Instability Threshold Research Articles

Disconjugacy of Eye Movements during Attempted Fixation: A Sufficient Marker for Amblyopia?

To investigate whether detection of disconjugacy of eye movements during attempted fixation, or interocular position instability, may serve as a single sensitive test for amblyopia. Binocular eye movements were recorded at 500 Hz using the EyeLink 1000 eye tracker (SR Research Ltd., Kanata, Ontario, Canada) and analyzed using EyeLink software and Matlab (MathWorks, Natick, MA, USA). Eight subjects (four amblyopes, one successfully treated amblyope, and three non-amblyopes: 7 - 44 years) were asked to fixate on a stationary cross subtending 0.5° at 57 cm. Interocular position instability was quantified by calculating the minimum area bivariate contour ellipse (BCEA) encompassing 68% of the difference between right and left eye position points during 20-second viewing epochs. For statistical analysis, BCEA values, as well as visual acuity and stereoacuity, were normalized by base-10 logarithm transformation. The amblyopic subjects with persistent vision loss (one anisometropic, two strabismic, one deprivation; uncorrected visual acuity range 20/60 - 20/300, corrected stereoacuity range nil-400 arcsec) showed significantly higher interocular position instability (larger 68% BCEAs) than the non-amblyopic subjects (uncorrected visual acuity range 20/20 - 20/800, corrected stereoacuities of 20 arcsec) and the successfully treated strabismic amblyope (to the 20/20 level of visual acuity and 70 arcsec of stereoacuity) during binocular viewing trials; p < 0.01. Interocular position stability was strongly correlated with stereoacuity (in that better stereoacuity was associated with lower 68% BCEAs; r = 0.95), but not with visual acuity (r = 0.20). Interocular position instability appears to differentiate amblyopic from non-amblyopic subjects and appears to improve after successful treatment. Interocular position instability may therefore prove to be a single sensitive test for the presence of amblyopia. As a difference measure, it is inherently less susceptible to head motion and calibration error, as well as to conjugate eye motion, and as such is expected to be somewhat immune to latent nystagmus. Interocular position instability may also be useful to guide treatment, especially in preverbal children, and to assess the efficacy of novel treatments. Further research is required to establish optimal interocular position instability thresholds and to determine how specific this measure is to amblyopia.

Chiral topographic instability in shrinking spheres

Many biological structures exhibit intriguing morphological patterns adapted to environmental cues, which contribute to their important biological functions and also inspire material designs. Here, we report a chiral wrinkling topography in shrinking core–shell spheres, as observed in excessively dehydrated passion fruit and experimentally demonstrated in silicon core–shells under air extraction. Upon shrinkage deformation, the surface initially buckles into a buckyball pattern (periodic hexagons and pentagons) and then transforms into a chiral mode. The neighbouring chiral cellular patterns can further interact with each other, resulting in secondary symmetry breaking and the formation of two types of topological network. We develop a core–shell model and derive a universal scaling law to understand the underlying morphoelastic mechanism and to effectively describe and predict such chiral symmetry breaking far beyond the critical instability threshold. Moreover, we show experimentally that the chiral characteristic adapted to local perturbation can be harnessed to effectively and stably grasp small-sized objects of various shapes and made of different stiff and soft materials. Our results not only reveal chiral instability topographies, providing fundamental insights into the surface morphogenesis of the deformed core–shell spheres that are ubiquitous in the real world, but also demonstrate potential applications of adaptive grasping based on delicate chiral localization.

Natural convection in a fluid saturating an anisotropic porous medium in LTNE: effect of depth-dependent viscosity

Thermal convection in a fluid saturating an anisotropic porous medium in local thermal nonequilibrium (LTNE) is investigated, with specific attention to the effect of variable viscosity on the onset of convection. Many fluids show a remarkable dependence of viscosity on temperature that cannot be neglected. For this reason, we take into account a fluid whose viscosity decreases exponentially with depth, according to Straughan (Acta Mech. 61:59–72, 1986), Torrance and Turcotte (J. Fluid Mech. 47(1):113–125, 1971). The novelty of this paper is to highlight how variable viscosity coupled with the LTNE assumption affects the onset of convection. A numerical procedure shows the destabilising effect of depth-dependent viscosity. Moreover, it comes out that the LTNE hypothesis makes the influence of viscosity more intense. Linear instability analysis of the conduction solution is carried out by means of the Chebyshev-tau method coupled to the QZ algorithm, which provides the critical Rayleigh number for the onset of convection in a straightforward way. The energy method is employed in order to study the nonlinear stability. The optimal result of coincidence between the linear instability threshold and the global nonlinear stability threshold is obtained. The influence of anisotropic permeability and conductivity, weighted conductivity ratio, and interaction coefficient on the onset of convection is highlighted.

Investigation on vibration parameters in aluminum finned tube arrays subjected to water cross flow

PurposePredicting the critical velocity is crucial at the instability threshold for shell and tube heat exchangers in order to prevent tube failure due to vibrations. In this study, the vibration response of an aluminum tube bundle subjected to water cross flow was analyzed experimentally. Aluminum tubes are preferred over steel tubes because of aluminum tubes' excellent corrosion resistance, ease of manufacture, and high thermal efficiency.Design/methodology/approachThe fluid elastic instability and vortex shedding mechanisms in a finned tube array of aluminum tubes with a base tube diameter of 19.05 mm and pitch of 34 mm were investigated. The current study considers parallel triangular finned tube arrays with fin heights of 3 mm and 6 mm with a uniform fin thickness and fin pitch. The plain tube array was tested to compare the finned tube array results. The tube vibration response was measured using an accelerometer mounted on the middle tube of the third row. In order to define the fluid elastic instability behavior of various tube arrays, the critical velocity at the instability threshold is measured. By finding the Strouhal number at the small peaks before instability, the vortex shedding behavior of the tube arrays is examined.FindingsThe results reveal that the critical velocity at instability for coarse finned tube arrays increases as the fin height increases. The effect of the tube material is evaluated by comparing the results with those previously reported for parallel triangular tube arrays made of steel. Finally, the occurrence of vortex shedding in a tube array is confirmed based on the Reynolds number and Strouhal number relationship. The instability constant K for the plain tube array of steel and aluminum material are 4.97 and 4.87, respectively.Originality/valueThis paper provides the research findings on the effect of fin height on coarse density finned tube array. This will add substantial knowledge to the literature in the field of fluid elastic instability and vortex shedding, which is needed for the safe functioning of shell and tube heat exchangers.

Stability Analysis of Double Diffusive Convection in Local Thermal Non-equilibrium Porous Medium with Internal Heat Source and Reaction Effects

Abstract The internal heat source and reaction effects on the onset of thermosolutal convection in a local thermal non-equilibrium porous medium are examined, where the temperature of the fluid and the solid skeleton may differ. The linear instability and nonlinear stability theories of Darcy–Brinkman type with fixed boundary condition are carried out where the layer is heated and salted from below. The D 2 {D^{2}} Chebyshev tau technique is used to calculate the associated system of equations subject to the boundary conditions for both theories. Three different types of internal heat source function are considered, the first type increases across the layer, while the second decreases, and the third type heats and cools in a nonuniform way. The effect of different parameters on the Rayleigh number is depicted graphically. Moreover, the results detect that utilizing the internal heat source, reaction, and non-equilibrium have pronounced effects in determining the convection stability and instability thresholds.

Scenario-free analysis of financial stability with interacting contagion channels

Financial stress tests that capture multiple interactions between contagion channels are conditional on specific, subjectively-imposed stress scenarios. Eigenvalue-based approaches, in contrast, provide a scenario-independent measure of systemic stability, but so far only handle a single contagion mechanism. We develop an eigenvalue-based approach that brings the best of both worlds, enabling the analysis of multiple interacting contagion channels without the need to impose a subjective stress scenario. Our model captures the solvency-liquidity nexus, which allows us to demonstrate that the instability due to interacting channels can far exceed that of the sum of the individual channels acting in isolation. The framework we develop is flexible and allows for calibration to the microstructure and contagion channels of real financial systems. Building on this framework, we derive an analytic stability criterion in the limit of a large number of institutions that gives the instability threshold as a function of the relative size and intensity of contagion channels. This analytical formula requires comparatively little data to elucidate the mechanisms that drive instability in real financial systems and thus complements the insights gained from traditional stress tests.

The onset of double diffusive convection in a rotating bi-disperse porous medium

It is well known that when a horizontal layer of fluid is heated from below, a thermal boundary layer of less dense and hot fluid rises up. When this boundary layer becomes unstable, convective motion in the fluid above sets in. Forecasting when instabilities take place is essential. When a salt dissolved in a fluid saturating a porous medium heated from below is considered, simultaneous mass diffusion and thermal diffusion occur. Unlike the diffusion of heat, the diffusion of salt can take place only through the fluid phase, so an additional physical effect has to be considered: the Soret effect, that is the mass flux created by a temperature gradient. In the present paper the onset of convection in a rotating layer of bi-disperse porous medium saturated by a binary fluid mixture, taking into account the Soret effect, is analysed. Linear stability analysis is performed in order to determine the instability thresholds for the onset of convection via a steady state (stationary convection) and via an oscillatory state (oscillatory convection). Nonlinear stability analysis is performed to obtain the global stability threshold with respect to the L^2-norm.

Optimization of Composite Cylindrical Shell Structures for Hydrostatic Pressure Loading

Abstract Deep-sea structures will collapse/implode under hydrostatic pressure when the structure dives below an instability threshold, leading to catastrophic failure. To better understand how the layup angle of composite cylindrical shells influences this instability threshold, this work explores how composite cylinders can achieve the highest (optimum) critical collapse pressure under hydrostatic loading conditions. To perform this analysis, a closed-form analytical cylinder buckling solution developed by previous work is used in conjunction with different cylindrical geometrical configurations and composite properties for glass, carbon, and intraply hybrid composite properties for woven and unidirectional structures. The results show that a composite structure's optimum layup configuration is unique to the structure's geometry and material system. However, general trends are observed for these different systems, such as how symmetric and asymmetric constructions place the axial-resistant layers near the neutral plane of the composite system. In addition, both constructions need an increase in shear-resistance layers as the L/D ratio decreases regardless of the material system. Lastly, the analytical approach presented in this work can be used to accurately determine the optimum layup angle for thin composite cylindrical structures that are subjected to external hydrostatic pressure.

Direct Measurement of the Return Current Instability in a Laser-Produced Plasma

Measurements were made of the return current instability growth rate, demonstrating its concurrence with nonlocal transport. Thomson scattering was used to measure a maximum growth rate of 5.1×10^{9} Hz, which was 3 times less than classical Spitzer-Härm theory predicts. The measured plasma conditions indicate the heat flux was nonlocal, and Vlasov-Fokker-Planck simulations that account for nonlocality reproduce the measured growth rates. Furthermore, the threshold for the return current instability was measured (δ_{T}=0.017±0.002) to be in good agreement with previous theoretical models.

Hot electron and x-ray generation by sub-ns kJ-class laser-produced tantalum plasma

This paper presents experimental investigation of temperature scaling and threshold of instability in hot electron and bremsstrahlung radiation from the interaction of sub-nanosecond and kilo-joule class laser pulses with a tantalum foil target at Prague Asterix Laser System. The laser intensity was varied between and W · cm−2 at the target focus. The energy distribution functions of electrons were measured by an angular array of magnetic spectrometers indicating the electron temperature in the range between 30 keV and 70 keV. The bremsstrahlung spectrum was characterized using a scintillator-based calorimeter. In particular, we show the laser-energy scaling of the total flux of hot electrons in the forward and backward directions with respect to the laser vector, the conversion efficiency of the laser energy to the energy carried by hot electrons, and the temperature of hot electrons as well as the unfolded bremsstrahlung temperature using a Monte Carlo code consistent with signals of the scintillator detector. The scaling shows that the electron flux increases discontinuously with increasing laser intensity from W · cm−2 with consequent instability in the production of hot electrons and bremsstrahlung radiation.

On Gait Stability: Correlations between Lyapunov Exponent and Stride Time Variability

Abstract Lyapunov exponent is a promising parameter to ascertain the stability of the human gait. In this work, we use a time-series model based on a second-order delay-system with inertial measurement units placed on the foot and wrist. Stability is analyzed in a localized sense, with the Lyapunov exponent computed in the temporal region between two heel-strike points, which are determined using a peak-detection algorithm. We have attempted to show correlations between variations in the stride time and stability of the gait under normal and abnormal conditions. In the latter case, we attach a weight on foot to emulate weakness. On comparison between both cases, we observe a statistical significance of p=0.0039 using Wilcoxon’s rank-sum test. Moreover, on observing the correlations between Lyapunov Exponent and Stride Time Variability, we notice a left-shift in the abnormal case, indicating a lower threshold for instability, with the Stride Time Variability being 0.07 as compared to 0.11 in the normal case.The results indicate that by exploiting the correlation between stride time variability and Lyapunov exponents, one can establish a threshold for gait stability.

Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains

Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. To this end, as illustrating examples, the instability dynamics of the N/2 mode in both the Fermi–Pasta–Ulam–Tsingou-α and -β chains under fixed boundary conditions are studied systematically. Applying the Floquet theory, we show that for both models the stability time T as a function of the perturbation strength λ follows the same behavior; i.e., , where λ c is the instability threshold. The dependence of λ c on N is also obtained. The results of T and λ c agree well with those obtained by the direct molecular dynamics simulations. Finally, the effect of instability dynamics on the thermalization properties of a system is briefly discussed.

Slow electron holes in the Earth's bow shock

We present analysis of about one hundred bipolar structures of positive polarity identified in ten quasi-perpendicular crossings of the Earth's bow shock by the Magnetospheric Multiscale spacecraft. The bipolar structures have amplitudes up to a few tenths of local electron temperature, spatial scales of a few local Debye lengths, and plasma frame speeds of the order of local ion-acoustic speed. We argue that the bipolar structures of positive polarity are slow electron holes, rather than ion-acoustic solitons. The electron holes are typically above the transverse instability threshold, which we argue is due to high values of the ratio ωpe/ωce between electron plasma and cyclotron frequencies. We speculate that the transverse instability can strongly limit the lifetime of the electron holes, whose amplitude is above a certain threshold, which is only a few mV/m in the Earth's bow shock. We suggest that electron surfing acceleration by large-amplitude electron holes reported in numerical simulations of high-Mach number shocks might not be as efficient in realistic shocks, because the transverse instability strongly limits the lifetime of large-amplitude electron holes at ωpe/ωce values typical of collisionless shocks in nature.

700 W single-frequency all-fiber amplifier at 1064 nm with kHz-level spectral linewidth

In this work, a single-frequency fiber amplifier with output power of 703 W was demonstrated at 1,064.4 nm in an all-fiber configuration. Cascaded Yb3+-doped fiber structure with different dopant concentration and hybrid 915/976 nm pump scheme were employed in power scaling stage to improve the gain saturation for higher transverse mode instability threshold. An overall optical efficiency of 67.5% was achieved at the maximum output power and the M2 was measured to be ∼1.4. A spectral linewidth of 2 kHz was obtained from the 703-W single-frequency laser. To the best of our knowledge, this is the first time that a single-frequency all-fiber amplifier with kHz-level spectral linewidth is achieved at such high output power.

Density inversion phenomenon in porous penetrative convection

Penetrative convection occurs in many natural phenomena where an unstable stratified fluid moves into a stable one. This topic is of interest in many research fields like, for example, in geophysics and astrophysics. In the present paper, on taking into account for quadratic density law, the onset of penetrative convection in a horizontal porous layer is investigated. For the problem at stake, since the principle of exchange of stabilities has been proved, the convection can occur only through a secondary stationary motion. The critical Rayleigh numbers for the onset of stationary convection have been found via the linear instability analysis of the conduction solution. Moreover, the nonlinear stability of the motionless state has been investigated via the energy method. Numerical simulations have been performed through Chebyshev-τ spectral method in order to analyse the behaviour of stability and instability thresholds with respect to the upper plane temperature.

Falling film on an anisotropic porous medium

The stability and dynamics of a falling liquid film over an anisotropic porous medium are studied using a one-domain approach. Our stability analysis shows a significant departure from the effective no-slip boundary condition in the isotropic case. Anisotropy does not affect the threshold of linear instability. However, a non-trivial dual effect of anisotropy on the film stability is observed depending on the permeability of the porous medium. This dual effect results from the net balance of the enhancement of viscous diffusion at the top Brinkman sublayer and the mitigation of viscous damping in the core Darcy sublayer. Three-equation models have been derived from the lubrication theory approximation in terms of the exact mass balance and averaged momentum balances in the porous and liquid layers. In the nonlinear regime, anisotropy has a dual effect by damping capillary waves at large permeabilities and enhancing them at low permeabilities. Anisotropy also affects wave speeds and shapes, modifies travelling-wave branches of solutions, affects the development of a time-periodic wavetrain by inlet forcing and alters the noise-driven dynamics of the flow. These effects result from the mitigation of mass exchange at the liquid–porous interface and the contribution of the cross-stream permeability in the Brinkman top sublayer to the viscous diffusion.

Threshold of transverse mode instability considering four-wave mixing.

In this work, the influence of four-wave mixing (FWM) effects on the transverse mode instability (TMI) is incorporated into the TMI model based on stimulated thermal Rayleigh scattering. The model is capable of analyzing the gain characteristics of different high-power fiber amplifiers, based on which the physical mechanism and functioning boundary of FWM are theoretically investigated. Consequently, a new TMI threshold formula is defined to resolve the inconsistencies in the previous TMI models. It is revealed that it is extremely necessary to consider the influence of FWM on TMI in ultra-large mode field laser systems.

Falling liquid films on a slippery substrate with variable fluid properties

We investigate the stability of a gravity-driven, thin, Newtonian liquid flowing on a uniformly heated slippery inclined plane. We construct a mathematical model of the flow that comprises the Navier–Stokes equation coupled with the equation of energy. While the rest of the boundary conditions are standard for thin-film problems, we apply a Navier slip boundary condition at the solid–liquid interface. We assume that the fluid thermophysical properties — density, dynamical viscosity, surface tension, and thermal diffusivity vary linearly with temperature as long as the change in temperature is small. In the analysis part, we follow the standard long-wave theory and construct a nonlinear evolution equation for the film thickness. This is followed by a linear and weakly nonlinear stability analysis. The linear analysis allows us to compute the critical Reynolds number of our problem and from this study, we conclude that the slippery substrate destabilizes the film flow. The weakly nonlinear stability analysis finds a finer description of various stable/unstable zones. Finally, we perform a numerical simulation of the evolution equation in a periodic domain using spectral methods. Our numerical results support the analytical predictions of the instability threshold using the linear and weakly nonlinear theories. The influence of the small Biot number is also investigated in presence of the slip length together with the variable fluid properties.

On anomalous microwave scattering in the edge transport barrier in O-mode ECRH and CTS experiments

We investigate the induced scattering parametric decay instability of ordinary microwaves leading to excitation of lower hybrid or electron plasma waves localized within a tokamak edge transport barrier. Numerical estimates of the instability threshold and growth rate for this scenario are given for the conditions of O1-mode ECRH at ITER and O2-mode ECRH and CTS experiments at ASDEX Upgrade, where investigation of these phenomena is shown to be possible.

Low-numerical aperture confined-doped long-tapered Yb-doped silica fiber for a single-mode high-power fiber amplifier.

A low-numerical aperture (NA) confined-doped long-tapered (LCT) Yb-doped fiber is proposed and fabricated by modified chemical vapor deposition combined with solution doping technique. The LCT fiber owns the core NA of ∼0.05 and the gain dopant doping diameter ratio of ∼77%, with a core/cladding diameter of 25/400 µm at both ends and 37.5/600 µm in the middle. The laser performance is demonstrated by a bidirectional pumping all-fiber amplifier, of which a 4.18-kW single-mode (M2 factor ∼1.3) laser output is achieved with a slope efficiency of ∼82.8%. Compared with the conventional fiber, the co-pumped and counter-pumped transverse mode instability thresholds and beam quality of the LCT fiber are remarkably enhanced. Throughout the continuous operation, the LCT fiber amplifier presents high power stability with fluctuation of < 1%. These results indicate that LCT fiber has great potential in power scaling remaining excellent beam quality.