Stability Threshold Research Articles

Double diffusive convection in bidispersive porous media with couple stresses effect and relatively large macropores

In this study, we have investigated the problem of double-diffusive convection in a porous medium that exhibits bidispersive characteristics and is influenced by couple stresses. The model employed considers the Darcy theory in the micropores, while utilizing the Brinkman theory in the macropores. The system encompasses two competing effects: a temperature gradient that induces instability and a salt gradient that enhances system stability. The study involved conducting analyses of linear instability and nonlinear stability. The eigenvalue systems obtained from both the linear and nonlinear theories were solved using the Chebyshev collocation method. To ensure the accuracy of this numerical method, the results were cross-validated by comparing them with the analytical solution of the eigenvalue system derived from the linear instability theory. Notably, the Chebyshev collocation method exhibited high accuracy even in the presence of high-order derivatives arising from the couple stresses term. Finally, numerical computations were performed to determine and extensively discuss the linear instability thresholds and global nonlinear thresholds. The findings contribute valuable insights into the behavior of the system under investigation. The results show that the stability thresholds of bidisperse flow in porous media are lower than those of single-phase flow. Moreover, the results confirm the stabilizing effect of the Brinkman parameter, couple stresses parameter, and permeability ratio parameter. It has also noted the stabilizing effect of the concentration Rayleigh number if the layer is salted below and the destabilizing effect if the layer is salted above.

Physics-Guided Neural Network for Load Margin Assessment of Power Systems

The power system load margin is an important index used in power system operation centers. Traditional load margin calculation involves solving a set of differential-algebraic equations where not all information is always available. Data-driven methods such as Neural Networks (NNs) have been proposed but present poor performance and lack of generalization, especially in cases other than the operating history of power systems. In this article, we propose a Physics-Guided Neural Network (PGNN) to calculate the load margin of power systems. The PGNN is regularized by an auxiliary process that aims to reconstruct the power flow equations at the stability threshold that defines the load margin. In the PGNN training stage, there are two error functions that must be minimized, one related to the empirical knowledge of the system and the other related to the physical knowledge of the system associated with the guarantee of power flow. Case studies are presented for two test power systems, IEEE 68-bus system and Brazilian interconnected power system, considering a set of operating conditions, signal noise and outliers. The results show the superior performance of PGNN over traditional NNs.

Computing the Load Margin of Power Systems Using Golden Jackal Optimization

The Load Margin (LM) is an important stability index applied in power systems. The calculation of LM has always been associated with voltage stability studies, but the increase in load can also cause the emergence of poorly damped oscillation modes studied in stability at small signals that can destabilize the power system. This article proposes an optimization model to determine the LM considering jointly the voltage stability and small signal stability thresholds. The bio-inspired algorithm called Golden Jackal Optimization is applied to solve the optimization model. The IEEE 39-bus test system is used for case studies and discussions.

Thermal stability of a two-dimensional multilayer diffusion-reaction problem

Multilayer diffusion-reaction problems appear commonly in heat and mass transfer analysis, including in thermal management of Li-ion batteries, drug delivery and reacting systems. Thermal stability of diffusion-reaction problems is of much interest due to the potential for thermal runaway in such systems. While there is some past work on investigating thermal instability in a one-dimensional multilayer body, practical systems such as Li-ion cells are often two- or even three-dimensional. Therefore, it is important to develop a theoretical understanding of when a two-dimensional multilayer diffusion-reaction system may be thermally unstable. This work addresses this important question by deriving a solution for the transient temperature field in this problem, followed by pole analysis in the Laplace domain. An explicit threshold for thermal stability of the system is determined on the basis of the determinants associated with a set of algebraic equations. The impact of key non-dimensional numbers on thermal stability is determined, including those associated with heat generation and boundary cooling, as well as ratios of thermal properties of the layers. Good agreement with past papers for special cases of the general problem considered here is shown. A stability curve that separates stable and unstable regions in the thermal design space of a two-dimensional two-layered body, such as a stack of Li-ion cells is presented. This work extends the state-of-the-art in the theoretical understanding of thermal stability, and may also contribute towards design for safety of practical engineering systems.

Weakly Nonlinear Analysis of Flow-Driven Porous Anodic Oxide

Porous anodic oxide (PAO) films are formed by the electrochemical oxidation of metals such as titanium, aluminum, and other metals in acidic solutions. The optimal selection of parameters leads to the formation of submicron-sized pores arranged in a parallel hexagonal array within these films. Porous anodic oxide has enormous industrial applications in the development of functional nanodevices. The present study builds upon the flow-driven porous anodic oxide model proposed by Mishra and Hebert. They have shown through a linear stability analysis of the model that the inter-pore distance in PAO is successfully determined by the competition between stabilizing oxide formation and destabilizing viscous flow. In this work, we investigate the weakly nonlinear analysis of the model to determine the nature of instability arising in flow-driven porous anodic films beyond the stability threshold. For formation of well- developed pores, the nature of instability must be subcritical. However, the results of weakly nonlinear analysis show that the solutions resulting from neutral stability exhibit a supercritical nature for the practical range of anodizing control parameters as shown in Figure 1. Thus, in order to make accurate nonlinear predictions about the formation of pores, it is imperative to incorporate additional physics into the viscous flow model. We also determine the Hadamard stability criteria by tracking the neutral wavenumber to ascertain the regions of well- posedness of the viscous flow model. Figure 1

Penetrative and Marangoni convection in a fluid film over a phase boundary

We study the effects of buoyancy, surface-tension gradients and phase boundary on the stability of a layer of water that is confined between air at the top and a layer of ice at the bottom. The temperature of the overlying air and flux condition at the free surface of the water layer are such that the layer is susceptible to both thermal and thermocapillary instabilities. We perform a linear stability analysis to identify these modes of instability and investigate the effects of the phase boundary on them. We find that with increasing thickness of the ice layer, the critical Rayleigh and Marangoni numbers for the instabilities are found to first decrease and then asymptote to constant values for ice thicknesses much larger than the thickness of the water layer. In the case of thermocapillary instability, we find that the thickness of the ice layer has negligible influence on the stability threshold for dimensionless wavenumber $k \gg 1$ , and that the presence of an unstably stratified liquid layer significantly alters the stability threshold for $k = O (1)$ . Furthermore, the inclusion of Marangoni stresses reduces the stability threshold of the thermal instability.

A simulation-based approach to assess the stability of marine food-webs and inform Good Environmental Status

The European Union Marine Strategy Framework Directive (MSFD) recognises that maintaining marine food-webs in Good Environmental Status (GES) is fundamental to ensure the long-term provision of essential ecosystem goods and services. However, operationalising food-web assessments is challenging due to difficulties in i) implementing simple but complete monitoring programmes, ii) identifying thresholds in monitoring indicators that inform when perturbations are diverting food-web state from GES and iii) in providing an integrative and complete picture of the (health) status of food-webs. In this context, stability assessments of marine food-webs could be useful to identifying the indicators that best track perturbation-induced changes in food-web state and the threshold boundaries that should not be exceeded to minimise the likelihood of losing stability. Yet, there is still a lack of systematic methods to perform such assessments. Here, we evaluate the potential of a simulation-based protocol to be used as a methodological standard for assessing the stability of marine food-webs. The protocol draws on the principles of ecological stability theory and provides a framework for assessing the trajectories of individual indicators during perturbation regimes and their robustness in detecting stability thresholds for marine food-webs. We tested the protocol on an open-ocean and deep-sea food-web modelled with the Ecopath with Ecosim suite. We concluded that indicators that quantify transfer efficiency through the food-web and measure the average trophic level of the community are optimal proxies for trophic functioning and structure to assess the stability of the system. Furthermore, we show how the approach can be applied to i) determine the impact of a loss of stability on the balance between trophic levels and ii) identify the biological components of the food-web that are most affected in scenarios of stability loss. Our findings could be useful for the ongoing debate on how trophic models and derived indicators can play a concrete and practical role in the food-web assessments in European seas.

Analysis of some biochemical properties of recombinant siberian roe deer (Capreolus pygargus) chymosin obtained in the mammalian cell culture (CHO-K1)

The structure of the Siberian roe deer (Capreolus pygargus) chymosin gene has been established for the first time and its exon/intron organization has been determined. The coding part of the C. pygargus chymosin gene was reconstructed and obtained as a DNA clone using the Golden Gate method. Comparative analysis of the sequences of prochymosins of roe deer, cow and single-humped camel revealed a number of amino acid substitutions in the sites forming the substrate-binding cavity of the enzyme and affecting the specificity subsites S4 and S1′ + S3′. The recombinant plasmid pIP1-Cap was constructed using the integration vector pIP1 for the expression of the roe deer prochymosin gene in CHO-K1 cells. A polyclone of CHO-K1-CYM-Cap cells was obtained, providing synthesis and secretion of recombinant prochymosin into the culture fluid of the producer. As a result of zymogen activation, a recombinant roe deer chymosin preparation with a total milk-clotting activity of 468.4 ± 11.1 IMCU/ml was obtained. The yield of recombinant roe deer chymosin was 500 mg/liter or ≈ 468,000 IMCU/liter, which exceeds the yield of genetically engineered chymosins in most of the expression systems used. The main biochemical properties of the obtained enzyme were compared with commercial preparations of recombinant chymosins of single-humped camel (Camelus dromedarius) and cow (Bos taurus). The specific milk-clotting activity of recombinant C. pygargus chymosin was 938 ± 22 IMCU/mg of protein and was comparable with the indicators of comparison enzymes. The nonspecific proteolytic activity of recombinant roe deer chymosin was 1.4-4.5 times higher than that of cow and camel enzymes. In terms of coagulation specificity, the recombinant C. pygargus chymosin occupied an intermediate position between the genetically engineered analogues of B. taurus and C. dromedarius chymosins. The threshold of thermal stability of recombinant roe deer chymosin was equal to 55°C. At 60°C, the enzyme retained

Influence of fluidelastic vibration frequency on predicting damping controlled instability using a quasi-steady model in a normal triangular tube array

Researchers have applied theoretical and CFD models for years to analyze the fluidelastic instability (FEI) of tube arrays in steam generators and other heat exchangers. The accuracy of each approach has typically been evaluated using the discrepancy between the experimental critical flow velocity and the predicted value. In the best cases, the predicted critical flow velocity was within an order of magnitude comparable to the measured one. This paper revisits the quasi-steady approach for damping controlled FEI in a normal triangular array with a pitch ratio of P/d=1.375. The method addresses the fluidelastic frequency at the stability threshold as an input parameter for the approach. The excellent agreement between the estimated stability thresholds and the equivalent experimental results suggests that the fluidelastic frequency must be included in the quasi-steady analysis, which requires minimal computing time and experimental data. In addition, the model allows a simple time delay analysis regarding flow convective and viscous effects.

Nonlinear EHD stability of a cylindrical interface separating two Rivlin-Ericksen fluids: A novel analysis

The NS of a cylindrical interface separating two liquids of the RE type is scrutinized in the present article. Through the presence of uniform streaming, the two electrified liquids are acted upon by an unchanged longitudinal EF. Density, viscoelasticity, and electrical features of the two liquids are all diverse; the ST at the interface is maintained. The motivation behind the present study lies in the numerous potential applications of this topic in manufacturing, engineering, and practical physics. The viscoelastic participation, also recognized via the VPF, can merely be constructed at the interface owing to the complexity of the theoretical process. The GEMs are inspected by the LS approach, then the nonlinear BCs are reached. A nonlinear equation of the interface movement is created by this technique. As well-known, the LS performance was extensively discussed in numerous publications. Accordingly, we exclusively study the nonlinear intelligence in the present work. A new methodology grounded in the NPA is employed to scrutinize the interface deviation in numerous frameworks and to estimate the NS. The last equation is an instance of a PDE with composite quantities. This equation is signified as a nonlinear HRHO, subject to specific constraints. A linear equation that corresponds to the measured NPA is created. The two equations are confirmed by a numerical analogous. At this stage, the linear equation is established to investigate the framework of a liquid flow along with the dimensionless fundamental numerals. Numerous non-dimensional physical numbers, used to characterize the system, are likewise determined. The physical significance of certain amounts aids in certain physical explanations. A set of charts is adopted to theoretically inspect and numerically display of the stability thresholds. The apprehension of instability/stability is portrayed by organizing the EF strength against the travelling wave numeral. To validate the stability profile, several polar representations are depicted. In our opinion, the current analysis is simple, operative, hopeful, and may be employed in a diversity of circumstances.

Predicting stability of synchronous nonlinear vibration in vertical rotating shaft system with journal bearing

Journal bearings (JBs) play a vital role in rotating machines across various fields. In vertical rotating shaft systems with JB, synchronous vibration experiences stages of destabilization and stabilization as rotational speed increases due to self-excited vibration. The onset speed of instability (OSI1) can be predicted via conventional eigenvalue analysis around static equilibrium positions. However, conventional analysis cannot determine the stabilizing and destabilizing speeds (OSS and OSI2) at which self-excited vibration disappears and reappears; numerical and experimental methods suffice. No other theory adequately explains these phenomena. This paper proposes an analytical method based on linearizing JB force and generalized eigenvalue analysis to efficiently predict synchronous vibration stability in vertical rotating shaft systems. The extended eigenvalue analysis directly determines synchronous orbit stability. Demonstrating accuracy and efficiency, a characteristic curve representing stability changes within an unbalance range is calculated, compared with numerical results. Our method serves as an input to rotor dynamic software, calculating rotating shaft-bearing stability thresholds.

Mechanism and risk assessment of baffle-jetting-induced vibrations in fuel rods

As nuclear reactor cores approach the end of their lifespans, it is a crucial aspect to ensure that the structural integrity of the reactor internals is not affected. The baffle-former bolts are subjected to significant mechanical stress and neutron irradiation from the reactor core during the plant operation. These circumstances can cause the bolts to degrade and lose some of their load-bearing capacity over the reactor lifespan. The degraded baffle-former bolts can lead to separation/openings between the baffle plates which cause water jet cross-flow injecting through these openings. This phenomenon is called baffle jetting. This jet flow can induce the vibration of fuel rods located near the baffle gaps, resulting in grid-to-rod fretting and, in extreme cases, fuel rod failures.This paper investigates the risk of baffle jetting-induced fluidelastic instability in fuel assemblies. A 6 × 5 axisymmetric flexible rod bundle having a prototypical nuclear fuel assembly is designed and fabricated to simulate a part of a fuel assembly under combined axial flow and baffle jetting. A special displacement mechanism is used to vary the position of jet flow relative to the array (i.e. jet eccentricity). Two cases, the jet-gap aligned case, and the jet-rod aligned case, are investigated to determine the variation of critical jet velocity with the jet eccentricity. In addition, three axial flow velocity cases, VAxial = 1.0 m/s, 1.5 m/s, and 2.0 m/s are tested in order to determine the stability effect of axial flow velocity on jet-induced instability. The experiments show that the mock-up array response resembles fluidelastic instability behavior. The stability threshold of the mock-up array depends strongly on the relative position of the jet flow with respect to the array centerline. In the jet-rod aligned case, the axial flow shows a strong effect on the combined flow-induced instability.

Effect of bearing shell deformation and ER fluid behavior on two-lobed slot-entry hybrid journal bearing

The present article deals with the effects of deformable bearing shells on the performance of lobed slot-entry hybrid journal bearing systems. The influence of the deformation coefficient [Formula: see text] has been studied using the thin liner elasticity model, which measures the flexibility of the bearing liner. Recently, smart fluid, that is, electrorheological (ER) fluid has been used in various tribological systems to obtain better performance. Therefore, the influence of ER lubricant on the bearing performance characteristics has also been studied in this work. Bingham model constitutive relation has been used to analyze the non-Newtonian behavior of ER fluid. The performance of fluid film bearings is greatly influenced by the noncircularity of the bearings. Therefore, the behavior of deformable bearing shells in a slot-entry journal bearing for lobed conditions has also been studied in the present study. The results reveal that considering deformation in the bearing shell reduces the value of frictional torque, whereas the value of stiffness coefficients and stability threshold speed increases. However, ER lubricant enhances the value of film thickness, stiffness/damping coefficients, and stability threshold speed margin.

A dynamical approach to the study of instability near Couette flow

AbstractIn this paper, we obtain the optimal instability threshold of the Couette flow for Navier–Stokes equations with small viscosity , when the perturbations are in the critical spaces . More precisely, we introduce a new dynamical approach to prove the instability for some perturbation of size with any small , which implies that is the sharp stability threshold. In our method, we prove a transient exponential growth without referring to eigenvalue or pseudo‐spectrum. As an application, for the linearized Euler equations around shear flows that are near the Couette flow, we provide a new tool to prove the existence of growing modes for the corresponding Rayleigh operator and give a precise location of the eigenvalues.

Stability of the scattering transform for deformations with minimal regularity

The wavelet scattering transform introduced by Stéphane Mallat is a unique example of how the ideas of harmonic and multiscale analysis can be ingeniously exploited to build a signal representation with provable geometric stability properties, such as the Lipschitz continuity to the action of small C2 diffeomorphisms – a remarkable result for both theoretical and practical purposes, inherently depending on the choice of the filters and their arrangement into a hierarchical architecture. In this note, we further investigate the intimate relationship between the scattering structure and the regularity of the deformation in the Hölder regularity scale Cα, α>0. We are able to precisely identify the stability threshold, proving that stability is still achievable for deformations of class Cα, α>1, whereas instability phenomena can occur at lower regularity levels modeled by Cα, 0≤α<1. While the analysis at the threshold given by Lipschitz (or even C1) regularity remains beyond reach, we are able to prove a stability bound in that case, up to ε losses.

Weakly nonlinear bifurcation behaviour at the onset of instability in horizontal convection using an advective buoyancy approximation

Horizontal free convection is studied under an extended buoyancy approximation constructed to capture centrifugal effects in strongly rotating regions within buoyancy driven flows. Under this approximation, the Gay-Lussac parameter (Ga) arises in the momentum equation to characterise non-Boussinesq behaviour. The scaling of average Nusselt numbers (Nuavg) are determined, as is its dependence on Ga. Increasing Ga is found to decrease Nuavg when convection dominates the flow, while no influence is detected in the low Rayleigh number regime dominated by conduction. The influence of Ga on the onset of the time-dependent regime is investigated and the critical Rayleigh number corresponding to different Ga are determined. Results demonstrate that increasing Ga stabilises the flow, delaying transition to the time-dependent regime. An Orr–Sommerfeld type stability analysis is performed to determine the local stability at different horizontal stations. A zone of convective instability is first detected, growing from the hot end of the enclosure, at Rayleigh numbers three orders of magnitude lower than the predicted global stability threshold at the maximum investigated Ga value. Ga is found to play a key role in determining the preferred orientation of instability roll structures, with increasing Ga being accompanied by a bias toward transverse-roll instabilities over longitudinal rolls. The Stuart—Landau model is used to reveal that the non-linear characteristics of this unsteady transition are consistent with a supercritical Hopf bifurcation.

Biochemical Properties of a Promising Milk-Clotting Enzyme, Moose (Alces alces) Recombinant Chymosin.

Moose (Alces alces) recombinant chymosin with a milk-clotting activity of 86 AU/mL was synthesized in the Kluyveromyces lactis expression system. After precipitation with ammonium sulfate and chromatographic purification, a sample of genetically engineered moose chymosin with a specific milk-clotting activity of 15,768 AU/mg was obtained, which was used for extensive biochemical characterization of the enzyme. The threshold of the thermal stability of moose chymosin was 55 °C; its complete inactivation occurred after heating at 60 °C. The total proteolytic activity of moose chymosin was 0.332 A280 units. The ratio of milk-clotting and total proteolytic activities of the enzyme was 0.8. The Km, kcat and kcat/Km values of moose chymosin were 4.7 μM, 98.7 s-1, and 21.1 μM-1 s-1, respectively. The pattern of change in the coagulation activity as a function of pH and Ca2+ concentration was consistent with the requirements for milk coagulants for cheese making. The optimum temperature of the enzyme was 50-55 °C. The introduction of Mg2+, Zn2+, Co2+, Ba2+, Fe2+, Mn2+, Ca2+, and Cu2+ into milk activated the coagulation ability of moose chymosin, while Ni ions on the contrary inhibited its activity. Using previously published data, we compared the biochemical properties of recombinant moose chymosin produced in bacterial (Escherichia coli) and yeast (K. lactis) producers.

Turing patterns in hyperbolic reaction-transport vegetation models with cross-diffusion

In this paper, the pattern formation process in arid environments on flat terrains is investigated. In particular, a class of one-dimensional hyperbolic reaction-transport vegetation model with a cross-diffusion term accounting for plant roots’ suction in the soil water diffusion feedback is considered. To characterize the emerging Turing patterns, linear stability analysis on the uniform steady states is first addressed. Then, multiple-scale weakly nonlinear analysis is performed to describe the time evolution of the pattern amplitude close to the stability threshold. Finally, to validate analytical predictions, a modified Klausmeier model which takes also into account the internal competition rate is studied. The effects of the inertial times as well as the cross-diffusion and the internal competition rate are illustrated both analytically and numerically.

Catchment-scale patterns of geomorphic activity and vegetation distribution in an alpine glacier foreland (Kaunertal Valley, Austria)

The interaction between geomorphological and ecological processes plays a significant role in determining landscape patterns in glacier forelands. However, the spatial organization of this biogeomorphic mosaic remains unclear due to limited catchment-scale data. To address this gap, we used a multi-proxy analysis to map potential geomorphic activity related to surface changes induced by sediment transport on drift-mantled slopes and a glaciofluvial plain. High-resolution vegetation data were used to generate a catchment-scale map delineating vegetation cover and stability thresholds. The two maps were integrated, and an exploratory regression analysis was conducted to investigate the influence of geomorphic activity on vegetation colonization. The multi-proxy analysis resulted in an accurate mapping of catchment-wide geomorphic activity, with a validation accuracy ranging from 75.3% through field mapping to 85.9% through plot sampling. Through vegetation cover mapping, we identified biogeomorphic stability thresholds, revealing a mosaic of vegetation distribution. Distinct colonization patterns emerged across different geomorphic process groups, influenced by process magnitude and the time since the last disturbance event. The exploratory regression analysis showed that vegetation distribution is significantly affected by geomorphic processes. Based on the overlay of results regarding geomorphic activity and vegetation distribution, we suggest an age-independent framework that indicates four potential situations of biogeomorphic succession.

Thermo-electric convection in a cylindrical annulus during a sounding rocket flight

An experiment on convective flows induced by the dielectrophoretic force was performed under the microgravity condition provided during a sounding rocket flight. The dielectrophoretic force possesses a non-conservative term that can be seen as resulting from an electric gravity. That gravity can be responsible for an electric Rayleigh–Bénard convection between a hot inner cylinder and a cold outer cylinder when an electric field is applied in the radial direction. Four cells with independent temperature and electric field controls allowed the investigation of eight different values of the electric Rayleigh number relatively close to the onset of the thermo-electric instability. A linear stability analysis is performed to predict the stability threshold and the evolution of the growth rate of the instability. The three-dimensional structure of the flow is captured by simultaneous particle image velocimetry and by shadowgraphy. The amplitude of the instability modes and the time evolution of the flow is analysed, and various methods are proposed to extrapolate the experimental critical value of the electric Rayleigh number for the onset of convection. The measured critical electric Rayleigh number is in agreement with the prediction of the linear stability theory. The comparison of the new experimental results with previous ones from parabolic flight campaigns highlights the importance of long-term microgravity for the achievement of thermal convection at low values of the control parameters.