Linear Stability Research Articles

Investigation of Magneto-convection in Viscoelastic Fluid Saturated Anisotropic Porous Layer Under Local Thermal Non-equilibrium Condition

The problem of magneto-convection in viscoelastic fluid saturated anisotropic porous layer under local thermal non-equilibrium (LTNE) effect is investigated. Extended Darcy model with time derivative term for viscoelastic fluid of the Oldroyd type with an externally imposed vertical magnetic field is used to model the momentum equation. The entire investigation has been split into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. We perform normal mode technique to examine linear stability analysis while truncated representation of Fourier series method is used for weakly non-linear stability analysis. The onset of convection is set in through oscillatory rather than stationary mode due to competition between the processes of thermal, magnetic effect and viscoelasticity. A comparative study between anisotropic and isotropic porous medium is made as a function of Q (Chandrasekhar number), 𝛤 (non dimensional inter phase heat transfer coefficient), 𝜆1 (Relaxation time) and λ2 (Retardation time). Apart from this, Q, 𝛤 and λ2 stabilize the system in oscillatory case while 𝜆1 destabilize the system. Furthermore 𝜉 (mechanical anisotropic parameter), 𝜂s (thermal anisotropic parameter for solid phase), destabilizes the system and 𝜂f (thermal anisotropic parameter for fluid phase) stabilizes the system. The effect of Q, 𝜆1, λ2, 𝛤, 𝜉, 𝜂f and 𝜂s on heat transfer is also examined.

Highly Sensitive Room-Temperature Detection of Ammonia in the Breath of Kidney Disease Patients Using Fe2Mo3O8/MoO2@MoS2 Nanocomposite Gas Sensor.

A novel Fe2Mo3O8/MoO2@MoS2 nanocomposite is synthesized for extremely sensitive detection of NH3 in the breath of kidney disease patients at room temperature. Compared to MoS2, α-Fe2O3/MoS2, and MoO2@MoS2, it shows the optimal gas-sensing performance by optimizing the formation of Fe2Mo3O8 at 900°C. The annealed Fe2Mo3O8/MoO2@MoS2 nanocomposite (Fe2Mo3O8/MoO2@MoS2-900°C) sensor demonstrates a remarkably high selectivity of NH3 with a response of 875% to 30ppm NH3 and an ultralow detection limit of 3.7 ppb. This sensor demonstrates excellent linearity, repeatability, and long-term stability. Furthermore, it effectively differentiates between patients at varying stages of kidney disease through quantitative NH3 measurements. The sensing mechanism is elucidated through the analysis of alterations in X-ray photoelectron spectroscopy (XPS)signals, which is supported by density functional theory (DFT) calculations illustrating the NH3 adsorption and oxidation pathways and their effects on charge transfer, resulting in the conductivity change as the sensing signal. The excellent performance is mainly attributed to the heterojunction among MoS2, MoO2, and Fe2Mo3O8 and the exceptional adsorption and catalytic activity of Fe2Mo3O8/MoO2@MoS2-900°C for NH3. This research presents a promising new material optimized for detecting NH3 in exhaled breath and a new strategy for the early diagnosis and management of kidney disease.

On traveling wave solutions with stability and phase plane analysis for the modified Benjamin-Bona-Mahony equation.

The modified Benjamin-Bona-Mahony (mBBM) model is utilized in the optical illusion field to describe the propagation of long waves in a nonlinear dispersive medium during a visual illusion (Khater 2021). This article investigates the mBBM equation through the utilization of the rational [Formula: see text]-expansion technique to derive new analytical wave solutions. The analytical solutions we have obtained comprise hyperbolic, trigonometric, and rational functions. Some of these exact solutions closely align with previously published results in specific cases, affirming the validity of our other solutions. To provide insights into diverse wave propagation characteristics, we have conducted an in-depth analysis of these solutions using 2D, 3D, and density plots. We also investigated the effects of various parameters on the characteristics of the obtained wave solutions of the model. Moreover, we employed the techniques of linear stability to perform stability analysis of the considered model. Additionally, we have explored the stability of the associated dynamical system through the application of phase plane theory. This study also demonstrates the efficacy and capabilities of the rational [Formula: see text]-expansion approach in analyzing and extracting soliton solutions from nonlinear partial differential equations.

Light induced self-assembly of one-dimensional PT-symmetric optical system exhibiting pulling force

Light induced self-assembly’s non-contact and non-invasive nature, along with its versatility and dynamic assembly capabilities, make it particularly well-suited for the self-organization of particles. Previous self-assembly configurations are either in a static equilibrium state or in a dynamic equilibrium state driven by a pushing force. In this study, we introduce a one-dimensional parity-time symmetric (PT-symmetric) multilayer optical system consisting of balanced gain and loss, enabling the generation of a total pulling force on the structure. By conducting molecular dynamics simulations, we achieve the self-organized structure exhibiting pulling force. Furthermore, by reversing the direction of the incident light, we realized pushing force induced binding. The stability of the bound structure is also analyzed using linear stability analysis. Additionally, the light induced self-assembly exhibiting pulling and pushing force is achieved in the one-dimensional multilayer system with unbalanced gain and loss. This work provides an additional degree of freedom in the self-organization of particles.

Stability of plane Couette flow under anisotropic superhydrophobic effects

We study the linear stability of plane Couette flow subject to an anisotropic slip boundary condition that models the slip effect of parallel microgrooves with a misalignment about the direction of the wall motion. This boundary condition has been reported to be able to destabilize channel flow far below the critical Reynolds number of the no-slip case. Unlike channel flow, the no-slip plane Couette flow is known to be linearly stable at arbitrary Reynolds numbers. Nevertheless, the results show that the slip can cause linear instability at finite Reynolds numbers also. The misalignment angle of the microgrooves that maximizes the destabilizing effect is nearly π/4, and the unstable modes are of small streamwise wavenumbers and relatively large spanwise wavenumbers. The flow is always more destabilized by two slippery walls compared to a single slippery wall. These observations are in qualitative agreement with the slippery channel flow with the same boundary condition, indicating that such an anisotropic superhydrophobic effect has a rather general destabilizing effect in shear flows regardless of the profile of the base flow. The absence of the Tollmien–Schlichting instability allows us to reveal the inverse relationship between the critical Reynolds number and the slip length as well as the misalignment in the small-parameter regime. The results suggest that arbitrary nonvanishing slip length and misalignment, with arbitrarily weak anisotropy, may suffice to destabilize plane Couette flow.

Large eddy simulation and linear stability analysis of active sway control for wind turbine array wake

The convective instability of wind turbine wakes allows specific upstream forcing to amplify downstream, leading to increased wake meandering and replenishment, thereby providing a theoretical basis for active wake control. In this study, the active sway control—a strategy previously proven to enhance wake recovery at the single wind turbine level—is analyzed at the turbine array level. The similarity and differences between individual turbine wakes and the wake array are analyzed using large eddy simulations and linear stability analysis, considering both uniform and turbulent inflow conditions. For cases with uniform inflow, large eddy simulations reveal significant meandering motion in the wake array induced by active sway control at a motion amplitude of 1% rotor diameter, consistent with previous studies of standalone wind turbine wakes. Nevertheless, the sensitive frequency for the wake array extends down to St = 0.125 below the limit of St > 0.2 for a single wake, and the optimal control frequency for the standalone turbine wake becomes suboptimal for the array. Linear stability analysis reveals the underlying mechanism of this frequency shift as changes in the shear-layer instability due to the overlap of upstream and downstream wakes and is capable to provide fast estimation of optimal control frequencies. When inflow turbulence intensity increases, the gain of active sway control is reduced, underscoring the importance of low-turbulence environment for successfully implementing the active sway control. The reduction in wake response is captured by the linear stability analysis if the base flow accounts for the faster wake expansion caused by inflow turbulence.

Nonlinear spatial evolution of degenerate quartets of water waves

In this manuscript we investigate the Benjamin-Feir (or modulation) instability for the spatial evolution of water waves from the perspective of the discrete, spatial Zakharov equation, which captures cubically nonlinear and resonant wave interactions in deep water without restrictions on spectral bandwidth. Spatial evolution, with measurements at discrete locations, is pertinent for laboratory hydrodynamic experiments, such as in wave flumes, which rely on time-series measurements at fixed gauges installed along the facility. This setting is likewise appropriate for experiments in electromagnetic and plasma waves. Through a reformulation of the problem for a degenerate quartet, we bring to bear techniques of phase-plane analysis which elucidate the full dynamics without recourse to linear stability analysis. In particular we find hitherto unexplored breather solutions and discuss the optimal transfer of energy from carrier to sidebands. We show that the maximal energy transfer consistently occurs for smaller side-band separation than the fastest linear growth rate. Finally, we discuss the observability of such discrete solutions in light of numerical simulations.

Linear stability of turbulent channel flow with one-point closure

Linear stability of turbulent channel flow with one-point closure

On the role of different nonlinear damping forms in the dynamic behavior of the generalized Beck’s column

The influence of internal and external nonlinear damping forms on the dynamics of a generalized Beck’s column, namely a visco-elastic cantilever beam, subjected to conservative and non-conservative loads at its free end, is investigated. A variational principle provides the equations of motion of the system, which are properly recast into an integro-differential form. The linear stability analysis of the system is then carried out and bifurcation points are detected in the space of parameters associated with the conservative and non-conservative loads. Starting from Hopf’s bifurcation points, a post-critical analysis, based on the Method of Multiple Scales is directly performed on the continuous system, avoiding any a-priori discretization. This method provides the bifurcation equations whose analysis reveals the double nature of nonlinear damping, which can be beneficial or detrimental in terms of stable or unstable bifurcated equilibria. It is found that both the internal and external forms of nonlinear damping can turn a supercritical instability of the system into a subcritical one, thus revealing another destabilizing effect of damping, beyond the very well-known one occurring in the linear field. Numerical simulations, grounded on a Galerkin discretization of the original system, confirm the analytical findings.

Modulation instability and extraction of fractional optical solitons in the presence of generalized Kudryashov’s law and dual form of non-local nonlinearity

This research delves into the study of optical solitons governed by Kudryashov’s law of nonlinear refractive index, incorporating a conformable fractional derivative, perturbed terms, and a quadrupled-power law in optical fibers. Employing a novel approach known as the generalized exp(− S(ζ) ) expansion method, we identify novel optical soliton solutions characterized by exponential, rational, and hyperbolic functions featuring a conformable fractional derivative. These solutions manifest as unified bright-dark, singular, singular periodic, kink, anti-kink, and novel solitary waves. We employ 3D, contour, and 2D plots to analyze the behavior of these solutions across different temporal and fractional-order derivative parameters, offering an understanding of their physical interpretations. Furthermore, we perform modulation instability (MI) analysis that depends on standard linear stability analysis to derive the MI gain spectrum, demonstrating how well our methodology works for nonlinear problems in the natural sciences and engineering domains. This approach provides an effective way to investigate optical solutions in various integer and fractional Schrödinger equations.

The Effect of Heavy Inclusions in the Upper Crust on Thermoconvective Instability of the Lithosphere

The method of linear theory for small perturbations is used to study the stability of heavy inclusions in the upper crust. The existence of such inclusions of increased density is associated with chemical heterogeneity or phase transitions. At small deformations considered in the linear stability theory, the material undergoes transient creep which is described by the Andrade rheological model. Under this rheology, the convective instability of thickened segments of the lithosphere is oscillatory: the increment is a complex number whose real part is close to zero (threshold instability). Heavy inclusions in the upper crust introduce a small complex correction to the increment that determines the convective instability of the lithosphere, slightly increasing the real and imaginary parts of the increment, enhancing the instability and increasing the oscillation frequency.

Throughflow effect on bi-disperse convection in Rivlin-Ericksen fluid

In this investigation, we delve into the influence of throughflow on the phenomenon of bi-disperse convection within Rivlin-Ericksen fluid. In the context of examining bi-disperse convection within this specific type of fluid, the throughflow effect is considered to have a uniform vertical distribution. The primary focus of this study centers on evaluating the system’s linear stability. To achieve this, we employ normal mode analysis to compute the Darcy-Rayleigh number at the onset of convection. This Darcy-Rayleigh number is computed for both stationary and oscillatory convection modes. Furthermore, we conduct a comprehensive analysis and present the results in graphical form to illustrate the impact of various parameters, including Peclet number and kinematic viscoelastic parameter, on both stationary and oscillatory convection. Our research findings demonstrate that when Peclet number Pr1 < 0, it leads to destabilising effect on both stationary and oscillatory convections. Conversely, when Peclet number Pr1 > 0, it induces stabilising effect on both stationary as well as oscillatory convections.

Development of a neural network model for peeling–ballooning stability analysis in the KSTAR tokamak pedestals

The neural network model, MISHKA-NN is developed to mitigate the computational burden associated with the linear ideal magnetohydrodynamic (MHD) stability analysis of the pedestal based on the peeling–ballooning (P–B) model. By utilizing both 1D plasma profiles (current density, pressure gradient, and safety factor) and 0D parameters (plasma geometry, total current, and toroidal mode number), the model predicts linear growth rate of edge-localized ideal MHD instability in a given equilibrium state. By enabling the prediction of each instability within a second, the model reduces the time required for plotting a pedestal P–B stability diagram ( j−α diagram) from approximately 100 CPU hours to a few CPU minutes. Notably, even with the utilization of parametric pressure and current profiles and plasma boundary shapes for the training dataset, the model shows a satisfactory level of performance in benchmarking the j−α diagram for the reconstructed equilibrium from a KSTAR tokamak experiment. We anticipate the model to serve as a versatile alternative to 2D linear MHD stability codes, alleviating numerical costs.

Rotating Stall Inception Prediction Using an Eigenvalue-Based Global Instability Analysis Method

The accurate prediction of rotating stall inception is critical for determining the stable operating regime of a compressor. Among the two widely accepted pathways to stall, namely, modal and spike, the former is plausibly believed to originate from a global linear instability, and experiments have partially confirmed it. As for the latter, recent computational and experimental findings have shown it to exhibit itself as a rapidly amplified flow perturbation. However, rigorous analysis has yet to be performed to prove that this is due to global linear instability. In this work, an eigenanalysis approach is used to investigate the rotating stall inception of a transonic annular cascade. Steady analyses were performed to compute the performance characteristics at a given rotational speed. A numerical stall boundary was first estimated based on the residual convergence behavior of the steady solver. Eigenanalyses were then performed for flow solutions at a few near-stall points to determine their global linear stability. Once the relevant unstable modes were identified according to the signs of real parts of eigenvalues, they were examined in detail to understand the flow destabilizing mechanism. Furthermore, time-accurate unsteady simulations were performed to verify the obtained eigenvalues and eigenvectors. The eigenanalysis results reveal that at the rotating stall inception condition, multiple unstable modes appear almost simultaneously with a leading mode that grows most rapidly. In addition, it was found that the unstable modes are continuous in their nodal diameters, and are members of a particular family of modes typical of a dynamic system with cyclic symmetries. This is the first time such an interesting structure of the unstable modes is found numerically, which to some extent explains the rich and complex results constantly observed from experiments but have never been consistently explained. The verified eigenanalysis method can be used to predict the onset of a rotating stall with a CPU time cost orders of magnitude lower than time-accurate simulations, thus making compressor stall onset prediction based on the global linear instability approach feasible in engineering practice.

Linear temporal stability of Jeffery–Hamel flow of nanofluids

Flow stability plays a key role in transition to turbulence in various systems. This transition initiates with disturbances appearing in the laminar base flow, potentially amplifying over time based on flow and fluid parameters. In response to these amplified disturbances, the flow undergoes successive stages of different laminar flows, ultimately transitioning to turbulence. One influential parameter affecting flow stability is the nanoparticle volume fraction (ϕ) in nanofluids, extensively employed in thermofluid systems like cooling devices to enhance fluid thermal conductivity and the heat transfer coefficient. Focusing on the impact of nanoparticles on Jeffery–Hamel flow stability, this study assumes fluid properties are temperature- and pressure-independent, exclusively examining the momentum transfer aspect. The analysis commences by deriving the base laminar flow solution. Subsequently, linear temporal stability analysis is employed, imposing infinitesimally-small perturbations on the base flow as a modified form of normal modes. A generalized Orr–Sommerfeld equation is derived and solved using a spectral method. Results indicate that, assuming nanofluid viscosity as μnf=μf/(1−ϕ)2.5, nanoparticle effects on momentum transfer and flow stability hinge on the ratio of nano-solid particle density to base fluid density (Rρ=ρs/ρf). For ϕ∈(0,0.1], flow stabilization occurs with ϕ when Rρ<3.5000, while destabilization is observed when Rρ>4.0135. Notably, nanoparticles exhibit a negligible impact on flow stability when 3.5000≤Rρ≤4.0135.

Macroscopic trends of linear tearing stability in cylindrical current profiles

The likelihood of realising tokamak power-plants will be greatly improved by the discovery of high-gain equilibria that resist the formation of small islands and hence avoid the disruptive neoclassical tearing mode. We propose a series of studies to understand how simple tokamak design can leverage aspects of tearing onset physics to maximise passive resistance to island formation. Here we investigate the variation that current profiles can bring about in preventing tearing onset through the cylindrical linear tearing stability parameter Δ′ . A database of 159148 realistic pilot-plant current profiles was generated with Monte Carlo sampling, and the distribution of Δ′ values was linked with interpretable profile characteristics. In agreement with prior theoretical and experimental studies, Δ′ was found to be strongly correlated with the existence and steepness of a local toroidal current well or hill, with the former destabilising and the latter stabilising. In the absence of these two cases, the remaining Δ′ values were linearly bounded by the toroidal current gradient at the rational surface.

Stability of asymmetric Schwarzschild–Rindler–de Sitter thin shell wormhole

The paper examines the dynamics of asymmetric thin shell wormholes that connect two distinct spacetimes using the cut and paste technique. The focus is on analyzing the linear stability of these wormholes by considering radial perturbations and utilizing the modified generalized Chaplygin gas equation of state. The specific case of an asymmetric wormhole connecting Schwarzschild–Rindler spacetime to Schwarzschild–Rindler–de Sitter space–time is analyzed using this formalism. Our investigation uncovers the existence of both stable and unstable regions, which are contingent upon the appropriate selection of various parameters within the metric spacetime and equation of state. Additionally, we determine that stability regions exist as a consequence of the square speed of sound. By increasing the value of the cosmological constant, the stability region is expanded. Furthermore, the stability regions are augmented by the influence of Rindler parameters, while the stability regions are also affected by adjustments in the equation of state parameters, leading to their enlargement.

Some optical solitons and modulation instability analysis of (3 + 1)-dimensional nonlinear Schrödinger and coupled nonlinear Helmholtz equations

In this study, we acquired some optical solitons of (3 + 1) dimensional nonlinear Schrödinger equation (3DNLSE) and coupled nonlinear Helmholtz equations (CNLHE) by using generalized G′G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(\\frac{{G}^{\\prime}}{G}\\right)$$\\end{document}-expansion method (GEM). We are able to derive exponential, trigonometric, and hyperbolic solutions. We notice that Mathematica 11.2 offer the equations for these answers. Aside from that, we display some of the solution’s graphic performance. Recently, accurate traveling-wave solutions for nonlinear partial differential equations (NLPDEs) have been acquired using this technique. Through linear stability analysis, we derive an analytical expression for the instability gain and analyze its main characteristics. Finally, we assess the robustness and stability of the solitary waves through numerical simulations and compare the accuracy of the analytical and numerical results. The obtained ultra-short optical solitons can be widely used as a guide for practical applications in telecommunications domain.

Gravitating kinks with asymptotically flat metrics

In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term is modified by an additional derivative coupling term . In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti-de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

Stability of fluid flow in a porous medium with uniform cross-flow and velocity slip

This work examines the evolution of small perturbations in a plane Poiseuille flow through a porous medium bounded by porous walls implemented with the Brinkman flow model. The effect of uniform cross-flow across the channel along with slip imposed on the channel walls is examined for the associated fluid flow. The modified Orr–Sommerfeld equation for the flow system under consideration is derived and then solved numerically using Chebyshev spectral collocation method. The acquired sufficient conditions ensure that fluid motion will remain stable even when the flow system is widely perturbed. The linear stability characteristics and the onset of instability is discussed for a wide range of cross-flow Reynolds number, slip length and porosity parameter. The above mentioned flow parameters have a significant stabilizing effect on the fluid flow that is depicted with neutral stability curves, growth rate dispersion curves and eigenspectrums. Asymmetric slip allows the critical Reynolds number to increase rapidly when the upper channel wall experiences more slip than the lower.