封闭圆内开缝圆自然对流的非线性特性研究

本文通过数值计算对封闭圆内开缝圆自然对流的非线性特性进行了研究。数值计算以整个流场为计算区域,采用非稳态数学模型和具有QUICK差分格式的SIMPLE算法。计算结果表明,在不同参数下流动和换热存在稳态定常解、周期性振荡解、拟周期性振荡解和非周期性振荡解。稳态定常解的相图是一个点;周期性振荡解的相图是一个极限环,对应功率谱含一个基频及其谐波;拟周期性振荡解的相图为环面,对应功率谱含两个不相关的频率及它们的线性组合频率;非周期性振荡解的功率谱为无规则的宽带连续谱。     

Eigenfunctions of Unbounded Support for Embedded Eigenvalues of Locally Perturbed Periodic Graph Operators

It is known that if a locally perturbed periodic self-adjoint operator on a combinatorial or quantum graph admits an eigenvalue embedded in the continuous spectrum, then the associated eigenfunction is compactly supported—that is, if the Fermi surface is irreducible, which occurs generically in dimension two or higher. This article constructs a class of operators whose Fermi surface is reducible for all energies by coupling several periodic systems. The components of the Fermi surface correspond to decoupled spaces of hybrid states, and in certain frequency bands, some components contribute oscillatory hybrid states (corresponding to spectrum) and other components contribute only exponential ones. This separation allows a localized defect to suppress the oscillatory (radiation) modes and retain the exponential ones, thereby leading to embedded eigenvalues whose associated eigenfunctions decay exponentially but are not compactly supported.     

Geometric Stability Analysis for Periodic Solutions of the Swift-Hohenberg Equation

In this paper we describe invariant geometrical structures in the phase space of the Swift-Hohenberg equation in a neighborhood of its periodic stationary states. We show that in spite of the fact that these states are only marginally stable (i.e., the linearized problem about these states has continuous spectrum extending all the way up to zero), there exist finite dimensional invariant manifolds in the phase space of this equation which determine the long-time behavior of solutions near these stationary solutions. In particular, using this point of view, we obtain a new demonstration of Schneider's recent proof that these states are nonlinearly stable. Received: 30 January 1997 / Accepted: 6 April 1997     

Phase Space Compression in One-Dimensional Complex Ginzburg-Landau Equation

The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.     

Dynamics of a deformable body in a fast flowing soap film

We study the behavior of an elastic loop embedded in a flowing soap film. This deformable loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a two-dimensional flexible body interacting in a two-dimensional flow. This coupled fluid-structure system shows bistability, with both stationary and oscillatory states. In its stationary state, the loop remains essentially motionless and its wake is a von Kármán vortex street. In its oscillatory state, the loop sheds two vortex dipoles, or more complicated vortical structures, within each oscillation period. We find that the oscillation frequency of the loop is linearly proportional to the flow velocity, and that the measured Strouhal numbers can be separated based on wake structure.     

Nonlinear dynamics in wurtzite InN diodes under terahertz radiation

We carry out a theoretical study of nonlinear dynamics in terahertz-driven n+ nn+ wurtzite InN diodes by using time-dependent drift diffusion equations.A cooperative nonlinear oscillatory mode appears due to the negative differential mobility effect,which is the unique feature of wurtzite InN aroused by its strong nonparabolicity of the Γ 1 valley.The appearance of different nonlinear oscillatory modes,including periodic and chaotic states,is attributed to the competition between the self-sustained oscillation and the external driving oscillation.The transitions between the periodic and chaotic states are carefully investigated using chaos-detecting methods,such as the bifurcation diagram,the Fourier spectrum and the first return map.The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitude as the control parameter.     

Nonlinear dynamics in wurtzite InN diodes under terahertz radiation

We carry out a theoretical study of nonlinear dynamics in terahertz-driven n⁺nn⁺ wurtzite InN diodes by using time-dependent drift diffusion equations. A cooperative nonlinear oscillatory mode appears due to the negative differential mobility effect, which is the unique feature of wurtzite InN aroused by its strong nonparabolicity of the Γ₁ valley. The appearance of different nonlinear oscillatory modes, including periodic and chaotic states, is attributed to the competition between the self-sustained oscillation and the external driving oscillation. The transitions between the periodic and chaotic states are carefully investigated using chaos-detecting methods, such as the bifurcation diagram, the Fourier spectrum and the first return map. The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitude as the control parameter.     

方腔内双扩散混合对流非线性格子Boltzmann研究

采用格子Boltzmann方法对方腔内双扩散混合对流的非线性特性进行数值模拟.发热圆位于方腔中心,流体从方腔左侧底部流进,流出位置分别为顶部右侧、中间和左侧三种情况.结果表明,不同参数下的双扩散混合对流存在稳态定常解、周期性振荡解和非周期性振荡解,监测点速度相图分别表现为最终到达一个点、一个封闭环和没有规律的曲线.     

Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.     

无反馈作用下混沌系统的振幅死亡

考虑了一种无反馈的作用机理，通过分析定常强迫作用下R?ssler系统的分岔图和Lyapunov指数谱，发现定常强迫能够导致混沌系统产生振幅死亡.这种现象的产生类似于耦合的极限环系统和耦合的R?ssler系统，弱定常强迫作用下的R?ssler系统经由一个周期运动被驱动到系统自身的一个平衡点上.进一步对受迫系统时间序列的研究表明，当定常强迫强度超过一个临界值时，系统的状态不断在小振幅周期运动与静止之间交替出现. 关键词： 振幅死亡 定常强迫 R?ssler系统     

Die Relaxation der Geschwindigkeitsverteilungsfunktion der Elektronen im homogenen Feld mit elastischen und anregenden Stößen. III. Die Einstellung des periodischen Verhaltens der Elektronen-komponente im elektrischen Feld großen Modulationsgrades

To continue the kinetic investigations concerning the periodic behaviour of the electron component of a low ionized Ne-plasma of a glow discharge column in a periodic electric field [4] with high degree of modulation in this paper the adjustment of the isotropic distribution function of the electrons and by the latter determined macroscopic quantities are calculated and discussed. Starting with the non-stationary Boltzmann equation the adjustment process is considered using different direct components of the field but nearly constant degree of modulation. In the whole range from a nearly momentary adjustment to an adjustment in the high frequency limit of only small modulated distribution function we obtained results concerning the adjustment behaviour and its characteristic times by variation of the cycle time of the electric field starting from the different stationary states. At the other hand the influence of the different degrees of modulation on the adjustment process and its characteristic times was investigated and interpreted. For this interpretation the spectrum of adjustment times of stationary states corresponding to all momentary values of the periodic electric field strength in one cycle plays a dominant role. From the investigations follows that the adjustment times of periodic states can alter their values by some orders of magnitudes in dependence on the parameters of the electric field.     

Magnetic surface levels

As is well known, the energy spectrum of conduction electrons in a metal in a magnetic field is split into the Landau levels. These levels give rise to several phenomena whose essence is in the oscillatory dependence of some property of the metal characteristics on the strength of the magnetic field, in the range of strong and medium fields. Of these the most famous are the de Haas-van Alphen effect, and the Shubnikov-de Haas effect. Electronic transitions between the Landau levels give rise to the cyclotron resonance.

In a surface layer of a metal placed in a weak magnetic field another system of levels appears for electrons moving along shallow arcs, with their ends resting upon the surface of the metal. These levels originate from the quantized periodic motion of electrons along such ‘skipping’ trajectories due to a specular reflection at the metal surface. The spectrum of the system of magnetic surface levels manifests itself in an oscillatory dependence of the surface impedance on a weak magnetic field. The oscillations are due to a resonant absorption of microwave radiation in transitions of electrons between the magnetic levels occurring at discrete values of the magnetic field.

This new quantum effect discovered in several metals in both the normal and superconducting states should, in principle, be common to all the conductors. Studies of the effect are being extended rapidly, and one foresees a discovery of some new phenomena due to the surface bound states of charged quasiparticles, arising in a conductor when exposed to a weak magnetic field.     

Eigenstates of spherical delta-shells

We study the exact solution of the Schrödinger equation with a δ-potential in the spherical coordinate system. We consider both stationary and nonstationary problems. We obtain solutions for bound states described by functions decreasing rapidly with the radius and solutions characterized by an oscillatory asymptotic behavior.     

Specific Features of the Quasilocal State Densities in the Presence of Defects in Media with Spatial Dispersion

The density of stationary quasilocal states of the continuous spectrum arising due to the presence of defects in a medium with spatial dispersion is analyzed. The influence of plane and point defects on the specific features of the spectral quasilocal state density is studied. It is demonstrated that the spectral density has a strict maximum caused by the quasilocal energy level arising in the system. For a plane defect, the energy of the quasilocal level is displaced from the resonance energy of total quasi-particle reflection from the defect. The influence of the quasilocal state on the electronic heat capacity in the presence of the point defect is analyzed.     

Time-resolved spectrum for resonant light scattering in an exciton-phonon system

A formula is given for the time-resolved spectrum of the resonantly- scattered radiation from an exciton-phonon system, and it is applied to the calculation of two-LO-phonon assisted spectrum. Both the Raman component associated with virtual intermediate states and the luminescence with real intermediate states are obtained. A Raman-like component with an oscillatory behavior can be seen, when the exciton relaxation time is shorter than the excitation pulse duration. It is proposed that the energy dependence of exciton relaxation rate can be directly measured from the time decay of a hot luminescence spectrum.     

Nonclassical degrees of freedom in the Riemann Hamiltonian

The Hilbert-Pólya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum Hamiltonian. If so, conjectures by Katz and Sarnak put this Hamiltonian in the Altland-Zirnbauer universality class?C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.     

Spatially Periodic Inhomogeneous States in a Nonlinear Crystal with a Nonlinear Defect

Spatially periodic inhomogeneous stationary states are shown to exist near a thin defect layer with nonlinear properties separating nonlinear Kerr-type crystals. The contacts of nonlinear self-focusing and defocusing crystals have been analyzed. The spatial field distribution obeys a time-independent nonlinear Schrödinger equation with a nonlinear (relative to the field) potential modeling the thin defect layer with nonlinear properties. Both symmetric and asymmetric states relative to the defect plane are shown to exist. It has been established that new states emerge in a self-focusing crystal, whose existence is attributable to the defect nonlinearity and which do not emerge in the case of a linear defect. The dispersion relations defining the energy of spatially periodic inhomogeneous stationary states have been derived. The expressions for the energies of such states have been derived in an explicit analytical form in special cases. The conditions for the existence of periodic states and their localization, depending on the defect and medium characteristics, have been determined.     

Continuous feedback control of KdV Burgers system

The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationary points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment separately.