of a Three level Ladder Atomic System with Incoherent Population Pumping in a Squeezed Vacuum

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Simple Waves and a Characteristic Decomposition of the Two Dimensional Compressible Euler Equations

We present a characteristic decomposition of the potential flow equation in the self-similar plane. The decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for the adiabatic Euler system. This result is a generalization of the well-known result on 2-d steady potential flow and a recent similar result on the pressure gradient system.Research partially supported by NSF of China with No. 10301022, NSF from Beijing Municipality, Fok Ying Tong Educational Foundation, and the Key Program from Beijing Educational Commission with no. KZ200510028018.Research partially supported by NSF-DMS-0305497, 0305114.     

Focusing of an oscillating shock wave emitted by a toroidal bubble cloud

An analysis of pressure-field dynamics is performed for an axially symmetric problem of interaction between a shock wave and a “free” bubble system (toroidal cluster) giving rise to a steady oscillating shock wave. The results of a numerical study of near-axis wave structure are presented for a focusing shock wave emitted by a bubble cluster. It is shown that the wave reflected from the axis has irregular structure. The Mach disk developing on the axis has a core of finite thickness with a nonuniform radial pressure distribution. The evolution of the Mach-disk core is analyzed, and the maximum pressure in the core is computed as a function of the gas volume fraction in the cluster. The effect of geometric parameters of the toroidal bubble cloud on the cumulative effect is examined.     

湍流系统中的阵发非完美位相同步和能量爆发

湍流现象广泛地存在于自然界的各个领域，关于湍流发生的机制成为一个多世纪以来人们不断探索但尚未完全解决的难题之一，在强湍状态下，系统不时地会突然聚集起巨大的能量，这对人类活动可能产生重大影响，作者利用一个典型的模型说明，在适当的参照系下，湍流波动可以等价地变换为在势阱中相互耦合的一组振子的运动；作为非线性系统自组织的结果，不同空间尺度的振子可以阵发地调节到非完美的位相同步，在同步发生的瞬间，虽然每个振子的位相和振幅的运动看起来仍很紊乱，但振子间的位相差却很小，并且它们的振幅几乎同时达到极大，引起系统整体能量爆发。     

Capillary-gravity waves generated by a slow moving object

We investigate theoretically and experimentally the capillary-gravity waves created by a small object moving steadily at the water-air interface along a circular trajectory. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity c(min)=23 cm s(-1). We demonstrate that no such velocity threshold exists for a steady circular motion, for which, even for small velocities, a finite wave drag is experienced by the object. This wave drag originates from the emission of a spiral-like wave pattern. Our results are in good agreement with direct experimental observations of the wave pattern created by a circularly moving needle in contact with water. Our study leads to new insights into the problem of animal locomotion at the water-air interface.     

Controlling spatio-temporal chaos via small external forces

The spatio-temporal chaos in the system described by a one-dimensional nonlinear-drift wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a carrier steady wave and its perturbation, we find that the controlling mechanism can be explained by a slaving principle. The critical controlling time for a perturbation mode increases exponentially with its wave number.     

Influence of the adiabatic index on switching between different types of shock wave reflection in a steady supersonic gas flow

A comprehensive pattern of different types of shock wave reflection in a steady supersonic gas flow is analytically constructed with regard to a new wave configuration found by the authors-negative-angle irregular reflection. A double Mach reflection with a negative reflection angle in a steady supersonic gas flow is numerically obtained for the first time.     

Wave number selection in Rayleigh-Bénard convection: A numerical study

A phenomenological amplitude equation introduced earlier to calculate steady states of convection in a finite container, is studied numerically as a function of space and time. The effect of sidewalls on wave number selection is demonstrated by observing the response of the system to the sudden imposition of boundary conditions. The wave vectors of stable steady states are studied as a function of Rayleigh number near threshold, and it is shown that more than one state can be stable for fixed Rayleigh number.     

Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.     

三能级Upper-ladder型系统中的

三能级Upper-ladder型系统中,在旋波、慢变振幅近似下,求解了考虑驱动场相位扩散后的系统密度矩阵运动方程,并给出了这个三能级梯型系统稳态线性解析解.利用对密度矩阵运动方程的稳态线性解析解的数值模拟结果,研究相位扩散对无反转激光增益、色散和粒子数差的影响;利用对密度矩阵运动方程的数值模拟结果,分析相位的扩散对无反...     

On-off collective imperfect phase synchronization and bursts in wave energy in a turbulent state

A new type of synchronization, on-off collective imperfect phase synchronization, is found in a turbulent state. In the driver frame the nonlinear wave system can be transformed to a set of coupled oscillators moving in a potential related to the unstable steady wave. In "on" stages the oscillators in different spatial scales adjust themselves to collective imperfect phase synchronization, inducing strong bursts in the wave energy. The interspike intervals display a power-law distribution. In addition to the embedded saddle point, it is emphasized that the delocalization of the master mode also plays an important role in developing the on-off synchronization.     

180°圆弧形钝感炸药的爆轰波传播

 采用贴体坐标下与Level Set方法相结合的爆轰冲击波动力学（DSD）计算方法,研究了180°圆弧形钝感炸药中非理想爆轰波的传播过程。通过数值模拟计算和实验测量的对比分析,得到了180°圆弧形炸药中爆轰波传播的一些规律：圆弧形钝感炸药可以实现定常爆轰,即在极坐标中整个爆轰波以固定角速度转动。这种定常阵面的形状和角速度与圆弧的外半径无关,定常体系依赖于圆弧形炸药的内半径和覆盖圆弧的外壳物质。对描述圆弧形炸药中爆轰波传播规律的经验公式进行了研究,结果表明这些经验公式能够准确描述爆轰波速度的变化,在实验测量和预估方面具有一定的参考价值。     

微扰法解由正弦波驱动的非线性漂移波的分岔

在以驱动波相速度运动的坐标系中,用微扰法讨论。在正弦波驱动下的非线性漂移波的分波方程。结果表明,在文献[1]中观察到的波包能量的滞后分岔和由定态向周期态的分岔可以统一地解析描述,它们分别对应某一非线性共振模式在时间维上的鞍结点分岔和Hopf分岔。波包能量失稳的频率是该模式的本征频率,除多普勒移动外,它的大小还因非线性效应而不同于其在实验室坐标系中的线性值。 关键词：     

氢氧爆轰波在激波管中的成长机制研究

 针对气相爆轰波成长机制研究,采用压力传感器和高速摄影技术,测试了氢氧混合气体在点火后的火焰波、前驱冲击波以及爆轰波的成长变化过程,计算了冲击波过程参数和气体状态参数,分析了火焰加速机制。实验结果表明,APX-RS型高速摄影系统可用于拍摄气相爆轰波的成长历程;氢氧爆轰波的产生是由于湍流火焰和冲击波的相互正反馈作用,导致反应区内多处发生局部爆炸,爆炸波与冲击波相互耦合,最终成长为定常爆轰波。     

Generalized WKB method in the three-dimensional case. I

The possibility of using the generalized WKB method for studying the steady states of a single-frequency system in three-dimensional potential fields which do not allow the variables to be separated in the Schrödinger equation is considered. Approximate wave functions are constructed; these transform into the well-known van Horn wave functions in the quasiclassical case.     

Nonsteady-state self-interaction in a medium with striction nonlinearity

An analytic and numerical investigation is made of the self-focusing of a wave beam allowing for the inertia of the nonlinear response of the medium described by an acoustic type of equation. Some characteristics of the dynamics of self-interaction of the wave fields are analyzed in the paraxial optics approximation and the self-similar structures and space-time instability of a plane wave are considered. The stages of instability buildup, structure formation, and the establishment of a steady state are studied numerically.     

Irregular dynamics in a one-dimensional Bose system

We study many-body quantum dynamics of delta-interacting bosons confined in a one-dimensional ring. Main attention is paid to the transition from the mean-field to the Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wave function and the momentum distribution depend on time for weak and strong interactions. We show that the transition from regular (quasiperiodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime, the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.     

Diffraction of a two-shock configuration by a convex cylindrical surface

The subject of this work is numerical investigation into the diffraction of a shock-wave configuration by a convex cylindrical surface. The diffraction is a stage of interaction of a shock wave with a two-dimensional body. It is preceded by the stage of shock wave reflection from the front surface of the body, the back surface of which has a convex cylindrical shape. The two-or three-shock configuration formed on the front surface diffracts by the back cylindrical surface. The emphasis is on studying the diffraction of the two-shock wave configuration with the diffraction angle varying continuously. The object under study a wedge with an inclined front surface and convex cylindrical back surface. The results of numerical investigation are obtained by integrating the Euler equations. Flow features associated with the simultaneous diffraction of the incident and reflected shock waves are revealed. The evolution of the gasdynamic system (stagnation wave + TU layer) arising inside the diffraction area is studied. Breakaway and vorticity initiation are considered. It is shown that the positions of the line of separation and TU layer change in the course of diffraction. They merge together at the stage of steady flow. Comparison is made between the flow formed upon diffraction of the two-shock configuration by the cylindrical surface and the flow generated upon diffraction by horizontal and vertical surfaces.     

模式的反转运动和波包的双稳态

在系统定态存在的坐标系中,用本征值分析说明,正弦波驱动的非线性漂移波方程出现的双稳态解是与一定模式的相速度在参数空间反转相联系的。     

Weak pressure wave in a gas filled elastic tube

The propagation of a small but finite shock disturbance through gas contained within a cylindrical tube is examined theoretically for the case where both the hoop elasticity and radial inertia of the tube are taken into account. Governing equations so derived are found to admit a non-dispersive wave of variable pressure behind the advancing shock front in direct contrast with the situation existing for an initially sharp-fronted infinitesimal disturbance where no steady wave form is possible. Detailed calculations are carried out for the case where the gas filling the tube is air. Results show that increases in either the tube or shock strength are sufficient to make the pressure distribution behind the wave front approach that which would exist in a rigid tube under similar conditions.