Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. II. Energetic Analysis of Certain Types of Monoenergetic Beam-Plasma Interactions Based on the Čerenkov Resonance Condition

The energy and momentum balance equations for a potential wave in a monoenergetic electron beam-plasma system are considered in the linear approximation, when the wave is in ?erenkov resonance with the beam particles. An energetic analysis of certain types of beam-plasma instabilities is given. It is shown that the energy and momentum balance equations are consistent with the dispersion relation for all unstable waves. From this fact follows that the energy and momentum densities of all linear unstable waves in reactive beam-plasma systems are equal to zero. An interpretation and a possible classification of beam-plasma instabilities are given.     

Resonant absorption of shear instabilities in flow systems with energy dissipation

It is shown that hydrodynamic and electrohydrodynamic waves excited in two-layer dissipative systems due to shear instabilities experience resonant absorption of two types: at the rotational frequency of particles of the medium and the frequency of their collision with the lattice.     

Localization in physical systems described by discrete nonlinear Schrodinger-type equations

Following a short introduction on localized modes in a model system, namely the discrete nonlinear Schrodinger equation, we present explicit results pertaining to three different physical systems described by similar equations. The applications range from the Raman scattering spectra of a complex electronic material through intrinsic localized vibrational modes, to the manifestation of an abrupt and irreversible delocalizing transition of Bose-Einstein condensates trapped in two-dimensional optical lattices, and to the instabilities of localized modes in coupled arrays of optical waveguides.     

Coulomb self-energy of a uniformly charged three-dimensional cylinder

We calculate exactly the Coulomb self-energy of a uniformly charged three-dimensional cylinder. We derive a general analytical formula which, in the limit of zero length, gives also the correct result for the Coulomb self-energy of a uniformly charged two-dimensional disk. The exact analytical expression that we derive can be used in models that incorporate finite thickness effects in studies of two-dimensional electronic systems in the fractional quantum Hall regime as well as models that describe cylindrical beams of charged particles, certain colloidal suspensions of charged rigid rod-like particles and biological systems consisting of macromolecules with cylindrical symmetry.     

Study of the instabilities of collisionless systems on the basis of stochastic trajectories

We propose a practical method for distinguishing stochastic and regular subsystems in the entire set of particles for numerical modeling of the development of physical instabilities in collisionless systems with self-consistent fields. The method of subdividing the phase space into subsystems is based on the comparison of the results of two computational experiments with identical initial conditions but different realizations of rounding errors. An example of establishing the spatial and temporal domains of the development of collective instability and determining the instability increments is offered by a gravitating disk.     

Magnetic Fluid and Nanoparticle Applications to Nanotechnology

Magnetic field based micro/nanoelectromechanical systems (MEMS/NEMS) devices are proposed that use 10 nm diameter magnetic particles, with and without a carrier fluid, for a new class of nanoduct flows, nanomotors, nanogenerators, nanopumps, nanoactuators, and other similar nanoscale devices. A few examples of macroscopic ferrohydrodynamic instabilities that result in patterns, lines, and structures are shown that can be scaled down to sub-micron dimensions.     

Parabolic resonances and instabilities

A parabolic resonance is formed when an integrable two-degrees-of-freedom (d.o.f.) Hamiltonian system possessing a circle of parabolic fixed points is perturbed. It is proved that its occurrence is generic for one parameter families (co-dimension one phenomenon) of near-integrable, two d.o.f. Hamiltonian systems. Numerical experiments indicate that the motion near a parabolic resonance exhibits a new type of chaotic behavior which includes instabilities in some directions and long trapping times in others. Moreover, in a degenerate case, near a flat parabolic resonance, large scale instabilities appear. A model arising from an atmospherical study is shown to exhibit flat parabolic resonance. This supplies a simple mechanism for the transport of particles with small (i.e. atmospherically relevant) initial velocities from the vicinity of the equator to high latitudes. A modification of the model which allows the development of atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities are clearly observed. (c) 1997 American Institute of Physics.     

相干与非相干激光成丝不稳定性的数值模拟研究

利用二维三温磁流体力学激光靶程序（ＣＡＳＴＯＲ）数值模拟了相干光和诱导空间非相干（ｉｎｄｕｃｅｄ ｓｐａｔｉａｌ ｉｎｃｏｈｅｒｅｎｃｅ ＩＳＩ）光的成丝不稳定性．用求解激光传播方程和简化流体模型的方法研究了随机相位板（ｒａｎｄｏｍ ｐｈａｓｅ ｐｌａｔｅ ＲＰＰ）光滑化技术对成丝不稳定性的影响，结果表明ＩＳＩ和ＲＰＰ去相干方法可以有条件地减弱或抑制成丝不稳定性． 关键词：     

Flow-controlled growth in Langmuir monolayers

We propose a hydrodynamic mechanism, based on the Marangoni flow, to describe growth instabilities of liquid-condensed islands in the supercooled liquid-expanded phase of two-dimensional Langmuir monolayers. This Marangoni instability is intrinsic to Langmuir monolayers and is not controlled by the expulsion of chemical impurities from the liquid-condensed phase. The hydrodynamic transport of the insoluble surfactants is shown to overwhelm passive diffusion and to provide a mechanism for fingering instabilities. The model can explain the observations by Brewster-angle microscopy of ramified liquid-condensed islands in monolayers that do not contain the fluorescent dye impurities, which are normally believed to be responsible for Langmuir-film growth instabilities. Received 21 May 2000 and Received in final form 18 June 2001     

Phase instabilities in small particles

In this review we consider the existing theories for the structure of small particles and the nature of morphological instabilities as the size is reduced. The various electron microscopic observations confirming the stability of a new phase, the so called ‘Multiply twinned structure’, in small particles is discussed. A theoretical model is presented to calculate the free energy surfaces for a series of asymmetric and single crystal structures using a modified Curie-Wulff construction for the surface energy, and a disclination model for the elastic strain energy. Depending on the activation barrier heights and the Boltzmann occupancy factors for the various local minima on the energy surface, the idea of ‘quasi-melting’ is introduced and compared with the structural instabilities in molecular clusters seen recently by various authors using computer simulations. A phase diagram for small particles as a function of size and temperature is presented and the effect of statistical fluctuations on stability is discussed. Finally a phenomenological discussion relating the phase instabilities to various melting and related phase transitions is given.     

Nonlinear hydrodynamic phenomena in Stokes flow regime

We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a single deformed drop and collective dynamics of arrays of hydrodynamically coupled particles. To explore physical mechanisms of system instabilities, chaotic drop evolution, and structural transitions in particle arrays we use simple models, such as small-deformation equations and effective-medium theory. We find numerical and analytical solutions of the simplified governing equations. The small-deformation equations for drop dynamics are analyzed using results of dynamical systems theory. Our investigations shed new light on the dynamics of complex fluids, where the nonlinearity often stems from the evolving boundary conditions in Stokes flow.     

Long wavelength instabilities of perfectly square planforms in nonlinear convection

The long wavelength instabilities of square planforms are studied using amplitude equations which describe the general interaction of two orthogonal coupled roll patterns. In addition to the zig-zag, two-dimensional and three-dimensional Eckhaus instabilities, a truly three-dimensional rectangular instability is found. Nonlinear phase diffusion equations are derived close to the onset of the instabilities.University of Gambridge, Gambridge, United Kingdom. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 788–792, August, 1993.     

How are spin gap and pairing correlations of doped Mott insulators controlled by the geometry of the lattice structure?

Proposals to enhance the spin excitation gap and the pairing correlations in doped Mott insulators are reviewed. Design and tuning of flat dispersions near the Fermi level extend the critical region of the metal-to-Mott insulator transition thereby inducing stronger pairing instabilities. Several one- and two-dimensional decorated lattices are studied. We also discuss the tuning for stronger d-wave pairing instabilities in a microscopic model of high-T_c cuprates.     

Parity-breaking bifurcation and global oscillation in patterns of ion channels

Stationary spatiotemporal pattern formation emerging from the electric activity of biological membranes is widespread in cells and tissues. A known key instability comes from the self-aggregation of membrane channels. In a two-dimensional geometry, we show that the primary pattern undergoes four secondary instabilities: Eckhaus-like, period-halving, drift instabilities, and a global oscillation. The stability diagram is determined. The parity-breaking (drift) bifurcation of channel density is characterized analytically and numerically.     

Localization of particles in a two-dimensional random potential

A recently proposed theory of the density response of particles moving in a random potential is applied to two-dimensional systems. The particles are found to be localized for arbitrary small disorder. By decreasing the potential fluctuations we find an abrupt transition from an insulating state to a quasi-conducting state exhibiting exceedingly small values for the inverse susceptibility, the inverse localization length and the excitation gap of the dynamical conductivity.     

任意Atwood数Rayleigh-Taylor和 Richtmyer-Meshkov 不稳定性气泡速度研究

本文将Layzer气泡模型推广到任意界面Atwood数情形,得到了自洽的微分方程组.该模型描述了气泡从早期的指数增长阶段到气 泡以渐近速度上升的非线性阶段的发展过程,给出了Rayleigh-Taylor(RT)和Richtmyer-Meshkov(RM)不稳定性的二维和 三维气泡速度渐近解,还求出了二维和三维RT不稳定性气泡顶点附近速度的解析解.     

Density instabilities in a two-dimensional dipolar Fermi gas

We study the density instabilities of a two-dimensional gas of dipolar fermions with aligned dipole moments. The random phase approximation (RPA) for the density-density response function is never accurate for the dipolar gas, and so we incorporate correlations beyond RPA via an improved version of the Singwi-Tosi-Land-Sj?lander scheme. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.     

Anomalous transport in heterogeneous media

The diffusion dynamics of particles in heterogeneous media is studied using particle-based simulation techniques. A special focus is placed on systems where the transport of particles at long times exhibits anomalies such as subdiffusive or superdiffusive behavior. First, a two-dimensional model system is considered containing gas particles (tracers) that diffuse through a random arrangement of pinned, disk-shaped particles. This system is similar to a classical Lorentz gas. However, different from the original Lorentz model, soft instead of hard interactions are considered and we also discuss the case where the tracer particles interact with each other. We show that the modification from hard to soft interactions strongly affects anomalous-diffusive transport at high obstacle densities. Second, non-linear active micro-rheology in a glass-forming binary Yukawa mixture is investigated, pulling single particles through a deeply supercooled state by applying a constant force. Here, we observe superdiffusion in force direction and analyze its origin. Finally, we consider the Brownian dynamics of a particle which is pulled through a two-dimensional random force field. We discuss the similarities of this model with the Lorentz gas as well as active micro-rheology in glass-forming systems.     

Dissipative instabilities in a mesospheric plasma with the aerosol charging processes taken into account

We consider dissipative instabilities of a flow of large aerosol particles as a possible mechanism for generation of electric-field and charged-particle density irregularities in the middle atmosphere. A dispersion equation describing the properties of the spectral component of a quasistatic electric field with allowance for the aerosol charging inertia and external stationary electric field is obtained. The equation is used to study characteristics of two possible instabilities, namely, the instability of a dust-acoustic mode and the instability of an additional low-frequency mode stimulated by the charging inertia. Dependences of the growth rates of both instabilities on the parameters of the medium and the external stationary electric field are obtained. Quantitative estimates for the parameters of the aerosol, ion, and electron components and external factors that are necessary for the excitation of instabilities in the region of the existence of summer polar mesospheric echo, as well as those for spatial scales of unstable perturbations, are given.