Results Of Stability Analysis Research Articles

CMMSE: New Properties of Auto‐Wave Solutions in Activator‐Inhibitor Reaction‐Diffusion Systems With Fractional Derivatives

ABSTRACTIn this article, we analyze new properties of auto‐wave solutions in fractional reaction‐diffusion systems. These new properties arise due to a change in fractional derivative order and do not occur in systems with classical derivatives. It is shown that the stability of steady‐state solutions and their evolution are mainly determined by the eigenvalue spectrum of a linearized system and the fractional derivative order. It is also demonstrated that the basic properties of auto‐wave solutions in fractional‐order systems can essentially differ from those in standard systems. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol–FitzHugh–Nagumo mathematical model. A common picture of possible instabilities and auto‐wave solutions in time‐fractional two‐component activator‐inhibitor systems is presented.

Linear stability analysis of turbulent mean flows based on a data-consistent Reynolds-averaged Navier–Stokes model: prediction of three-dimensional stall cells around an airfoil

Stall cells are transverse cellular patterns that often appear on the suction side of airfoils near stalling conditions. Wind-tunnel experiments on a NACA4412 airfoil at Reynolds number ${Re}=3.5 \times 10^5$ show that they appear for angles of attack larger than $\alpha = 11.5^{\circ }\ (\pm 0.5^{\circ })$ . Their onset is further investigated based on global stability analyses of turbulent mean flows computed with the Reynolds-averaged Navier–Stokes (RANS) equations. Using the classical Spalart–Allmaras turbulence model and following Plante et al. (J. Fluid Mech., vol. 908, 2021, A16), we first show that a three-dimensional stationary mode becomes unstable for a critical angle of attack $\alpha = 15.5^{\circ }$ which is much larger than in the experiments. A data-consistent RANS model is then proposed to reinvestigate the onset of these stall cells. Through an adjoint-based data-assimilation approach, several corrections in the turbulence model equation are identified to minimize the differences between assimilated and reference mean-velocity fields, the latter reference field being extracted from direct numerical simulations. Linear stability analysis around the assimilated mean flow obtained with the best correction is performed first using a perturbed eddy-viscosity approach which requires the linearization of both RANS and turbulence model equations. The three-dimensional stationary mode becomes unstable for angle $\alpha = 11^{\circ }$ which is in significantly better agreement with the experimental results. The interest of this perturbed eddy-viscosity approach is demonstrated by comparing with results of two frozen eddy-viscosity approaches that neglect the perturbation of the eddy viscosity. Both approaches predict the primary destabilization of a higher-wavenumber mode which is not experimentally observed. Uncertainties in the stability results are quantified through a sensitivity analysis of the stall cell mode's eigenvalue with respect to residual mean-flow velocity errors. The impact of the correction field on the results of stability analysis is finally assessed.

Effect of filler loading on the frictional, thermal and mechanical properties of ABS/boron nitride (h-BN) nanocomposites

The effect of hexagonal boron nitride (h-BN) nanoparticles in acrylonitrile butadiene styrene (ABS) polymer matrix is investigated. ABS/h-BN nanocomposites were prepared with h-BN content ranging from 0.5 to 5 wt% and their frictional, thermal and mechanical properties were evaluated. XRD analysis showed that the 'd' spacing in h-BN stacks increased in the ABS nanocomposite due to the interpenetration of ABS polymer chains. The tensile properties and thermal stability of ABS matrix showed better improvement with 0.5 wt% addition of h-BN nanoparticles. The tensile fracture mechanism in ABS/h-BN nanocomposites was predicted using tensile fracture surface analysis. Coats-Redfern approach was applied to support the thermal stability analysis results. Significant enhancement (28 %) in frictional property of ABS was observed in the nanocomposite with h-BN. Wettability and flame retardancy of the ABS/h-BN nanocomposites were also investigated.

The influence of disks deformation on the stability analysis of an aircraft braking system

Friction-induced vibration emanating from aircraft braking system is a key issue in the design phase, due to the significant damage it can cause to the brake structure. Although the problem of unstable vibrations in aircraft braking systems has been studied by a number of researchers, the suitability of the mechanical modeling strategy for predicting instabilities remains an open problem. The need for relevant numerical models is therefore essential in order to be as predictive as possible during the design phase. Preliminary studies must therefore be carried out to validate or invalidate the modeling hypotheses traditionally used. Indeed the stability analysis of an aircraft braking system is performed in order to study a low-frequency instability. An industrial model is used, hence reducing the number of degrees of freedom (DoF) is of utmost importance in order to have reasonable computation times. When studying low-frequency phenomena, this can be achieved by neglecting the deformations of the disks. However, no current study has shown that this hypothesis is realistic. So the aim of this paper is to assess the effect of the rigidity hypothesis on the results predicted by the stability analysis. In order to do so, the stability analysis results of a model with rigid disks and one with non-rigid disks are compared, with a particular attention on the main instability phenomenon. It is found that considering rigid disks has a very limited influence on the frequency of the low-frequency eigenmodes, but it over-predicts the real part of the unstable eigenmode. Besides, a component mode synthesis (CMS) technique is shown to reduce significantly the size of the non-rigid disks model while ensuring a satisfying precision regarding eigenmodes prediction.

Geomorphological management strategies for cyclone-impacted sea turtle nesting habitat along the eastern seaboard of India.

Sea turtles are globally vulnerable due to climate change uncertainties and anthropogenic threats. The present study highlights the impacts of a very severe tropical cyclone (VSCS) on a potential sea turtle rookery and suggests management strategy for protection and conservation of rookery habitat under changing spit geomorphology. The results show that VSCS has short-term impact on rookery and spit geomorphology, while long-term precarious impact over the coastal sedimentology due to debris pollution. Study on geomorphology, sedimentology, and debris pollution indicates that plastic pollution and change in sediment characteristics are the most probable cause for failure of arribada events during post-cyclone year. Further, study identified that reduced estuary mouth and elongation of sand spit are the potential cause for coastal flooding and loss of nesting habitat. Therefore, locational stability of estuary cross-section under varying dimension of inlet channel and width are estimated for better management of uncertainties arises from the extreme events. Results of stability analysis show that observed cross Sect.(207-1728 m2) is often fall within unstable regimes compared to the estimated equilibrium cross-sectional area (790-1085 m2) under natural estuary condition. Considering the severity of long-shore transport and fast migration of sand spit, study further recommends cross-sectional area of magnitude (951-965 m2) is highly essential while inlet channel oscillates between 3500 and 7500m. Similarly, for siltation issues, cross-sectional area (769-969 m2) is highly required for the varying dimension of estuary widths (50-600m). In addition, involvement of local community in cleaning coast following cyclonic storm could be best approach instead of mechanical way to unalter the rookery sedimentology. This comprehensive approach addresses immediate cyclone-induced threats while promoting the long-term sustainability of sea turtle nesting habitats, offering actionable management recommendations for maintaining estuary stability and preserving critical nesting environments in face of increasing coastal disasters.

Delay-tolerant hierarchical distributed control for DC microgrid clusters considering microgrid autonomy

A microgrid cluster (MGC) is formed by interconnected geographically adjacent microgrids (MGs), which can effectively improve power supply reliability. To fulfill the requirements of coordination between MGs while exerting the autonomy ability of each MG, this paper proposes a hierarchical distributed control method for DC MGCs with MG autonomous-cooperative mode switching. The proposed method can not only realize the proportional current sharing between the MGs and the voltage regulation of the common bus but also allow MGs to operate in autonomous or cooperative mode by establishing and disconnecting the inter-MG communication links. In addition, considering that the delay of inter-MG communication links affects multiple control links of the proposed control method, a delay-dependent stability analysis method based on Padé approximation and eigenvalue spectrum comparison is proposed. By stability analysis, the time delay margin (TDM) is determined, and the key link that determines the TDM is identified as the observer based on the proportional-integral (PI) consensus algorithm. On this basis, the scattering transformation (ST) is introduced to improve the stability of the observer under delay and thus enhance the TDM of DC MGCs, which is confirmed by stability analysis based on a new system model integrating node variables and edge variables. Finally, the performance of the proposed control method and stability analysis results are verified by hardware-in-loop (HIL) tests and MATLAB/Simulink simulations

Mixed Grass Species Enhances Root Production and Plant–Soil Reinforcement

ABSTRACTVegetation is a widely used eco‐friendly approach for slope reinforcement and ecological restoration. As a potential planting strategy, mixed planting of plants is often recommended to improve biodiversity, but the effects of mixed planting on soil reinforcement and slope stability are not yet clear. To address this issue, a study on two typical herbaceous slope protection plants, Chrysopogon zizanioides and Cynodon dactylon, were conducted. The biomechanical characteristics of different herbaceous plants were analyzed, and their root distribution and soil reinforcement performance under single and mixed planting were explored. Results show that mixed planting could significantly increase the number and root area ratio of root systems. At 0.1 cm depth after 42 days, the root number under mixed planting increased by 111.42% compared to vetiver grass monoculture and by 19.57% compared to bermuda grass monoculture. Mixed planting can provide stronger soil reinforcement by increasing apparent cohesion, with a maximum increase in apparent cohesion of 47.9%. The results of slope stability analysis showed that vegetation mainly relied on mechanical reinforcement in the root zone and hydrological reinforcement outside the root zone. After 42 days of growth, mixed planting at 0.1 m depth increased slope stability by 11.94% compared to vetiver grass monoculture and by 27.12% compared to bermuda grass monoculture, with both mechanical and hydrological effects of vegetation significantly enhanced. These findings suggest that mixed planting can promote plant development and growth, improve root production, and enhance plant–soil reinforcement and slope stability during the early establishment of vegetation. Therefore, in formulating slope reinforcement and ecological restoration strategies, more consideration can be given to mixed planting of plants, maximizing the utilization of competition characteristics between plants, and reducing the risk of shallow landslides while improving biodiversity.

Modified Target Pressure Distribution for Supersonic Natural Laminar Flow Wing Design

Natural laminar flow (NLF) is an important technique for reducing drag of the next-generation supersonic transport aircraft. However, achieving NLF on supersonic transport wings is challenging due to the large swept angles and high-Reynolds-number conditions, which significantly amplify Tollmien–Schlichting (TS) and crossflow (CF) instabilities. To address this problem, this paper proposes a modified target pressure distribution to attenuate the TS and CF instabilities. Compared with conventional targets defined using empirical functions, it is derived in two steps: the first step is to prescribe an initial flat target pressure distribution with a narrow leading-edge flow acceleration region and conduct inverse designs; the second step is to modify the target pressure distribution according to the stability analysis results of the designed wing in order to achieve a balance of disturbance growth at positive and negative wave angles. The proposed approach is validated on a 60°-swept infinite-span wing at Ma=2 and Re=1.39×107. Results demonstrate that TS and CF instabilities are well-suppressed under the modified target pressure distribution, with the transition location delayed from xtr/c=0.26 on the baseline wing to xtr/c=0.95 on the designed wing, suggesting that the proposed method is effective for NLF design on supersonic highly swept wings.

Investigation of the Sigma Approximation Technique for the Solution of the Time Spectral Equation System

Abstract The time spectral method (TSM) is commonly utilized to analyze periodic unsteady flows within turbomachines. However, the time spectral solutions in regions with large temporal and spatial gradients, such as wakes, shocks, and boundary layers, can be plagued with unphysical oscillations, known as the Gibbs phenomenon. This paper presents an investigation into the sigma approximation technique, which is capable of significantly attenuating the Gibbs phenomenon by dampening high-frequency nonlinear components in time spectral solutions. Central to this technique are three sigma parameters: the exponent, the cutoff number, and the number of harmonics, which collectively determine the damping effects for each frequency. However, the optimal combination of them remains to be ascertained considering the tradeoff between the accuracy of solutions and the reduction of unphysical oscillations. In this study, a two-row compressor configuration is first selected, and numerical simulations are performed to evaluate the efficacy of this technique under near-peak efficiency and near-stall operating conditions. It is found that Gibbs-type unphysical oscillations can be effectively mitigated without notably compromising solution accuracy through an optimal combination of sigma parameters. The NASA Stage 35 case study further verifies the effectiveness of the proposed optimal sigma parameter combination in preserving the accuracy of time spectral solutions based on the data from test rig. Moreover, the von Neumann analysis reveals that the sigma approximation technique can enhance the numerical stability of the time spectral equation system, thereby allowing the use of aggressive numerical parameters to accelerate convergence. The stability analysis results are verified by a two-dimensional bump under two different flow conditions and further assessed using the two-row compressor.

Studying the Antioxidant and Antimicrobial Activity of Lipsticks Made with Phycoerythrin Under the Influence of Different Magnetic Fields

Background: Several studies have shown the benefits of magnetic treatment on the productivity of secondary metabolites, growth, and the state of microalgae cultures Objective: This study examined the antioxidant and antimicrobial activity of lipsticks made with phycoerythrin (PE) extracted from the cyanobacterium Nostoc sp. under the influence of different magnetic fields (30 mT and 60 mT). Material and Methods: After cyanobacterial culture under magnetic fields of 30 mT and 60 mT, the PE was extracted and lipsticks were formulated. The primary evaluation methods used in this study are melting point, breaking point, linoleic acid peroxidation assay, force of application, stability, surface abnormalities, skin irritation, thixotropy character, dispersibility test, perfume stability, colorimetric assay, antioxidant, and microbial analysis Results: The 30 mT treatment showed the highest concentration, purity, dry weight, antioxidant activity, and percentage of PE extraction compared to control cultures. No significant differences were found in the melting point, stability, thixotropy character, dispersibility, or perfume stability tests. The breaking point and force of application decreased significantly during 30 days. Peroxidation assay tests revealed lipstick increased oxidation and antioxidant activity after 30 days of 30 and 60 mT treatments compared to non-PE cultures. The study found that the amount of ΔE increased significantly in cultures without PE over time, while this increase was lower in magnetic field-treated cultures. However, no signs of crystal formation, surface wrinkles, liquid secretion, itching, or skin irritation were observed in 30 days of 30 and 60 mT magnetic treatments compared to control cultures with PE. Microbial analyzes over 30 days showed a significantly lower number of bacteria under magnetic fields than control cultures. In addition, the results of counting Escherichia coli and coliform bacteria were negative for thirty days. The antioxidant activity of PE was significantly higher in magnetic field-treated cultures. The number of Staphylococcus aureus decreased significantly in all cultures under magnetic field influence. Conclusions: The overall results of this study showed that magnetic fields had a significant effect in many evaluation tests on the culture of cyanobacteria Nostoc sp. As a result, lipsticks made with extracted PE have more antioxidant and antimicrobial activity

Применение высокопрочной стали для создания полувагонов повышенной грузоподъемности

Purpose: substantiation of the possibility to increase the load capacity of gondola cars using high-strength steel in the car body structure. Methods: gondola cars load capacity changing analysis. Numerical research of the effect of the steel yield strength value on the mass of the beam structure according to the criteria of strength and stiffness for a beam on two hinged supports operating in bending, and also according to the buckling criteria of a compressed beam. Gondola car body structure finite element analysis in order to confirm the strength and buckling parameters with the normative requirements. Results: the analysis of load capacity of universal fouraxle gondola cars built in the period from the beginning of production of the first Russian cars up to the present time was performed. Results of the analysis of the effect of steel yield strength on the mass of the structure according to the strength criteria and stiffness for a beam on two hinged supports operating in bending, and also according to the buckling criteria of a compressed beam was presented. High-strength steel technical requirements for welded structures of freight wagons is considered. Parameters for evaluating the suitability of rolled high-strength steel for freight wagon construction are given. The results of strength and stability analysis of the gondola car model 12-6744 with high-strength steel, which confirm the design compliance of the car in terms of normative parameters of strength and stability with the requirements of the existing standards are given. The gondola car model 12-6744 advantages are described, as well as the economic effect of its operation for the consignor. Practical importance: the possibility of using high-strength steel to increase the load capacity of gondola cars is substantiated. The gondola car model 12-6744 with high-strength steel was designed. Its advantages are given, and the economic effect of operating such a wagon for the consignor is shown.

Impedance modeling and quantitative stability analysis of grid-connected voltage source converters under complex unbalanced conditions

The stability issues caused by voltage source converters (VSCs), which are commonly used in renewable energy systems, are investigated in this paper. Much literature has investigated the impedance models and quantitative stability analysis for converters under the weak and unbalanced grid. However, on the one hand, harmonic-transfer-function (HTF)-based modeling methods are complex, and the established infinite-order models may suffer from unreasonable truncation. On the other hand, these existing impedance models without considering all unbalance factors are inaccurate. Both of these may bring wrong stability analysis results. Therefore, this paper proposes a simple impedance extension method and considers all unbalance factors to derive the impedance model of the converter. However, due to the established higher-order impedance model, the traditional impedance-ratio based stability analysis method is not applicable to multi-input multi-output (MIMO) systems. The commonly used eigenvalue-based GNC and diagonalization-based methods applicable to MIMO systems are cumbersome and not suitable for quantitative analysis. Therefore, in this paper, a quantitative analysis tool of system stability based on the phase-frequency characteristics of determinants is developed. Then, stability regions in the multi-parameter space are obtained. Finally, the established impedance model and the quantitative analysis results are validated via both simulations and hardware experiments.© 2017 Elsevier Inc. All rights reserved.

Non-smooth self-excited vibration of a novel dynamical model for a disc brake

This paper proposes a new dynamic model for the study of friction-induced self-excited vibration of a disc brake system, where the pad’s motions in both radial and circumferential/tangential directions are included, which is in stark contrast to the previous studies that normally consider the pad’s motion in the tangential/circumferential direction only. The non-smooth dynamics of the system including three different states of motion, i.e., stick, slip and separation, is investigated. Both the linear stability analysis and the transient dynamic analysis are performed. The numerical results in the linear stability analysis indicate that the inclusion of pad’s radial motion in the present brake model significantly expands the ranges of operating parameters for dynamic instability than the brake model with only circumferential/tangential motion for the pad. For the transient dynamic analysis, two different methods, i.e., the time integration method and the shooting method, are employed for the calculation of steady-state response. The accuracy and efficiency of the shooting method are subsequently examined. The numerical results show rich bifurcation behaviours of the steady-state response in the present brake model with the variations of brake pressure and disc speed , and (the stiffness of the inclined spring in the radial direction) is a key parameter for controlling the occurrence of chaotic vibration in the system. Conflict of Interest Statement The authors declare no conflicts of interest.

Landslide Analysis with Incomplete Data: A Framework for Critical Parameter Estimation

Landslides are one of the most common geohazards, posing significant risks to infrastructure, recreation, and human life. Slope stability analyses rely on detailed data, accurate materials testing, and careful model parameter selection. These factors are not always readily available, and estimations must be made, introducing uncertainty and error to the final slope stability analysis results. The most critical slope stability parameters that are often missing or incompletely constrained include slope topography, depth to water table, depth to failure plane, and material property parameters. Though estimation of these values is common practice, there is limited guidance or best practice instruction for this important step in the analysis. Guidance is provided for the estimation of: original and/or post-failure slope topography via traditional methods as well as the use of open-source digital elevation models, water table depth across variable hydrologic settings, and the iterative estimation of depth to failure plane and slope material properties. Workflows are proposed for the systematic estimation of critical parameters based primarily on slide type and scale. The efficacy of the proposed estimation techniques, uncertainty quantification, and final parameter estimation protocol for data-sparse landslide analysis is demonstrated via application at a landslide in Colorado, USA.

Research on upper bound limit analysis of slope stability in open-pit mine based on least square principle

So as to extend the application of upper bound limit analysis for slope stability in open-pit mine, this paper analyzed failure mechanism of rock mass when shear failure occurred based on plastic mechanics principles, and combined with discrete mathematical theory and least square principle to propose a visualization method of logarithmic spiral. At the same time, the visualization method was applied to engineering practice for slope stability in open-pit mine, and cycle algorithm of stability analysis for open-pit mine slope was proposed through energy balance conditions, then stability analysis results were evaluated reasonably through uniting with limit equilibrium method. The results show that visualization method of logarithmic spiral proposed in this paper is highly consistent with original curve, and can ensure correlation coefficient square is greater than 0.9995. What is more, upper bound limit analysis method has a superhigh accuracy in slope engineering. At the same time, the most dangerous sliding surface obtained by this method can satisfy the requirements of velocity separation, which solved velocity problems during the process of slope evolution. Therefore, the method proposed in this paper has a stronger application in the field of open-pit mining.

Investigation on the Preparation and Performance of a Novel Sustained-Release Type Fluid Loss Agent for High-Temperature Resistant Oil Well Cement

Fluid loss agents (FLA) can reduce the fluid loss of cement paste by adsorption on the surface of the cement particles during cementing and decreasing the permeability of the cement cake, ensuring the safety of the cementing. As the exploration of the use of cement is progressing toward deeper and ultra-deeper layers, the use of FLA at high temperatures is urgently necessary. Hence, in this article, we describe the preparation of FLA with an organic/inorganic intercalated microstructure to meet the requirements of cementing at 210 °C. The anionic polymer FLA (ASDA) consists of 2-acrylamido-2-methylpropane sulfonic acid, sodium p-styrenesulfonate, N, N-dimethylacrylamide, and sodium 3-allyloxy-1-hydroxy-1-propylene. Organic-inorganic hybrid FLA, magnesium/aluminum-ASDA-hydrotalcite (Mg/Al-ASDA-LDHs) was prepared by intercalating ASDA into the interlayers of magnesium/aluminum layered double hydroxides (Mg/Al-LDHs) via an anion-exchange reaction. The results of thermal stability analysis showed that Mg/Al-ASDA-LDHs had better thermal stability than ASDA, with a decomposition temperature of 416 °C. In addition, the structure effectively mitigated the decrease in compressive strength of the mud caused by the carboxyl groups in the polymer. The Mg/Al-LDHs structure avoids the problem of reduced compressive strength of hardened cements due to conventional polymer FLA. The compressive strength of the cement containing Mg/Al-ASDA-LDHs increased by 57.4% after 7 days of curing compared with the cement containing 3% bwoc (“% bwoc” is defined as “by the weight of cement”) ASDA.

Nonlinear flow phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface

In this paper, we present a comprehensive study of the fingering phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface. A theoretical analysis is firstly carried out and the governing equation describing the film thickness is established for the non-Newtonian fluid denoted by a power-law index n. Using the lubrication theory with dimensionless variables, the partial differential equation for the film thickness is derived, and both two-dimensional flow and three-dimensional flow are investigated. The traveling wave characteristic of the two-dimensional flow is displayed by using the finite difference scheme associated with a Newton iteration technique. The effect of changing the radius of the cylinder, precursor-layer thickness and power-law index is then considered through examining the variation of the capillary waves. Furthermore in three-dimensional complex flow, the fingering patterns for different parameters are simulated. The linear stability analysis based on the traveling wave solutions is given to elucidate the influence of different physical parameters, explaining the physical mechanism of nonlinear flow behaviors in two dimension and three dimension. Results from linear stability analysis show that the power-law index reinforces the fingering instability whether the fluid is shear-thinning or shear-thickening. Moreover, the numerical results illustrate that increasing the radii of the cylinder expands the unstable region. The flow profiles for different power-law coefficients are consistent with the result of the linear stability analysis, proving the unstable role of the power-law coefficient.

Nonmodal linear stability analysis of hypersonic flow over an inclined cone

Nonmodal linear stability analysis results are presented for hypersonic flow over a cone at 6° angle of attack complementing earlier modal stability analysis. Based on the parallel flow assumption, singular value decomposition is applied to obtain the optimal linear combination of global crossflow modes. The optimal disturbance exhibits significant transient growth in the initial short distance and progressively follows the path of the most unstable mode downstream. The largest transient energy gain is observed for disturbances at around 40 kHz close to the most amplified modal frequency and tends to increase with the Reynolds number. The optimal disturbance initially exhibits two amplitude peaks in the azimuthal direction, one lying in the leeward region where the unstable crossflow modes reside and the other in the windward region where the adjoint modes exist. As the optimal disturbance travels downstream, the second amplitude peak rapidly shifts toward the leeward side and reaches the optimal energy gain when it eventually merges with the first amplitude peak. The evolution process of the optimal disturbance indicates that the optimal disturbance might have exploited the locally crossflow instability through traveling from the windward side to the leeward side.

Amplification factor transport equation modelling of Mack mode disturbances in hypersonic boundary layers

In the hypersonic boundary layer, the streamwise instability modes are mainly the Mack first mode and the Mack second mode. After the Mach number exceeds 4.0, the Mack second mode becomes the dominant instability mode for boundary layer transition. Currently, there is no complete analytical method to establish an amplification factor transport equation for the second mode. In order to improve the application of the amplification factor transport (AFT) model in hypersonic boundary layer transition prediction, this paper employs boundary layer similarity solutions to conduct stability analysis on the second mode and introduces a function to calculate the growth rate of disturbances. Additionally, a transport equation for the amplification factor of the second mode is formulated. For the non-local variables appearing in the equation, a local calculation method is provided. Combined with the intermittency factor transport equation, a transition prediction model for the second mode is formed. Hypersonic flat plate, wedge, and flared wedge are selected for model validation. The computed results show good agreement with standard stability analysis or experimental results, demonstrating the rationality of the transition model and its high prediction accuracy and reliability.

Existence and stability of dissipative solitons in a dual-waveguide lattice with linear gain and nonlinear losses

In this study, we investigate the existence and stability of in-phase and out-of-phase dissipative solitons in a dual-waveguide lattice with linear localized gain and nonlinear losses under both focusing and defocusing nonlinearities. Numerical results reveal that both types of dissipative solitons bifurcate from the linear amplified modes, and their nonlinear propagation constant changes to a real value when nonlinearity, linear localized gain, and nonlinear losses coexist. We find that increasing the linear gain coefficient leads to an increase in the power and propagation constant of both types of dissipative solitons. For defocusing nonlinearity, in-phase solitons are stable across their entire existence region, while focusing nonlinearity confines them to a small stable region near the lower cutoff value in the propagation constant. In contrast, out-of-phase solitons have a significantly larger stable region under focusing nonlinearity compared to defocusing nonlinearity. The stability regions of both types of dissipative solitons increase with increasing nonlinear losses coefficient. Additionally, we validate the results of linear stability analysis for dissipative solitons using propagation simulations, showing perfect agreement between the two methods.