Unstable Band Research Articles

Discussing the limitations of unconditional stability indicators in evaluating thermoacoustic quality of burners with flames

Assessing the thermoacoustic performance of designed combustors, with a focus on the stability quality factor, is crucial. Thermoacoustic instability in combustion appliances arises from intricate interactions among unsteady combustion, heat transfer, and (maybe) acoustic modes within the system. Accurate prediction of system stability requires modeling all components, including the burner with flame. Traditionally, the burner in the presence of combustion is represented as an acoustically (active) two-port block with passive upstream and downstream acoustic terminations. The dispersion relation of the thermoacoustic system is commonly used for anticipating eigen-frequencies and assessing stability. However, practical scenarios often lack specific information about upstream and downstream terminations during development. This raises a critical question: How can the thermoacoustic performance of burners and their associated flames be evaluated without specified acoustics? This article addresses this question by exploring the concept of unconditional stability in a generic two-port thermoacoustic system. The unconditional stability criteria have been used as quality indicators in designing electrical devices. This rich toolbox has been introduced in thermoacoustics. We first scrutinize assumptions underlying two most known unconditional stability-based criteria called [Formula: see text] and [Formula: see text] factors, connecting them to the general thermoacoustic problems. Then, the application of these criteria in assessing the thermoacoustic quality of burners with flames are discussed. This investigation revealed that while they are able to accurately predict the histogram of unstable frequencies and critical frequency bands, their use as reliable indicators to assess thermoacoustic quality in burners are not recommended due to their mathematical limitations and high level of conservatism of these factors.

Optimization Design of Phononic Crystals Based on BPNN‐MPA in Applied Mathematical Analysis

Traditional finite element analysis methods have the problem of expensive and unstable band structure diagram calculation when generating phononic crystals. Therefore, this study combines back propagation neural networks with ocean predator algorithms to optimize the geometric structure of phononic crystals. The results show that the coefficient of determination for the predicted bandgap width and lower bound of Model 3 is 1.00, which is better than the comparison model. However, Models 2 and 5 have poor predictive performance for bandgap width due to overfitting during actual training. Therefore, after using the ocean predator algorithm for hyperparameter adjustment, it is found that the maximum number of failures in the validation set of Model 5 is 30, the number of hidden layer nodes is 30, and after 500 experiments, the average error of the bandgap width is 5.26%, and the average error of the lower bound of the bandgap is 1.33%. The average error of the bandgap width after hyperparameter adjustment is 4.89%, and the average error of the lower bound of the bandgap is 1.21%, both of which are effectively reduced and better than the comparison model. Overall, the combination model has high computational efficiency and stability in phononic crystal optimization and can be practically applied in the design and optimization of phononic crystal geometric structures.

Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics

This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion effect is presented. The findings demonstrate that the self-steepening effect may also produce an asymmetric unstable frequency band. Combined with the modulation instability, the rogue wave, rational soliton and mixed interaction of localized waves have a quantitative relationship with plane-wave parameters. Various exact solutions can be accurately located and obtained according to the generalized Darboux transformation. The asymptotic analysis of rational solutions demonstrates the state transition of higher-order rogue waves. This paper illustrates the significance of modulation instability for studying the integrable systems by the Darboux transformation. It is a new guidance to solve the difficulty of exact excitation of asymmetric localized waves in complex integrable systems. The results have prospective applications and references for the emergence, amplification and compression of asymmetric pulses in optical experiments.

Coexistence of stationary Görtler and crossflow instabilities in boundary layers

The coexistence of stationary Görtler and crossflow instabilities in boundary layers covering incompressible to hypersonic regimes is investigated by varying the local sweep angle, pressure gradient, wall curvature, and wall temperature using linear stability analysis. The results show that increasing the local sweep angle under a fixed concave curvature in incompressible boundary layers leads to the appearance of two unstable modes at certain sweep angles, which is conventionally known as the “changeover” regime between the crossflow and Görtler modes. This study identifies a synchronization between the two modes under this condition, which is similar to multiple Görtler modes and thus referred to as Görtler–crossflow modes. Three scenarios are presented to describe the possible development of these modal instabilities. In addition, increasing the concave curvature destabilizes the instability, while introducing a pressure gradient stabilizes the instability and results in a shrinkage of the unstable band of the spanwise wavenumber, as reported in the literature. In supersonic and hypersonic boundary layers, synchronization can occur near specific sweep angles and under cold wall conditions in supersonic boundary layers. As Mach number increases, the synchronization regime shifts toward lower sweep angles and wall temperature, in which the former reflects a decline in crossflow strength relative to Görtler instability, while the latter indicates the influence of thermal effects on synchronization. In hypersonic boundary layers, the crossflow instability is insignificant compared with the Görtler instability. No synchronization is identified under various parameter changes, and the first Görtler–crossflow mode dominates across the entire spanwise wavenumber ranges.

In-situ compression with acoustic emission detection of high pressure torsion deformed Cu38Zr54Al8 metallic glass micropillars

In-situ compression of Cu38Zr54Al8 metallic glass micropillars in a scanning electron microscope was performed together with continuous acoustic emission recording on samples in the as-cast state and after pre-deformation by high pressure torsion. A size effect was detected in both shear band operation and acoustic emission signal, irrespective of the preliminary deformation. This phenomenon was explained by the size dependent compliance of the pillar/indenter system. Differences between acoustic emission signals from the as-cast and pre-deformed states indicated changes in the shear band formation mechanism due to high pressure torsion. These differences were clear in the elastic regime of the in-situ compression and supported the role of rejuvenation in stabilization of unstable shear bands.

A Hot-Wire Anemometer with Automatically Adjusted Dynamic Properties for Wind Energy Spectrum Analysis

Hot-wire anemometric measurements are often related to the determination of flow parameters in a high frequency range. Such knowledge is particularly important when analyzing the flow phenomena in the vicinity of wind turbines. The reliability of obtained results is determined by the knowledge of the properties of the system used for measurements. It concerns both the static and dynamic characteristics of individual measurement channels. In studies of hot-wire anemometric systems, a problem related to the unstable transmission bands of such systems and their high dependence on measurement conditions and the system configuration itself has been commonly indicated. This paper presents the results of an investigation of a new type of hot-wire anemometer, allowing for automatic adjustment of its dynamic characteristics under real working conditions. The presented system is dedicated to the analysis of the wind energy spectrum in experimental laboratory tests on reduced-scale models and to specialized in situ measurements.

Four-wave mixing and coherently coupled Schrödinger equations: Cascading processes and Fermi-Pasta-Ulam-Tsingou recurrence.

Modulation instability, breather formation, and the Fermi-Pasta-Ulam-Tsingou recurrence (FPUT) phenomena are studied in this article. Physically, such nonlinear systems arise when the medium is slightly anisotropic, e.g., optical fibers with weak birefringence where the slowly varying pulse envelopes are governed by these coherently coupled Schrödinger equations. The Darboux transformation is used to calculate a class of breathers where the carrier envelope depends on the transverse coordinate of the Schrödinger equations. A "cascading mechanism" is utilized to elucidate the initial stages of FPUT. More precisely, higher order nonlinear terms that are exponentially small initially can grow rapidly. A breather is formed when the linear mode and higher order ones attain roughly the same magnitude. The conditions for generating various breathers and connections with modulation instability are elucidated. The growth phase then subsides and the cycle is repeated, leading to FPUT. Unequal initial conditions for the two waveguides produce symmetry breaking, with "eye-shaped" breathers in one waveguide and "four-petal" modes in the other. An analytical formula for the time or distance of breather formation for a two-waveguide system is proposed, based on the disturbance amplitude and instability growth rate. Excellent agreement with numerical simulations is achieved. Furthermore, the roles of modulation instability for FPUT are elucidated with illustrative case studies. In particular, depending on whether the second harmonic falls within the unstable band, FPUT patterns with one single or two distinct wavelength(s) are observed. For applications to temporal optical waveguides, the present formulation can predict the distance along a weakly birefringent fiber needed to observe FPUT.

Effect of Different Fuels on Combustion Instabilities in an Annular Combustor

Abstract Combustion instability in annular combustors of jet engines is a recurring issue. In this study, the characteristics of instabilities for different fuels are investigated by combining the instability maps obtained in a laboratory-scale annular combustor equipped with multiple swirling spray injectors (MICCA-spray) and flame describing functions (FDFs) from a single sector configuration (SICCA-spray). Two types of liquid fuels are injected as hollow cone sprays: heptane, which is fairly volatile, and dodecane, which is less volatile. Experiments are also conducted with gaseous propane, perfectly premixed with air, which serves as a reference. An instability map is systematically drawn by varying the global equivalence ratio and thermal power. The data indicate that the amplitude and frequency of instabilities depend, for the same operating point, on the fuel injection conditions (premixed or spray) and fuel type. Overall trends show that premixed propane is unstable in a broad operating domain. Injection of liquid fuels induces changes in flame time lag that modifies the unstable regions. For heptane, the instability map is closer to the propane reference map, whereas dodecane exhibits wider stable regions. An attempt is made to understand these features by examining the FDF, which gives the ratio of relative fluctuations in heat release rate to the relative fluctuations in velocity. The FDFs measured in a single sector configuration give access to gain and phase information that can be used to determine unstable bands and calculate an instability index guiding the interpretation of the differences in instabilities of the three fuels.

Effect of Phosphorus Doped Poly Annealing on Threshold Voltage Stability and Thermal Oxide Reliability in 4H-SiC MOSFET

We have investigated the effect of high temperature annealing of phosphorus doped poly on gate oxide integrity and device reliability. In NMOS capacitance analysis, unstable flat band voltage characteristics and lower oxide breakdown electric field were observed in wafers which received high temperature poly annealing at 1100 °C. Gate oxide integrity (GOI/Vramp) tests and time dependent dielectric breakdown (TDDB) tests were performed to evaluate wafer level reliability. Degraded GOI characteristics and poor gate oxide lifetime were obtained for the high temperature poly annealed condition. To evaluate package level reliability, high temperature gate bias (HTGB) stress tests were conducted. Some samples failed in positive gate bias stress and more severe negative threshold voltage shift was observed in negative gate bias stress for the high temperature poly annealed condition.

Atomic elastic stiffness analysis to predict twinning in Fe single crystal under shear

As a series study that discusses local instability by atomic elastic stiffness, Bija=Δσia/Δεj, molecular dynamics simulations of simple shear on Fe perfect lattice are performed to discuss twin deformation. In the simulation of extremely low temperature of 0.1K, many twin boundaries are nucleated in a periodic slab cell of stacked (1¯1¯2) planes just after the stress drop or elastic limit under shear. The 1st eigenvalue ηa(1) of the 6×6 matrix Bija shows fluctuation in each (1¯1¯2) planes just before the elastic limit. At the stress-strain peak, ηa(1)<0 or unstable layers emerge and twin deformation occurs at these unstable “band” in the simulation cell. The period of the ηa(1) fluctuation is almost constant even if the cell size is expanded in the [1¯1¯2] and [11¯0] direction, while the unstable band arrays tilt normal to the diagonal line of the simulation cell, under the cell expansion in the [111] direction. At the elevated temperature of 300K, the simultaneous periodic band never appears but a few unstable bands appear locally in time sequence and bring twinning there.

Superconducting transition in a non-superconducting PrBa2Cu3O7 film triggered by interfacial carrier injection

The discovery in 1986 of high-temperature superconductivity in cuprates above liquid nitrogen temperature brought about a new chapter in high-temperature superconductivity research, bringing applications that bit closer. However, how to further improve the superconducting transition temperature of high-temperature superconductors is a huge challenge in condensed matter physics and materials science. Recently, interface-enhanced high-temperature superconductivity in one-unit-cell FeSe film on a SrTiO3 substrate has created a new avenue for improving the superconducting transition temperature. Here, a transition from an originally non-superconducting state to a superconducting state triggered by the interfacial injection of charge carriers was observed in a PrBa2Cu3O7/Nb-doped SrTiO3 heterostructure, and the non-superconducting to superconducting transition temperature increases with increase in the injection current. Current–voltage characteristics indicate that several conduction mechanisms coexist. In the proposed mechanism, the injected electrons are self-trapped in an unstable quasiconduction band which has a direct influence on the intrinsic properties, such as resistance and superconductivity, of the PrBa2Cu3O7 film. Our findings offer an alternative strategy for manipulating the superconducting state in oxides by the injection of charge carriers through the oxide interfaces, and can also help us to understand the mechanism of high-temperature superconduction.

Characterization of velocity fluctuations and the transition from transient to steady state shear banding with and without pre-shear in a wormlike micelle solution under shear startup by Rheo-NMR

AbstractRheo-NMR velocimetry was used to study shear banding of a 6 wt.% cetylpyridinium chloride (CPCl) worm-like micelle solution under shear startup conditions with and without pre-shear. 1D velocity profiles across the fluid gap of a concentric cylinder Couette shear cell were measured every 1 s following shear startup for four different applied shear rates within the stress plateau. Fitting of the velocity profiles allowed calculation of the shear banding characteristics (shear rates in the high and low shear band, the interface position and apparent slip at the inner rotating wall) as the flow transitioned from transient to steady state regimes. Characteristic timescales to reach steady state were obtained and found to be similar for all shear banding characteristics. Timescales decreased with increasing applied shear rate. Large temporal fluctuations with time were also observed and Fourier transform of the time and velocity autocorrelation functions quantified the fluctuation frequencies. Frequencies corresponded to the elastically driven hydrodynamic instabilities,i.e.vortices, that are known to occur in the unstable high shear band and were dependent upon both applied shear rate and the pre-shear protocol.

Asymmetric effect of static radial eccentricity on the vibration characteristics of the rotor system of permanent magnet synchronous motors in electric vehicles

Considering static radial eccentricity, a Jeffcott rotor model is established for the rotor system of the permanent magnet synchronous motors in electric vehicles. The system conservative force, including unbalanced magnetic pull, which results in nonlinearity is analyzed, and center manifold theorem and Lyapunov method are used to determine the stabilities of multiple equilibrium points. This analysis shows that static eccentricity spoils the symmetry of the equilibrium points, although they are distributed in the line along the direction of the static eccentricity. This asymmetry leads to the pitchfork bifurcation of equilibrium points to a generic bifurcation with a defect. This analysis provides two stability conditions for the rotor system. Furthermore, the effect of the asymmetry on the dynamic characteristics that can induce backward whirling motion coupled with forward whirling motion is quite different from the case without static eccentricity. These characteristics are investigated by multi-scale method. As a result, the analytical solution of the system at steady state is obtained. The frequency characteristics of the main resonance are analyzed, and the stability of the solution is determined using Routh–Hurwitz criterion and the geometric constraint of the rotor whirling motion. The characteristics reveal that a globally unstable frequency band appears due to the geometric constraint. However, this frequency band narrows and even vanishes with increases in damping and electromagnetic stiffness and decreases in mass imbalance, mechanical stiffness and static eccentricity. The analysis by multi-scale method is based on the assumption of the time invariance of the forward and backward whirling amplitudes, which is validated by the numerical method. The results of the two methods agree well, which indicates that this assumption and the analysis are reasonable.

Pattern formation for a two-dimensional reaction-diffusion model with chemotaxis

This paper is devoted to study the formation of stationary patterns for a chemotaxis model with nonlinear diffusion and volume-filling effect over a bounded rectangular domain. By using linear stability analysis around the homogeneous steady states we establish conditions for the existence of unstable mode bands that lead to the formation of spatial patterns. We derive the Stuart-Landau equations for the pattern amplitudes by means of weakly nonlinear multiple scales analysis and Fredholm theory. In particular, we find asymptotic expressions for a wide range of patterns sustained by the system. These patterns include mixed-mode, square, hexagonal, and roll stationary configurations. Our analytical results are corroborated by direct simulations of the underlying chemotaxis system.

Cubic plasma membrane domains stabilize and restrict zones for pH band formation in Chara internodal cells

ABSTRACTCharacean internodal cells display acid and alkaline regions along their surface when exposed to light. The acidification facilitates uptake of carbon required for photosynthesis. In the genus Chara, cubic plasma membrane domains, known as charasomes, were first described five decades ago. Their size and abundance varies along the cell surface and it has been conjectured that the charasome coverage correlates with the pH banding pattern. In this study, we used fluorescein isothiocyanate-dextran (FITC-dextran) and confocal laser scanning microscopy to map the pH profile at high spatial and temporal resolution. In parallel, we stained the charasomes with styryl dyes and investigated their distribution in relation to the fluorescence pattern of FITC-dextran. In both internodal cells of the branchlets and of the main axis, we found that charasomes were small and sparse at the alkaline bands but large and abundant at the acidic regions. Our findings confirm the existence of cell surface regions predisposed to generate either high or low pH zones. We provide evidence that areas with high charasome abundance stabilize and restrict the position of the acidic bands whereas regions with low charasome abundance allow the formation of either stable or unstable alkaline bands.

Strato-hyperbolic instability: a new mechanism of instability in stably stratified vortices

The stability of stably stratified vortices is studied by local stability analysis. Three base flows that possess hyperbolic stagnation points are considered: the two-dimensional (2-D) Taylor–Green vortices, the Stuart vortices and the Lamb–Chaplygin dipole. It is shown that the elliptic instability is stabilized by stratification; it is completely stabilized for the 2-D Taylor–Green vortices, while it remains and merges into hyperbolic instability near the boundary or the heteroclinic streamlines connecting the hyperbolic stagnation points for the Stuart vortices and the Lamb–Chaplygin dipole. More importantly, a new instability caused by hyperbolic instability near the hyperbolic stagnation points and phase shift by the internal gravity waves is found; it is named the strato-hyperbolic instability; the underlying mechanism is parametric resonance as unstable band structures appear in contours of the growth rate. A simplified model explains the mechanism and the resonance curves. The growth rate of the strato-hyperbolic instability is comparable to that of the elliptic instability for the 2-D Taylor–Green vortices, while it is smaller for the Stuart vortices and the Lamb–Chaplygin dipole. For the Lamb–Chaplygin dipole, the tripolar instability is found to merge with the strato-hyperbolic instability as stratification becomes strong. The modal stability analysis is also performed for the 2-D Taylor–Green vortices. It is shown that global modes of the strato-hyperbolic instability exist; the structure of an unstable eigenmode is in good agreement with the results obtained by local stability analysis. The strato-hyperbolic mode becomes dominant depending on the parameter values.

Uncovering Instabilities in the Spatiotemporal Dynamics of a Shear-Thickening Cornstarch Suspension

Recent theories predict that discontinuous shear-thickening (DST) involves an instability, the nature of which remains elusive. Here, we explore unsteady dynamics in a dense cornstarch suspension by coupling long rheological measurements under constant shear stresses to ultrasound imaging. We demonstrate that unsteadiness in DST results from localized bands that travel along the vorticity direction with a specific signature on the global shear rate response. These propagating events coexist with quiescent phases for stresses slightly above DST onset, resulting in intermittent, turbulent-like dynamics. Deeper into DST, events proliferate, leading to simpler, Gaussian dynamics. We interpret our results in terms of unstable vorticity bands as inferred from recent model and numerical simulations.

Association between Genomic Instability and Evolutionary Chromosomal Rearrangements in Neotropical Primates.

During the last decades, the mammalian genome has been proposed to have regions prone to breakage and reorganization concentrated in certain chromosomal bands that seem to correspond to evolutionary breakpoints. These bands are likely to be involved in chromosome fragility or instability. In Primates, some biomarkers of genetic damage may be associated with various degrees of genomic instability. Here, we investigated the usefulness of Sister Chromatid Exchange as a biomarker of potential sites of frequent chromosome breakage and rearrangement in Alouatta caraya, Ateles chamek, Ateles paniscus, and Cebus cay. These Neotropical species have particular genomic and chromosomal features allowing the analysis of genomic instability for comparative purposes. We determined the frequency of spontaneous induction of Sister Chromatid Exchanges and assessed the relationship between these and structural rearrangements implicated in the evolution of the primates of interest. Overall, A. caraya and C. cay presented a low proportion of statistically significant unstable bands, suggesting fairly stable genomes and the existence of some kind of protection against endogenous damage. In contrast, Ateles showed a highly significant proportion of unstable bands; these were mainly found in the rearranged regions, which is consistent with the numerous genomic reorganizations that might have occurred during the evolution of this genus.

Spanwise flow development within a laminar separation bubble under natural and forced transition

The variation of streamwise and spanwise characteristic wavelengths of a NACA 0018 laminar separation bubble under natural and periodic excitation conditions is investigated experimentally. Periodic forcing is applied with an AC-DBD plasma actuator, and the response of the bubble is characterised in two orthogonal planes by means of time-resolved particle image velocimetry. Periodic excitation results in substantial time-averaged size reduction of the bubble. Linear stability analysis is used to establish that the most notable flow deformation is achieved when excitation is applied at the most unstable frequency, which does not significantly vary (<4%) for the range of excitation parameters investigated. At excitation frequencies well below the unstable frequency band, the shear layer does not lock to the excitation and is, instead, modulated. Lock-in is achieved at higher forcing frequencies, which are within the unstable band. For the case of modulated shedding, spanwise deformations become more significant than in the natural case; whereas when shedding becomes locked to the excitation frequency, the coherence of the rollers along the span increases. Characteristic streamwise and spanwise wavelengths are statistically quantified by means of spatial wavelet analysis, demonstrating that spanwise deformations attain wider range of wavelengths than the respective streamwise rollers. Analysis of these results suggests that spanwise deformation is associated to both the incoming boundary layer and shear layer stability characteristics.

Stable and Unstable Vortex Knots in a Trapped Bose Condensate

The dynamics of a quantum vortex torus knot ${\cal T}_{P,Q}$ and similar knots in an atomic Bose-Einstein condensate at zero temperature in the Thomas-Fermi regime has been considered in the hydrodynamic approximation. The condensate has a spatially nonuniform equilibrium density profile $\rho(z,r)$ due to an external axisymmetric potential. It is assumed that $z_*=0$, $r_*=1$ is a maximum point for function $r\rho(z,r)$, with $\delta (r\rho)\approx-(\alpha-\epsilon) z^2/2 -(\alpha+\epsilon) (\delta r)^2/2$ at small $z$ and $\delta r$. Configuration of knot in the cylindrical coordinates is specified by a complex $2\pi P$-periodic function $A(\varphi,t)=Z(\varphi,t)+i [R(\varphi,t)-1]$. In the case $|A|\ll 1$ the system is described by relatively simple approximate equations for re-scaled functions $W_n(\varphi)\propto A(2\pi n+\varphi)$, where $n=0,\dots,P-1$, and $iW_{n,t}=-(W_{n,\varphi\varphi}+\alpha W_n -\epsilon W_n^*)/2-\sum_{j\neq n}1/(W_n^*-W_j^*)$. At $\epsilon=0$, numerical examples of stable solutions as $W_n=\theta_n(\varphi-\gamma t)\exp(-i\omega t)$ with non-trivial topology have been found for $P=3$. Besides that, dynamics of various non-stationary knots with $P=3$ was simulated, and in some cases a tendency towards a finite-time singularity has been detected. For $P=2$ at small $\epsilon\neq 0$, rotating around $z$ axis configurations of the form $(W_0-W_1)\approx B_0\exp(i\zeta)+\epsilon C(B_0,\alpha)\exp(-i\zeta) + \epsilon D(B_0,\alpha)\exp(3i\zeta)$ have been investigated, where $B_0>0$ is an arbitrary constant, $\zeta=k_0\varphi -\Omega_0 t+\zeta_0$, $k_0=Q/2$, $\Omega_0=(k_0^2-\alpha)/2-2/B_0^2$. In the parameter space $(\alpha, B_0)$, wide stability regions for such solutions have been found. In unstable bands, a recurrence of the vortex knot to a weakly excited state has been noted to be possible.