Stability Threshold Research Articles

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.

A Revised Work on the Rayleigh-Bénard Instability of Nanofluid in a Porous Medium Layer

To reveal the mechanism of the enhanced heat transfer in nanofluids, Buongiorno (ASME J. Heat Transfer, vol. 128, 2006, pp. 240–250) developed a convective transport model by considering the slip mechanisms of nanoparticles migration. By now, many extended researches are based on his model. Among them, the study on porous medium flow pioneered by Nield & Kuznetsov (Int. J. Heat & Mass Transfer, vol. 52, 2009, pp.5796–5801) has received much attention. Their work employed the Darcy model and Buongiorno’s model to investigate the thermal instability in a horizontal porous medium layer saturated by a nanofluid. Through a sophisticated analysis, they obtained an approximate formula capable of predicting the stability threshold. However, a potential contradiction exists in their analysis owing to an improper assumption about the thermophoretic coefficient, which may lead to an unphysical result. To date, much of current works still adopted this improper assumption in various extended problems. To resolve this contradiction, the present study revises their work by considering the dependence of thermophoretic coefficient on the volume fraction of nanoparticles. A nonlinear basic-state solution of concentration is obtained and then used to implement the linear stability analysis. In comparison with Nield’s formula, the present result shows that the threshold of instability shifts to a lower concentration by more than one order of magnitude. The mechanism causing the shift is discussed and the novelty of the present study is stressed.

Stability threshold of Couette flow for 2D Boussinesq equations in Sobolev spaces

Consider the nonlinear stability of the Couette flow in the Boussinesq equations with vertical dissipation on T×R. We prove that if the initial perturbations uin and θin to the Couette flow vs=(y,0)⊤ and θs=1, respectively, satisfy ‖uin‖HN+1+ν−12‖θin‖HN+ν−13‖|∂x|13θ‖HN≪ν13, N>7, then the resulting solution remains close to the Couette flow in L2 at the same order for all time.

Simulation of foil bearing supported rotor systems considering tilting motions

AbstractAn accurate model of a foil bearing supported rotor needs to cover rotor dynamics of the shaft, structure dynamics of the foil as well as hydro‐ and thermo dynamics in the fluid film. The paper addresses the incorporation of tilting motions of the shaft and its influence on the foil deflection, which in turn results in a more accurate prediction of the stability threshold of the rotor‐bearing system.

The parametric analysis on angular vibration stability of spiral groove dry gas seal with real gas model

To accurately grasp the vibration stability of spiral groove dry gas seals (S-DGSs), the angular vibration stability thresholds of S-DGSs, which vary with the operating and structural parameters, were investigated by using carbon dioxide and hydrogen real gases as lubricants. The numerical results show that the vibration stability of the S-DGS in angular direction is independent of spring stiffness. Under the same conditions, the real gas effect enhances critical transverse moment of inertia and frequency ratio in carbon dioxide case, whereas it reduces both stability thresholds in hydrogen case. A spiral groove number Ng, land-to-groove ratio κ, and spiral angle δ that are too large or too small all contribute to an increased risk of S-DGS angular instability. By considering critical frequency ratio as the target, the optimal range of spiral groove structure parameters have been obtained by using a single factor analysis method.

A QGIS -plugin for gully erosion modeling

Gully erosion affects the landscape and human life in many ways, including the destruction of agricultural land and infrastructures, altering the hydraulic potential of soils, as well as water availability. Due to climate change, more areas are expected to be affected by gully erosion in the future, threatening especially low-income agricultural regions. In the past decades, quantitative methods have been proposed to simulate and predict gully erosion at different scales. However, gully erosion is still underrepresented in modern GIS-based modeling and simulation approaches. Therefore, this study aims to develop a QGIS plugin using Python to assess gully erosion dynamics. We explain the preparation of the input data, the modeling procedure based on Sidorchuk’s (Sidorchuk A (1999) Dynamic and static models of gully erosion. CATENA 37:401–414.) gully simulation model, and perform a detailed sensitivity analysis of model parameters. The plugin uses topographical data, soil characteristics and discharge information as gully model input. The plugin was tested on a gully network in KwaThunzi, KwaZulu-Natal, South Africa. The results and sensitivity analyses confirm Sidorchuck’s earlier observations that the critical runoff velocity is a main controlling parameter in gully erosion evolution, alongside with the slope stability threshold and the soil erodibility coefficient. The implemented QGIS plugin simplifies the gully model setup, the input parameter preparation as well as the post-processing and visualization of modelling results. The results are provided in different data formats to be visualized with different 3D visualization software tools. This enables a comprehensive gully assessment and the derivation of respective coping and mitigation strategies.

Effect of the density ratio on the oscillatory Saffman–Taylor instability in vertical conical Hele–Shaw cell

The stability of an oscillating interface between two immiscible liquids with a high viscosity contrast in an axisymmetric conical Hele–Shaw cell in dependence on the density ratio is studied experimentally. The symmetry axis of the cell is vertical, while the tangential component of the gravy acts on the axisymmetric interface. The contact line is almost motionless, while the low-viscosity liquid penetrates a high-viscosity one in the form of an axisymmetric “tongue” in the course of an oscillating cycle. The increase in the oscillation amplitude leads to the development of azimuthal patterns (fingers) at the interface. Fingers of a low-viscosity liquid appear when a viscous liquid is being squeezed out of the cell and reach their maximum length at the maximum displacement of the interface. Then, the fingers decrease and are replaced by small depressions penetrating into the low-viscosity liquid in the phase of maximum boundary displacement toward the low-viscosity liquid. The increase in the density ratio of liquids has a stabilizing effect on the interface: The instability threshold is shifted to the higher oscillation amplitudes. Also, the stability threshold is independent of whether the high-viscosity or low-viscosity liquid is denser than the other one. We propose a new dimensionless parameter that controls the stability of the interface—the multiplication of the square root of the capillary number and the dimensionless amplitude of interface oscillations. It is revealed that the critical value of the stability parameter increases linearly with an increase in the density ratio of liquids.

Effect of outer-cylinder rotation on the radially heated Taylor–Couette flow

A Taylor–Couette setup with radial heating is considered where a Boussinesq fluid is sheared in the annular region between two concentric, independently rotating cylinders maintained at different temperatures. Linear stability analysis is performed to determine the Taylor number for the onset of instability. Two radius ratios corresponding to wide and thin gaps with several rotation rate ratios are considered. The rotation of the outer cylinder is found to have a general stabilizing effect on the stability threshold as compared to pure inner-cylinder rotation, with a few exceptions. The radial heating sets up an axial flow which breaks the reflection symmetry of isothermal Taylor–Couette flow in the axial coordinate. This symmetry breaking separates linear stability thresholds, and we find the fastest growing modes with both positive and negative azimuthal numbers for different parameters. Another important finding of the current study is the discovery of unstable modes in the Rayleigh-stable regime. Furthermore, closed disconnected neutral curves (CDNCs) are observed for both wide and thin gaps which can separate from or merge into open neutral–stability curves. Alternatively, CDNCs can also morph into open neutral stability curves as the rotation rate ratio is changed. CDNCs are observed to be sensitive to changes in control parameters, and their appearance/disappearance is shown to induce discontinuous jumps in the critical Taylor number. For both wide and thin gaps, the fastest-growing modes found in the pure corotation case are shown to have their origins in the instability islands at smaller values of rotation rate ratios.

Comparison of Biochemical Properties of Recombinant Alpaca (<i>Vicugna pacos</i>) Chymosins Produced in Pro- and Eukaryotic Expression Systems

Based on the yeast Kluyveromyces lactis, a strain-producer of recombinant alpaca prochymosin (Vicugna pacos) was developed. A comparative analysis of the biochemical properties of recombinant alpaca chymosin obtained in the expression systems of K. lactis and Escherichia coli was carried out. It was found that the recombinant alpaca chymosin synthesized in K. lactis exceeds the analog obtained in E. coli by 12.9 times in the number of enzyme turnovers, and by 2.9 times in catalytic efficiency. Compared to chymosin expressed in E. coli, the enzyme obtained in a eukaryotic producer has a thermal stability threshold increased by 5°C. Replacing a prokaryotic producer with a eukaryotic one enhances the negative sensitivity of the milk-clotting activity of recombinant alpaca chymosin to an increase in substrate pH in the range of 6.1–6.9, which is accompanied by an increase in the duration of coagulation by 8–35%. With an increase in the concentration of CaCl2 in the substrate, the coagulation activity of the target enzyme synthesized in E. coli was 12–14% higher than that of its analogue obtained in K. lactis.

Thermohaline convection of a Casson fluid in a porous layer: Linear and non-linear stability analyses

The study investigates the thermosolutal convection of a Casson fluid in a horizontal layer that is heated and salted from below. Both linear and non-linear analyses are performed using the method of normal modes to solve the governing equations. Interestingly, the study demonstrates that the linear and non-linear stability thresholds coincide. To solve the differential eigenvalue problem for linear theory, a one-term Galerkin approach is employed. Meanwhile, for the eigenvalue problem of non-linear instability, a numerical solution is obtained using the bvp4c routine in MATLAB. The results reveal some important findings. First, the Casson parameter is shown to destabilize the flow, leading to instability. However, the Darcy number and solutal Rayleigh number are found to have a stabilizing effect on the system. Furthermore, the study develops a weakly non-linear theory using multiple scale analysis to investigate heat and mass transport, offering valuable insight into these transport phenomena within the context of the system under consideration.

Proton Temperature Anisotropy within the Interplanetary Coronal Mass Ejections Sheath at 1 au

The sheath plasma of interplanetary coronal mass ejections (ICMEs) is highly compressed, heated, turbulent, and magnetically intense relative to the ambient solar wind. In this Letter, we perform a detailed study of proton temperature anisotropy within the 333 ICME sheath regions observed on board the Wind spacecraft spanning the years 1995–2015. Our observations show that marginal stability thresholds of mirror mode and firehose instabilities predominantly constrain the proton temperature anisotropy within these sheath regions regardless of ICME sheath plasma speed. This is true even when the plasma beta values are less than 2, a parameter space that should have favored the prevalence of parallel firehose and proton cyclotron instabilities according to linear stability analysis. This investigation demonstrates the critical role played by distinct plasma instabilities in shaping the evolution of ICME sheath plasma compared to the broader solar wind environment.

The Impact of Sintering Conditions on the Inner Microstructure of Composites: LSM:YSZ Electrode Case Study

High-temperature solid oxide cells (SOCs) is in the center of scientific attention for a while as a promising technology related to sustainable society. In this case, SOCs consist of two closely interlinked technologies: solid oxide fuel cells and solid oxide electrolysis cells. Both technologies share several similar traits such as high electrical efficiency and fast reaction kinetics due to the high operating temperature (600–900 °C) without the need for PGM catalysts. These cells basically consist of two porous composite electrodes and a dense ion conducting electrolyte. In particular, the inner microstructure of the electrodes predetermines the SOCs performance owing to its governing effect on the electrical conductivity and/or electrocatalytic activity. Despite its importance, contemporary understanding of the development of the emerging microstructure during the fabrication of these composite materials is far from sufficient.Lanthanum-strontium-manganite (LSM, La1-xSrxMnO3-δ) paired with yttria stabilized zirconia (YSZ, ZrO2:Y2O3) is the typical example of the state-of-the art porous oxygen electrode exhibiting a mixed ion-electron conductivity suitable for SOCs. The fabrication process of LSM:YSZ electrodes involves a crucial step – the sintering, which principle lies in the thermal treatment of the precursor particles for a defined period of time. The LSM:YSZ composite is usually sintered at 1150 °C. At this temperature, exclusively LSM particles tend to soften and form an interlinked solid framework between individual particles, while the YSZ particles remain unaffected by the temperature treatment due to their high melting point (around 2500 °C).Despite the sintering process belongs among the oldest known fabrication techniques, there is no hard evidence on how the sintering proceeds over time at different temperatures while employing materials with significantly different melting points, such as LSM and YSZ. In addition, the sintering temperature along with the sintering time directly influences the resulting inner microstructure and consequently the electrical conductivity of such electrode. Prediction of the resulting inner microstructure is frequently performed by postmortem analyses of multiple samples sintered at different temperatures. However, such practice results only in indirect proofs of the impact of the sintering temperature and is significantly time consuming. The goal of this study is, therefore, to investigate the sintering process of LSM:YSZ composite in situ and to set into relation the resulting inner microstructure with the applied thermal treatment.To answer the present goal, a novel combination of SEM paired with inbuilt MEMS heating chip was developed. This setup allows for online monitoring of the LSM:YSZ sintering process. The results show that at 900 °C the LSM particle agglomerates begin to shrink as the individual LSM particles start to adhere to each other. At this point, significant porosity emerges in the composite, which is considered essential to ensure a sufficient mass transfer during the SOCs operation. On the other hand, the degree of the emerged porosity can be beyond the threshold of mechanical stability of the electrode body, rendering such an electrode unusable. At 1150 °C the densification of the composite occurs, which is essentially a self-healing process resulting in a well-interlinked and mechanically stable composite. The densification is related to the adhesion of the LSM particles to the YSZ particles, thus forming a solid framework, ensuring ample mixed ionic-electronic conductivity of the fabricated electrode. Based on the results, a slight variation in sintering temperature and/or time leads to a significant difference in the electric conductivity of the electrode due to a different sintering degree or, in other words, due to the different void fraction in the body of the electrode. Within the literature, this outcome is reflected by a major inconsistency in reported electric conductivity of the commonly utilized 50:50 wt.% ratio of LSM:YSZ.An interesting insight into the sintering process of the LSM:YSZ composite has provided the SEM paired with inbuilt MEMS heating chip. This experimental technique is very promising for in situ studies of sintering and/or synthesis processes of various materials related to numerous technologies.This work was supported by the Technology Agency of the Czech Republic under project no. TK04030143.

Voltage Controlled Ab-Initio Simulations of Metal-Insulator Interfaces Immersed in Electrolyte for Corrosion and Battery Applications Via the Quantum Continuum Approximation (QCA)

While Density Functional Theory (DFT) has been an invaluable tool for exploring atomic interaction of defects and interfaces, it has been difficult to include information about the voltage of the larger electrochemical system into these calculations. This is because the electric field at any given simulation region is dependent on the broader interface, which is usually 10s of nm long. Fully simulating this interface with DFT is computationally prohibitive, and most studies simulate smaller portions. This reduction eliminates the information about the surrounding electric field, however, and thus the interaction with the global potential is unaccounted for. In this talk, we introduce the Quantum Continuum Approximation (QCA) as a methodology for including interface voltage information into limited-size DFT calculations by self-consistently coupling DFT calculations of defect/interface regions to Poisson-Boltzmann descriptions of the surrounding insulating and electrolyte regions. By reducing the number of atoms needed to incorporate voltage information into DFT calculations by an order of magnitude, QCA makes the voltage-dependent first-principles study of full electrochemical interfaces viable. We demonstrate this methodology to examine Cl- ion insertion into aluminum/aluminum oxide interfaces as a function of voltage. We find good agreement between the voltage threshold for stability predicted by QCA and those found experimentally. We then demonstrate QCA as a tool for measuring Li+ ion transport barriers through different solid-electrolyte interface (SEI) regions in battery chemistry as a function of voltage. Our work demonstrates the ability to attach a potentiostat to DFT calculations of interfaces relevant to simulations of electrochemical applications at reasonable computational cost. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525

Instability analysis of vibrated thermo-convection in Casson nanofluid suspension

This work is motivated by the importance of vertical vibration in nanofluids suspension, because of its wide applications in heat exchangers from one fluid to another, controlling the mixing in microvolumes, pharmaceutical industry, and engineering. The current study analyzes the effects of high-frequency vertical vibration on a horizontal Casson nanofluid layer heated from below saturated between rigid-rigid, rigid-free, and free-free boundary conditions. Field equations are derived by using time-average method, which describes the vibrational thermo-convection. These field equations are solved by utilizing linear stability analysis and Galerkin technique to obtain the thermal stability curve. By using this curve, the impacts of vertical vibration and physical governing factors on temperature profile are discussed. High-frequency vertical vibration is observed to have a stabilizing effect on Casson nanofluid suspension, thereby reducing thermo-convective heat transfer from one fluid to another. Stability threshold of vibrated suspension is increased approximately as [Formula: see text] and [Formula: see text] when [Formula: see text] and [Formula: see text], respectively. The significance of Brownian motion and thermophoretic force on convective heat transfer with vertical vibration is discussed. The resisting nature of Casson nanofluid on vibrational convective heat transfer is also tabulated.

Energetic bounds on gyrokinetic instabilities. Part 3. Generalized free energy

Free energy, widely used as a measure of turbulence intensity in weakly collisional plasmas, has been recently found to be a suitable basis to describe both linear and nonlinear growth in a wide class gyrokinetic systems. The simplicity afforded by this approach is accompanied by some drawbacks, notably the lack of any explicit treatment of wave–particle effects, which makes the theory unable to describe things like stability thresholds or dependence on the geometry of the background magnetic field. As a step toward overcoming these limitations, we propose an extension of the theory based on a generalization of the free energy. With this, it is demonstrated that resonance effects are recovered, and the bounds on growth are significantly reduced. The simplicity and efficient computation of the associated ‘optimal’ growth rates makes the theory potentially applicable to stellarator optimization.

Dynamical Behaviors in a Stage-Structured Model with a Birth Pulse

This paper presents an exploitation model with a stage structure to analyze the dynamics of a fish population, where periodic birth pulse and pulse fishing occur at different fixed time. By utilizing the stroboscopic map, we can obtain an accurate cycle of the system and investigate the stability thresholds. Through the application of the center manifold theorem and bifurcation theory, our research has shown that the given model exhibits transcritical and flip bifurcation near its interior equilibrium point. The bifurcation diagrams, maximum Lyapunov exponents and phase portraits are presented to further substantiate the complexity. Finally, we present high-resolution stability diagrams that demonstrate the global structure of mode-locking oscillations. We also describe how these oscillations are interconnected and how their complexity unfolds as control parameters vary. The two parametric planes illustrate that the structure of Arnold’s tongues is based on the Stern–Brocot tree. This implies that the periodic occurrence of birth pulse and pulse fishing contributes to the development of more complex dynamical behaviors within the fish population.

Substrate-mediated leg interactions play a key role in insect stability on granular slopes.

Locomotion on granular inclines is a subject of high relevance in ecological physics as well as in biomimmetics and robotics. Enhancing stability on granular materials represents a huge challenge due to the fluidization transition when inclination approaches the avalanche angle. Our motivating example is the predator-prey system made of the antlion, its pit, and its prey. Recent studies have demonstrated that stability on granular inclines strongly depends on the pressure exerted on the substrate. In this work we show that for multilegged locomotion, along with pressure, the distance between the leg contacts on the substrate also plays a major role in the determination of the stability threshold. Through a set of model experiments using artificial sliders, we determine a critical distance below which stability is importantly affected by the interactions between the perturbed regions generated by each contact point. A simple model based on the Coulomb method of wedges allows us to estimate a stability criterion based on pressure, interleg distance, and substrate characteristics. Our work suggests that mass to leg-length allometric relationships, as the ones observed in ants, may be an important key in determining the locomotion success of multilegged locomotion on granular inclines.