Linear Stability Research Articles

MEMS fast steering mirror with a large optical aperture and high surface quality for free-space optical communication

This work presents a MEMS fast steering mirror fabricated by an 8-inch AlScN platform, with a large optical aperture of up to 10 mm and high surface quality (RMS < 20 nm, PV < 120 nm), intended for free-space optical communication. The device comprises a high reflective mirror plate, a pillar and four cantilever beams with AlScN thin films. This device is prepared by a wafer-level eutectic bonding process. A reinforcement structure is proposed to increase the resonant frequency and the resistance to deformation. The mechanical performance, including resonant frequency, step response, linearity, and long-term stability are characterized. The maximum tilting angle is 1.38 mrad at 68 V, the settling time is improved from 400 ms in the open-loop control mode to 0.5 ms with the double step algorithm. The relationship of the resonant frequency, surface figure, and the depth of reinforced ribs is studied through characterizing devices with different depths of reinforced ribs. The bonding quality and the mutual melting states of bonding layers interface are investigated.

Stability and eigenvalue bounds for micropolar shear flows

AbstractWe prove eigenvalue bounds for two‐dimensional linearized disturbances of parallel flows of micropolar fluids, deriving the Orr‐Sommerfeld equations and providing a sufficient condition for linear stability of such flows. We also derive wave speed bounds.

Baroclinic instability in the Eady model for two coupled flows

ABSTRACT The linear instability of baroclinic flows in two superimposed and coupled, immiscible fluids is studied theoretically. These flows are westerlies, and they are thermally or mechanically coupled. The fluids are stably stratified, internally and mutually (the upper fluid is lighter than the lower fluid). In each fluid, two-level surface quasi-geostrophy governs the evolution of the perturbed westerly flow. The perturbations are horizontal normal modes. Firstly, the models are not coupled and the flow instability in each fluid is validated separately against the results of the classical Eady model of baroclinic instability. Secondly, the two fluids are thermally and/or mechanically coupled. With thermal coupling, and for meridionally uniform perturbations, a new mode of instability appears for long waves. This pair of unstable modes converges towards the modes of the uncoupled fluids at medium wavelengths. For perturbations with a non trivial meridional structure, the thermal coupling essentially damps the instability. For an upper flow with a larger deformation radius than in the lower flow, the growth rates of the perturbation are therefore more strongly altered in the former than in the latter. With mechanical coupling, the instability is essentially damped at large to medium scales, while the short-wave cut-off is extended towards smaller waves. When the fluids are both thermally and mechanically coupled, these effects add up. This very idealised study is a first step towards studying more realistic cases.

Deeper but smaller: Higher-order interactions increase linear stability but shrink basins.

A key challenge of nonlinear dynamics and network science is to understand how higher-order interactions influence collective dynamics. Although many studies have approached this question through linear stability analysis, less is known about how higher-order interactions shape the global organization of different states. Here, we shed light on this issue by analyzing the rich patterns supported by identical Kuramoto oscillators on hypergraphs. We show that higher-order interactions can have opposite effects on linear stability and basin stability: They stabilize twisted states (including full synchrony) by improving their linear stability, but also make them hard to find by markedly reducing their basin size. Our results highlight the importance of understanding higher-order interactions from both local and global perspectives.

Effect of an external axial magnetic field on thermal convection of an electric conducting fluid in a rotating spherical shell

We investigated the interaction between the thermal convection structure in a rotating spherical shell and a uniformly applied magnetic field acting externally toward the axis of rotation. We considered a system that the inner and outer spherical boundaries are heated and cooled both isothermally and the effects of induced magnetic fields are neglected. The convection structure of this system is characterized by the generation of travelling waves around the axis of rotation. We numerically investigated how this is affected under the magnetic field. The characteristics of the disturbance (i.e., growth rate and phase velocity) were estimated from the exponential amplification period using three-dimensional (3D) simulations and compared with those obtained from linear stability analyses (LSA). In particular, the effects of the magnetic field on the kinetic energy and Nusselt number were investigated for a quasi-steady state using 3D simulations. Our numerical results revealed that the applied magnetic field destabilizes the flow field and enhances heat transfer. This is noteworthy, contrary to the common sense that magnetic field stabilizes the flow field and reduces the heat transfer coefficient. However, the magnetic field strengths at which the kinetic energy and heat transfer coefficient took their maximum values differ slightly.

Contribution of machine learning and physics-based sound simulations for the optimization of brass instruments

Sound simulations by physical model are interesting to transcribe the physics underlying the functioning of a musical instrument. These simulations make it possible to create virtual sounds with a mode of operation representative of the interaction musician/instrument (driving a sound by the causes that create it). The work consists in studying the contribution of machine learning (ML) methods in the optimization of a musical instrument. The application concerns the brass instruments (trumpets). From a training set of virtual instruments, ML methods are trained to model the intonation (represented by the equivalent fundamental pitch) and the ease of emission (represented by the threshold pressure obtained by linear stability analysis) of sounds, according to the modal parameters of the input impedance. With the ML models, an optimization with genetic algorithms is next carried out to improve the intonation and the ease of emission. The last stage of the approach consists in the optimization of the bore of the instrument (optimization of the shape of the leadpipe). The results show that the approach gives promising results: optimal instruments are actually efficient when re-simulated with the physical model. The manufacturing of an optimal instrument is in progress to confirm the validity of the approach

The effect of Lévy index coefficient on modulational instability and rogue wave excitation in nonlocal media with cubic–quintic nonlinearities

This paper explores the modulational instability (MI) of a plane wave and its behavior in the nonlinear Schrödinger equation (NLSE) with a fractional diffraction term quantified by its Lévy index coefficient and nonlocal cubic–quintic nonlinearities. First, we analyze the stability of the plane wave solution and examine how nonlocal nonlinearities and the Lévy index coefficient affect the MI gain. We observe that the stability in the fractional NLSE exhibits new features that differ from those in the standard NLSE. Specifically, when dealing with competing cubic and quintic nonlinearities, the interaction between nonlocality and the Lévy index coefficient α can eliminate MI for low values of α, unlike the classical NLSE with α=2, where we find the plane wave to be unstable. Besides the linear stability analysis, numerical simulations are performed to understand further the plane wave dynamics from its nonlinear stage in this model. The results reveal the generation of periodic chains of localized peaks. Guided by analytical predictions and using the plane wave solution subject to Gaussian perturbation, we numerically investigate the possibility of exciting rogue waves in the parameter spaces where MI exists. We find that the different combinations of signs of the cubic and quintic nonlinearities (focusing and defocusing) and the fractional diffraction term significantly impact the formation of rogue waves. These results may pave the way for the theoretical and experimental study of nonlinear phenomena in physical models with fractional derivatives and nonlocal nonlinearities.

Linear instability of viscous parallel shear flows: revisiting the perturbation no-slip condition

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities that could be sufficient to explain turbulence transition. In many cases, the near-wall behaviour of the discovered instabilities is empirically indistinguishable from the classical no-slip condition. The ability of these alternative boundary conditions to predict linear instabilities that are consistent with turbulence transition suggests that the no-slip condition may be an overly simplified model of fluid–solid interface physics, particularly as a description of the flow perturbations that lead to turbulence transition in wall-bounded flows.

Linear stability theory and molecular simulations of nanofilm dewetting with disjoining pressure, strong liquid–solid slip and thermal fluctuations

The dewetting of thin nanofilms is significantly affected by thermal fluctuations, liquid–solid slip and disjoining pressure, which can be described by lubrication equations augmented by appropriately scaled noise terms, known as stochastic lubrication equations. Here molecular dynamics simulations along with a newly proposed slip-generating method are adopted to study the instability of nanofilms with arbitrary slip. These simulations show that strong-slip dewetting is distinct from weak-slip dewetting by faster growth of perturbations and fewer droplets after dewetting, which cannot be predicted by the existing stochastic lubrication equation. A new stochastic lubrication equation considering the strong-slip boundary condition is thus derived using a long-wave approximation to the equations of fluctuating hydrodynamics. The linear stability analysis of this equation, i.e. surface spectrum, agrees well with molecular simulations. Interestingly, strong slip can break down the usual Stokes limits adopted in weak-slip dewetting and bring the inertia into effect. The evolution of the standard deviation of the film height $W^2(t)={\overline {h^2}-{\bar {h}}^2}$ at the initial stage of the strong-slip dewetting is found to be $W\sim t^{1/4}$ in contrast to $W\sim t^{1/8}$ for the weak-slip dewetting.

B-254 Analytical and Clinical Performance Evaluation of Plasma pTau217 in a Clinical Diagnostic Laboratory

Abstract Background Blood-based biomarkers provide an accessible and cost-effective tool for diagnosing Alzheimer’s disease (AD). Among these biomarkers, phosphorylated tau 217 (pTau217) shows promise for both AD diagnosis and differential diagnosis, as well as for facilitating access to emerging disease-modifying therapies. The ALZpath SIMOA pTau-217 v2 assay is a digital immunoassay designed for quantifying pTau-217 in human EDTA plasma samples. This study assesses the analytical performance of plasma pTau217 assays as a Laboratory Developed Test (LDT) appropriate for diagnostic application. Methods In this analytical study, we evaluate accuracy, precision, detection limits, linearity, and analyte stability. Plasma pTau217 levels were measured using the ALZpath pTau217 v2 assay on a single Quanterix HD-X SIMOA Analyzer platform at BC Neuroimmunology Lab. Inc. Vancouver, British Columbia, Canada. As a clinical testing laboratory, our validation procedures are in accordance with CAP and CLIA requirements, with a primary focus on adhering to CLSI guidelines for both analytical and clinical performance testing. To determine a reference range and cut-off, samples of Amyloid PET-confirmed cases (n=263) and healthy subjects between the ages of 55 and 95, with a roughly equal ratio of males to females (n=219), were tested. Results The ALZpath pTau217 assay demonstrates an analytical measurement range of 0.0046 - 3.4056 ng/L, with a limit of blank (LoB) of 0.0019 ng/L, a limit of detection (LoD) of 0.0046 ng/L, and a limit of quantification (LoQ) of 0.03 ng/L. Linearity spans from 0.06 to 1.75 ng/L, with repeatability showing intra-laboratory precision above LoQ ≤ 20% CV. Stability is maintained at 4⁰C for ≤ 1 week, at room temperature for ≤ 72 hrs, at -20⁰C for ≤ 2 weeks, and at -70⁰C for ≤ 3 weeks, with freeze/thaw cycles tolerated up to 6 times. Moreover, interference is not detected at the maximum concentrations tested for albumin, unconjugated bilirubin, biotin, hemoglobin, creatinine, and heterophilic antibodies. The reference range was determined using the 95% reference interval, resulting in 0.398 ng/L. ROC analysis yielded an AUC of 0.932 with a Youden index of 0.338 ng/L. At the Youden index, sensitivity was 90.0% with a specificity of 85.6%. Specificity reached 95.5% at the upper cut point of 0.471 ng/L, while sensitivity was 94.8% at the lower cut point of 0.242 ng/L. Conclusions The outstanding analytical performance of pTau217 supports its adoption as a reliable screening and diagnostic tool in clinical practice, aiding clinicians in the accurate diagnosis of AD.

A systematic investigation of the freezing process of silty clay through unidirectional stepwise freezing method combined with digital imaging processing technology

Soil freezing represents a complex thermo-hydro-mechanical coupling process that encompasses a range of physical and mechanical phenomena, such as heat transfer, moisture migration, cryostructure development, ice lens segregation, frost heave, and consolidation, all of which interact and influence one another throughout the freezing process. This study conducted a unidirectional stepwise freezing test, comprising three distinct freezing stages, to investigate the freezing behavior of Qinghai-Tibet silty clay using digital imaging processing technology (DIPT), which includes an image acquisition system and a digital image processing system. The results demonstrate that the stepwise freezing test provides a more comprehensive insight into the physical and mechanical processes occurring during unidirectional soil freezing. At various stages of freezing, the temperature distribution within the sample achieves a linear stabilization, with the frozen zone exhibiting a slightly larger extent compared to the unfrozen zone. The longitudinal section of the sample developed layered cryogenic cracks, whereas the horizontal section revealed interconnected cryogenic polygonal cracks of varying sizes, which facilitated moisture migration and ice segregation. Furthermore, ice lenses can segregate within a broad temperature range below the soil freezing point in the frozen zone, resulting in frost heave within the frozen zone and consolidation of the unfrozen zone. This study proposes an experimental method to clarify the complex phenomenon and mechanisms of frost heave during soil freezing.

Linear and nonlinear stability of double diffusive convection in a micropolar fluid saturated porous layer with magnetic field and throughflow effects

The linear and nonlinear stability of double-diffusive convection in a porous layer saturated with micropolar fluid is examined. A transverse magnetic field is applied to the flow together with vertical throughflow. The normal mode technique is employed for linear stability analysis, whereas the energy method is used for nonlinear stability analysis. The resulting eigenvalue problems corresponding to linear and nonlinear stability theories are solved numerically by employing the bvp4c routine in MATLAB 2022(b). The critical thermal Rayleigh numbers for both linear and nonlinear analyses are computed for the different values of the governing parameters and presented graphically. A comparison is made between linear and nonlinear stability results. It is observed that the flow is more stable whenever a magnetic field is added to the flow, although the subcritical instability region also slightly increases. Increasing the Darcy number, Lewis number, coupling number, and absolute value of the throughflow parameter destabilizes the flow. On the other hand, raising the porosity of the medium and micropolar parameters stabilizes the flow. Furthermore, there is no subcritical gap in the absence of the throughflow effect, which is a good agreement between the linear and nonlinear thresholds.

Stability analysis for viscoelastic fluid with thermorheological effects: Linear and nonlinear approaches

This study investigates the stability analysis of Rayleigh-Bénard configuration for a viscoelastic fluid subject to thermorheological effects, using the D2-Chebyshev-τ method. The fluid is modeled as a third-order viscoelastic fluid. This study accentuates how salting the fluid layer affects the thresholds for the onset of instability in a fluid of third order encompassing physically realistic rigid boundaries. The dynamic model incorporates advection-diffusion of temperature and solute concentration and a modified Navier–Stokes equation. We determine instability thresholds for the complex non-Newtonian fluid by analyzing the linear stability of the steady-state conduction solution. Our analysis proves the strong form of the principle of exchange of stabilities, demonstrating that convective motions can only occur through stationary motion. Additionally, a nonlinear stability analysis using the energy method is performed, deriving an unconditional nonlinear stability criterion. The results provide a comprehensive understanding of how variable viscosity and viscoelasticity impact system stability. Both the viscosity parameter and the third-grade fluid parameter exhibit stabilizing effects. Notably, we observe a discrepancy between the linear and global nonlinear stability results, indicating the presence of a subcritical instability region. This study contributes to the understanding of complex fluid dynamics in non-linear mechanical systems, with potential applications in various industrial and natural processes.

Scrutinizing black hole stability in cubic vector Galileon theories

In a subclass of generalized Proca theories where a cubic vector Galileon term breaks the U(1) gauge invariance, it is known that there are static and spherically symmetric black hole (BH) solutions endowed with nonvanishing temporal and longitudinal vector components. Such hairy BHs are present for a vanishing vector-field mass (m=0) with a non-zero cubic Galileon coupling β 3. We study the linear stability of those hairy BHs by considering even-parity perturbations in the eikonal limit. In the angular direction, we show that one of the three dynamical perturbations has a nontrivial squared propagation speed c Ω,1 2, while the other two dynamical modes are luminal.We could detect two different unstable behaviors of perturbations in all the parameter spaces of hairy asymptotically flat BH solutions we searched for. In the first case, an angular Laplacian instability on the horizon is induced by negative c Ω,1 2. For the second case, it is possible to avoid this horizon instability, but in such cases, the positivity of c Ω,1 2 is violated at large distances. Hence these hairy BHs are generally prone to Laplacian instabilities along the angular direction in some regions outside the horizon. Moreover, we also encounter a pathological behavior of the radial propagation speeds c r possessing two different values of c r 2 for one of the dynamical perturbations. Introducing the vector-field mass m to cubic vector Galileons, however, we show that the resulting no-hair Schwarzschild BH solution satisfies all the linear stability conditions in the small-scale limit, with luminal propagation speeds of three dynamical even-parity perturbations.

Flow of fluids with pressure-dependent viscosity down an incline: Long-wave linear stability analysis

In this paper, we investigate the linear stability of a gravity-driven fluid with pressure-dependent viscosity flowing down an inclined plane. The linear stability analysis is formulated using the long-wave approximation method. We show that the onset of instability occurs at a critical Reynolds number that depends on the material and geometrical parameters. Our results suggest that the dependence of the viscosity on pressure can influence the stability characteristics of the flow down an incline.

Reverse iontophoresis sensing electrode for joint detection of pH, NH4+, and lactic acid

With the rapid development of integrated electronic circuit technology, biological fluid-electricity integrated detection systems have gradually become a research hotspot. Researchers have integrated biological fluid electrical detection methods into circuits and developed small, low-power, portable detection devices equipped with sensing electrodes, which can achieve continuous monitoring of human health parameters. In recent years, the integration of reverse iontophoresis technology that can be used to extract body fluids with electrochemical sensors has opened up the possibility of flexible, portable biochemical sensing with excellent detection sensitivity. Herein, we present a method for extracting biofluids based on reverse iontophoresis technology, coupled with electrochemical sensing techniques for the simultaneous detection of various biomarkers in body fluids. The multi-channel sensing electrode was modified layer by layer using nitrogen-doped graphene (N-Gr), ion-selective membrane, or lactate oxidase for rapid and sensitive detection of pH (3–8), ammonium ion (NH4+) (0.1 mM–50 mM), and lactic acid (1 mM–50 mM). Subsequently, an integrated system for electrical stimulation extraction and sensing analysis based on reverse iontophoresis was established and experimentally tested. Experimental results demonstrated that the multi-channel joint detection sensing electrode has excellent sensing linearity, specificity, repeatability, and long-term stability. Finally, a smartphone-based WeChat applet was developed, which can realize parameter setting, function selection, and result display of sensor detection. In this study, reverse iontophoresis technology was used to collect body fluids, and the important biomarkers pH, NH4+, and lactic acid in the body fluids were detected. Overall, this research presents an integrated detection system and a multi-channel sensing scheme for the detection of important biochemical markers in bodily fluids, thereby providing potential value for health monitoring applications.

A Fluorescent Probe Containing Triphenylamine-Benzofuranone Moiety for Detecting Cysteine and Imaging in Living Pulmonary Cells Under Hypercapnia.

In this work, a fluorescent probe TPB-Cys derived from triphenylamine-benzofuranone was developed for monitoring the cysteine (Cys) level and imaging in living pulmonary cells under hypercapnia condition. A systematic hypoxia module was tried to cover both the in-solution test and pulmonary cellular imaging. The hypoxia condition did not obviously affect the fluorescence response signal during the in-solution test. The fluorescence signal at 540 enhanced in a dose-dependent enhancement along with the increase of the Cys concentration. The probe showed the advantages including relatively long linear range, high sensitivity, high stability, and high selectivity. With low cyto-toxicity, TPB-Cys achieved the monitoring of the endogenous Cys level in living pulmonary cells. Furthermore, it also realized the visualization of the affection of the hypoxia and hypoxia recovered conditions. This work was informative for both the accurate diagnosis and potential medical techniques.

Stability of asymptotic waves in the Fisher–Stefan equation

We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher–Stefan equation. All stability analysis is in terms of the limiting equations that the asymptotic waves satisfy.

Congested traffic patterns of mixed lattice hydrodynamic model combining the perceptual range differences with passing effect

With the aid of Vehicle-to-everything (V2X) technologies for network connectivity, connected autonomous vehicles (CAVs) can broaden the drivers' perceptual boundaries and receive a greater quantity of exogenous vehicle information, thereby governing the vehicle's acceleration information of the next moment. Nonetheless, constrained by contemporary communication networks and sophisticated vehicle control technology, the process of promoting CAVs is long-lasting, and throughout this stage of transition, both CAVs and human-driven vehicles (HDVs) will happen on the road. Moreover, passing behaviour is uncommon in the traffic flow model despite being a fundamental microscopic driving behaviour, particularly within mixed-traffic situations. To bridge that hole, we introduce the percentage ratios of CAVs into the lattice hydrodynamic model by integrating the perceptual range differences between two different types of vehicles with passing effects. Subsequently, the stability norm associated with the new model is ascertained by performing the linear stability analysis. When the above-mentioned stability condition is not achieved, we investigate the complex behaviour of the new model, and the associated existing conditions, as well as the modified Korteweg-de Vries (mKdV) equation, are determined simultaneously. When the passing ratio is inadequate, no jam and kink jam make up the whole phase region; while when the passing ratio surpasses the minimum, the initial unstable region can be segregated into two extra segments: the chaotic sub-region and the kink jam sub-region, the density wave progressively transitioned from being a kink-Bando traffic wave to a chaotic phase. Lastly, the findings of the numerical experiment identify with the theoretical derivation made above.

Stability analysis of Rayleigh–Bénard–Marangoni convection in fluids with cross-zero expansion coefficient

Cross-zero expansion coefficient Rayleigh–Bénard–Marangoni (CRBM) convection refers to the convective phenomenon where thermal convection with stratified positive and negative expansion coefficients in a liquid layer is coupled with the Marangoni convection. In the Bénard convection, fluids with a cross-zero expansion coefficient contain a neutral expansion layer where the expansion coefficient (α) is zero, and the local buoyancy-driven convection is coupled with the Marangoni convection, leading to unique flow instability phenomena. This paper uses linear stability theory to analyze the CRBM convection in a horizontal liquid layer under a vertical temperature gradient and performs numerical calculations for fluids under different Bond numbers (Bd) in both bottom-heated and bottom-cooled models, obtaining the critical destabilization conditions and modes. In the bottom-heated model, different combinations of buoyancy instability mechanism (BIM), tension instability mechanism, and coupled instability mechanism (CIM) appear depending on the dimensionless temperature for the neutral expansion layer (Tα0) and the Bd. In the bottom-cooled model, two mechanisms occur according to the variation of Tα0: BIM and CIM.