Kind Of Instability Research Articles

The electronic structure and the phases of [formula omitted

BaVS 3 is a moderately correlated d-electron system with a rich phase diagram. To construct the corresponding minimal electronic model, one has to decide which d-states are occupied, and to which extent. The ARPES experiment presented here shows that the behavior of BaVS 3 is governed by the coexistence of wide-band ( A 1 g ) and narrow-band (twofold degenerate E) d-electrons. We sketch a lattice fermion model which may serve as a minimal model of BaVS 3 . This serves foremost for the understanding of the metal–insulator in pure BaVS 3 and its absence in some related compounds. The nature of the low-temperature magnetic order differs for several systems which may be described in terms of the same electron model. We describe several recent experiments which give information about magnetic order at high pressures. In particular, we discuss field-induced insulator-to-metal transition at slightly subcritical pressures, and an evidence for magnetic order in the high-pressure metallic phase. The phase diagram of Sr-doped BaVS 3 is also discussed. The complexity of the phases of BaVS 3 arises from the fact that it is simultaneously unstable against several kinds of instabilities.

Physical interpretation of unstable modes of a linear shear flow in shallow water on an equatorial beta-plane

Unstable modes of a linear shear flow in shallow water on an equatorial $\beta$-plane are obtained over a wide range of values of a non-dimensional parameter and are interpreted in terms of resonance between neutral waves. The non-dimensional parameter in the system is $E \,{\equiv}\, \gamma^{4} / (gH\beta^{2})$, where $\gamma$, $g$, $H$ and $\beta$ are the meridional shear of basic zonal flow, gravitational constant, equivalent depth and the north–south gradient of the Coriolis parameter, respectively. The value of $E$ is varied within the range $-2.50 \,{\le}\,\log E \,{\le}\,7.50$.The problem is solved numerically in a channel of width $5\gamma/\beta$. The structures of the most unstable modes, and the combinations of resonating neutral waves that cause the instability, change according to the value of $E$ as follows. For $\log E \,{<}\, 2.00$, the most unstable modes have zonally non-symmetric structures; the most unstable modes for $\log E \,{<}\, 1.00$ are caused by resonance between equatorial Kelvin modes and continuous modes, and those for $1.00 \,{\le}\,\log E \,{<}\, 2.00$ are caused by resonance between equatorial Kelvin modes and westward mixed Rossby–gravity modes. The most unstable modes for $\log E \,{\ge}\, 2.00$ have symmetric structures and are identical with inertially unstable modes. Examinations of dispersion curves suggest that non-symmetric unstable modes for $1.00 \,{\le}\,\log E \,{<}\, 2.00$ and inertially unstable modes for $\log E \,{\ge}\, 2.00$ are the same kind of instability.

Direct observation of a precursor in a complex system

A precursor is a kind of instability in a nonequilibrium system observed prior to a bifurcation. It has been observed in important natural phenomena such as earthquakes and epileptic seizures. In most cases just qualitative results were reported, with the exception of some quantitative observations of noisy precursors. We report the observation of precursors excited by a deterministic perturbation. Quantitative characterization of this type of precursor is important in predicting a bifurcation in advance. This predicting ability comes from a dynamical structure present on the perturbed system.

Traitement arthroscopique de l'instabilité glénohumérale antérieure

Arthroscopic treatment of anterior shoulder instability is now well defined but its learning curve remains long. This technique should only be used for a certain kind of instability. Surgical gesture should be acquired such as the different devices that are proposed. Arthroscopic techniques are still in progress and results are improving with the selection of patient who could benefit by it.

Measurement of fluctuations in the supersonic poloidal flow driven by a hot cathode

The density and potential fluctuations were measured in hot-cathode biasing plasma at the Tohoku University Heliac. In the improved mode, high-frequency fluctuations (>100 kHz) appeared in the density signal. On the other hand, low-frequency fluctuations (<100 kHz) in the density and potential signals were suppressed. The characteristics of high-frequency fluctuation were compared with three kinds of instability, and they were consistent with those of the flute instability driven by the supersonic poloidal rotation. The suppression of low-frequency fluctuations in improved mode is considered the effect of E × B poloidal rotation or its shear. The profile of the anomalous particle flux was estimated by analysing the low-frequency fluctuation signals. The flux decreased in the improved mode in most of the region, although the decrease in flux was small near the rational surface (n/m = 5/3).

Metallic State of the Three-Band Hubbard Model with Super-Lattice Structure

We investigate the dynamical superlattice correlation in the two-dimensional three-band Hubbard model on the basis of the unrestricted fluctuation exchange approximation. We calculate the one-particle spectral function, the spin correlation function and the charge correlation function at finite temperature. We find that some experimental results can be reproduced consistenly by taking inhomogenous distribution of Cu 3d electrons into account. The correlation functions suggest that several kinds of instabilities with spatial inhomogenieties exist in some regions, where these instabilities significantly affect the one-particle spectral fuctions.

Discrete breathers in two-dimensional anisotropic nonlinear Schrödinger lattices

We study the structure and stability of discrete breathers (both pinned and mobile) in two-dimensional nonlinear anisotropic Schrödinger lattices. Starting from a set of identical one-dimensional systems we develop the continuation of the localized pulses from the weakly coupled regime (strongly anisotropic) to the homogeneous one (isotropic). Mobile discrete breathers are seen to be a superposition of a localized mobile core and an extended background of two-dimensional nonlinear plane waves. This structure is in agreement with previous results on one-dimensional breather mobility. The study of the stability of both pinned and mobile solutions is performed using standard Floquet analysis. Regimes of quasi-collapse are found for both types of solutions, while another kind of instability (responsible for the discrete breather fission) is found for mobile solutions. The development of such instabilities is studied, examining typical trajectories on the unstable nonlinear manifold.

Parameter study on Kelvin–Helmholtz instability in solar wind type flowing structures

The stability behaviour of the wave modes that propagate in the solar wind plasma is considered in the framework of the Hall-magnetohydrodynamics. The Hall-MHD theory extends the wave frequency limit up to or higher than the ion cyclotron frequency. Due to the different flow velocities of the adjacent media in the solar wind, a Kelvin–Helmholtz instability is naturally expected to arise. The behaviour of the wave modes due to this particular kind of instability is studied under solar wind conditions typical for 1 AU. This is a preliminary study on the stability problem in the solar wind flowing structures and it could be relevant for the interplanetary and space weather research.

The integrated and local estimations of instability for a class of autonomous delay systems

Abstract The Lyapunov stability of a partly nonlinear delay system is investigated both analytically and numerically for the sake of calculation of (i) integrated and (ii) local estimates. The improvement of numerical scheme for calculation of characteristic exponents is achieved within the integrated analysis and the properties of mutual similarity of the internal product are proved. At the local instabilities investigation, two kinds of instability for the delay system with high-power nonlinearity are detected. The intermittency of the chaotic behavior is also explored numerically and analogy with hydrodynamic turbulence is shown.

Cold Gas Simulations of the Influence of Inhibitor Shape in Combustor Combustion

A cold-gas setup is used to analyze the internal acoustic response of small-scale solid propellant rocket motors. These motors are characterized by a forward, a central, and an aft segment, with nonablative inhibitors on the last segment forward face. Investigations have been carried out with four inhibitors with different protrusions and shapes, each leading to specific pressure oscillation behavior. The cold-flow setup has been designed to reproduce the general features of the internal geometry of the combustors corresponding to two burning times. It is found that pressure measurements reproduce the acoustic response of firing tests with satisfactory agreement. Velocity fluctuations are used to analyze vortex-shedding-driven pressure oscillations. Measurements in the shear layer generated downstream from the inhibitors and in the vicinity of the injecting wall allow identification of the development of two vortex fields. Experiments with small inhibitors show the development of only one kind of instability, combining the vortex development of the shear layer with an effect of vorticity amplification due to the wall injection. Finally, an estimation of the convection velocity is proposed to explain resonance frequency evolution during the combustion.

A numerical method for the computation of bifurcation points in fluid mechanics

Two original algorithms are proposed for the computation of bifurcation points in fluid mechanics. These algorithms consist of finding the zero values of a specific indicator. To compute this indicator a perturbation method is used which leads to an analytical expression of this indicator. Two kinds of instability are considered: stationary and Hopf bifurcations. To prove the efficiency and advantages of such numerical methods several numerical tests are discussed.

The coupling instability of Rossby and topographic Rossby waves in the equatorial area

In case of considering the fact that the tropical ocean thermocline or the lower atmosphere height field has the meridional variation, the topographic Rossby wave will be excited. Also the background geostrophic current emerges. Under such conditions, the topographic Rossby wave can interact with the classical Rossby wave at some parameter band and thus brings a new kind of instability, which may be of potential application in understanding some phenomena of the ENSO cycle.

Vertical stability of bubble chain: Multiscale approach

Linear stability is investigated of a uniform chain of equal spherical gas bubbles rising vertically in unbounded stagnant liquid at Reynolds number Re = 50–200 and bubble spacing s > 2.6 bubble radii. The equilibrium bubble positions are questioned for their stability with respect to small displacements in the vertical direction, parallel to the chain motion. The transverse displacements are not considered, and the chain is assumed to be laterally stable. The bubbles are subjected to three kinds of forces: buoyant, viscous, inviscid. The viscous and inviscid forces have both pairwise (local) and distant (nonlocal) components. The pairwise forces are expressed by the leading-order formulas known from the literature. The distant forces are expressed as a linear superposition of the pairwise forces taken over several farther neighbours. The stability problem is addressed on three different length scales corresponding to: discrete chain (microscale), continuous chain (mesoscale), bubbly chain flow (macroscale). The relevant governing equations are derived for each scale. The microscale equations are a set of ODE’s, the Newton force laws for the individual discrete bubbles. The mesoscale equation is a PDE for bubbles continuously distributed along a line, obtained by taking the continuum limit of the microscale equations. The macroscale equations are two PDEs, the mass and momentum conservation equations, for an ensemble of noninteracting mesoscale chains rising in parallel. This transparent two-step process (micro → meso → macro) is an alternative to the usual one-step averaging, in obtaining the macroscale equations from microscale information. Here, the scale-up methodology is demonstrated for 1D motion of bubbles, but it can be used for behaviour of 2D and 3D lattices of bubbles, drops, and solids. It is found that the uniform equilibrium spacing results from a balance between the attractive and repulsive forces. On all three length scales, the equilibrium is stabilized by the viscous drag force, and destabilized by the viscous shielding force ( shielding instability). The inviscid forces are stability neutral and generate conservative oscillations and concentration waves. The stability region in the parameter plane s − Re is determined for each length scale. The stable region is relatively small on the microscale, larger on the mesoscale, and shrinks to zero on the macroscale where the bubbly chain flow is inherently unstable. The shielding instability is expected to occur typically in intermediate Re flows where the vertical bubble interactions dominate over the horizontal interactions. This new kind of instability is studied here in a great detail, likely for the first time. Its relation to the elasticity properties of bubbly suspension on different length scales is discussed too. The shielding force takes the form of a negative bulk modulus of elasticity of the bubbly mixture.

Thermodynamic instabilities of a binary mixture of sticky hard spheres

The thermodynamic instabilities of a binary mixture of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA) and the Percus-Yevick (PY) approximation are investigated using an approach devised by Chen and Forstmann [corrected] [J. Chem. Phys. [corrected] 97, 3696 (1992)]. This scheme hinges on a diagonalization of the matrix of second functional derivatives of the grand canonical potential with respect to the particle density fluctuations. The zeroes of the smallest eigenvalue and the direction of the relative eigenvector characterize the instability uniquely. We explicitly compute three different classes of examples. For a symmetrical binary mixture, analytical calculations, both for mMSA and for PY, predict that when the strength of adhesiveness between like particles is smaller than the one between unlike particles, only a pure condensation spinodal exists; in the opposite regime, a pure demixing spinodal appears at high densities. We then compare the mMSA and PY results for a mixture where like particles interact as hard spheres (HS) and unlike particles as SHS, and for a mixture of HS in a SHS fluid. In these cases, even though the mMSA and PY spinodals are quantitatively and qualitatively very different from each other, we prove that they have the same kind of instabilities. Finally, we study the mMSA solution for five different mixtures obtained by setting the stickiness parameters equal to five different functions of the hard sphere diameters. We find that four of the five mixtures exhibit very different type of instabilities. Our results are expected to provide a further step toward a more thoughtful application of SHS models to colloidal fluids.

Dynamic behavior of a liquid metal interface under the influence of a high-frequency magnetic field

We present experimental results on the stability of a free liquid metal surface influenced by an alternating magnetic field. The field is generated by an inductor fed by a high-frequency electrical current. The experimental setup consists of an annulus filled with the liquid metal galinstan. We observe three kinds of instabilities: exciting of capillary waves, a static high-amplitude surface deformation, and eventually an electromagnetic pinch at a critical inductor current I(cp). The data show that I(cp) correlates directly with the current frequency and the geometric parameters.

Instability phenomena during the conical expansion of circular cylindrical shells

Pushing a conical die into a tube is a forming process that is suitable for changing the shape of a thin cylindrical tube into that of a conical shell. The degree of expansion that is achievable without destroying the tube is limited by two mechanisms: (a) loss of global stability due to elasto-plastic ‘Concertina’ buckling of the straight part of the tube, and (b) diffuse necking caused by local loss of material stability in the conical part of the tube. The former mechanism is characterized by a periodic buckling pattern, that is similar to the one observed in typical crash elements, while the latter mechanism leads to the formation of periodic necks and subsequent failure by strain localization and rupture. In this study experimental evidence for both kinds of instabilities is presented along with corresponding simulation results obtained with the finite element method. For long tube specimens ‘Concertina’ buckling was found to be the dominant instability mode while for short tube specimens failure by necking and rupture occurred. The critical circumferential strain for the onset of necking at the expanding tube end was markedly higher than the one expected from uniaxial tension results. This finding is attributed to the supporting effect of the tube sections that are subjected to lower strains.

Combustion Modes and Reaction Paths of the Self-Sustained High-Temperature Synthesis of Intermetallic Compounds: A Computer Simulation Study of the Effect of Exothermicity

The effect of the thermodynamic aspects on the SHS of intermetallic compounds is investigated by computer simulation using an heterogeneous model. The exothermicity of the process is explored by changing heat of formation of the solid compound and mixing enthalpy in the liquid phase, while the kinetics is left unmodified. Different dynamic behaviors have been identified: steady propagation, pulsed propagation, extinction. Two different kinds of instabilities are shown: longitudinal instabilities and transversal instabilities. The ranges of existence of these two dynamic behaviors appear to be mutually exclusive. The occurrence of different dynamic behaviors is related to the predominant process taking place in the different cases.

The escaping disaster: A problem related to state-dependent delays

We study a second order state-dependent delay equation with an in general unbounded delay that describes an idealized one-dimensional motion. Although governed by a negative feedback mechanism, the set of equilibria, formed by the so called constant velocity solutions, is unstable and a new kind of instability, called the escaping instability, evolves.

The Breakdown of Migdal's Theorem and the Divergence of Electron Polarizations in HTSC

We assume that Fermi surface nesting is a common feature in all oxide high temperature superconductors (HTSC) of perovskite or layered-perovskite structure. We show that this feature results in the breakdown of the Migdal's theorem, and the singularity of some electronic polarizations. These singularities trigger various kinds of instabilities in these materials.

Dielectric spectroscopy of concentrated cosmetic W/O‐emulsions: possibilities to distinguish product changes caused by coalescence, sedimentation and variation of ingredients

A quick result whether a newly developed cosmetic water-in-oil (W/O)-emulsion shows constant sensory behavior (stable) or whether it changes its behavior over time (instable) is an important aspect in cosmetic research. In order to observe changes as quickly as possible, analytic methods are used. An established method is rheology, a sensitive method that gives direct information on sensory aspects. Additional information concerning the kind of instability allows a more focused improvement of formulation in the case of instabilities. In order to gain this information, an additional analytic method with a more ingredient specific focus is needed. In this article, the possibilities of using dielectric spectroscopy in order to get additional information are discussed. For concentrated W/O-emulsions a dependence of emulsion behavior from volume median droplet diameter d(v50) is visible by both methods: rheology and dielectric spectroscopy. A variation of droplet size distribution at constant volume median droplet diameter d(v50) does not change the results for the examined emulsions. Quantitative information about mean droplet size is possible with calibration. Because of their different physical forci, rheology and dielectric spectroscopy complement each other in high-sensitive detection of coalescence. In contrast to the mechanical properties of W/O-emulsion, dielectric spectroscopy gives additional information concerning some reasons of change in emulsion structure. Mechanism like sedimentation and coalescence can be distinguished and the phase where changes take place (oil phase or water phase) can be located. The latter is possible by a new parameter - the correlation between maximum of dielectric loss epsilon''(f(R)) and the relaxation frequency f(R). Their correlation can be described by a simple power law. By coupling rheology and dielectric spectroscopy, an improvement in fast emulsion development and production control may be achieved without losing the advantage of a quick and easy measurement procedure.