Linear Stability Research Articles

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.

Nonlinear Evolution of Instabilities in a Laminar Separation Bubble at Hypersonic Speeds

The development of both convective stationary perturbation and global instabilities in the vicinity of a laminar separation bubble above an axisymmetric compression corner in hypersonic flow was investigated using numerical simulations. The flow configuration of interest corresponded to the cone–cylinder–flare model used in experimental measurements in the Boeing/U.S. Air Force Office of Scientific Research Mach-6 Quiet Tunnel (BAMQT) at Purdue University. For a flare angle of 10 deg and unit Reynolds number of 11.5×106 m−1, their surface flow visualizations identified the presence of streamwise elongated thermal streaks near the reattachment location that had a dominant azimuthal wave number m=36. Previous linear stability analyses predicted that the amplification characteristics of small-amplitude, unsteady, and convective instabilities within this flow were consistent with the surface pressure fluctuations measured in the experiment. However, their accompanying investigation of global instabilities showed that the separation bubble was weakly unstable at the 10 deg flare angle, with the most unstable global mode corresponding to a stationary disturbance with m≈5–6 (i.e., well below the measured wave number of m=36. Besides characterizing the global instability for selected flare angles, the present numerical simulations quantify the details of the stationary equilibrium state associated with supercritical bifurcation resulting from the nonlinear saturation of the unstable global mode. Although velocity perturbations associated with the saturated global mode are dominated by the fundamental spanwise wavelength associated with the linear global instability, the surface heat flux downstream of the reattachment is dominated by m=36, in agreement with the experimental measurements.

Spectral and linear stability of peakons in the Novikov equation

AbstractThe Novikov equation is a peakon equation with cubic nonlinearity, which, like the Camassa–Holm and the Degasperis–Procesi, is completely integrable. In this paper, we study the spectral and linear stability of peakon solutions of the Novikov equation. We prove spectral instability of the peakons in . To do so, we start with a linearized operator defined on and extend it to a linearized operator defined on weaker functions in . The spectrum of the linearized operator in is proven to cover a closed vertical strip of the complex plane. Furthermore, we prove that the peakons are spectrally unstable on and linearly and spectrally stable on . The result on is in agreement with previous work about linear instability and our result on is in line with past work on orbital stability.

Inertia and slip effects on the instability of a liquid film coated on a fibre

To investigate the influence of inertia and slip on the instability of a liquid film on a fibre, a theoretical framework based on the axisymmetric Navier–Stokes equations is proposed via linear instability analysis. The model reveals that slip significantly enhances perturbation growth in viscous film flows, whereas it exerts minimal influence on flows dominated by inertia. Moreover, under no-slip boundary conditions, the dominant instability mode of thin films remains unaltered by inertia, closely aligning with predictions from a no-slip lubrication model. Conversely, when slip is introduced, the dominant wavenumber experiences a noticeable reduction as inertia decreases. This trend is captured by an introduced lubrication model with giant slip. Direct numerical simulations of the Navier–Stokes equations are then performed to further confirm the theoretical findings at the linear stage. For the nonlinear dynamics, no-slip simulations show complex vortical structures within films, driven by fluid inertia near surfaces. Additionally, in scenarios with weak inertia, a reduction in the volume of satellite droplets is observed due to slip, following a power-law relationship.

Linear and nonlinear stability analyses of micropolar fluid flow in horizontal porous layers

The linear and nonlinear stability analyses of micropolar fluid flow in a horizontal porous layer heated from below in the presence of throughflow is numerically investigated. The Brinkman model is considered to govern the micropolar fluid flow within the porous region. The main purpose of the present study is to investigate the behavior of the subcritical region for micropolar fluid parameters in the presence of throughflow. The energy approach is used to analyze nonlinear stability, whereas the normal mode scheme is used to investigate linear stability. The obtained eigenvalue problems related to linear and nonlinear stability analyses are solved numerically using the bvp4c routine in MATLAB. Finally, the critical thermal Rayleigh number is determined for the given values of the governing parameters. It is observed that the subcritical area decreases as the Darcy number (Da), micropolar parameter (m), and absolute value of throughflow parameter (|Pe|) decrease. Furthermore, there is no subcritical gap in the absence of the throughflow effect for micropolar fluid flow, which is a good agreement for the linear and nonlinear thresholds.

A comprehensive examination of the linear and numerical stability aspects of the bubble collision model in the TRACE-1D two-fluid model applied to vertical disperse flow in a PWR core channel under loss of coolant accident conditions

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.

Stability of low-pressure turbine boundary layers under variable Reynolds number and pressure gradient

The free-stream turbulence induced transition occurring under typical low-pressure turbine flow conditions is investigated by comparing linear stability theory with wind tunnel measurements acquired over a flat plate subjected to high turbulence intensity. The analysis was carried out, accounting for three different Reynolds numbers and four different adverse pressure gradients. First, a non-similarity-based boundary layer (BL) solver was used to compute base flows and validated against pressure taps and particle image velocimetry (PIV) measurements. Successively, the optimal disturbances and their spatial transient growth were calculated by coupling classical linear stability theory and a direct-adjoint optimization procedure on all flow conditions considered. Linear stability results were compared with experimental particle image velocimetry measurements on both wall-normal and wall-parallel planes. Finally, the sensitivity of the disturbance spatial transient growth to the spanwise wavenumber of perturbations, the receptivity position, and the location where disturbance energy is maximized were investigated via the built numerical model. Overall, the optimal perturbations computed by linear stability theory show good agreement with the streaky structures surveyed in experiments. Interestingly, the energy growth of disturbances was found to be maximum for all the flow conditions examined, when perturbations entered the boundary layer close to the position where minimum pressure occurs.

Propeller wake impact on transition location

This work has been carried out within ESTRO Clean Sky 2 CfP project, whose goal was to develop an innovative future green regional aircraft configuration based on several new technologies able to match the very demanding and challenging objectives ACARE 2020 in terms of environmental impact. In details, an automatic numerical procedure for the evaluation of the detrimental effect of the propeller on transition location of a laminar turbo-prop wing is proposed here. The evaluation of transition location is based on a well-known procedure, based on the use of eN method implemented in a Linear Stability (LST) solver. The input data for the LST solver are represented by the pressure distribution as derived from high-fidelity Reynolds-Averaged Navier–Stoke (RANS) solutions and the velocity profiles in the boundary layer derived from a conical formulation of the boundary layer equations.

Modeling dedicated lanes for connected autonomous vehicles with poly-information uncertainties and electronic throttle dynamics

Numerous studies have demonstrated that connected autonomous vehicles and human-driven vehicles are now coexisting throughout a transitional phase. Traffic flow can be improved, the system can be stabilized, and less energy will be used with dedicated lanes for connected autonomous vehicles. Additionally, with few communication resources, no communication delivery is ever perfect, leading to issues with poly-information uncertainty. First, this paper provides a macroscopic model of heterogeneous traffic flow from the perspective of vehicle dynamics employing electronic throttle dynamics and poly-information uncertainty with/without dedicated lanes. Second, the mixed traffic flow linear stability criterion is derived using the linear stability theory. The third portion, which was based on the theoretical analysis, focused on the consequences of dedicated lane configurations on traffic flow as well as a discussion of the effects of various parameters on the stability of mixed traffic flow and energy consumption emissions. Finally, we modeled the Huanshan Road in Jinan, China using the experimental VISSIM platform. The analysis and demonstration of a two-way, four-lane road with or without dedicated lanes. The findings demonstrate that increasing connected autonomous vehicles penetration and dedicated lanes construction can increase traffic capacity, enhance the stability of traffic flow, and lower energy use and additional emissions. It is important to keep in mind that dedicated lanes must be built at an appropriate connected autonomous vehicle penetration rate to boost traffic flow without squandering resources.

Analysis of Tolfenamic Acid using a Simple, Rapid, and Stabilityindicating Validated HPLC Method.

Tolfenamic acid (TA) belongs to the fenamates class of non-steroidal anti-inflammatory drugs. Insufficient information is available regarding the availa-bility of a reliable and validated stability-indicating method for the assay of TA. A relatively simple, rapid, accurate, precise, economical, robust, and stability-indicating RP-HPLC method has been developed to determine TA in pure and tablet dosage forms. The method was validated according to the ICH guideline, and parameters like linearity, range, selectivity, accuracy, precision, robustness, specificity, and solution stability were determined. TLC and FTIR spectrometry were used to ascertain the purity of TA. The specificity was determined with known impurities and after performing forced degradation, while the robustness was established by Plackett-Burman's experimental design. The mobile phase used for the analysis was acetonitrile and water (90:10, v/v) at pH 2.5. The detection of the active drug was made at 280 nm using a C18 column (tR = 4.3 min.). The method's ap-plicability was also checked for the yellow polymorphic form of TA. The results indicated that the method is highly accurate (99.39-100.80%), precise (<1.5% RSD), robust (<2% RSD), and statistically comparable to the British Pharmacopoeia method with better sensitivity and specificity. It was observed that the stress degradation studies do not affect the method's accuracy and specificity. Hence the proposed method can be used to assay TA and its tablet dosage form.

Modification of the resistive tearing instability with Joule heating by shear flow

We investigate the influence of background shear flow on linear resistive tearing instabilities with Joule heating for two compressible plasma slab configurations: a Harris current sheet and a force-free, shearing magnetic field that varies its direction periodically throughout the slab, possibly resulting in multiple magnetic nullplanes. To do so, we exploit the latest version of the open-source, magnetohydrodynamic spectroscopy tool Legolas. Shear flow is shown to dramatically alter tearing behavior in the presence of multiple magnetic nullplanes, where the modes become propagating due to the flow. Finally, the tearing growth rate is studied as a function of resistivity, showing where it deviates from analytic scaling laws, as well as the Alfvén speed, the plasma-β, and the velocity parameters, revealing surprising nuance in whether the velocity acts stabilizing or destabilizing. We show how both slab setups can produce growth rate regimes, which deviate from analytic scaling laws, such that systematic numerical spectroscopic studies are truly necessary, for a complete understanding of linear tearing behavior in flowing plasmas.

Simulations of tokamak edge plasma turbulent fluctuations based on a minimal 3D model

A new simulation model for tokamak boundary plasma, SOLT3D, is implemented in the BOUT++ framework (Dudson et al 2009 Comput. Phys. Commun. 180 1467). The simulation model includes a set of dynamic equations describing collisional boundary plasma and neutral gas in the tokamak scrape-off layer and divertor region. The model is verified against standard linear plasma instabilities and available nonlinear results. For L-mode like conditions, SOLT3D reproduces characteristics of boundary plasma turbulent fluctuations that are similar to published experimental data, in terms of the amplitude and spatial dependence of the fluctuations. It also reproduces realistic plasma fluxes on material surfaces and expected Bohm-like effective radial transport. Plasma fluctuations inferred from the simulations imply inevitably a significant level of intrinsic ‘noise’ for axisymmetric tokamak plasma transport modeling, introducing errors on the order of unity. In particular, the toroidally averaged atomic rates below 5–10 eV are strongly modified by turbulent plasma fluctuations, which should significantly affect the standard axisymmetric modeling of the tokamak edge plasma and divertor.