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The friction-induced vibration of a continuous system consisting of two flexible beams in sliding contact to represent a brake system is studied in this paper. Besides the motion of relative sliding when the two beams are in contact, the separation of beams may also happen in the system dynamics. The complex eigenvalue analysis for the stability of the steady sliding state and the transient dynamic analysis for the characteristics (intensity and periodicity) of the steady-state responses of the system are carried out. Moreover, the results obtained using different numbers of beam modes are acquired and compared. It is found that only a few low-order beam modes need to be incorporated to get accurate results of the stability of the steady sliding state and the steady-state responses of the continuous frictional system, which therefore theoretically justify the omission of high-order modes of continuous structures when investigating the friction-induced vibration of continuous systems and thereby greatly reduce the computational cost. Additionally, the inclusion of the separation and re-contact behavior has a significant effect on the number of required modes for accurate steady-state responses compared with that when no separation is considered, which also verifies the important role of the separation and re-contact behavior in the system dynamics. Besides, a reduced dynamic model that can produce identical dynamic behaviors to those of the continuous frictional system is constructed, with the structural parameters of the reduced model derived from the several key low-order modes of beams. [ABSTRACT FROM AUTHOR]

Buoyancy‐driven Rayleigh–Bénard convection in the presence of a magnetic field, rotation, and temperature‐dependent viscosity has applications in the field of crystal growth, space laboratory experiments, and atmospheric convection. It also has potential applications in heat transfer and magnetohydrodynamics, which can occur in planetary and stellar interiors. The present work aims to study the combined effect of magnetic fields and rotation on the onset of Rayleigh–Bénard convection in temperature‐dependent viscosity Newtonian liquids with internal heat sources/sinks. Both linear and weak nonlinear stability analyses of convection are performed in the problem. The minimal representation of the Fourier series for the stream function and the magnetic potential allows us to derive the analytical expression for the thermal Rayleigh number (Ra $Ra$) and the generalized Lorenz model. In linear theory, the critical Rayleigh number and the wave number are tabulated for different values of the Chandrasekhar number (Q $Q$), the Taylor number (Ta $Ta$), and the thermorheological parameter (V $V$), and the onset of stability is analyzed. It is found that the instability manifests at Rac=657.51124 $R{a}_{c}=657.51124$ when Q=V=Ta=0 $Q=V=Ta=0$ for stress‐free and isothermal boundaries. In nonlinear theory, the generalized Lorenz model obtained is not amenable to analytical treatment; therefore, the classical fourth‐order Runge–Kutta method is applied to solve the Lorenz model. It is found that the internal Rayleigh number, the thermorheological parameter, and the Taylor number influence the onset of convection and heat transfer coefficient. It is also demonstrated that the joint increase in rotational force and magnetic field strength stabilizes the system strongly, thereby reducing heat transfer. However, increasing the heat source and the variable viscosity parameter have antagonistic influences. [ABSTRACT FROM AUTHOR]

A one-equation transition model is proposed for high-speed transitional flows. The model is based on the amplification-factor-transport framework and involves only one transport equation for the amplification factor of streamwise instabilities. A new algebraic intermittency factor is established and applied to a turbulence model to predict transition, and the model is tested by applying it to several cases over a wide speed range. Comparisons with linear stability theory and available experimental data indicate that the model handles first- and second-mode-induced transitions in supersonic and hypersonic flows and reasonably captures the effects of Mach number, wall-to-edge temperature ratio, and nose bluntness. The new one-equation model offers reduced computational burden and simpler implementation while retaining a reasonable prediction accuracy. [ABSTRACT FROM AUTHOR]

Viscous fingering is a common instability event that occurs during the process of water-drive oil for oil recovery, significantly limiting the efficiency of oil extraction. In this study, we propose a film flow model that accounts for the variation in height at the water-oil two phase interface, enabling the calculation and analysis of the triggering mechanism and flow evolution process of this unstable phenomenon. We theoretically derive the equation of water film flow, which can be used to explore the flow evolution of the two-phase interface in the process of oil displacement. By numerically solving the two-dimensional flow equation, we obtain the traveling wave profile and find that the morphology of the two-phase interface is significantly affected by the plane's inclined angle, capillary number and density ratio of the two-phase liquid. Furthermore, we perform linear stability analysis and finite element numerical simulation considering small initial disturbances to explore the triggering conditions of viscous fingering phenomenon and the full time from gentle displacement to unstable flow. The results reveal that the moving contact line of the driven liquid front is more stable when the viscosity of the oil is less different from the driven liquid and has a smaller density, thereby improving of the driving efficiency in the water-driven oil process. These insights have significant implications for guiding efforts to enhance oil recovery efficiency, and we provide concrete engineering suggestions to achieve this aim. ● The equation of water film flow during water driving oil is derived considering the height of the two-phase interface. ● The traveling wave profile of the water film is explored to analysis the water-oil interface at a certain time in the water driving oil process. ● The linear stability analysis of water-oil interface is studied to investigate the evolution of small perturbations and explain the triggering mechanism of viscous fingering. ● We simulate the evolution of the two-phase interface in water driving oil to follow the full time evolution from smooth flow to the formation of viscous fingering. [ABSTRACT FROM AUTHOR]

During the 2022 monkeypox (Mpox) outbreak in non-endemic countries, sexual transmission was identified as the dominant mode of transmission, and particularly affected the community of men who have sex with men (MSM). This community experienced the highest incidence of Mpox cases, exacerbating the public health burden they already face due to the disproportionate impact of HIV. Given the simultaneous spread of HIV and Mpox within the MSM community, it is crucial to understand how these diseases interact. Specifically, since HIV is endemic within this population, understanding its influence on the spread and control of Mpox is essential. In this study, we analyze a mechanistic mathematical model of Mpox to explore the potential impact of HIV on the dynamics of Mpox within the MSM community. The model considered in this work incorporates the transmission dynamics of the two diseases, including antiretroviral therapy (ART) for HIV. We assumed that HIV was already endemic in the population at the onset of the Mpox outbreak. Through our analysis, we derived the Mpox invasion reproduction number within an HIV-endemic setting and established the existence and local asymptotic stability of the Mpox-free equilibrium under these conditions. Furthermore, we demonstrated the existence and local asymptotic stability of an Mpox-endemic equilibrium in an HIV-endemic regime. Notably, our findings revealed that the model exhibits a backward bifurcation, a phenomenon that may not have occurred in the absence of HIV within the population. The public health significance of our results is that the presence of HIV in the MSM community could hinder efforts to control Mpox, allowing the disease to become endemic even when its invasion reproduction number is below one. Additionally, we found that Mpox might be more challenging to control in scenarios where HIV increases susceptibility to Mpox. Finally, consistent with previous studies, our analysis confirms that reducing sexual contact can be effective for controlling the spread of Mpox within the MSM community.

This paper presents a novel segment-based Eulerian-Lagrangian transition method for predicting the primary and secondary breakup behavior of a flat nozzle spray. It combines the Volume of Fluid (VOF) method for simulating liquid sheet disintegration and primary breakup with the Discrete Phase Model (DPM) method for secondary breakup. The VOF simulation predicts the varying thickness and local velocity characteristics of the liquid sheet from the center region to the edge region near the nozzle exit. Meanwhile, the proposed segment-based linear stability analysis in this study is capable of predicting the initial droplet variation resulting from primary breakup, considering the varying behavior of the liquid sheet from different regions. The simulation results match reasonably well with experimental data at both macroscopic and microscopic levels, effectively predicting the overall spray structure, mass flow rate, and droplet size variations across different regions with good accuracy. Both experimental and numerical data show that the Sauter mean diameter (SMD) values differ between the center and edge regions, with the edge region displaying larger droplets than the center region. This indicates that the segment-based approach is crucial for successfully predicting the spatial distributions of droplet size characteristics. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the nonlinear transition to turbulence in generalized 3D Kolmogorov flow. The difference between this and classical Kolmogorov flow is that the forcing term in the x direction sin (y) is replaced with sin (y) cos (z) . This drastically complicates the problem. First, a stability analysis is performed by deriving the analog of the Orr–Sommerfeld equation. It is shown that for infinite stretching, the flow is stable, contrary to classical forcing. Next, a neutral curve is constructed, and the stability of the main solution is analyzed. It is shown that for the cubic domain, the main solution is linearly stable, at least for 0 < R ≤ 100 . Next, we turn our attention to the numerical investigation of the solutions in the cubic domain. The main feature of this problem is that it is spatially periodic, allowing one to apply a relatively simple pseudo-spectral numerical method for its investigation. We apply the method of deflation to find distinct solutions in the discrete system and the method of arc length continuation to trace the bifurcation solution branches. Such solutions are called disconnected solutions if these are solutions not connected to the branch of the main solution. We investigate the influence of disconnected solutions on the dynamics of the system. It is demonstrated that when disconnected solutions are formed, the nonlinear transition to turbulence is possible, and dangerous initial conditions are these disconnected solutions. [ABSTRACT FROM AUTHOR]

This paper explores an analytical approach for obtaining multiple solutions for a three-wave interaction system in (1 + 1) dimensions. We introduce a novel approach that expresses wave solutions in terms of Jacobi elliptic functions and explores specific cases involving hyperbolic functions. Additionally, this paper focuses on analyzing the linear stability of two kinds of solutions: (a) periodic and (b) one or two-hump bright solitons influenced by group velocity and group velocity dispersion. The method of separation of variables along with the ansatz method is employed to derive extract analytical solutions of this model. For linear stability analysis, the eigenvalue problem is solved using the Fourier collocation method, where Fourier coefficients are defined analytically and validated numerically. Moreover, linear stability is verified through direct numerical simulations using the pseudospectral method with special derivatives in the temporal direction (t) and the 4th-order Runge–Kutta method in the spatial direction (z), further confirmed by the Crank-Nicholson finite difference method. All these investigations within the framework of our current model yield novel insights and present breakthrough research opportunities in the realm of nonlinear optics. A key finding of this study is the discovery of stable analytical solutions, which are presented here for the first time. Furthermore, we introduce a special case known as constant magnitude wave solution and examine its modulational instability in the presence of group velocity dispersion. We also investigate the influence of group velocities and wave vector mismatches. All the results obtained are new and interesting, and the concept opens new possibilities for results in the field of nonlinear optics and nonlinear dynamics. [ABSTRACT FROM AUTHOR]

As the core of reproducing the real nonlinear phenomena of traffic congestion, the investigation of car-following models, which take into account human factors, has consistently assumed a central role within the domain of transportation science. Nevertheless, it is noteworthy that prior studies have invariably employed a fixed value for driver reaction time to stimuli, whereas it is imperative to recognize the dynamic nature of this parameter, closely associated with the instantaneous vehicle speed. To address this issue, this paper constructs a dynamic sensitivity coefficient (DSC), and further develops a nonlinear human factoring car-following model to reveal the relation between the reaction time and the current speed. Firstly, the linear critical stability condition and the mKdV equation of the model are derived by the linear stability analysis and kink–antikink solution analytic method, respectively. Then, the numerical experiments are conducted to demonstrate that the proposed model is more practical and can reproduce the real driving behavior and phenomena. Finally, calibration and validation results exhibit the actual vehicle trajectory can be simulated well. [ABSTRACT FROM AUTHOR]

Summary: Stomatal closure during drought inhibits carbon uptake and may reduce a tree's defensive capacity. Limited carbon availability during drought may increase a tree's mortality risk, particularly if drought constrains trees' capacity to rapidly produce defenses during biotic attack.We parameterized a new model of conifer defense using physiological data on carbon reserves and chemical defenses before and after a simulated bark beetle attack in mature Pinus edulis under experimental drought. Attack was simulated using inoculations with a consistent bluestain fungus (Ophiostoma sp.) of Ips confusus, the main bark beetle colonizing this tree, to induce a defensive response.Trees with more carbon reserves produced more defenses but measured phloem carbon reserves only accounted for c. 23% of the induced defensive response. Our model predicted universal mortality if local reserves alone supported defense production, suggesting substantial remobilization and transport of stored resin or carbon reserves to the inoculation site.Our results show that de novo terpene synthesis represents only a fraction of the total measured phloem terpenes in P. edulis following fungal inoculation. Without direct attribution of phloem terpene concentrations to available carbon, many studies may be overestimating the scale and importance of de novo terpene synthesis in a tree's induced defense response. [ABSTRACT FROM AUTHOR]

In this paper, two novel classes of implicit exponential Runge–Kutta (ERK) methods are studied for solving highly oscillatory systems. First of all, symplectic conditions for two kinds of exponential integrators are derived, and we present a first-order symplectic method. High accurate implicit ERK methods (up to order four) are formulated by comparing the Taylor expansion of the exact solution, it is shown that the order conditions of two new kinds of exponential methods are identical to the order conditions of classical Runge–Kutta (RK) methods. Moreover, we investigate the linear stability properties of these exponential methods. Numerical examples not only present the long time energy preservation of the first-order symplectic method, but also illustrate the accuracy and efficiency of these formulated methods in comparison with standard ERK methods. [ABSTRACT FROM AUTHOR]

We present LinStab2D, an easy-to-use linear stability analysis MATLAB tool capable of handling complex domains, performing temporal and spatial linear stability, and resolvent analysis. We present the theoretical foundations of the code, including the linear stability and resolvent analysis frameworks, finite differences discretization schemes, and the Floquet ansatz. These concepts are explored in five different examples, highlighting and illustrating the different code capabilities, including mesh masking, mapping, imposition of boundary constraints, and the analysis of periodic flows using Cartesian or axisymmetric coordinates. These examples were constructed to be a departure point for studying other flows. [ABSTRACT FROM AUTHOR]

Last December 27th, 2023, Ebru Cavlak Aslan et al. have published the article in the Journal "Optical and Quantum Electronics" the article titled "Analysing of different wave structures to the dissipative NLS equation and modulation instability" (Opt Quantum Electron 56:254, 2024. https://doi.org/10.1007/s11082-023-06035-6) where they tried to present analytical solutions of a dissipative nonlinear Schrödinger equation and study the modulational instability of the continuous wave solution of that equation. After analyzing their results, we found a number of shortcomings about both the modulational instability study and the analytical solutions. For analytical solutions, we found that all their found exact solutions were about the standard nonlinear Schrödinger equation and may contain errors/mistakes since at least one of their found dark soliton solutions was done in the region of modulational instability of the standard nonlinear Schrödinger equation. We also found that all their results about the modulational instability were obtained on an erroneous plane wave solution of their model equation, leading thus to obsolete results. It is the aim of the present comment to correct all shortcomings found in that study on the modulational instability. [ABSTRACT FROM AUTHOR]

We examine the genesis of coherent vortices in submerged vegetated flows by means of a linear stability analysis. The mathematical framework is comprised of the conservation equations of fluid mass and momentum. The problem is tackled by imposing normal mode perturbations over an underlying undisturbed flow. We find that the growth rate of perturbations takes maximum magnitude for a specific wavenumber, termed as the critical wavenumber. The critical wavenumber indicates the most favorable wavenumber of coherent vortices emerging in submerged vegetated flows. The critical wavenumber amplifies as the flow Reynolds number, and vegetation height and density augment. The migration velocity of incipient coherent vortices characterizes minimum magnitude for a selected value of the vegetation height. The unstable zone in the stability diagram embarks beyond a critical Reynolds number. The critical Reynolds number designates the onset of coherent vortex appearance in submerged vegetated flows. The predictions of the present study are congruent with the existing theoretical and experimental works. [ABSTRACT FROM AUTHOR]

Articulated heavy vehicles exhibit poor lateral stability, which may lead to unstable motion modes, e.g., trailer-sway and jackknifing, causing severe accidents. Varying relevant vehicle parameters improves the static stability but degrades the dynamic stability. The past studies focused either on the static or dynamic stability alone. However, little attention has been paid to exploring the trade-off between the static and dynamic stabilities. To gain design insights for active safety systems for AHVs, this article studies this trade-off systematically. To this end, a systematic method is proposed to conduct the linear stability and trade-off analysis. To implement and demonstrate the proposed method, a linear three-degrees-of-freedom yaw-plane model is generated to represent a tractor/semi-trailer. A trade-off analysis is conducted considering two tractor rear-axle configurations and three trailer payload arrangements. In each case, simulation is performed in both steady-state and transient testing maneuvers. To validate the linear stability analysis based on the linear yaw-plane model, two nonlinear TruckSim models are introduced, and the corresponding simulation is conducted. Insightful understanding of the trade-off is gained through analyzing the simulation results, and the linear stability analysis will provide valuable guidelines for the design and development of active safety systems for AHVs. [ABSTRACT FROM AUTHOR]

The one-dimensional Two-Fluid concept uses an area-average approach to simplify the time and phase-averaged Two-Fluid conservation equations, making it more suitable for addressing difficulties at an industrial scale. Nevertheless, the mathematical framework has inherent weaknesses due to the loss of details throughout the averaging procedures. This limitation makes the conventional model inappropriate for some flow regimes, where short-wavelength perturbations experience uncontrolled amplification, leading to solutions that need to be physically accurate. The critical factor in resolving this problem is the integration of closure relations. These relationships play a crucial function in reintroducing essential physical characteristics, thus correcting the loss that occurs during averaging and guaranteeing the stability of the model. To improve the accuracy of predictions, it is essential to assess the stability and grid dependence of one-dimensional formulations, which are particularly affected by closure relations and numerical schemes. The current research presented in the text focuses on improving the well-posedness of the TFM, specifically within the TRACE code, which is widely utilized for nuclear reactor safety assessments. Incorporating a bubble collision model in the momentum equations is demonstrated to enhance the TFM's resilience, especially in scenarios with high void fractions where conventional TFMs may face challenges. The analysis presents a linear stability analysis performed for the transient one-dimensional Two-Fluid Model of system code TRACE within the framework of vertically dispersed flows. The main emphasis is on evaluating the stability characteristics of the model while also acknowledging its susceptibility to closure relations and numerical techniques.

It is proved analytically that the complex growth rate n = nr + ini (nr and ni are the real and imaginary parts of n , respectively) of an arbitrary neutral or unstable oscillatory disturbance of growing amplitude in rotatory electrothermoconvection in a dielectric fluid layer saturating a sparsely distributed porous medium heated from below, for the case of free boundaries, is located inside a semicircle in the right half of the nrni − plane, whose centre is at the origin and radius = maxTaPr2,ReaPrA\sqrt {\max \left( {{T_a}P_r^2,{{{R_{ea}}{P_r}} \over A}} \right)} , where Ta is the modified Taylor’s number, Pr is the modified Prandtl number, Rea is electric Rayleigh number and A is the ratio of heat capacities. The upper limits for the case of rigid boundaries are derived separately. Furthermore, similar results are also derived for the same configuration when heated from above.

The present study investigates the impact of a magnetic field on double‐diffusive convection in an inclined porous layer, employing linear instability theory. The perturbed state is solved using the normal mode technique, and the stability eigenvalue problem is numerically analyzed for longitudinal and traveling rolls using the Runge‐Kutta method coupled with the shooting method. Various dimensionless physical parameters, including solutal and thermal Rayleigh numbers, inclination angle, Hartmann number, and Lewis number, are examined for their influence on system stability. The findings reveal that, for Le<1 $Le\lt 1$, the Hartmann number, solute Rayleigh number, and inclination angle act as stabilizing factors, with greater stability observed for traveling rolls compared to longitudinal rolls. In the case of Le=1 $Le=1$, the critical Rayleigh number shows a monotonic relationship with the solute Rayleigh number and inclination angle, while its relationship with the Hartmann number is non‐monotonic for traveling rolls. Moreover, for Le>1 $Le\gt 1$, the Hartmann number stabilizes the system by raising the onset threshold value, favouring longitudinal modes. The solute Rayleigh number also contributes to system stability. The impact of the inclination angle on system stability is contingent upon its magnitude, with small angles favouring the stability of longitudinal rolls and larger angles leading to an initial transition from traveling to longitudinal rolls, indicating a complex non‐monotonic behavior. [ABSTRACT FROM AUTHOR]

Liquid crystalline polymer (LCP) solutions undergo uniaxial elongation in fiber spinning, yielding highly oriented fibril-structured fibers with enhanced orientation and mechanical properties. This study explores how initial fiber orientation and Frank elasticity influence the dynamics and stability of the isothermal spinning process for LCP solutions. The simplified Larson-Doi mesoscopic model is employed, capable of capturing elastic stress emerging from domain structure evolution. Two main factors, inlet orientation and the Ericksen number as a parameter representing Frank elasticity, significantly affect steady-state fiber orientation profiles and the onset of draw resonance instability, as determined through linear stability analysis. The sensitivity of spinline flow to a sinusoidal disturbance is assessed using the frequency response method. Changes in stability onset concerning these two main factors are reasonably correlated with the extensional behavior of the LCP solution in the spinline and the results of the frequency response. [ABSTRACT FROM AUTHOR]

Linear stability analysis of the steady flow past elliptic cylinders of different aspect ratio (A r) has been conducted for the flow Reynolds number (R e) in the range 30–200. A new unstable mode, which we refer as tertiary wake mode, has been discovered. Two other unstable modes (the primary wake mode and the secondary wake mode), already reported in the literature, are also found. The critical R e for the onset of instability of these modes and the corresponding Strouhal number (S t) have been reported. Modes that have large growth rates tend to come close to the cylinder surface, and the extent to which they spread downstream in the wake is less compared to the weaker modes. The size of the vortical structures in a mode is inversely related to its S t. The change in the characteristics of these modes with respect to change in A r and R e , as well as their evolution leading to the fully developed flow, has been studied. Selective suppression of the unstable modes is effected using a slip-plate placed on the wake centerline. For R e = 150, it is shown that selective suppression of the unstable modes leads to different fully developed unsteady flows. [ABSTRACT FROM AUTHOR]

Spatially overlapped coupled matter‐wave bright solitons are considered in binary Bose‐Einstein condensates with nonlinear optical lattices(NOLs) and study the properties of scattering patterns due to a localized defect. It is shown that spatially overlapped solitons become separated and exhibit different scattering patterns with the variation of inter‐species interaction. The NOL interplays with the defect and tends to influence the scattering properties. However, the effect of NOL varies with strength of inter‐component interaction. It is found that, if this interaction is weak then the scattering center gets shifted outside the defect. However, for a stronger inter‐component interaction, the scattering takes place from the defect and leads to different scattering patterns. [ABSTRACT FROM AUTHOR]

The paper investigates the effects of the Forchheimer term (form drag) and vertical pressure gradient on the buoyancy‐induced instability of power‐law saturating fluid in a porous plane medium. Two isobaric permeable layers are assumed to sandwich the horizontal porous plane. In the meantime, Dirichlet and Neumann equations are the thermal boundary conditions considered for the lower and upper layers. A base flow developed analytically via the governing equations is just in function of the Péclet number P $P$, with no dependence on the characteristic parameter of the power law fluid. A linear stability analysis consists of substituting a base flow with a small perturbation into the governing equations leads to a four‐order eigenvalue problem. An analytical solution is performed for the asymptotic cases of an infinite wavelength. The Runge–Kutta solver is applied together with the shooting technique to evaluate numerical solutions for the general case of nonnegligible wave numbers. Among the findings is the contribution of the Forchheimer term in the variation of the threshold Péclet number whose value can switch the wave numbers from zero to nonzero and increase the stability of the system. [ABSTRACT FROM AUTHOR]

While low‐resolution climate models at present struggle to appropriately simulate convectively coupled large‐scale atmospheric disturbances such as equatorial Kelvin waves (EKWs), superparameterization helps better reproduce such phenomena. To evaluate such model differences based on physical mechanisms, a linearized theoretical framework of convectively coupled EKWs was developed in a form readily applicable to model evaluation by allowing background stability and diabatic heating to have arbitrary vertical profiles rather than assuming simplified ones. A system of linearized equations of convection‐coupled gravity waves was derived as a two‐dimensional model of the convectively coupled EKWs. In this work, the basic states are taken from observations, CTL‐MIROC and SP‐MIROC experiments introduced in Part 1. The tendency of convectively coupled gravity waves to grow faster under top‐heavy heating is confirmed for realistic stratification profiles, as found in previous studies under constant stratifications. A comparison of linear unstable solutions with basic states taken from SP‐MIROC and CTL‐MIROC shows that the top‐heavy heating profile in SP‐MIROC largely contributes to the enhancement of the EKW‐like unstable modes, while subtle differences of stratification profiles considerably affect EKW behaviors. The bottom‐heavy heating bias in the CTL‐MIROC likely originates from insufficient modeling of subgrid stratiform precipitation in tropical organized systems. It is desirable to incorporate such stratiform components in cumulus parameterizations to achieve better EKW reproducibility. Plain Language Summary: Present global climate models (GCMs) cannot resolve small‐scale cumulus convection. Hence, they cannot reproduce sufficient amplitudes of convectively coupled large‐scale atmospheric disturbances such as the equatorial Kelvin wave (EKW). In contrast, high‐resolution models that explicitly simulate cumulus convection can reproduce these disturbances better. In this study, a linearized theoretical framework of the convectively coupled EKW was developed to interpret and evaluate model behavior. Using this framework, EKWs simulated by different models were compared based on their physical mechanisms. The basic states were taken from observations and MIROC simulations introduced in Part 1. The tendency of EKWs to grow under a top‐heavy heating condition was confirmed under realistic stratification profiles as found in previous studies under constant stratifications. A comparison of linear unstable solutions with the basic states taken from the MIROC simulations showed that the heating altitude is the most important factor for enhancing the EKW‐like unstable modes, while stratification profiles can sometimes considerably affect EKW growth. Bottom‐heavy heating bias in the conventional MIROC likely originates from insufficient parameterization of organized precipitating systems in the tropics. It is desirable to incorporate such stratiform components in the cumulus parameterization to achieve better EKW reproducibility. Key Points: A linearized model of the EKW is derived in a form readily applicable to evaluation of numerical simulationsSuperparameterized MIROC enhanced EKW amplitudes through top‐heavy heating profilesTo improve EKW reproducibility, GCMs need better representation of tropical stratiform precipitation [ABSTRACT FROM AUTHOR]

We have studied the dynamics of various kinds of optical dark solitons like, chirped, chirp-free, M-shaped & wing shaped dark solitons using higher-order nonlinear Schrödinger equation. To obtain the exact analytical solution, we employed mathematical techniques such as the extended rational sinh-cosh and sin-cos methods. Our investigation shows that one can manipulate the shape of both chirp and chirp free dark solitons by properly tuning the magnitude of the self steepening and self phase modulation. The stability of the obtained dark soliton solutions are verified by using linear stability analysis. [ABSTRACT FROM AUTHOR]

This study describes direct numerical simulation (DNS) of radially inward spiralling corotating disk flow with a narrow disk spacing, using the open source solver Nek5000 and the supercomputer SuperMUC-NG at Leibniz Supercomputing Centre. Knowledge about laminar and turbulent regime boundaries in this flow scenario is important for modelling and performance prediction of friction turbines. Simulations are performed in differently sized sections of the flat annulus that is formed by two opposing corotating disk surfaces. Three sets of operating conditions are covered, from the laminar, transitional and turbulent region of a previously determined stability chart respectively. Directly downstream of the inlet boundary, the flow is artificially perturbed with a random body force acting normal to the disk surfaces. Fourier analysis of the DNS flow field reveals that the artificial perturbation is dampened across all wavenumbers for the laminar conditions, while at the transitional conditions a small range of modes is weakly amplified towards the outlet. The identified unstable modes were previously correctly predicted by linear stability analysis. Comparison to experimental velocity profile measurements from a previous study at the same transitional operating conditions suggests strongly perturbed flow during the experiment. For inflow conditions leading to turbulent flow, average velocity profiles from DNS coincide with those from experiment and from commercial fluid simulation software with turbulence modelling (ANSYS CFX). Close to the walls, turbulent dissipation and turbulent kinetic energy distributions do not agree with the ANSYS CFX results. Friction Reynolds number settles at about 118 after turbulent flow has developed from the initial perturbation. Two point correlations and corresponding energy spectra are presented. [ABSTRACT FROM AUTHOR]

Evaluating the physical mechanisms that link hydraulic fracturing (HF) operations to induced earthquakes and the anticipated form of the resulting events is significant in informing subsurface fluid injection operations. Current understanding supports the overriding role of the effective stress magnitude in triggering earthquakes, while the impact of change rate of effective stress has not been systematically addressed. In this work, a modified critical stiffness was brought up to investigate the likelihood, impact, and mitigation of induced seismicity during and after hydraulic fracturing by developing a poroelastic model based on rate-and-state fraction law and linear stability analysis. In the new criterion, the change rate of effective stress was considered a key variable to explore the evolution of this criterion and hence the likelihood of instability slip of fault. A coupled fluid flowedeformation model was used to represent the entire hydraulic fracturing process in COMSOL Multiphysics. The possibility of triggering an earthquake throughout the entire hydraulic fracturing process, from fracturing to cessation, was investigated considering different fault locations, orientations, and positions along the fault. The competition between the effects of the magnitude and change rate of effective stress was notable at each fracturing stage. The effective stress magnitude is a significant controlling factor during fracturing events, with the change rate dominating when fracturing is suddenly started or stopped. Instability dominates when the magnitude of the effective stress increases (constant injection at each fracturing stage) and the change rate of effective stress decreases (the injection process is suddenly stopped). Fracturing with a high injection rate, a fault adjacent to the hydraulic fracturing location and the position of the junction between the reservoir and fault are important to reduce the Coulomb failure stress (CFS) and enhance the critical stiffness as the significant disturbance of stresses at these positions in the coupled process. Therefore, notable attention should be given to the injection rate during fracturing, fault position, and position along faults as important considerations to help reduce the potential for induced seismicity. Our model was verified and confirmed using the case of the Longmaxi Formation in the Sichuan Basin, China, in which the reported microseismic data were correlated with high critical stiffness values. This work supplies new thoughts of the seismic risk associated with HF engineering. [ABSTRACT FROM AUTHOR]

The study delves into the impact of couple stress on the commencement of convection in a porous material oriented horizontally. This layer contains a chemically reactive ferromagnetic fluid and experiences bottom heating. The investigation utilizes small perturbation methodology to explore and understand the impact of couple stress on the initiation of convection in this specific system. With the assumption of a non-autocatalytic exothermic reaction, eigenvalues are determined utilizing the Galerkin method. The analysis explores the effects of magnetic and couple stress parameters, as well as the Frank-Kamenetskii number. The observation indicates that the acceleration of the onset of ferroconvection is influenced by both magnetic forces and chemical reactions. Simultaneously, the presence of the couple stress component serves to stabilize the system. Moreover, when the nonlinearity of magnetization is sufficiently pronounced, the destabilization of the fluid layer is observed to be marginal. [ABSTRACT FROM AUTHOR]

The stability of thermocapillary flow in a liquid bridge under a transverse rotating magnetic field (RMF) was numerically investigated by the linear stability analysis using the spectral element method. Three commonly used RMF models, namely, the infinite model, the simplified finite model and the Φ1-Φ2 model, are employed to describe the RMF and their results are compared. Additionally, for the Φ1-Φ2 model, the uniform and non-uniform RMF were also compared. The numerical results show that with the increase of magnetic Taylor number Ta, the critical Marangoni number (Mac) for the three RMF models increases firstly, then decreases sharply to a minimum, finally increases again when the RMF is strong enough to suppress the radial and axial convection induced by thermocapillary force. Two transitions between the wavenumber k=1 and k=2 mode are observed with increasing Ta. The results obtained by the simplified finite model are in good agreement with those of the Φ1-Φ2 model, however, the infinite model has a significant deviation compared to the Φ1-Φ2 model. Besides, the results indicate that the non-uniform RMF has a relatively weak action compared with the uniform RMF. [ABSTRACT FROM AUTHOR]

The stability of steady, fully developed flow in a long cylindrical pipe for a shear-thinning fluid (which approximates a class of viscoplastic materials) is studied using linear stability analysis. The eigenvalues of the frequency of the perturbation of the steady-state solution are obtained using the shooting method. The eigenvalues are negative in the Reynolds number range studied and asymptotically tend to zero as the Reynolds number increases. This shows the pipe flow is stable in the Reynolds number range studied. A qualitatively similar trend is shown by the eigenvalues of a Navier–Stokes fluid of equivalent viscosity. However, the eigenvalues are much lesser than those of the shear-thinning fluid, and this shows that the flow of the Navier–Stokes fluid can be expected to be stable over a much larger Reynolds number range than the shear-thinning fluid.

Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and efficiency on non-diffusive equations to date. In this paper we apply linear stability analysis to showcase the poor stability properties of exponential integrators on non-diffusive problems. We then propose a simple repartitioning approach that stabilizes the integrators and enables the efficient solution of stiff, non-diffusive equations. To validate the effectiveness of our approach, we perform several numerical experiments that compare partitioned exponential integrators to unmodified ones. We also compare repartitioning to the well-known approach of adding hyperviscosity to the equation right-hand-side. Overall, we find that the repartitioning restores convergence at large timesteps and, unlike hyperviscosity, it does not require the use of high-order spatial derivatives.