Velocity distributions in dissipative granular gases

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution eta and q=N(H)/N(C), the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find between uniform and boundary heating can then be understood as different limits of q, for q>1 and q less, similar 1, respectively.     

颗粒气体的团簇行为

颗粒体系由于粒子间非弹性碰撞和摩擦等内秉的能量耗散特性,由宏观粒子形成的颗粒气体体系经常会有局部凝聚现象,这是颗粒气体体系与分子气体体系的最大区别之一。理解和预测这一现象的发生将有助于人们对远离平衡态体系的复杂现象(如有序结构、斑图和团簇形成)的认知。这种局部凝聚现象可以类比于分子气体中亚稳分解形成的液滴,将气液相分离用于解释和寻求局部凝聚现象的模型得到了分子动力学模拟的校验。但是实验的校验却由于宏观粒子运动受重力作用的影响难以在实验室中实现。实践十号卫星为我们提供了长时稳定微重力条件,使得实验观察成为可能,有望获得团簇形成及颗粒冷却行为等颗粒动力学重要实验结果。     

Drift dissipative instability in a two temperature plasma

The presence of a small amount of relatively cold electrons in an otherwise hot plasma reduces the ion sound speed in the medium and hence reduces the growth rate of the drift dissipative ion acoustic mode in an inhomogeneous weakly ionized plasma. This is expected to improve the confinement time in certain magnetic confinement schemes. The propagation of a small but finite amplitude mode in the presence of ion viscosity is also investigated by using reductive perturbation method. It is shown that, when the damping due to ion viscosity is stronger than the growth due to collisions, there exists a stationary shock solution.     

The dissipative instability of a relativistic electron beam

The theory of the wall instabilities of surface waves excited by an electron beam is developed. Their classification, linear, quasilinear and nonlinear theory is given. It is shown that dissipative instabilities convert practically all the energy lost by the beam into the heating of the lossy walls confining the beam.     

Beam instability of afterglow plasma in inert gases

The paper considers the conditions under which the development of beam instabilities of the after-glow plasma in inert gases is possible. The validity of assumptions has been experimentally confirmed.     

Surface tension and instability of shock waves in gases

The pressure anisotropy within a shock layer results in an additional property of the shock wave: the surface tension. Its value amounts to 10³ dyn/cm for Mach number 10. The surface tension term in the characteristic equation causes an absolute shock wave instability in the spontaneous sound emission regime.     

Thermal effects in the dissipative instability of the electron beam-plasma systems

The effects of the thermal motion of the charged particles in the dissipative instability of the under and over-limiting currents of a relativistic electron beam in a fully magnetized beam-plasma waveguide is investigated. It is shown that by increasing the temperature of the plasma electrons, the resonant frequency of the waveguide slightly increases and the growth rates of the instability development decreases. In addition, an increase of the temperature of the plasma electron can change the dissipative hydrodynamic instability to the collisionless kinetic instability. Furthermore, the dissipative instability of the overlimiting electron beam is shown to be more sensitive with respect to the electron plasma temperature compared to the underlimiting electron beam case.     

Growth of ordered domains beyond a dynamic instability in dissipative systems

We furnish evidence supporting our conjecture that the growth of structure which results at the onset of a center manifold in driven systems operating far from equilibrium can be described by a power law with a single exponent. More specifically, if the dissipative structure is contained in a center manifold and thus its stability is warranted, the linear dimensions for domains of organized spatial cells increase ast ^1/2.     

The D'yakov-kontorovich instability of shock waves in real gases

In the 1950s, D'yakov and Kontorovich predicted that under certain conditions perturbed shock waves in nonideal gases can become unstable by emitting undamped sound and entropy-vortex waves. For the last 45 years, though, little progress has been made in the identification and numerical modeling of physical conditions for which this phenomenon might occur. Using a van der Waals equation of state, we present for the first time a dynamical simulation of a D'yakov-Kontorovich instability. The two-dimensional emission pattern of acoustic waves appearing in the simulation agrees with the prediction of a linearized theory.     

A remark on the drift dissipative instability of weakly ionized plasma

The author takes into account ion motion along the magnetic lines in the dispersion equation. It is shown that the drift branch of waves joins the ion acoustic branch in the weakly ionized plasma, too, and that the term describing this motion has a stabilizing effect. These results are independent on the relation of the wave length to the mean free path of the electrons.The author would like to express his sincere thanks to Dr. J. Václavík for his valuable comments.     

Nonlinearly saturated dynamical state of a three-wave mode-coupled dissipative system with linear instability

Linearly unstable dissipative systems with quadratic nonlinearity occurring in plasma physics, optics, fluid mechanics, etc. are often modeled by a general set of three-wave mode-coupled ordinary differential equations for complex variables. Bounded attractors of the set approximate nonlinearly saturated turbulent states of real physical systems. Exact criteria for boundedness of the attractors are found. Fundamentally different kinds of asymptotic behavior of the wave triad are classified in the parameter space and quantitatively assessed.     

Electron thermal diffusion instability and standing striations in the plasma of a dc discharge in molecular gases

A linear theory of waves in the positive column of dc discharge in molecular gases is presented. Full account is taken of local electron hydrodynamics (s.c. quasi-homogeneous equations), which is derived on the basis of a local non-equilibrium distribution of the electron gas. The production term on the right-hand-side of the ion balance equation gives the familiar ionization wawes, but the ion drift enhanced by the high value of the logitudinal field strength, together with the modification of the pertubed electric field incurred by the electron thermal diffusion, causes the dispersion curve to inersect thek-axis. This provides a natural explanation of the amplified low frequency anode directed wave commonly observed in molecular gas discharges as well as of the standing striation pattern. Numerical examples are given for the case of nitrogen.     

Dynamic instability of supercritical driveshafts mounted on dissipative supports—Effects of viscous and hysteretic internal damping

The case of a rotating shaft with internal damping mounted either on elastic dissipative bearings or on infinitely rigid bearings with viscoelastic suspensions is investigated in order to obtain the stability region. A Euler-Bernoulli shaft model is adopted, in which the transverse shear effects are neglected and the effects of translational and rotatory inertia, gyroscopic moments, and internal viscous or hysteretic damping are taken into account. The hysteretic damping is incorporated with an equivalent viscous damping coefficient. Free motion analysis yields critical speeds and threshold speeds for each damping model in analytical form. In the case of elastic dissipative bearings, the present results are compared with the results of previous studies on finite element models. In the case of infinitely rigid bearings with viscoelastic suspensions, it is established that viscoelastic supports increase the stability of long shafts, thus compensating for the loss of efficiency which occurs with classical bearings. The instability criteria also show that the effect of the coupling which occured between rigid modes introducing external damping and shaft modes are almost more important than damping factor. Lastly, comparisons between viscous and hysteretic damping conditions lead to the conclusion that an appropriate material damping model is essential to be able to assess these instabilities.     

Temperature effect on dissipative holographicscreening-photovoltaic solitons in a biased dissipative system

In a biased dissipative photovoltaic-photorefractive system, this paper investigates the temperature effect on the evolution and the self-deflection of the dissipative holographic screening-photovoltaic （DHSP） solitons. The results reveal that, the evolution and the self-deflection of the bright and dark DHSP solitons are influenced by the system temperature. At a given temperature, for a stable DHSP soliton originally formed in the dissipative system, it attempts to evolve into another DHSP soliton when the temperature change is appropriately small, whereas it will become unstable or break down if the temperature departure is large enough. Moreover, the self-deflection degree of the solitary beam centre increases as temperature rises in some range, while it is decided by the system parameters and is slight under small-signal condition. The system temperature can be adjusted to change the formation and the self-deflection of the solitary beam in order to gain certain optical ends. In a word, the system temperature plays a role for the DHSP solitons in the dissipative system.     

Geometric phases in dissipative systems

It is shown that a phenomenon analogous to the geometric phase shifts of Berry and Hannay occurs for dissipative oscillatory systems and can be detected in numerical simulations of chemical oscillators. The approach herein to the theory of geometric phases begins with a study of simple first-order differential equations on the circle (circle dynamics). It is shown how more complicated systems exhibit geometric phases through reduction to a circle dynamics. In this way, the various manifestations of the phenomenon are seen from a single unified perspective. The results are illustrated in numerical experiments on several model systems ranging from analytically solvable, but contrived, to realistic models of chemical oscillators.     

Structure effects in dissipative collisions

An ansatz representing a generalisation of the one-body recoil formula is proposed on the basis of the total kinetic energy loss versus σ_Z² correlation systematics observed in collisions between very heavy nuclei. It is shown that such correlations are surprisingly sensitive to the shell structure of the colliding nuclei. The mechanism of energy dissipation appears also to be strongly influenced by the structure effects.     

Intermittency in dissipative dynamical systems

We show that the intermittency displayed by a differential system proposed by Yamada and Fujisaka can be interpreted in the general framework of intermittent transitions to turbulence studied by Pomeau and the author.     

Ericson fluctuations in dissipative collisions

We generalize Ericson's theory of fluctuations to deep inelastic reactions. Following Ericson we assume that theS-matrixS _βα(E, l) can be written as a sum of pole terms in the complex energy plane, but the dependence ofS _βα (E, l) on the angular momentuml is assumed to be coherent. Semi-classical approximations for the summation of the angular momenta lead to a simple formula for the energy autocorrelation function. It contains the average widthΓ(l) describing the lifetimeτ(l) of the intermediate dinuclear system and the numberN _eff of unresolved primary channels. These quantities can be determined from a measurement of the autocorrelation function.