Stability of superflow for ultracold fermions in optical lattices

We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.     

Periodic droplet formation in chemically patterned microchannels

Simulations show that, when a phase-separated binary AB fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give rise to the simultaneous, periodic formation of monodisperse droplets of A in B and B in A. The system bifurcates between time-independent behavior and different types of regular, nondecaying oscillations in the structural characteristics. The surprisingly complex behavior is observed even in the absence of hydrodynamic interactions and arises from the interplay between the fluid flow and patterned substrate, which introduces nonlinearity into the dynamical system.     

The dynamics of clusters of flexible cylinders in axial flow: Theory and experiments

This paper presents an outline of the theory for the dynamics of clusters of independently supported flexible cylinders in axial flow, and an extensive discussion of the behaviour of such systems with increasing flow velocity, with special emphasis placed on the modal forms of free coupled motions of the cylinders and on the onset of instabilities. Results of an experimental study of the problem are also presented, involving systems of two, three or four cylinders supported at both ends and positioned symmetrically in the cylindrical test section of a water tunnel; experiments were conducted with different inter-cylinder gaps and support conditions. Both theory and experiment show that with increasing flow the system loses stability by buckling in one of its coupled modes, commonly in a pattern where cylinders move towards one another symmetrically, maximum displacement occurring just downstream of their midpoints. With increasing flow, theory predicts that other buckling instabilities are superimposed on the first; in the experiments the system remains buckled, changing modal patterns constantly; some of them correspond to those predicted by theory. At sufficiently high flow, oscillatory motion is observed, corresponding to theoretical flutter. Theory and experiment agree qualitatively in most essential features of the dynamical behaviour of the system, and quantitative agreement in the critical flow velocities for the onset of the first buckling instability is remarkably good.     

不相溶系统内酸碱中和反应驱动动力学的不稳定性

采用含Mach-Zehnder干涉光路和Hele-Shaw反应器的实验系统,研究了重力场作用下,在Hele-Shaw系统内沿水平界面发生的由酸碱中和反应驱动的动力学不稳定性.反应器内包含上下两层反应物,即下层密度较大的四甲基氢氧化铵水溶液和上层密度较小的溶解于有机相的丙酸溶液. 研究了在伴随有界面传质的中和反应过程中,化学组分对于动力学不稳定性的影响. 观察发现了由于反应物初始浓度不均引起的多种形式的Marangoni对流结构,包含有胞状结构和各种震动波形式的结构.测量了不稳定性发生过程中碱溶液的浓度. 结果表明不稳定性对流的产生可以显著提高系统内的传质效率,并造成传质结 构的剧烈变形.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Stability Diagrams of a Bose-Einstein Condensate in Excited Bloch Bands

Landau and dynamical instabilities o/a Bose-Einstein condensate （BEC） in the excited bands of a one-dimensional optical lattice are investigated by the Gross Pitaevskii theory. Our results show that there always exists Landau instability for a BEC in the whole region of excited bands. We also map out the dangerous zones of the dynamical instability. The experimental implications of the stability diagram are discussed.     

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.     

Spiral structures in magnetized rotating plasmas

A theory of spiral structure formation has been formulated to show that spiral structures are rather basic entities in magnetized rotating plasmas subjected to various types of instabilities such as collisional drift wave instability, flute mode instability due to centrifugal force, and Kelvin-Helmhotz instability. The characteristic features of spiral structures observed experimentally in electron cyclotron resonance plasmas are reproduced by our theory.     

Modification of pattern formation in doubly resonant second-harmonic generation by competing parametric oscillation

We analyze pattern formation in doubly resonant intracavity second-harmonic generation in the presence of competing nondegenerate parametric downconversion. We show that for positive cavity detuning of the fundamental frequency the threshold for parametric oscillation is lower than that of transverse, pattern forming instabilities. The parametric oscillation strongly modifies the pattern dynamics found previously in a simplified analysis that neglects parametric instability [Phys. Rev. E 56, 4803 (1997)]. Stationary and dynamic patterns in the presence of parametric oscillation are found numerically.     

稠密颗粒射流倾斜撞击颗粒膜特征

采用高速摄像仪对稠密颗粒射流倾斜撞击形成的类液体颗粒膜特征进行实验研究,考察了颗粒粒径、射流速度以及射流含固率等因素对颗粒膜形态及动态特征的影响.结果表明:随着颗粒粒径增大,稠密颗粒倾斜撞击流由颗粒膜向散射模式转变;随着射流速度增加,气固不稳定增强,射流流量出现脉动,正面与侧面分别表现为颗粒膜的非轴对称振荡和表面波纹结构;颗粒膜非轴对称振荡的振荡频率和振荡幅度随射流速度的增大而增大;表面波纹速度和波长沿传播方向增大,波纹间存在叠加现象.颗粒膜出现非轴对称振荡主要是因为喷嘴出口由气固不稳定性引起的射流流量脉动,射流流量脉动频率与撞击面振荡频率基本相当.     

Dynamical systems and complex systems theory to study unsteady combustion

Reacting flow fields are often subject to unsteadiness due to flow, reaction, diffusion, and acoustics. Further, flames can also exhibit inherent unsteadiness caused by various intrinsic instabilities. Interaction between various unsteady processes across multiple scales often makes combustion dynamics complex. Characterizing such complex dynamics is essential to ensure the safe and reliable operation of high efficiency combustion systems. Tools from nonlinear dynamics and complex systems theory provide new perspectives to analyze and interpret the data from real systems. They could also provide new ways of monitoring and controlling combustion systems. We discuss recent advances in studying unsteady combustion dynamics using the tools from dynamical systems theory and complex systems theory. We cover a range of problems involving unsteady combustion such as thermoacoustic instability, flame blowout, fire propagation, reaction chemistry and flow flame interaction.     

Instabilities in a two-dimensional polar-filament-motor system

The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.     

Modal spectra extracted from nonequilibrium fluid patterns in laboratory experiments on Rayleigh-Bénard convection

We describe a method to extract from experimental data the important dynamical modes in spatiotemporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an experimental ensemble of Rayleigh-Bénard convection patterns with nearby initial conditions close to the onset of secondary instability. An analysis of the ensemble evolution reveals the spatial structure of the dominant modes of the system as well as the corresponding growth rates. The extracted modes are related to localized versions of instabilities found in the ideal unbounded system. The approach may prove useful in describing instability in experimental systems as a step toward prediction and control.     

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.     

Absolute instability of a liquid jet in a coflowing stream

Cylindrical liquid jets are inherently unstable and eventually break into drops due to the Rayleigh-Plateau instability, characterized by the growth of disturbances that are either convective or absolute in nature. Convective instabilities grow in amplitude as they are swept along by the flow, while absolute instabilities are disturbances that grow at a fixed spatial location. Liquid jets are nearly always convectively unstable. Here we show that two-phase jets can breakup due to an absolute instability that depends on the capillary number of the outer liquid, provided the Weber number of the inner liquid is >O(1). We verify our experimental observations with a linear stability analysis.     

Structures of a continuously fed two-dimensional viscous film under a destabilizing gravitational force

We study the gravity induced instability of a liquid film formed below a plane grid which is used as a porous media in an original hydrodynamic experiment. The film is continuously supplied with a controlled flow rate. We give through a phase diagram the full spectrum of the different flow regimes and we investigate the dynamics of the observed structures. True secondary instabilities of a 2D periodic pattern are described. The control parameters are the flow rate and the viscosity.     

Stabilities of one-dimensional stationary states of Bose-Einstein condensates

We explore the dynamical stabilities of a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) consisting of fixed N atoms with time-independent external potential. For the stationary states with zero flow density the general solution of the perturbed time evolution equation is constructed, and the stability criterions concerning the initial conditions and system parameters are established. Taking the lattice potential case as an example, the stability and instability regions on the parameter space are found. The results suggest a method for selecting experimental parameters and adjusting initial conditions to suppress the instabilities.     

Convection in horizontally shaken granular material

In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically. Using two dimensional molecular dynamics we show that the convection pattern depends crucially on the inelastic properties of the material. The concept of restitution coefficient provides arguments for the change of the behaviour with varying inelasticity. Received 3 March 1999