Instability Criterion Research Articles

How Does the Critical Torus Instability Height Vary with the Solar Cycle?

The ideal magnetohydrodynamic torus instability can drive the eruption of coronal mass ejections. The critical threshold of magnetic field strength decay for the onset of the torus instability occurs at different heights in different solar active regions, and understanding this variation could therefore improve space weather prediction. In this work, we aim to find out how the critical torus instability height evolves throughout the solar activity cycle. We study a significant subset of Helioseismic and Magnetic Imager (HMI) and Michelson Doppler Imager Space-Weather HMI Active Region Patches (SHARPs and SMARPs) from 1996 to 2023, totaling 21,584 magnetograms from 4436 unique active-region patches. For each magnetogram, we compute the critical height averaged across the main polarity inversion line, the total unsigned magnetic flux, and the separation between the positive and negative magnetic polarities. We find the critical height in active regions varies with the solar cycle, with higher (lower) average critical heights observed around solar maximum (minimum). We conclude that this is because the critical height is proportional to the separation between opposite magnetic polarities, which in turn is proportional to the total magnetic flux in a region, and more magnetic regions with larger fluxes and larger sizes are observed at solar maximum. This result is noteworthy because, despite the higher critical heights, more coronal mass ejections are observed around solar maximum than at solar minimum.

Unstable Regions of Anisotropic Relativistic Spheres in Higher-Dimensions

Abstract In this work, we consider the collapse of a $\mathbb{D}$-dimensional sphere in the framework of a higher dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the $\mathbb{D}$-dimensional modified term.
This work investigates the criteria for dynamical instability of
anisotropic relativistic sphere systems with
$\mathbb{D}$-dimensional modified gravity. The certain conditions are
applied that lead to the collapse equation and their effects on
adiabatic index $\Gamma$ in both Newtonian (N) and Post-Newtonian
(PN) regimes by using a perturbation scheme. The study explores that
the $\Gamma$ plays a crucial role in determining the degree of
dynamical instability. This index characterizes the fluid's
stiffness and has a significant i7mpact on defining the ranges of
instability. This systematic investigation demonstrates the
influence of various material properties such as anisotropic
pressure, kinematic quantities, mass function, $\mathbb{D}$-dimensional modified gravity parameters, and the radial profile of energy density on the
instability of considered structures during their evolution. This
work also displays the dynamical behavior of spherically symmetric
fluid configuration via graphical approaches.

Validating the Definition of Lumbar Instability-A Cross-Sectional Study with 420 Healthy Volunteers.

Background/Objectives: Low back pain is thought to be caused by lumbar instability. To date, multiple definitions of radiological lumbar instability have been used without verifying the "normal range" of the lumbar segmental mobility. Ideally, normative data for lumbar mobility in healthy individuals are required to establish an acceptable threshold for lumbar instability. This study aims to elucidate (i) the prevalence of so-called radiological lumbar instability at each lumbar spine level in conventional criteria and (ii) a practical radiological threshold for lumbar instability in healthy individuals. Methods: Participants completed a questionnaire and underwent standard active dynamic radiography of the lumbar spine in the standing position. Intervertebral range of motion (IROM) and sagittal translation distance (ΔST) were measured at each intervertebral level. Nachemson's criteria of radiological lumbar instability were applied. Results: This study involved four hundred and twenty participants (249 males and 171 females); 76% (320/420) met the criteria for radiological lumbar instability. The definition of lumbar instability based on IROM and ΔST was achieved by 0.2% and 1.7% of participants at the L5-sacrum (L5-S) level, respectively. Conclusions: The normative data of lumbar mobility were obtained from a large number of participants who had less LBP-related ADL disability. The widely accepted criteria for lumbar instability were not applicable except for the L5-S level. Further studies of lumbar mobility, including patients with severe LBP, might prove the relationship between hypermobility of the lumbar spine and LBP.

Differentiating the Structural and Functional Instability of the Craniocervical Junction.

This paper presents the anatomical and biomechanical aspects of chronic instability of the craniocervical junction (CCJ) with a discussion on clinical diagnostics based on mobility tests and provocative tests related to ligamentous system injuries, as well as radiological criteria for CCJ instability. In addition to the structural instability of the CCJ, the hypothesis of its functional form resulting from cervical proprioceptive system (CPS) damage is discussed. Clinical and neurophysiological studies have shown that functional disorders or organic changes in the CPS cause symptoms similar to those of vestibular system diseases: dizziness, nystagmus, and balance disorders. The underlying cause of the functional form of CCJ instability may be the increased activity of mechanoreceptors, leading to "informational noise" which causes vestibular system disorientation. Due to the disharmony of mutual stimulation and the inhibition of impulses between the centers controlling eye movements, the cerebellum, spinal motoneurons, and the vestibular system, inadequate vestibulospinal and vestibulo-ocular reactions occur, manifesting as postural instability, dizziness, and nystagmus. The hyperactivity of craniocervical mechanoreceptors also leads to disturbances in the reflex regulation of postural muscle tone, manifesting as "general instability". Understanding this form of CCJ instability as a distinct clinical entity is important both diagnostically and therapeutically as it requires different management strategies compared to true instability. Chronic CCJ instability significantly impacts the quality of life (QOL) of affected patients, contributing to chronic pain, psychological distress, and functional impairments. Addressing both structural and functional instability is essential for improving patient outcomes and enhancing their overall QOL.

Thermal Processing Map Study of the GH99 Nickel-Based Superalloy Based on Different Instability Criteria

The thermal compression experiments of the GH99 alloy were carried out at different strains from 1020 °C to 1170 °C and 0.001 s−1–1 s−1 conditions using a Gleeble-3800 thermal compression simulation tester. Construction of thermal processing maps with four instability criteria were superimposed on Murty, Prasad, Gegel, and Malas at different strains based on stress-strain data. Based on the theoretical basis, prediction results, and EBSD microstructure characterization method of four instability criteria, the suitable forming processing region and rheological instability region of the alloy were predicted. It was found that the Prasad instability criterion had the most accurate prediction results. The instability range predicted by Murty was accurate under minor strains, but as the strain increased, the expected instability range slightly increased compared to the actual range. However, the Gegel and Malas criteria have biases in predicting alloys under low-rate conditions at different strains. A scientific and rational optimization was carried out to select hot working process parameters for GH99 alloy in response to the influence of strain on its hot deformation behavior.

An Investigation on unstable flow during hot deformation of Inconel X750 superalloy using 3D processing map and shear band formation criterion

In this study, deformation efficiency and instability criteria were employed to delineate the unstable flow regions for Inconel X750 superalloy through high temperature deformation. High temperature stress–strain data attained from isothermal hot compression experiments in the temperature range of 950-1150 °C and strain rates between 0.0001 and 1s⁻¹ to identify safe and un-safe deformation domains in terms of an integrated 3D processing maps. These domains were validated through detailed microstructure observation and material tendency to shear band formation in terms of the competition between work hardening and strain rate sensitivity i.e. flow localization parameter. The superimposed effect of microstructure features like dynamic precipitation, dynamic recovery (DRV), and dynamic recrystallization (DRX) with destructive shear banding were responsible for controlling the material behaviour. Based on the TEM images, it was observed that material revealed stable flow at lower strain rates while adiabatic shear band and flow localization occurred at higher strain rates due to activation of slip systems and cell formation.

Investigation of Surge Phenomena in a Centrifugal Compressor by 3D-1D Coupling Approach

Abstract Critical instability, such as surge phenomena, can occur at low flow rates for a compressor system, leading to flow rate fluctuations and potential damage. To study this, traditional numerical analysis requires a comprehensive approach encompassing the compressor and its piping system. This demands extensive computational resources and time due to the complexity of capturing internal flow during surge, including separation and vortex generation. To overcome these limitations, this research proposes a computational strategy combining 3D and 1D analysis for enhanced efficiency and reduced computational demands, which employs 1D analysis for more straightforward flow regions like piping and 3D analysis for the more complex compressor section. This approach is facilitated using AMESim for 1D and STAR-CCM+ for 3D simulations, enabling seamless integration and data exchange between different dimensional analyses. The method improves computational efficiency and reasonably approximates surge phenomena compared to experimental data. The 3D and 1D coupled analysis closely aligns with experimental data, providing a viable and more effective alternative method for surge analysis in compressor systems. This methodology promises to streamline the study of compressor surge phenomena, providing a practical tool for engineers and researchers.

Triple-diffusive instabilities in Ellis fluid-saturated porous layers: Dynamics of oscillatory convection

Triple-diffusive convection in Ellis fluid-saturated porous layers has a wide array of real-world applications, including enhanced oil recovery, optimized geothermal energy extraction, and improved food processing and drug delivery systems. It also plays a crucial role in environmental management, particularly in controlling groundwater contamination and maintaining soil health by modeling pollutant transport and nutrient dynamics. This study explores the onset of convection in an Ellis fluid-saturated porous layer, influenced by three stratifying agents with differing diffusivities. A modified Darcy porous medium, salted from below, is subjected to horizontal throughflow driven by a prescribed pressure gradient. Through normal mode analysis, a linear stability analysis is conducted, resulting in explicit threshold conditions for the onset of convection. The findings reveal that convection begins with oscillatory motion, driven by the combined effects of the pressure gradient and solute concentration gradients. Notably, the study uncovers the emergence of disconnected, closed, heart-shaped oscillatory neutral curves, indicating the presence of three critical values of the solutal Darcy-Rayleigh number required to establish linear instability criteria and novel discovery for an Ellis fluid-saturated porous medium. Moreover, the results show that increasing the solutal Darcy-Rayleigh number and the Ellis power-law index stabilizes the system, while a higher Darcy-Ellis number leads to destabilization. The results obtained in the limiting cases are found to be consistent with those reported in previous studies.

New accents of security-oriented management of logistics activity entities in the conditions of digitalization

The paper focuses on management issues in the field of sustainable functioning and development of business entities on the basis of guaranteeing their economic security. The industry specialization of entities specializing in logistics activities is taken into account. New aspects of security-oriented management of logistics entities are defined and taken into account, in particular in the languages of digitalization, which bring to the fore the issues of information and cyber security, digital communications, as well as cashless electronic payments. On this basis, the purpose of the research is to identify new accents of security-oriented management of logistics entities in the conditions of digitalization. The components of the economic security of logistics entities that require priority attention in terms of strengthening during the digital transformation of the economy and society have been determined. The toolkit of safety-oriented management under modern conditions for subjects of logistics activity is indicated. It is shown that under modern conditions, business entities specializing in logistics activities should focus on two mega aspects when forming their own security-oriented management systems. These are: (1) operational challenges caused by critical instability and the consequences of a full-scale war; (2) new opportunities, realities, as well as challenges of global and comprehensive digital transformation of economic relations. It was concluded that the new emphasis of security-oriented management of logistics entities concerns all the leading components of their economic security.

Role of Higher-Order Scattering Coefficient and Residual Nonlinearities on Instability Criteria in Three-Body Bose-Einstein Condensates

We examine the instability characteristics in a three-body condensate and the effect of higher-order nonlinear effects caused by shape-dependent imprisonment and higher-order scattering coefficients such as S-wave scattering length and effective range for collisions. Using the linear stability technique, we study the spreading relations and gain profile of the adapted Gross Pitaevski equation with higher-order scattering coefficients and enduring nonlinearity. The role of higher-order interactions S-wave scattering length, residual nonlinearity, and effective range for collisions over the modulational instability in immiscible and miscible three-body Bose-Einstein condensates has been discussed in detail. MI can be excited in miscible condensates and changed in immiscible condensates because of residual nonlinearity, without taking into account higher-order nonlinearity and three-body condensates. However, the results of this work demonstrate that the influence of higher-order residual nonlinearity can cause the MI to change in both immiscible and immiscible condensates. The discovered MI spectrum reveals a new soliton production regime in three-body condensates. The results exhibit that higher-order scattering coefficient and remaining nonlinearity interplay can successfully switch the instability gain profile in miscible and immiscible condensates. This makes it possible to regulate the dynamics by varying the MI in a ternary combination of Bose-Einstein condensates.

Effect of Er on the Hot Deformation Behavior of the Crossover Al3Zn3Mg3Cu0.2Zr Alloy

The effect of an erbium alloying on the hot deformation behavior of the crossover Al3Zn3Mg3Cu0.2Zr alloy was investigated in detail. First of all, Er increases the solidus temperature of the alloy. This allows hot deformation at a higher temperature. The precipitates resulting from the Er alloying of the Al3Zn3Mg3Cu0.2Zr alloy were analyzed using transmission electron microscopy. Erbium addition to the alloy produces the formation of more stable and fine L12-(Al3(Zr, Er)) precipitates with a size of 20–60 nm. True stress tends to increase with a decline in the temperature and an increase in the deformation rate. The addition of Er leads to decreases in true stress at the strain rates of 0.01–1 s−1 due to particle-stimulated nucleation softening mechanisms. The effective activation energy of the alloy with the Er addition has a lower value, enabling an easier hot deformation process in the alloy with an elevated volume fraction of the intermetallic particles. The addition of Er increases the strain rate sensitivity, which makes the failure during deformation less probable. The investigated alloys have a significant difference in the dependence of the activation volume on the temperature. The flow instability criterion allows better deformability of Er-doped alloys and enables the alloys to be formed more easily. The evenly distributed particles prevent the formation of shear bands with elevated storage energy and decrease the probability of crack initiation during the initial stages of hot deformation when only one softening mechanism (dynamic recovery) is working. The microstructure analysis proves that dynamic recovery is the main softening mechanism.

Evolution of water wave packets by wind in shallow water

We use the Korteweg–de Vries (KdV) equation, supplemented with several forcing/friction terms, to describe the evolution of wind-driven water wave packets in shallow water. The forcing/friction terms describe wind-wave growth due to critical level instability in the air, wave decay due to laminar friction in the water at the air–water interface, wave stress in the air near the interface induced by a turbulent wind and wave decay due to a turbulent bottom boundary layer. The outcome is a modified KdV–Burgers equation that can be a stable or unstable model depending on the forcing/friction parameters. To analyse the evolution of water wave packets, we adapt the Whitham modulation theory for a slowly varying periodic wave train with an emphasis on the solitary wave train limit. The main outcome is the predicted growth and decay rates due to the forcing/friction terms. Numerical simulations using a Fourier spectral method are performed to validate the theory for various cases of initial wave amplitudes and growth and/or decay parameter ranges. The results from the modulation theory agree well with these simulations. In most cases we examined, many solitary waves are generated, suggesting the formation of a soliton gas.

Influence of Anisotropic Consolidation on the Instability of Loose Granular Soils Under Undrained and Drained Loading

Previous studies, mostly experimental, have reported conflicting observations on the effect of the initial anisotropic consolidation stress ratio (η<sub>0</sub>) on the stress ratio at the onset of instability (η<sub>f</sub>) for drained and undrained loading that involve static liquefaction. They indicate that as η<sub>0</sub> increases, η<sub>f</sub> could decrease, increase, or remain invariant, albeit without providing potential mechanistic factors. In this study, the anisotropic critical state theory (ACST) is used to investigate potential factors, including compressibility, state, and fabric anisotropy, that can explain the influence of η<sub>0</sub> on η<sub>f</sub> under undrained and drained loading. The assessments consider numerical simulations with the ACST-based SANISAND-F model, insights from SANISAND-F based instability criteria, the instability surface concept, and available experimental observations. Our findings show that compressibility and fabric anisotropy (and its evolution) are key factors in explaining the influence of η<sub>0</sub> on η<sub>f</sub>. In particular, the results show that if fabric evolution is not substantial, an increase in η<sub>0</sub> decreases η<sub>f</sub> for materials with significant compressibility, whereas the effect of η<sub>0</sub> in low compressibility materials is minimal. On the other hand, for materials that promote fabric evolution, the results suggest that the effect of fabric changes counteract compressibility effects, potentially increasing η<sub>f</sub>.

Winning the transition: Strategic state action in France and Germany amid the low carbon transition and energy shock

European economies are in flux, destabilized by the low carbon transition (LCT) and post-Ukraine energy shock. How are states responding to this instability? This article contributes to emerging environmentally focused Comparative Capitalisms (CC) scholarship by developing a novel framework for analysing how state action is shaped by the demand-competitiveness-energy nexus. We comparatively examine the cases of France and Germany since 2022, drawing upon 19 elite interviews and documentary analysis of stakeholder accounts, to advance three arguments. First, it is essential for CC frameworks to integrate energy supply dynamics to understand state action and processes of capitalist development. Second, the asymmetric impact of the LCT on France and Germany has shaped distinct state-led capitalist restructuring designed to protect and extend national competitive advantages. For Germany, this has primarily involved ‘greening’ its existing export-led model of growth, whereas French state actors are attempting to advance its interests via the ‘strategic autonomy’ (SA) agenda at the domestic and regional levels. Finally, the energy shock has initiated more interventionist state action in Germany that exposes critical instabilities in its export-led growth model. This analysis has significant implications for CC scholarship and its understanding of capitalist development by illustrating the significance of energy supply dynamics and advancing understanding of how disequilibrium can be theorized within the literature.

Flame propagation, explosion hazard, and pollutant emission characterization of typical clean fuels leaks in plateau low-pressure region

To accelerate energy transformation and sustainable development, various countries are rushing to lay hydrogen doped natural gas pipelines. However, the installation of pipelines will pass through plateau low-pressure region, and the impact of low-pressure environments on the flame propagation, explosion hazards, and pollutant emission characteristics of hydrogen doped natural gas is not yet clear. To solve this problem, a combination of constant volume combustion experiment and numerical simulations is used. The characterization parameters of flame, explosion and pollutant concentration of natural gas/H2/air under low-pressure environment are obtained, and their chemical reaction kinetics are analyzed. When the pressure drops, the laminar burning velocity (LBV) of them increases, and the Lewis number (Le) gradually increases by more than 1. Thermal diffusion is stronger than mass diffusion, and the growth rate of flame thickness exceeds 26 %. The effect of hydrodynamic instability enhances, causing an increment in the average size of flame cells, the critical instability radius, and the Markstein length (Lu). At the equivalent ratio (φ) of 1, there is a change from negative to positive in the Lu, and flame stability continuously strengthens. The explosion overpressure is reduced by 78 % to 90 %, the explosion temperature by 16 % to 20 %. As the φ increases, the LBV exhibits an inverted U-shaped relationship, reaching its maximum value near “φ = 1″. The flame stability first weakens and then strengthens. The explosion hazard is strongest in the range of ”φ = 1–1.2″. With a decrease in pressure, the total reaction rate of fuel consumption is reduced by more than 50 %. The continuous reaction distance is extended by 12 %. Changes in pressure have a relatively weak impact on the content of CO and CO2. The increase in the φ results in an increase in CO content of over 7 %. The content of CO2 reaches its maximum value around “φ = 1″. It is an essential reference for the safe delivery of hydrogen energy and the reduction of environmental pollution.

Negative available potential energy dissipation as the fundamental criterion for double diffusive instabilities

The background potential energy (BPE) is the only reservoir that double diffusive instabilities can tap their energy from when developing from an unforced motionless state with no available potential energy (APE). Recently, Middleton and Taylor linked the extraction of BPE into APE to the sign of the diapycnal component of the buoyancy flux, but their criterion can predict only diffusive convection instability, not salt finger instability. Here, we show that the problem can be corrected if the sign of the APE dissipation rate is used instead, making it emerge as the most fundamental criterion for double diffusive instabilities. A theory for the APE dissipation rate for a two-component fluid relative to its single-component counterpart is developed as a function of three parameters: the diffusivity ratio, the density ratio, and a spiciness parameter. The theory correctly predicts the occurrence of both salt finger and diffusive convection instabilities in the laminar unforced regime, while more generally predicting that the APE dissipation rate for a two-component fluid can be enhanced, suppressed, or even have the opposite sign compared to that for a single-component fluid, with important implications for the study of ocean mixing. Because negative APE dissipation can also occur in stably stratified single-component and doubly stable two-component stratified fluids, we speculate that only the thermodynamic theory of exergy can explain its physics; however, this necessitates accepting that APE dissipation is a conversion between APE and the internal energy component of BPE, in contrast to prevailing assumptions.

Younger age for the oldest magnetic white dwarfs

Abstract Sufficiently old white dwarfs cool down through a convective envelope that directly couples their degenerate cores to the surface. Magnetic fields may inhibit this convection by stiffening the criterion for convective instability. We consistently implemented the modified criterion in the stellar evolution code mesa, and computed the cooling of white dwarfs as a function of their mass and magnetic field B. In contrast to previous estimates, we find that magnetic fields can significantly change the cooling time t even if they are relatively weak $B^2\ll 8\pi P$, where P is the pressure at the edge of the degenerate core. Fields B ≳ 1 MG open a radiative window that decouples the core from the convective envelope, effectively lowering the luminosity to that of a fully radiative white dwarf. We identified a population of observed white dwarfs that are younger by Δt ∼ Gyr than currently thought due to this magnetic inhibition of convective energy transfer – comparable to the cooling delay due to carbon–oxygen phase separation. In volume-limited samples, the frequency and strength of magnetic fields increase with age. Accounting for magnetic inhibition is therefore essential for accurate cooling models for cosmic chronology and for determining the origin of the magnetic fields.

Local gravitational instability of two-component thick discs in three dimensions

Aims. The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study the local gravitational instability of two-component thick discs in three dimensions. Methods. We use as a starting point a recently proposed analytic three-dimensional (3D) instability criterion for discs with non-negligible thickness that takes the form Q3D < 1, where Q3D is a 3D version of the classical 2D Toomre Q parameter for razor-thin discs. Here, we extend the 3D stability analysis to two-component discs, considering first the influence on Q3D of a second unresponsive component, and then the case in which both components are responsive. We present the application to two-component discs with isothermal vertical distributions, which can represent, for instance, galactic discs with both stellar and gaseous components. Finally, we relax the assumption of vertical isothermal distribution, by studying one-component self-gravitating discs with polytropic vertical distributions for a range of values of the polytropic index corresponding to convectively stable configurations. Results. We find that Q3D < 1, where Q3D can be computed from observationally inferred quantities, is a robust indicator of local gravitational instability, depending only weakly on the presence of a second component and on the vertical gradient of temperature or velocity dispersion. We derive a sufficient condition for local gravitational instability in the midplane of two-component discs, which can be employed when both components have Q3D > 1.

EHD Instabilities in Two Layers of Insulating and Conducting Immiscible Liquids Subjected to Unipolar Charge Injection

In this paper, the instability of two layers of insulating and conducting immiscible liquids separated by a deformable interface and subjected to unipolar injection is examined. Taking into account the slight deformation of the interface between the two liquids, a system of equations and boundary conditions is derived at marginal state. Non zero numerical solutions for both layers exist only for eigenvalues of the instability parameter T, which depends on the following parameters: injection level C, Bond number Bo, a new non-dimensional parameter P proportional to interfacial tension and the ratio of the layers’ thickness and of liquids viscosity. The variations in the instability criterion Tc, corresponding to the smallest eigenvalue, are examined in detail as a function of the main characteristic parameters C, P and the Bond number. We find that for some values of P, two instability mechanisms convective and interfacial ones can take place. When the strength of interfacial tension or the liquid thickness ratio is very low, the critical number tends to a value corresponding to interfacial instability. The influence of injection-induced convection in the insulating layer and the effect of interfacial deformation on interfacial instability are also discussed.

Elastic Local Buckling Analysis of a Sandwich Corrugated Steel Plate Pipe-Arch in Underground Space

In underground spaces, corrugated steel plate (CSP) pipe-arches may experience local buckling instability, which can subsequently lead to the failure of the entire structure. Recently, sandwich CSP pipe-arches have been used to enhance the stability of embedded engineering outcomes, and their buckling behaviors require in-depth research. In this paper, we establish a theoretical model by simplifying soil support and using Hoff sandwich plate theory to focus on the local buckling stability of the straight segment in embedded sandwich CSP pipe-arches using the Rayleigh–Ritz method. Through stability analysis, the instability criteria for embedded sandwich CSP pipe-arches are analytically determined. Numerical calculations reveal that the critical buckling load of a sandwich CSP pipe-arch is affected by several factors, including the elastic modulus, thickness, Poisson’s ratio, rotational constraint stiffness, and the length of the straight segment. Specifically, increasing the thickness of the sandwich CSP pipe-arch can substantially enhance the critical buckling load. Meanwhile, the wavenumber is affected by the elastic modulus and the length of the straight segment. The analytical results are in agreement with those obtained from finite element analysis. These findings provide a theoretical basis and guidance for the application of sandwich CSP pipe-arches in fields such as subway stations, tunnel construction, underground passages, and underground parking facilities.