Streaming instability in quantum dusty plasmas

By using a quantum hydrodynamic (QHD) model, we derive a generalized dielectric constant for an unmagnetized quantum dusty plasma composed of electrons, ions, and charged dust particulates. Neglecting the electron inertial force in comparison with the electron pressure, and the force associated with the electron correlations at a quantum scale, we discuss two classes of electrostatic instabilities that are produced by streaming ions, and dust grains. The effects of the plasma streaming speeds, the thermal speed of electrons, and the quantum parameter are examined on the growth rates. The relevance of our investigation to dense astrophysical plasmas is discussed.     

Lateral shaping and stability of a stretching viscous sheet

We investigate the changes of shape of a stretching viscous sheet by controlling the forcing at the lateral edges, which we refer to as lateral shaping. We propose a one-dimensional model to study the dynamics of the viscous sheet and systematically address stability with respect to draw resonance. Two class of lateral forcing are considered: (i) for the case that the stress at the edges is specified, we show that a pure outward normal stress S_n is usually unfavorable to the draw resonance instability as compared to the case of stress-free lateral boundaries. Alternatively, a pure streamwise tangential stress S_t is stabilizing; (ii) for the case that the lateral velocity at the edges is specified, we show that the stability properties are problem specific but can be rationalized based on the induced stress components (S_n,S_t).     

Linear and non‐linear stability thresholds for thermal convection in a box

We analyse the problem of finding instability thresholds and global non‐linear stability bounds for thermal convection in a linearly viscous fluid in a finite box. The vertical walls are maintained at different temperatures which gives rise to a non‐uniform temperature field in steady state. This problem was previously analysed by Georgescu and Mansutti (Int. J. Non‐Linear Mech. 1999; 34 :603–613). In our work we determine the linear instability threshold to be well above the global stability boundary found by an energy method. Since the perturbed system is not symmetric we expect this to be the case, and our analysis yields a parameter region where possible sub‐critical instabilities may be found. Copyright © 2006 John Wiley & Sons, Ltd.     

激光等离子体不稳定性及其抑制方案研究

受激拉曼散射、受激布里渊散射等激光等离子体不稳定性（LPI）是激光等离子体物理领域最重要的研究课题之一。特别是在激光驱动的惯性约束聚变中,LPI会造成相当份额的激光能量损失,破坏辐射对称性,产生的超热电子还会预热靶丸,进而影响压缩效率和聚变能量增益。近期,在美国国家点火装置上开展的实验表明对LPI物理过程的充分理解和有效控制对成功实现ICF点火至关重要。我们对近期LPI方面的一系列研究进展进行了简单介绍与讨论。首先,回顾了描述LPI过程的三波耦合理论,由此得出了LPI在线性阶段的增长率。接着讨论了一些复杂情景下的LPI物理过程,譬如LPI的非线性发展阶段、级联LPI、多光束LPI以及LPI间的非线性耦合。最后,着重介绍了一系列抑制LPI的技术方案,包括束匀滑技术、光束时域整形、宽带激光、偏振旋转激光以及外加磁场等。     

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approx‐imation are studied, using the 16‐moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL‐MHD fluid model (single fluid equations by Chew, Goldberger, and Low [5,9]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes – strongly modified compared to the CGL model – and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL‐MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities ‐ incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes ‐ two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electron correlation in weakly coupled transition metal dimers: Bimetallocenylenes and bimetallocenes

The Hartree-Fock (HF) instabilities in a series of bimetallocenes (1) and bimetallocenylenes (2) with Fe, Co, Ni and Cr as 3d centers have been investigated by means of a semiempirical INDO Hamiltonian. The HF picture is only valid in the case of the iron dimers. Strong correlation effects are encountered in the Co, Ni and Cr complexes. The necessary conditions for singlet, non-singlet (triplet) and non-real variations of the HF orbitals are discussed in detail. Singlet fluctuations are the result of intraatomic angular correlation (short-range) at each 3d center. The violation of the spin symmetry corresponds to a long-range interaction between the transition metal centers. Only for MOs with large 3d _xz amplitudes there exists a channel for the interatomic spin decoupling. Consequences for polymetallocenes are shortly discussed.     

AUGMENTED LAGRANGIAN METHOD AND OPEN BOUNDARY CONDITIONS IN 2D SIMULATION OF POISEUILLE–BÉNARD CHANNEL FLOW

The main objective of this study is to compare the influence of different boundary conditions upon the incompressible Poiseuille –Bénard channel flow (PBCF) in a 2D rectangular duct heated from below. In a first technical part the algorithm used to carry out this work, based on the augmented Lagrangian method, is presented. The implementation details of the five different open boundary conditions (OBCs) and the periodic boundary conditions (PBCs) tested in the present paper are also given. The study is then carried out for 1800<Ra≤ 10,000, 0<Re≤10 and 0·67≤Pr≤6·4. The five selected OBCs, applied at the outlet of the computational domain, respectively express the following conditions: a square profile for the velocity (OBC1), mass conservation (OBC2), zero second derivative of the horizontal velocity component (OBC3), a mixed boundary condition combining Dirichlet and Neumann conditions (OBC4) and an Orlanski-type boundary condition (OBC5). A good estimation of the perturbation amplitude and of the length of the perturbed zone at the outlet boundary is proposed. It is shown that OBC5 causes very little perturbation in the recirculating flow compared with the other OBCs. © 1997 John Wiley & Sons, Ltd.     

Instabilities in viscoelastic flow past a square cavity

Elastic flow transitions in viscoelastic flow past a square cavity adjacent to a channel are reported. The critical conditions for the onset of flow transitions and the qualitative and quantitative characterization of the secondary flows generated by the instability have been examined using streakline photography and instantaneous pressure measurements. Cellular type of instabilities inside the cavity is observed for flow rates beyond a critical value. Small and large scale eddies are observed at high flow rates. The flow inside the cavity and in the channel upstream and downstream of the cavity becomes weakly time-dependent for high flow rates.     

Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities

Recently we studied time dependent structural changes that are coupled with flow instabilities (Fischer 1998; Wheeler 1998; Fischer 2000). Within a stability analysis, a classification scheme for the feedback circuit of coupled shear-induced structure and flow instabilities was derived by Schmitt et al. (1995) and applied to our samples. Here, inhomogeneous flow layers of different concentration and viscosity are generated by shear-induced diffusion (spinodal demixing) and, as consequence, one no longer observes a homogeneous solution but a type of shear banding that is seen here for the first time. In this paper we present the behaviour of the first normal stress difference observed in the critical shear-rate regime where transient shear-induced structure is coupled with flow instability. Similar to the oscillations of the shear stresses (strain-controlled rheometer) one observes oscillations in the first normal stress difference. This behaviour indicates that elastic structures are built up and destroyed while the shear-induced structures occur and that the induced phase is more elastic than the initial one. Oscillations of shear stress and first normal stress difference are in phase and indicate that both phenomena are caused by the same mechanism. Received: 30 June 1999/Accepted: 14 December 1999     

Nonstandard finite difference schemes for reaction‐‐diffusion equations having linear advection

We extend previous work on nonstandard finite difference schemes for one‐space dimension, nonlinear reaction–diffusion PDEs to the case where linear advection is included. The use of a positivity condition allows the determination of a functional relation between the time and space step‐sizes, and provides schemes that are explicit. The Fisher equation is used to illustrate the method. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 361–364, 2000