Softening induced instability of a stretched cohesive granular layer

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching. We present a simple model in which the mechanism responsible of the instability is the "strain softening" exhibited by humid granular materials above a typical strain. Our analysis indicates that such a type of instability should be observed in any system presenting a negative stress sensitivity to strain perturbations.     

Dynamical instability of shear-free collapsing star in extended teleparallel gravity

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f(T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.     

Emergence and decay of turbulence in stirred atomic Bose-Einstein condensates

We show that "weak" elliptical deformation of an atomic Bose-Einstein condensate rotating at close to the quadrupole instability frequency leads to turbulence with a Kolmogorov energy spectrum. The turbulent state is produced by energy transfer to condensate fragments that are ejected by the quadrupole instability. This energy transfer is driven by breaking the twofold rotational symmetry of the condensate. Subsequently, vortex-sound interactions damp the turbulent state leading to the crystallization of a vortex lattice.     

Numerical irreversibility in self-gravitating small N-body systems, II: Influence of instability affected by softening parameters

We investigate the fundamental characteristics of numerical irreversibility appearing in self-gravitating small N-body systems by means of a molecular dynamics method from the viewpoint of time-reversible dynamics. We reconsider a closed spherical system consisting of 250 point-particles interacting through the Plummer softened potential. To investigate the characteristics of numerical irreversibility, we examine the influence of the instability affected by the softening parameter for the softened potential (the instability considered here is the instability of a dynamical system in chaos theory, e.g., a separation rate of the distance between two nearby trajectories in phase space or speed space). To this end, under the restriction of constant initial energy, the softening parameter for the Plummer softened potential is varied from 0.005R to 0.050R, where R is the radius of the spherical container. We first confirm that the size of the softening parameter, i.e., the deviation of the potential from a pure gravitational potential, influences the virial ratio, the density, the pressure on the spherical container, etc., during an early stage of the relaxation process. Through a time-reversible simulation based on a velocity inversion technique, we demonstrate that numerical irreversibility due to round-off errors appears more rapidly with decreasing softening parameter. This means that the higher the instability of the system or the higher the separation rate of the distance between two nearby trajectories, the earlier the memory of the initial conditions is lost. We show that the memory loss time , when the simulated trajectory completely forgets its initial conditions, increases approximately linearly with the timescale of the chaotic system, i.e., the Lyapunov time t_λ. In a small self-gravitating system, propagation of numerical irreversibility or loss of reversibility depends on both the energy state of the system and the instability affected by the softening parameter.     

Convection in thick and in thin fluid layers with a free surface – The influence of evaporation

Convective systems are examined by stability analysis as well as numerical solutions of the hydrodynamic basic equations in three spatial dimensions. Instabilities caused by surface tension gradients (Marangoni effect) are analyzed. The effect of evaporation of a volatile oil is studied by a two-layer system as well as by means of an effective Biot number. In thin fluid layers (a few 100 nm), an instability caused by the interaction between free surface and solid substrate manifests itself in form of surface deformation. We discuss this situation using the lubrication approximation. Special emphasis is layed on the influence of evaporation which may stabilize the system and which may lead to interesting new periodic structures.     

Mass redistribution causes the structural richness of ion-irradiated surfaces

We show that the "sputter patterning" topographical instability is determined by the effects of ion impact-induced prompt atomic redistribution and that erosion--the consensus predominant cause--is essentially irrelevant. We use grazing incidence small angle x-ray scattering to measure in situ the damping of noise or its amplification into patterns via the linear dispersion relation. A model based on the effects of impact-induced redistribution of those atoms that are not sputtered away explains both the observed ultrasmoothening at low angles from normal incidence and the instability at higher angles.     

Nonlinear waves in nonequilibrium systems of the oscillatory type,part I

Nonlinear waves in mathematical models of nonequilibrium spatially uniform media with the oscillatory instability of the trivial state are considered. The models are based on the generalized Ginsburg-Landau equations. For the long-wave system, i.e. that described by two-component reaction-diffusion equations, we obtain the full stability conditions for monochromatic plane travelling waves. The basic part of the paper is devoted to the short-wave system which can be described by reaction-diffusion equations with not less than three components or by a two-component system with residual nonlocality. We construct the Ginsburg-Landau equation for this system, and we find its general quasistationary one-dimensional solution which is a travelling wave modulated by a travelling envelope wave. The stability of this solution is investigated with the especial emphasis on different important particular cases. The obtained results are compared with experimental observations of different waves on fronts of detonation and non-gaseous combustion (which also are characterized by the oscillatory short-wave instability of the trivial state), and the qualitative agreement between theoretical and experimental results is demonstrated.     

Modulational instability and localized breather in discrete Schrödinger equation with helicoidal hopping and a power-law nonlinearity

We investigate the discrete nonlinear Schrödinger model with helicoidal hopping and a power-law nonlinearity, motivated by the tunable nonlinearity in the model of DNA chain and ultra-cold atoms trapped in a helix-shaped optical trap. In the study of modulational instability, we find a successive destabilization along with increasing nonlinear-power. In particular, the critical amplitudes of second-stage instability decrease as nonlinear-power increases. Furthermore, it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. This link enable us to analytically estimate the critical parameters at which the breather solutions turn unstable, and find these parameters are dramatically influenced by the nonlinear-power. The stability properties of localized breathers perform an obvious change when the nonlinear power crosses a critical value ${\gamma }_{cr}$. It is reflected that at weak nonlinearity the breathers exhibit monostability, while exceeding ${\gamma }_{cr}$ the bistability and instability will set in. The interplay between nonlinear-power and long-range hopping on the stability properties of breathers is also discussed in detail.     

Radial and angular rotons in trapped dipolar gases

We study Bose-Einstein condensates with purely dipolar interactions in oblate traps. We find that the condensate always becomes unstable to collapse when the number of particles is sufficiently large. We analyze the instability, and find that it is the trapped-gas analogue of the "roton-maxon" instability previously reported for a gas that is unconfined in 2D. In addition, we find that under certain circumstances the condensate wave function attains a biconcave shape, with its maximum density away from the center of the gas. These biconcave condensates become unstable due to azimuthal excitation--an angular roton.     

Zero-sound condensate in a Fermi liquid

We consider a normal Fermi liquid with a local scalar interaction given by the Landau parameter f₀. The system becomes unstable for f₀ < ?1 against a growth of scalar-mode excitations (Pomeranchuk instability). We show that the instability may be tamed by the formation of a static Bose condensate of the scalar modes. We study a possible reconstruction of the isospin-symmetric nuclear matter owing to the appearance of the condensate. Possibility of a novel metastable state at subnuclear densities is demonstrated.     

Theory for the laser-induced femtosecond phase transition of silicon and GaAS

We analyze he femtosecond instability of the chamond lattice of silicon and GaAs, which is induced by a dense electron-hole plasma after excitation by a very imense laser pulse. We obtain that the electron-hole plasma causes an instability of both transverse acoustic and longitudinal optical phonons. So, within less than 200fs, the atoms are displaced more than 1 Å from their equilibrium position. The gap between the conduction and the valence band then vanishes and the symmetries of the diamond structure are destroyed, which has important effects on the optical reflectivity and second-harmonic generation. After that, the crystal melts very rapidly because of the high kinetic energy of the atoms. Note that mis is in good agreement with recent experiments done on Shand GaAs using a pump laser to excite a dense electron hole plasma and a probe laser to observe the resulting changes in the atomic and electronic structure.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Current-induced transverse spin-wave instability in a thin nanomagnet

We show that an unpolarized electric current incident perpendicular to the plane of a thin ferromagnet can excite a spin-wave instability transverse to the current direction if source and drain contacts are not symmetric. The instability, which is driven by the current-induced "spin-transfer torque," exists for one current direction only.     

Structure changes induced by external multiplicative noise in the electrohydrodynamic instability of nematic liquid crystals

We study the influence of external multiplicative noise on the electrohydrodynamic instability (EHD) in nematic liquid crystals. It turns out that the correlation time _n and the intensityQ of the noise are the crucial parameters to control the system. Different types of noise lead to minor quantitative changes when compared to Gaussian white noise, leaving the qualitative aspects unchanged. With increasing noise intensity the threshold for the onset of the first instability changes drastically. We observe that the curvature arising when the threshold of the various instabilities is plotted as a function of the noise intensity changes as one is going, e.g., from the onset of Williams domains (WD) to the onset of the grid pattern (GP). This result reflects the transition in the flow structure from two-dimensional (WD) to three-dimensional (GP, DSM) flow patterns. As the intensity of the noise is increased further, the onset of the first instability becomes more complex. The measurement of the nonlinear onset time shows a strong dependence on the noise intensityQ, which is linear for WD and GP well above onset. The linear onset time shows an unexpected dependence on the noise intensity close to the onset of the first instability. For sufficiently long correlation times of the noise, a destabilization by noise is obtained.     

Intrinsic route to melt fracture in polymer extrusion: a weakly nonlinear subcritical instability of viscoelastic poiseuille flow

As is well known, the extrusion rate of polymers from a cylindrical tube or slit (a "die") is in practice limited by the appearance of "melt fracture" instabilities which give rise to unwanted distortions or even fracture of the extrudate. We present the results of a weakly nonlinear analysis which gives evidence for an intrinsic generic route to melt fracture via a weakly nonlinear subcritical instability of viscoelastic Poiseuille flow. This instability and the onset of associated melt fracture phenomena appear at a well-defined ratio of the elastic stresses to viscous stresses of the polymer solution.     

Chaos and algorithmic complexity

Our aim is to discover whether the notion of algorithmic orbit-complexity can serve to define chaos in a dynamical system. We begin with a mostly expository discussion of algorithmic complexity and certain results of Brudno, Pesin, and Ruelle (BRP theorems) which relate the degree of exponential instability of a dynamical system to the average algorithmic complexity of its orbits. When one speaks of predicting the behavior of a dynamical system, one usually has in mind one or more variables in the phase space that are of particular interest. To say that the system is unpredictable is, roughly, to say that one cannot feasibly determine future values of these variables from an approximation of the initial conditions of the system. We introduce the notions of restrictedexponential instability and conditionalorbit-complexity, and announce a new and rather general result, similar in spirit to the BRP theorems, establishing average conditional orbit-complexity as a lower bound for the degree of restricted exponential instability in a dynamical system. The BRP theorems require the phase space to be compact and metrizable. We construct a noncompact kicked rotor dynamical system of physical interest, and show that the relationship between orbit-complexity and exponential instability fails to hold for this system. We conclude that orbit-complexity cannot serve as a general definition of chaos.     

Coherent Excitation of Optical Oscillations in a Metal Nanosphere by a 2D Electric Current

We propose a new concept of localized surface plasmon polariton (SPP) mode excitation in a spherical nanoparticle, which utilizes a collective mechanism of dissipative instability in an adjacent 2D plasma carrying a DC electric current. We show that 2D DC current becomes unstable at optical frequencies when the drift velocity exceeds the speed of sound in the 2D plasma. Dissipative instability emerges as a result of self-consistent 2D plasma oscillations coupled to the electromagnetic modes of the nanosphere, the material of which is absorbing at given frequency (i.e., the dielectric permittivity Imε > 0), and instability is absent in the case of transparent material. We derive the dispersion equation for this dissipative instability by a self-consistent solution of the Maxwell equations for the electromagnetic modes and the hydrodynamic equations for the 2D plasma current. Our estimates demonstrate attainment of very high instability increments Imω ~ 10¹⁵ s^?1, which makes the proposed concept very promising for excitation of plasmonic nanoantennas.     

Soft fermi surfaces and breakdown of Fermi-liquid behavior

Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.     

To the theory of cyclotron instability of trapped alpha-particles in tokamak reactor

The authors analyse numerically the cyclotron thermonuclear instability accompanying the interaction of fast magneto-acoustic waves with trapped alpha-particles for a tokamak of circular cross-section. It is shown that the instability is caused mainly by the strongly trapped particles. The influence of the thermal spread of alpha-particles on the cyclotron instability of fast magneto-acoustic waves is investigated.     

Cathode Sheath Instability at Frequencies Near the Ion Plasma Frequency

We consider steady-state and nonstationary processes in a near-cathode region. Equations describing the plasma dynamics near a cathode at frequencies close to the ion plasma frequency are derived, and solutions of these equations for various zones of a discharge gap are found. A piecewise-uniform model of a cathode sheath is developed, which points out the possibility of an instability at a frequency slightly less than the near-cathode ion plasma frequency. The gas pressure effect on the instability threshold with respect to the discharge current is considered. The obtained results are in good agreement with the data of experimental studies of the cathode sheath in a hollow-cathode discharge.     

Secondary instabilities of hexagonal patterns in a Bénard-Marangoni convection experiment

We have identified experimentally secondary instability mechanisms that restrict the stable band of wave numbers for ideal hexagons in Bénard-Marangoni convection. We use "thermal laser writing" to impose long wave perturbations of ideal hexagonal patterns as initial conditions and measure the growth rates of the perturbations. For epsilon=0.46 our results suggest a longitudinal phase instability limits stable hexagons at a high wave number while a transverse phase instability limits low wave number hexagons.