Linear Stability Research Articles

Convective instability of Ekman boundary layer flow of a Newtonian fluid over a stretchable rotating disk

ABSTRACT This paper examines a linear convective instability of an incompressible, Newtonian, viscous fluid rotating over a stretchy spinning disk in an Ekman boundary layer flow. First time in the literature, a numerical analysis of impacts of the stretching mechanism on the stability of the Ekman flow in the presence of the Coriolis force has been carried out, where the bottom disk is allowed to uniformly extend in radial direction. The von Kármán similarity transformations have been used to convert the governing equations of motion into a system of non-linear coupled ordinary differential equations (ODEs) in non-dimensional variables. Then velocity profiles of the flow have been obtained by numerically solving these dimensionless ODEs. The neutral stability curves were then obtained by performing a linear stability analysis for the convective mechanism by using the Chebyshev collocation method. Surface stretching has a globally stabilizing influence on both Type-I and Type-II instability modes of the Ekman flow, according to the stability curves. Then, the result established from the stability curves has been verified by calculating total kinetic energy change due to induced perturbations in the flow system. y.

Instability in an anisotropic Brinkman layer due to downward or upward throughflow and purely due to internal heat generation

A linear stability analysis using normal mode technique is applied on an internally heated anisotropic Brinkman porous layer with vertical throughflow. Four internal heat source functions are considered to model the problem with same temperature at the bounding plates. The basic temperature profile due to pure internal heating is seen to be disturbed by throughflow (upward or downward) and the impact of through flow on these profiles is studied. Downward through flow, in particular, is seen to disturb the instability criterion for different profiles. Effect of anisotropy and modified Darcy number on onset of convection is also discussed.

Stability of a photosurfactant-laden viscous liquid thread under illumination

This paper investigates the effects of a light-actuated photosurfactant on the canonical problem of the linear stability of a viscous thread surrounded by a dynamically passive fluid. A model consisting of the Navier–Stokes equations and a set of molar concentration equations is presented that capture light-induced switching between two stable surfactant isomer states, trans and cis. These two states display significantly different interfacial properties, allowing for some external control of the stability behaviour of the thread via incident light. Normal modes are used to generate a generalized eigenvalue problem for the growth rate which is solved with a hybrid analytical and numerical method. The results are validated with appropriate analytical solutions of increasing complexity, beginning with a solution to a clean interface, then analytical solutions for one insoluble surfactant, one soluble surfactant and a special case of two photosurfactants with a spatially uniform undisturbed state. Presenting each of these cases allows for a holistic discussion of the effect of surfactants in general on the stability of a liquid thread. Finally, the numerical solutions in the presence of two photosurfactants that display radially non-uniform undisturbed states are presented, and details of the impact of the illumination on the linear stability of the thread are discussed.

An electric kickscooter multibody model: equations of motion and linear stability analysis

AbstractIn this work, a detailed multibody model of an electric kickscooter is presented. The model includes toroidal wheels as well as rear and front suspensions. The equations of motion are derived and linearized along the steady forward motion of the vehicle. Using an efficient linearization approach, suitable for complex multibody systems with holonomic and nonholonomic constraints, allows for obtaining the reduced linearized equations of motion as a function of the geometric, dynamic, wheels’, and suspensions’ parameters. The proposed electric kickscooter multibody model is validated with the stability results of a previously presented electric kickscooter benchmark. Since the resulting eigenvalues are parameterized regarding the design parameters, a detailed linear stability analysis of the system is performed. In particular, the influence on the stability of the toroidal geometry of the wheels, the elliptic cross-section of the toroidal wheels, the rider model, the steering axis inclination angle, the inertia tensor of the front frame, and the rear and front suspensions is analyzed. The model presented, together with the linearized equations of motion obtained in this work, enables a systematic analysis of the stability of these vehicles, which helps design new electric kickscooters with improved vehicle safety conditions and oriented to a wider range of potential users.

LTNE effects on two‐layer configuration with throughflow

AbstractThe effect of throughflow on the beginning of convective motion in a fluid layer overlying a fluid‐saturated porous layer is examined theoretically in this article under the local thermal nonequilibrium model. We considered boundaries to be insulating to temperature perturbations. The normal mode approach is employed to analyze the governing equation for a composite configuration, with the solution sought through the regular perturbation technique to assess linear stability. The critical Rayleigh number, signifying the initiation of stationary convection, has been determined by solving the system of coupled equations. It is found that the system attains stability with increased porosity–conductivity ratios, regardless of the throughflow direction. This stability is consistently observed for depth ratios of 0.1 and 0.2. However, for higher depth ratios (0.5 and 1.0), the system exhibits dual nature stability when throughflow is present. Further, the stability of the system is enhanced by a graphical depiction illustrating how the throughflow parameter, porosity‐scaled conductivity ratio, depth ratio, Darcy number, and Prandtl number collectively influence the onset of convective motion.

A microscopic traffic flow model for explaining nonlinear traffic phenomena: Modeling, stability analysis and validation

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.

Nitrogen doped leather waste-derived carbon materials as electrocatalyst for oxygen evolution reaction

Nitrogen doped leather waste-derived carbon materials have been employed as eletrocatalyst for oxygen evolution reaction. Low current densities and complex synthesis routes of other carbon-based materials limit their practical applicability. We present herein a simple and cost-competitive design of a metal free nitrogen-doped carbon matrix (NCM). At 10 mA cm−2 of current density, the assembled NCM showed a low over potential of 330 mV. NCM provided 73 mV dec-1 of slope value according to Tafel analysis, with NCM slope value improved as compared to previously described electrocatalysts inclusive of graphene (113 mV dec−1) and carbon nanosheets (101 mV dec−1), under similar reaction conditions. Linear sweep voltamogram, stability test and electrochemical impedance spectra confirmed the potential of NCM in OER as a heterogeneous electrocatalyst.

Lie group and stability analysis of tangent hyperbolic fluid flow driven by a shrinking sheet

This study elaborates on the mathematical modeling of tangent hyperbolic fluid flow driven by a shrinking sheet in a porous medium. The roles of Soret-Dufour and thermal radiation are considered to model the energy and concentration equations. The primary objective is to find an appropriate similarity transformation through Lie group analysis, which helps to produce the self-similar equations from the governing nonlinear partial systems. The similarity solutions are calculated numerically using the “bvp4c” solver in Matlab. Additionally, adequate suction is required to obtain the similarity solutions. As expected, dual solutions are found within a certain range of the suction parameter. The skin friction coefficient, heat, and mass transfer rates at the sheet are observed for pertinent flow constraints of physical interest. It reveals that the dual solutions bifurcate from a critical point, and beyond this point, no solution exists. Furthermore, the branches of dual solutions on the nondimensional velocity, temperature, and concentration profiles depict different characteristics. Thus, a linear temporal stability analysis has been employed to test the flow stability, revealing that the upper branch is physically reliable. The heat transfer rate increases by 7.69% and 9.55% in the upper and lower branches, respectively, for Soret parameter changes from 0.6 to 0.9. Meanwhile, the mass transfer rate decreases by 85.30% and 324.60% in the upper and lower branches, respectively. The consequences of Weissenberg and suction parameters show an opposite character on the velocity, temperature, and concentration profiles in the upper branch.

Stable production of fluid jets with vanishing diameters via tip streaming

We study numerically the microjetting mode obtained when a fluid is injected through a tube submerged in a uniaxial extensional flow. The steady solution to the full nonlinear Navier–Stokes equations is calculated. We obtain the linear global modes determining the linear stability of the steady solution. For sufficiently large outer viscosity, the flow remains stable for infinitely small values of the injected flow rate. This implies that jets with vanishing diameters can be produced regardless of the jet viscosity and outer flow strength. For a sufficiently small inner-to-outer viscosity ratio, the microjetting instability is associated only with the flow near the entrance of the jet. The tapering meniscus stretches and adopts a slender quasiconical shape. Consequently, the cone tip is exposed to an intense outer flow, which stabilizes the flow in the cone–jet transition region. This work presents the first evidence that fluid jets with arbitrarily small diameters can be stably produced via tip streaming. The results are related to those of a droplet in a uniaxial extensional flow with its equator pinned to an infinitely thin ring. The pinning of the equator drastically affects the droplet stability and breakup.

Mechanobiological tortuosity of blood vessels with stress-modulated growth and remodeling

The stability of blood vessels is essential for maintaining their functions, while severe blood vessel tortuosity leads to various clinical complications. The growth and remodeling of blood vessels, which are regulated by mechanical and biochemical cues, cause residual stresses that affect vessel stability. In this paper, we combine theory and simulations to study the mechanobiological behavior of blood vessels with stress-modulated growth and remodeling. Effects of the volumetric growth of the matrix and the turnover and reorientation of collagen fibers are accounted for. Linear stability analysis is first carried out to investigate the mechanobiological stability of blood vessels. By developing a finite element method that incorporates stress-modulated growth and remodeling, we validate the theoretical solution of the critical state and further capture the postbuckling evolution of blood vessels. Our results show that an increased internal pressure can lead to the thickening of the vessel wall, which stabilizes the blood vessels mechanically, whereas the effect of internal pressure on the mechanobiological buckling is nonmonotonic. Compared to the mechanical instability, the mechanobiological buckling results in a larger mode number and a shorter wavelength, as usually observed in varicose veins. Vessels during postbuckling may exhibit non-uniform wall thicknesses, in consistency with the experimental observation on tortuous aortas. These findings highlight the crucial role of mechanical remodeling in tissue morphogenesis and could deepen the understanding of mechanobiological mechanisms underlying the formation and development of blood vessel tortuosity.

Filtering induced explosive death in coupled FitzHugh–Nagumo neurons: Theory and experiment

Explosive emergent behavior governed by discontinuous and irreversible phase transition is in the center of recent research. In this paper we show that explosive amplitude death (AD) can be induced in a system of coupled oscillators if diffusion is accompanied by low-pass filtering in the mutual coupling path. Here we consider a ring network of diffusively coupled FitzHugh–Nagumo oscillators, and through theoretical and experimental investigations explore how the low-pass filter induces and controls the transition to explosive AD state. We derive the conditions of getting AD in the network through linear stability analysis. Using one and two parameter bifurcation analysis we find the explicit parametric zone of explosive death in the limiting case of two neurons, which reveals that the explosive death arises through the saddle–node bifurcation of limit cycle. In the strong coupling limit, we observe an interesting semi-explosive death scenario, where both continuous and discontinuous transitions are present. Finally, using electronic hardware circuits, we demonstrate the first experimental observation of explosive amplitude death that establishes the robustness of the scenario in a practical setup.

Linear stability of compact shrinking Ricci solitons

Linear stability of compact shrinking Ricci solitons

THE RETROSPECTIVE ANALYSIS OF TRIGEN INTERTAN NAIL IN THE TREATMENT OF UNSTABLE INTERTROCHANTERIC FEMORAL FRACTURES AT HOSPITAL FOR TRAUMATOLOGY AND ORTHOPAEDICS.

Intertrochanteric fractures are highly prevalent among the elderly population, with approximately 90% occurring in individuals aged over 65. These geriatric fractures are associated with elevated mortality rates and significant functional impairment. Common treatment modalities for unstable intertrochanteric fractures include proximal femoral nail antirotation (PFNA) and the InterTan nail (IT). PFNA and IT are frequently employed due to their lower failure rates and favorable biomechanical properties, resulting in positive clinical outcomes for the management of unstable intertrochanteric fractures. The unique design of the IT nail, featuring two cephalocervical screws within an integrated mechanism, permits linear intraoperative compression and rotational stability of the neck and head fragment. In this study, we assess the clinical outcomes of IT nail utilization in the treatment of intertrochanteric fractures at the Hospital for Traumatology and Orthopedics. This study comprises a retrospective analysis and case series report. Between February 2021 and August 2021, we retrospectively evaluated 35 patients who underwent treatment with the IT nail for unstable intertrochanteric fractures. Epidemiological data, operative duration, intraoperative blood loss, intraoperative blood transfusion requirements, length of hospital stay, bone healing rates, and IT nail-related complications were recorded. The mean age of the patients was 70.97 ± 16.97 years, with a mean operative time of 60 minutes, mean intraoperative blood loss of 160.86 ± 72.8 ml, mean intraoperative blood transfusion volume of 203.43 ± 189.29 ml, and a mean hospital stay of 7 days. Bone healing was observed in 97.14% of cases. The treatment of unstable intertrochanteric fractures using the IT nail in elderly patients was successful. Our findings indicate favorable clinical outcomes in terms of surgical duration, intraoperative blood loss, hospitalization duration, and union rates for elderly patients. Further investigations are warranted to validate these early results.

Fabricating NiCoFe2O4 decorated PANI nanostructures for high-performance electrochemical detection of 3-Nitro-L-tyrosine biomarkers for rapid diagnosis

A recent development in novel catalytic nanostructures offers numerous opportunities to perform the electrochemical operations towards sensing applications. The organic material PANI has been endorsed as a conducting polymer as it has controlled electrical properties and low density which will be beneficial over the metallic nanostructures. Herein, Nickel Cobalt Ferrite (NiCoFe2O4 (NCF)) nanostructures were anchored on the surface of PANI and engineered for electrochemical sensing applications. 3-nitro-L-tyrosine (3-NT) is an important compound for diagnosing oxidizing biomarkers that plays a vital role in therapy and diagnosing pathogenesis. Due to NCF/PANI’s conductivity, and superior surface area. It was probed for electrochemical sensing of 3-NT. The NCF/PANI displayed an excellent LOD, broad linear range, better sensitivity, selectivity, and stability. Furthermore, the proposed sensor exhibits sensitive 3-NT detection in biological samples with satisfactory recovery rates.

Linear stability and numerical analysis of vertical dense particulate flows in hydraulic conveying

Linear stability and numerical analysis of vertical dense particulate flows in hydraulic conveying

Investigating the role of edge neutrals in exciting tearing mode activity and achieving flat temperature profiles in LTX-β

We present observations, numerical simulations, and analysis from experiments in the Lithium Tokamak Experiment-Beta (LTX-β) in which the electron temperature profile (Te (r)) shifts from flat to peaked and a tearing mode is also destabilized when the average density (ne ave ) exceeds ∼1019 m−3. Flat Te (r) is obtained routinely in LTX-β, with a lithium coated, low-recycling first wall, once the external fueling is stopped and density decays [Boyle et al 2023 Nucl. Fusion 63 056020]. In the present experiment, flat Te profiles can be sustained while maintaining constant ne ave below a line averaged density threshold (ne ave th ) of ∼1019 m−3. Above ne ave th, Te (r) shifts from flat to peaked and a tearing mode is destabilized. Due to low recycling, the achieved ne ave can be controlled precisely by external fueling and hence, a certain threshold of the edge neutral inventory from the external fueling is experimentally manifested through ne ave th . The goal of the present work is to investigate the role of edge neutrals in determining Te (r) and MHD stability in the unique low-recycling regime of LTX-β. Our hypothesis is that the peaking of Te (r) beyond ne ave th is due ultimately to the edge cooling by the cold neutrals beyond a critical fueling flux. At lower fueling flux, flat Te (r) results in broader pressure profile and lower resistivity, which in turn stabilizes the tearing mode. This hypothesis is supported by edge neutral density estimation by DEGAS 2 code. Mode analysis by singular value decomposition confirms the tearing mode structure to be m/n = 2/1 (m and n being the poloidal and toroidal mode numbers). Linear tearing stability analysis with M3D-C1 predicts that plasmas with ne ave > 1019 are highly susceptible to a n = 1 tearing mode. ORBIT simulations, however, confirmed that the tearing modes do not contribute to the loss of fast ions from neutral beam injection. This study shows for the first time that the neutral inventory at the edge could be one of the deciding factors for the achievability of the unique operation regime of flat Te (r) and the excitation of tearing activity that could be disruptive for the plasmas.

Influence of immersed particles on the stability of the liquid–liquid interface in a two-layer channel flow

The current study investigates the global linear stability of a two-layer channel flow with a train of solid particles flowing near the liquid–liquid interface. Three different mechanisms of instability (shear, interfacial and migration modes) are identified, and their interactions are examined. The interfacial instability, associated with the viscosity jump at the liquid–liquid interface, is found to be coupled to the migration of the particle. The stability of the flow configuration is evaluated for various governing parameters, including fluid viscosities and flow rate ratios, particle position, inter-particle distance, and Reynolds and capillary numbers. Our numerical results are compared with the particle-free flow configuration, indicating that the presence of the particle in the more viscous fluid promotes the destabilization of the interface. Remarkably, under certain flow parameters, the presence of the particle stabilizes the interface when flowing in the less viscous liquid. The impact of particles is more significant as the capillary number increases or the Reynolds number decreases.

Collective group drift in a partial-differential-equation-based opinion dynamics model with biased perception kernels.

In the age of technology, individuals accelerate their biased gathering of information, which in turn leads to a population becoming extreme and more polarized. Here we study a partial-differential-equationmodel for opinion dynamics that exhibits collective behavior subject to nonlocal interactions. We developed an interaction kernel function to represent biased information gathering. Through a linear stability analysis, we show that biased populations can still form opinionated groups. However, a population that is too heavily biased can no longer come to a consensus, that is, the initial homogeneous mixed state becomes stable. Numerical simulations with biased information gathering show the ability for groups to collectively drift towards one end of the opinion space. This means that a small bias in each individual will collectively lead to groups of individuals becoming extreme together. The characteristic time scale for a group's existence is captured from numerical experiments using the temporal correlation function. Supplementing this, we included a measure of how different each population is after regular time intervals using a form of the Manhattan and Euclidean distance metrics. We conclude by exploring how wall boundary conditions induce pattern formation initially on the most extreme sides of the domain.

EHD instability of a cylindrical interface separating two couple-stress fluids

This article is an attempt at examining the axi-symmetric and asymmetric streaming flows described by the CSF framework. A liquid that has microfibers implanted in it, like a fiber-reinforced composite substance, is so-called CSF. It is a system that consists of an endless vertical cylindrical interface that separates the two CSF structure. The CSFs are increasingly growing significant in modern manufacturing and technology, necessitating greater research into these fluids. An axial EF acts over the cylindrical contact in addition to the influence of CSF. The VPT is employed for the sake of convenience to minimize mathematical complexity. Combining the elementary linear equations of motion and the proper linear related BCs is the major procedure of the linear technique. A collection of physically dimensionless numbers is produced using a non-dimensional process. Subsequently, the requirements for hypothetical linear stability are developed. With the aid of the Gaster's theorem, the MS is applied in computing the dispersion relationships. After carefully examining a variety of effects on the stability investigation of the system at issue, it has been shown that the system is more unstable when a porous material is present than it would be without one. The resulting axisymmetric disturbance situation is more unstable. The linear techniques are depicted throughout a number of graphs.

Slip boundary conditions effect on bidispersive convection with local thermal non-equilibrium: Significant findings

We examine a theory concerning heat convection within a porous material characterized by a skeletal structure comprising macropores and, additionally, cracks or fissures leading to a network of micro pores. Brinkman theory and slip conditions were considered applicable within the macropores, while exclusively Darcy theory was applied within the micropores. This represents a scenario of thermal convection within a double-porosity porous medium. The theory accommodates non-equilibrium thermal conditions, allowing for the possibility that the temperature of the solid skeleton differs from that of the fluid present in either the macro or micro pores. Importantly, the model permits independent fluid velocities and pressures within both the macro and micro pores. We conducted both linear and nonlinear stability assessments, with a specific focus on assessing how slip boundary conditions affect the stability of the system. Once we pinpointed the onset of instability, we calculated the critical Rayleigh number as a variable dependent on the slip coefficient. Additionally, we provided numerical results that outline the thresholds for stability and instability.