Linear Stability Research Articles

Brattkus–Davis modes in the solution to the linear stability of plane stagnation-point flow

Brattkus–Davis modes in the solution to the linear stability of plane stagnation-point flow

Piezotronic Transistors Based on GaN Wafer for Highly Sensitive Pressure Sensing with High Linearity and High Stability.

Piezotronic effect utilizing strain-induced piezoelectric polarization to achieve interfacial engineering in semiconductor nanodevices exhibits great advantages in applications such as human-machine interfacing, micro/nanoelectromechanical systems, and next-generation sensors and transducers. However, it is a big challenge but highly desired to develop a highly sensitive piezotronic device based on piezoelectric semiconductor wafers and thus to push piezotronics toward wafer-scale applications. Here, we develop a bicrystal barrier-based piezotronic transistor for highly sensitive pressure sensing by p-GaN single-crystal wafers. Its pressure sensitivity can be as high as 19.83 meV/MPa, which is more than 15 times higher than previous bulk-material-based piezotronic transistors and reaches the level of nanomaterial-based piezotronic transistors. Moreover, it can respond to a very small strain of 3.3 × 10-6 to 1.1 × 10-5 with high gauge factors of 1.45 × 105 to 1.38 × 106, which is a very high value among various strain sensors. Additionally, it also exhibits high stability (current stability of 97.32 ± 2.05% and barrier height change stability of 95.85 ± 3.43%) and high linearity (R2 ∼ 0.997 ± 0.002) in pressure sensing. This work proves the possibility of designing a bicrystal barrier as the interface to obtain a strong piezotronic effect and highly sensitive piezotronic devices based on wafers, which contributes to their applications.

Turbulence and mixing from neighbouring stratified shear layers

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$ , approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\sim D_c$ , billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$ , neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.

Dark solitons and their bound states in a nonlinear fiber with second- and fourth-order dispersion

We study the excitations of dark solitons in a nonlinear optical fiber with the second- and fourth-order dispersion, and find the emergence of striped dark solitons (SDSs) and some multi-dark-soliton bound states. The SDSs can exhibit time-domain oscillating structures on a plane wave, and they have two types: the ones with or without the total phase step, while the multi-dark-soliton bound states exhibit different numbers of amplitude humps. By the modified linear stability analysis, we regard the SDSs as the results of the competition between periodicity and localization, and analytically give their existence condition, oscillation frequency, and propagation stability, which show good agreements with numerical results. We also provide a possible interpretation of the formation of the existing striped bright solitons (SBSs), and find that SBS will become the pure-quartic soliton when its periodicity and localization carry equal weight. Our results provide the theoretical support for the experimental observation of striped solitons in nonlinear fibers, and our method can also guide the discovery of striped solitons in other physical systems.

Formation of convective roll patterns over a longitudinal throughflow in an active inhomogeneous porous medium with weak clogging

The convective stability of a plane-parallel longitudinal throughflow in a system consisting of two porous sublayers with distinct permeability is studied taking into account the weak pore clogging effect and given a finite difference in concentration between the upper and lower boundaries of the system. A system of differential equations for convection is derived within the framework of the continuum approach and the nonlinear MIM model. A linear stability analysis of the basic longitudinal flow is carried out. The boundary value problem is solved using the numerical technique for constructing a fundamental system of solutions. The neutral stability curves of the basic flow with respect to the disturbances in the form of rolls with different wavelength are obtained. For the absence of pore clogging, the convective stability maps of the critical solutal Rayleigh-Darcy number versus the permeability ratio for the initial uncontaminated sublayers, as well as the plots of the critical disturbance frequency and wave number versus the permeability ratio for some values of the Peclet number, are constructed. It is shown that these results have symmetry with respect to the solution for equal initial permeability of sublayers. The clogging effect associated with the solute adsorption and desorption in a porous medium is studied in the two-layered systems with the values 0.1 and 10 of the ratio of initial permeabilities of the sublayers; convection localization occurs in distinct sublayers. It was found that clogging increases the stability of the longitudinal basic flow relative to solutal inhomogeneity and breaks the symmetry of solutions with respect to the case when the two-layered system is reduced to a single layer with the same filtration properties of the porous medium throughout its volume. The influence of sorption effects on the critical parameters of oscillatory convection is investigated by plotting the critical solutal Rayleigh-Darcy number, disturbance frequency and wave number against the adsorption coefficient at fixed values of the desorption coefficient. The isolines of the stream function are constructed to analyze convective flow patterns. It was established that there is a weak relationship between the typical size of local convective roll patterns and the clogging parameters. It is shown that the sorption processes, which can lead to clogging, have a significant impact on the velocity of convective rolls moving along the two-layered system at a slight variation in their sizes.

Gravitating kinks with asymptotically flat metrics

Abstract In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term $\mathcal{X}$ is modified by an additional derivative coupling term $\alpha\mathcal{X}^2$. 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-Indicating HPLC Method for Determination of Ibuprofen and Famotidine Degradation Products.

A new stability-indicating high-performance liquid chromatographic method for the quantitative determination of ibuprofen and famotidine degradation products in combined pharmaceutical products was developed and validated. The current aim of this study is to develop a rapid, accurate and robust analytical stability indicating impurity method that can separate ibuprofen, famotidine and their related impurities by using a reversed-phase high-performance liquid chromatography. A Zorbax SB-Phenyl column (4.6 × 150mm2, 5-μm particle size) with mobile phase containing phosphate buffer solution with a pH value of 3.0 and acetonitrile was used. The flow rate was 0.8mL/min and the analytes were detected by UV detector at 265nm. The retention times of ibuprofen and famotidine were 18.43 and 5.14min, respectively. This method was validated to confirm specificity, linearity, sensitivity (limit of detection and limit of quantitation), precision, accuracy, robustness and sample stability according to the International Conference on Harmonization guidelines. Studies have been completed and reported with two active substances in the combined dosage form and seven impurities in total. There is no method in the literature that simultaneously distinguishes and quantitatively analyzes both active substances and degradation products.

Acoustic tones generated by impinging jets: Differences between laminar and highly-disturbed nozzle-exit boundary layers

The differences between the acoustic tones generated by impinging jets with laminar and highly-disturbed nozzle-exit boundary layers are investigated. For that, jets at Mach numbers between 0.6 and 1.3 impinging on a flat plate at a distance of 8 nozzle radii from the nozzle exit are computed using large-eddy simulations. The amplitudes of the tones generated by the jets through feedback loops establishing between the nozzle and the plate are found to be significantly affected by the exit turbulent disturbances. In the present study, overall, they are lower for the initially laminar jets than for the initially disturbed ones. The level decrease varies from a few dB up to 15 dB, depending on the tones, which can change the frequencies of the dominant tones and the numbers and azimuthal structures of their associated feedback modes. For Mach numbers 0.75 and 0.8, for instance, the dominant tone frequencies are approximately two times lower for the initially laminar jets than for the other ones, yielding a better agreement with experiments of the literature in the former case. For a Mach number of 1.1, as a second example, the dominant tone is associated with the axisymmetric third feedback mode in the laminar case but with the helical fifth feedback mode in the disturbed case. The differences in the tone amplitude are finally discussed by estimating the power gains of the shear-layer instability waves between the nozzle and the plate using linear stability analysis for the axisymmetric mode. In most cases, at the frequency of a specific tone, the higher the gain, the stronger the acoustic tone.

Impact of a floating flexible plate on the stability of double-layered falling flow

The hydrodynamic stability behavior of a two-layer falling film is explored with a floating flexible plate on the top layer surface. The stress balance at the surface is modeled using a modified membrane equation. There is an insoluble surfactant at the liquid-liquid interface of the flow system. The linear instability of perturbation waves is captured by numerically solving the generalized Orr-Sommerfeld eigenvalue problem using the Chebyshev spectral collocation technique. Four different types of linear stability modes are identified: surface mode (SM), interface mode (IM), interface surfactant mode (ISM), and shear mode (SHM). The floating flexible plate has an inferior impact on all the existing modes in the longwave zone. However, a significant influence is noticed for the finite wave numbers. The surface and interface wave instabilities can be suppressed in the smaller wavenumber zone by imposing higher structural rigidity and uniform thickness of the flexible plate. The stabilizing nature of the surface mode becomes more powerful when the top layer viscosity is dominant. A new interfacial instability emerges when the top layer is less viscous than the lower one. At moderate Reynolds numbers, the behavior of interface mode is different in two different zones mr<1 and mr>1, where m and r denote the viscosity and density ratio, respectively. Further, the unstable shear modes induced by the top and bottom layers are detected under the low inclination angles with a strong inertia force. The occurrence of the shear modes requires the viscosity and density of the lower layer to be much higher than those of the upper layer. The influence of characteristic parameters of the flexible plate on the lower layer shear mode is not very sensitive. Finally, the competition between the different modes for dominance of stability boundaries is also discussed.

Linear stability of nonrelativistic self-interacting boson stars

Linear stability of nonrelativistic self-interacting boson stars

Periodic solutions in a 2D-symmetric Hamiltonian system through reduction and averaging method

We study a type of perturbed polynomial Hamiltonian system in 1:1 resonance. The perturbation consists of a homogeneous quartic potential invariant by rotations of π / 2 radians. The existence of periodic solutions is established using reduction and averaging theories. The different types of periodic solutions, linear stability, and bifurcation curves are characterized in terms of the parameters. Finally, some choreography of bifurcations are obtained, showing in detail the evolution of the phase flow.

Modulation instability in nonidentical metamaterial waveguide arrays by graph Laplacian approach

We theoretically investigate modulation instability (MI) in a nonidentical waveguide array, which is made up of positive and negative index metamaterial waveguides. The unit cell of the optical waveguide array consists of three waveguides arranged in a triangular manner. Waveguides 1 and 3 are made up of positive index material (PIM) channels and waveguide 2 is by negative index material (NIM) channels, as a result, they show different light propagation characteristics. We model this array of waveguides using a generalized nonlinear Schro¨dinger equation, replacing the Laplacian operator with the graph Laplacian. Following linear stability analysis, we will discuss MI for different values of transverse wave number, as it determines the order of the Brillouin zone. We also discuss the effect of input power on periodic MI in normal and anomalous dispersion regimes. Thus we report a comprehensive study on the MI and hence the better ways to generate and manipulate the solitons or ultra-short pulses in NIM PIM waveguide arrays.

When discrete fronts and pulses form a single family: FPU chain with hardening-softening springs

We consider a version of the classical Hamiltonian FPU (Fermi–Pasta–Ulam) problem with nonlinear force-strain relation in which a hardening response is taken over by a softening regime above a critical strain value. We show that in addition to pulses (solitary waves) this discrete system also supports non-topological and dissipation-free fronts (kinks). Moreover, we demonstrate that these two types of supersonic traveling wave solutions belong to the same family. Within this family, solitary waves exist for continuous ranges of velocity that extend up to a limiting speed corresponding to kinks. As the kink velocity limit is approached from above or below, the solitary waves become progressively more broad and acquire the structure of a kink–antikink bundle. Direct numerical simulations and Floquet analysis of linear stability suggest that all of the obtained solutions are effectively stable. To motivate and support our study of the discrete problem we also analyze a quasicontinuum approximation with temporal dispersion. We show that this model captures the main effects observed in the discrete problem both qualitatively and quantitatively.

A 3-D minimum-enstrophy vortex in stratified quasi-geostrophic flows

Applying a variational analysis, a minimum-enstrophy vortex in three-dimensional (3-D) fluids with continuous stratification is found, under the quasi-geostrophic hypothesis. The buoyancy frequency is held constant. This vortex is an ideal limiting state in a flow with an enstrophy decay while energy and generalized angular momentum remain fixed. The variational method used to obtain two-dimensional (2-D) minimum-enstrophy vortices is applied here to 3-D integral quantities. The solution from the first-order variation is expanded on a basis of orthogonal spherical Bessel functions. By computing second-order variations, the solution is found to be a true minimum in enstrophy. This solution is weakly unstable when inserted in a numerical code of the quasi-geostrophic equations. After a stage of linear instability, nonlinear wave interaction leads to the reorganization of this vortex into a tripolar vortex. Further work will relate our solution with maximal entropy 3-D vortices.

Premixed flames in narrow heated channels of circular cross-section: Steady-state solutions, their linear stability analysis and the multiplicity of stable dynamic modes

Premixed flames in narrow heated circular channels subjected to a Poiseuille flow are investigated within the constant density model for various Lewis numbers using irreversible one-step Arrhenius kinetics. A global stability analysis of steady-state axisymmetric solutions is carried out, together with time-dependent direct numerical simulations. The analysis reveals the criteria for the appearance of oscillatory and three-dimensional cellular flame structures. The problem is also studied separately within the framework of the narrow-channel approximation.Among the results obtained, the following can be singled out as the main ones. First, the multiplicity of stable dynamic modes, oscillatory and steady-state, taking place for the same set of parameters for flames with Le<1 is demonstrated. The actual occurrence of one mode or another depends on the initial conditions. Second, the appearance of chaotic regimes is shown for flames with Le>1. The chaotic dynamics occurs in a narrow range of values of the flow rate, with Feigenbaum period-doubling cascades taking place both before and after this interval. The results of this study could be useful in the development and use of small-scale combustion devices.Novelty and significance statement: A systematic study of premixed flames in narrow heated circular channels in the presence of Poiseuille flow is carried out for various Lewis numbers using irreversible one-step Arrhenius kinetics. One of the novelties presented in the paper is the linear global stability analysis of steady state axisymmetric solutions of this problem, which has not been reported before. Also, for the first time, the existence of multiple stable dynamic modes, oscillatory and time-independent, which occurs at the same parameter values, is demonstrated for flames with Lewis number smaller than one. For flames with a Lewis number greater than one, cases with chaotic dynamics are found that manifest themselves in a narrow range of the flow rate. Finally, it is demonstrated that the Feigenbaum cycle-doubling cascade can appear before and after this interval of chaotic dynamics. Such analysis has not been reported before for this problem of flames in partially heated channels.

Snap-induced flow in a closed channel

Snap-through is a buckling instability that allows slender objects, including those in plant and biological systems, to generate rapid motion that would be impossible if they were to use their internal forces exclusively. In microfluidic devices, such as micromechanical switches and pumps, this phenomenon has practical applications for manipulating fluids at small scales. The onset of this elastic instability often drives the surrounding fluid into motion – a process known as snap-induced flow. To analyse the complex dynamics resulting from the interaction between a sheet and a fluid, we develop a prototypical model of a thin sheet that is compressed between the two sides of a closed channel filled with an inviscid fluid. At first, the sheet bends towards the upstream direction and the system is at rest. However, once the pressure difference in the channel exceeds a critical value, the sheet snaps to the opposite side and drives the fluid dynamics. We formulate an analytical model that combines the elasticity of thin sheets with the hydrodynamics of inviscid fluids to explore how external pressure differences, material properties and geometric factors influence the system's behaviour. To analyse the early stages of the evolution, we perform a linear stability analysis and obtain the growth rate and the critical pressure difference for the onset of the instability. A weakly nonlinear analysis suggests that the system can exhibit a pressure spike in the vicinity of the inverted configuration.

Magnetic field influence on Casson fluid flow in rotating convection

The stability of buoyant flow in an infinite extended vertical fluid layer bounded by impermeable conducting isothermal rigid walls, known as magnetic field influence on Casson fluid flow in rotating convection, is investigated. A system of governing equations (Navier–Stokes, heat, and induction ones) is solved with isothermal rigid boundary conditions. When the majority of electrically conducting fluids are extremely small, the stability of governing equations can be simplified by taking the smallness of magnetic Prandtl number into account. In linear stability, the Chebyshev collocation method is used to solve numerically the system of eigenvalue problems. The Casson fluid parameter, Chandrasekhar number, magnetic Prandtl number, and Taylor number all have destabilizing effects on the system's basic velocity and basic magnetic field, resulting in instability. The critical Rayleigh number (Rc), critical wave number (ac), and critical wave speed (cc) are calculated using the influence of governing parameters. The Casson fluid parameter and magnetic Prandtl number were found to stabilize stationary disturbances in neutral stability curves.

In silico modelling of ciprofloxacin specific aptamer for the development of high-performance biosensor

Ciprofloxacin (CFX), a widely used fluoroquinolone antibiotic, is critical in healthcare settings for treating patients. However, improper treatment of wastewater from these facilities can lead to environmental contamination with CFX. This underscores the need for an efficient, straightforward method for early detection. In this study, a DNA aptamer was selected through a hierarchical docking workflow, and the stability and interactions were assessed by Molecular Dynamics (MD) simulation. The aptamer-CFX complex that showed the most promise had a docking score of −8.596 kcal/mol and was further analyzed using MD simulation and MM/PBSA. Based on the overall results, the identified ssDNA sequence length of 60 nt (CAGCGCTAGGGCTTTTAGCGTAATGGGTAGGGTGGTGCGGTGCAGATATCGGAATTGGTG) was immobilized over a gold transducer surface through the self-assembled monolayer (SAM; Au–S-ssDNA) method. The ssDNA-modified surface has demonstrated a high affinity towards CFX, which is confirmed by cyclic voltammogram (CV) and electrochemical impedance spectroscopy measurements (EIS). The DNA-aptamer modified electrode demonstrated a good linear range (10 × 10−9 – 200 × 10−9 M), detection limit (1.0 × 10−9 M), selectivity, reproducibility, and stability. The optimized DNA-aptamer-based CFX sensor was further utilized for the accurate determination of CFX with good recoveries in real samples.

Parametric analysis of the flow past a square cylinder in the interface of two different-velocity streams

We address the linear stability of the two-dimensional incompressible flow past a square cylinder immersed in the wake of an upstream splitter plate, which separates two streams of different velocities, UT (top) and UB (bottom), to three-dimensional perturbations. The analysis is done in the so-called wake transition regime, across which two-dimensional vortex shedding incorporates spanwise modulation. In addition to the top and bottom stream Reynolds numbers (ReT,B=DUT,B/ν, with D the square cylinder side and ν the kinematic viscosity of the fluid), a parametric analysis is conducted to gauge the effects of splitter plate length (S) and the gap between the trailing edge of the splitter plate and the front face of the cylinder (G) on the leading three-dimensionalizing instabilities. Modes akin to the A- and B-type instabilities that characterize the wake transition regime past circular and square cylinders in homogeneous incoming flow are observed only at very small values of the top-to-bottom Reynolds number ratio R=ReT/ReB, while a third mode, mode C, is ubiquitous beyond more than very mild values of R. Increasing S at constant small G has a stabilizing effect on mode C, whose onset is pushed to higher values of R. Only for long S is mode A observed. Fixing a short S and increasing G results instead in a destabilization of mode C, and mode B is favored over mode A.

Dynamics and Control of a Plant-Herbivore Model Incorporating Allee's Effect

This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect. We specifically investigate a model that incorporates a strong predator functional response to better understand the system's qualitative behavior at positive equilibrium points. In the present study, we explore the topological classifications at fixed points, stability analysis, Neimark-Sacker, Transcritical bifurcation and State feedback control in the two-dimensional discrete-time plant-herbivore model. It is proved that for all involved parameters ς1,ϱ1,γ1 and ϒ1, discrete-time plant-herbivore model has boundary and interior fixed points: c1=(0,0), c2=(ς1−1ϱ1,0) and c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1) respectively. Then by linear stability theory, local dynamics with different topological classifications are investigated at fixed points: c1=(0,0), c2=(ς1−1ϱ1,0) and c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1). Our investigation uncovers that the boundary equilibrium c2=(ς1−1ϱ1,0) experiences a transcritical bifurcation, whereas the unique positive steady-state c3=(ϒ1(1−γ1)2γ1−1,γ1(2ς1+ϱ1ϒ1−2)−ϱ1ϒ1+1−ς12γ1−1) of the discrete-time plant-herbivore model undergoes a Neimark-Sacker bifurcation. To address the periodic fluctuations in grapevine population density and other unpredictable behaviors observed in the model, we propose implementing state feedback chaos control. To support our theoretical findings, we provide comprehensive numerical simulations, phase portraits, dynamics diagrams, and a graph of the maximum Lyapunov exponent. These visual representations enhance the clarity of our research outcomes and further validate the effectiveness of the chaos control approach.