Rossby waves in the magnetic fluid dynamics of a rotating plasma in the shallow-water approximation

We have studied rotating magnetohydrodynamic flows of a thin layer of astrophysical plasma with a free boundary in the β-plane. Nonlinear interactions of the Rossby waves have been analyzed in the shallow-water approximation based on the averaging of the initial equations of the magnetic fluid dynamics of the plasma over the depth. The shallow-water magnetohydrodynamic equations have been generalized to the case of a plasma layer in an external vertical magnetic field. We have considered two types of the flow, viz., the flow in an external vertical magnetic field and the flow in the presence of a horizontal magnetic field. Qualitative analysis of the dispersion curves shows the presence of three-wave nonlinear interactions of the magnetic Rossby waves in both cases. In the particular case of zero external magnetic field, the wave dynamics in the layer of a plasma is analogous to the wave dynamics in a neutral fluid. The asymptotic method of multiscale expansions has been used for deriving the nonlinear equations of interaction in an external vertical magnetic field for slowly varying amplitudes, which describe three-wave interactions in a vertical external magnetic field as well as three-wave interactions of waves in a horizontal magnetic field. It is shown that decay instabilities and parametric wave amplification mechanisms exist in each case under investigation. The instability increments and the parametric gain coefficients have been determined for the relevant processes.     

On stochastic stabilization of the Kelvin-Helmholtz instability by three-wave resonant interaction

An analytical investigation of the effect of three-wave resonant interactions with the linearly unstable wave is proposed. We consider the waves in the Kelvin-Helmholtz model, consisting of two fluid layers with different densities and velocities. We suppose that the velocity shear is weakly supercritical, the instability is of the algebraic type, i.e., the amplitude of the unstable wave grows linearly, and the instability occurs within the framework of a single mode. The amplitudes of two other waves taking part in the nonlinear interaction are assumed to be stable. The initial amplitudes of these waves are supposed to be small in comparison with the initial amplitude of the unstable wave. We present an analysis of the system of amplitude equations derived for this case using JWKB-method. As a result, we obtain equations that couple solutions pre- and post-passing the singular point, i.e., the point where the amplitude of the unstable wave has a local minimum. These equations give us the transformation rule of a parameter that characterizes the phase shift between fast and slow waves and defines the behavior of the system. This parameter is constant between two singular points and varies by chance at a singular point. As long as it stays positive, the amplitude of the wave remains limited and performs stochastic oscillations. If this parameter passes over zero, then we leave the region of stabilization and turn out in the region, where the amplitude grows infinitely. Accordingly, the transition to the region of instability happens stochastically. However, if the time interval, when the amplitude remains bounded, is large enough, the proposed scenario can be treated as a partial stabilization of instability.     

Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. V. Excitation of Waves in Strong Dissipative Plasmas by a Monoenergetic Beam

A system of nonlinear equations derived in a previous paper which describes the evolution of the beam-plasma instability in strong dissipative plasmas is solved numerically. It is shown that there are three characteristic solutions of the system of equations: the resonant dissipative instability, the nonresonant instability with strong dissipation and the nonresonant dissipative instability. A physical interpretation of essential features of these instabilities is given. The interaction of resonant and nonresonant waves in the system electron beam-strong dissipative plasma is examined. Some conclusions for the transport problem of electron beams in strong dissipative plasmas are obtained in this paper.     

Development of instability in the problem of flow around a sphere

Multimoment hydrodynamics equations are used to solve the problem of flow around a quiescent solid sphere. The solutions to the multimoment hydrodynamics equations are found, which enable to interpret of the phenomenon of vortex shedding. The solutions give a pattern of instability development that qualitatively reproduces experimental data over a wide range of Reynolds numbers. The replacement of one unstable flow mode by another unstable mode is governed the tendency of the system to find the fastest way to depart from the state of statistical equilibrium. After stability loss, the system does not reach a new stable state. Such a scenario is at odds with the ideas of classical hydrodynamics, which interprets the development of instability in terms of a bifurcation transition from one stable state to another. This picture presented shows the direction of solving the problems faced by classical hydrodynamics in the interpretation of the phenomenon of vortex shedding.     

受激布里渊散射并行数值模拟研究

为了更深入地研究激光与等离子体相互作用中受激Brillouin散射不稳定性的物理机制,建立了受激Brillouin散射三波耦合数学模型,根据方程组的形式以及数学特征,采用算子分裂方法,坐标平移,高效的并行傅里叶变换和归约密度等算法,编制模拟受激Brillouin散射不稳定性的并行程序,并用数值算例证明其有效性,最后采用近3亿固定网格规模,扩展到4096个核上测试并行性能,并行效率达到81.6%。     

On the stability of Kolmogorov spectra of a weak turbulence

The stability problem of Kolmogorov spectra of a weak turbulence is analytically solved for the first time in the framework of a three-wave kinetic equation. The spectrum of isotropic perturbations of a stationary not-in-equilibrium distribution is found for the capillary waves on a shallow water surface. It is shown, in the isotropic case, that the Kolmogorov solution is stable with respect to excitations local in k-space. The perturbations drift to the damping region without growth of the magnitude. The structural instability of the isotropic spectrum is found by computer simulation: a small pumping anisotropy causes the spectrum to be essentially anisotropic within the inertial range.     

Stimulated scattering of light in a laser produced magnetoplasma

This note considers stimulated scattering of laser light in the ordinary mode by magnetosonic waves in a plasma. Problems of three-wave decay interaction and modulation instability are investigated. The growth rates and thresholds are obtained analytically. Application to laser-plasma interaction is discussed.     

Hamiltonian description of barotropic Rossby waves

A transformation into the normal canonical variables is found in the beta-plane approximation for barotropic Rossby waves of an arbitrary amplitude. This transformation is used to derive a matrix of three-wave interaction and to find an expression for the fourth-order term in the interaction Hamiltonian, which describes the modulation instability of Rossby waves. An increment of this instability has been calculated and estimated numerically.     

Stability analysis of the Randall–Sundrum braneworld in presence of bulk scalar

The stability problem of Randall–Sundrum braneworld is readdressed in the light of stabilizing bulk scalar fields. It is shown that in such scenario the instability in general persists because of back-reaction even when an arbitrary potential is introduced for a canonical scalar field in the bulk. It is further shown that a bulk scalar field can indeed stabilize the braneworld when it has a tachyon-like action. The full back-reacted metric in such model is derived and a proper resolution of the hierarchy problem (for which the Randall–Sundrum scenario was originally proposed) is found to exist by suitable adjustments of the parameters of the scalar potential.     

Experimental observation of motion of edge dislocations in Ge/Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>/Si(001) (<Emphasis Type="Italic">x</Emphasis> = 0.2–0.6) heterostructures

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.     

The inverse scattering solution for the full three dimensional three- wave resonant interaction

The direct and inverse scattering solution for the full three dimensional three-wave resonant interaction is solved, and an infinite set of conservation laws are found.     

Influence of Structural Defects on Martensitic Transformations in Systems with Low Elastic Moduli

We have developed a computational scheme within the Parrinello and Rahman molecular dynamics method allowing changes in the volume and shape of the model block. The scheme enables us to study the considerable structural rearrangement of the system in response to an arbitrary stress tensor. The effects of the type, symmetry, and interaction of regularly spaced point-defect complexes and stacking faults on the lattice stability and martensitic-transformation realization in bcc and B2-structures are investigated. It is shown that the defects can both stabilize the parent structure and contribute to its instability and development of the transformation by the shear mechanism. The actual scenario will depend on the defect type and symmetry. It is found that in the premartensite state, where the system approaches its stability limit, the interaction of strain fields occurring in the vicinity of defects may affect the choice of possible martensite-transition pathways.     

Dynamics of the free surface of a conducting liquid in a near-critical electric field

Near-critical behavior of the free surface of a perfectly conducting liquid in an external electric field is considered. Based on an analysis of three-wave processes using the method of integral estimates, sufficient criteria for hard instability of a planar surface are formulated. It is shown that the higher-order nonlinearities do not saturate the instability, for which reason the growth of disturbances has an explosive character.     

Parametric interaction and compression of optical pulses in field of high-power pump wave

It is shown that, in the undepleted pump approximation, the nonlinear problem of the three-wave parametric interaction under the conditions of phase mismatch can be reduced to a problem of linear interaction of the signal and idle waves with a strong low-frequency pump wave. The whole wave packet formed by the two waves breaks down to partial pulses whose dynamics is controlled by effective dispersion parameters. This can be accompanied by the compression of either one of the pulses that comprises the wave packet or the whole wave packet.     

Intermittency at the onset of stochasticity in nonlinear resonant coupling processes

A simple model for the nonlinear saturation of a plasma instability is studied via numerical solution of the resonant three-wave coupling equations. When parameters are varied the attractors of motion undergo bifurcations of several types. Intermittency is shown to occur in a transition from a limit cycle to a strange attractor. Such a transition might be indicative of an intermittent onset of turbulence in certain plasma experiments.     

空心旋转液体射流初始阶段运动规律的研究

应用质量守恒定律和动量守恒定律,建立了描述空心旋转液体射流初始阶段运动的非线 性常微分方程组;该方程组可以用数值方法方便地求解。理论计算结果与实验拍摄到的射流照片吻 合很好。本结果表示射流受挑动失稳破碎成液滴前的最基本运动状态,是进一步从理论上研究空心 旋转射流破碎雾化机理的基础。     

Vibration of a liquid with a free surface in a spinning spherical tank

The problem of forced fluid vibrations in a partially filled spinning spherical tank is solved numerically by using the finite element method. The governing equations include Coriolis acceleration and spatially homogeneous vorticity. An exponential instability is detected in the present simulation for fill ratios below 0·5 and centrifugal acceleration to thrust ratios less than 1·7. This fictitious instability appears in the model as a result of the homogeneous vortex assumption since the free slosh equations are neutrally stable in the Liapunov sense.     

Optical holography of diatomic small nanostructure objects and the near-field effect: Dimensional resonances at normal incidence of external optical radiation on a small object

The interaction of an atomic group occupying a volume with linear dimensions which are considerably smaller than the length of an external light wave is considered. On the basis of the joint set of equations for the electric field strength of the light wave and the optical equations for linear dipole oscillators, the self-consistent problem of determination of the field at the points of location of the atoms, as well as at different points of observation outside the atomic group (a small object) in the wave and near-field zones, is solved. An optical plane hologram of a small object is obtained by way of interference of the coherent field of dipoles of the object and a reference coherent wave in a certain plane of observation points far from the object in the wave zone. It is shown with the help of numerical experiments that a small object forms interference fringes with a good contrast, which allows one to use optical quasi-resonant emission for the development of a nondestructive method of investigation of small objects.     

Three-Wave Coupling Coefficients for Non-Uniform MHD Plasmas

Resonant three-wave interaction in a spatially non-uniform MHD plasma is considered, and the coupling coefficients are derived.     

Quantum Inverse Scattering Method for an Integrable Model

The exact eigenstates of the Hamiltonian for a quant um three-wave interaction system with boson-fermion operators are constructed by the quantum inverse scattering method. The Bethe-ansatz equations are obtained from the periodic boundary conditions.