Instability Threshold Research Articles

Probing the twist angle of confined prominence eruption using SDO/AIA data

In this context, we utilized a simplified representation of the curved cylinder flux tube to approximate the helical structure of the prominence. By considering the bright helical features as indicators of the magnetic field, we measured the average twist angle of the prominence legs. To gather the necessary data, we obtained image data with a wavelength of 171 Å from the Solar Dynamic Observatory (SDO)/Advanced Imaging Assembly (AIA) archive. We employed some IDL routines within the SolarSoft (SSW) package to determine the flux rope’s total twist angle for a confined prominence eruption. Specifically, we focus on a confined prominence eruption that occurred at the south-east limb of the Sun for an active region (AR) NOAA (AR 11 117) observed on October 21, 2010. The eruption commenced on 2010-10-21 at 21:56:18 UT and lasted until 2010-10-22 at 01:24:58 UT. During this event, a B2.6 flare class that occurred on 2010-10-21 at 23:17 UT, located at heliographic position of N20E84. Our results indicate that the distance between the two footpoints is up to 18 670 km. Initially, when the event began the height (h) was found to be 21 162.1 km, but the height was increased to reach 80 362.4 km at the end of eruption. The flux rope’s average twist angle (ϕ, in radian) at the beginning of eruption was ϕ = 13.4π. As the prominence ascended to higher levels, the twist angle was decreased gradually due to the magnetic field relaxation reached to ϕ = 3.6π. We determined that the flux ropes average twist angle (ϕ) that exceed the threshold for the helical kink instability. Therefore, we conclude that the eruption was caused by helical kink instability, as a result it is in consistent with other investigations.

Weakly nonlinear analysis of rotating magnetoconvection with anisotropic thermal diffusivity effect

The influence of anisotropic thermal diffusive coefficient on the stability of the horizontal fluid planar layer rotating about its vertical axis and permeated by the horizontal homogeneous magnetic field is studied. The linear stability analysis is carried out using the normal mode method. The stationary cross/oblique and parallel modes are calculated for different ranges of control parameters arising in the system. The SA (Stratification Anisotropy) parameter, α (the ratio of horizontal and vertical thermal diffusivities), plays a key role in deciding the boundaries between these modes and their instability regions when there is a combination of high and low rotation with weak and strong magnetic fields. The obtained isotropic results coincide with those obtained by pioneers in the literature. The weakly nonlinear behavior of the stationary convective motion in the vicinity of primary instability threshold is studied using the two-dimensional Landau–Ginzburg (LG) equation with cubic nonlinearity. This equation derived using the multiple scale analysis is similar to the one obtained in the literature having different relaxation time, nonlinear coefficient, and coherence lengths. These coefficients are used to study the heat transfer rate. In the case of high rotation, Nusselt number gets decreased from atmospheric (α < 1) to oceanic (α > 1) SA types. The domain for secondary instability of Eckhaus is obtained using the spatiotemporal LG equation and it is observed that the Eckhaus instability region decreases with increasing α.

Effects of gravity and anisotropy on the convective instability in a nanofluid porous medium

Controlling thermal loads in heat transfer systems that produce high heat flux is a real mechanical challenge. Various cooling/heating techniques are available to achieve the reliability requirements of electronic devices. Among them, the use of nanofluids is one of the important techniques that provide long term stability, higher cooling rates, decreased pumping power needs, and cost-effectiveness. Instability in fluids typically occurs when a disturbance affects the equilibrium of forces of external, inertial, or viscous origin acting on a system. The disturbances may arise from the surroundings due to small changes in the boundary conditions, surface roughness, free stream turbulence, noise, etc. In several circumstances, these disturbances are very small and hence cannot be measured with the available instruments but can be observed after the instability sets in. In this study, we focus on examining the effect of time-periodic vertical gravity modulation on the initiation of natural convection in a porous medium saturated with a nanofluid. The porous medium is characterized by being heated at the bottom and possessing anisotropic properties in terms of permeability and thermal diffusivity. Specifically, we investigate the onset of convection in water-based nanofluids that contain metallic (Cu) and metal oxide ( A l 2 O 3 ) particles. The Khanafer-Vafai-Lightstone (KVL) nanofluid model is employed to describe the behavior of the nanofluids, and the thresholds for convective instability are determined using the Mathieu functions. In addition, we study the instabilities of synchronous and subharmonic modes and explore their transitions along with practical applications.

Predictors of failed left bundle branch pacing implant in heart failure with reduced ejection fraction: Importance of left ventricular diameter and QRS morphology

BackgroundLeft bundle branch pacing (LBBP) is considered an alternative to cardiac resynchronization therapy (CRT). However, LBBP is not suitable for all patients with heart failure. ObjectiveThe aim of our study was to identify predictors of unsuccessful LBBP implantation in CRT candidates. MethodsA cohort of consecutive patients with indications for CRT were included. Clinical, echocardiographic, and electrocardiographic variables were prospectively recorded. ResultsA total of 187 patients were included in the analysis. LBBP implantation was successful in 152 of 187 patients (81.2%) and failed in 35 of 187 patients (18.7%). The causes of unsuccessful implantation were unsatisfactory paced QRS morphology (28 of 35 [80%]), inability to screw the helix (4 of 35 [11.4%]), lead instability (2 of 35 [5.7%]), and high pacing thresholds (1 of 35 [2.8%]). The left ventricular end-diastolic diameter (LVEDD), non-LBBB (left bundle branch block) QRS morphology, and QRS width were predictors of failed implantation according to the univariate analysis. According to the multivariate regression analysis, LVEDD (odds ratio 1.31 per 5-mm increase; 95% confidence interval 1.05–1.63 per 5-mm increase; P = .02) and non-LBBB (odds ratio 3.07; 95% confidence interval 1.08–8.72; P = .03) were found to be independent predictors of unsuccessful LBBP implantation. An LVEDD of 60 mm has 60% sensitivity and 71% specificity for predicting LBBP implant failure. ConclusionWhen LBBP was used as CRT, LVEDD and non-LBBB QRS morphology predicted unsuccessful implantation. Non-LBBB triples the likelihood of failed implantation independent of LVEDD. Caution should be taken when considering these parameters to plan the best pacing strategy for patients.

Taxis-driven complex patterns of a plankton model.

This paper reports an important conclusion that self-diffusion is not a necessary condition for inducing Turing patterns, while taxis could establish complex pattern phenomena. We investigate pattern formation in a zooplankton-phytoplankton model incorporating phytoplankton-taxis, where phytoplankton-taxis describes the zooplankton that tends to move toward the high-densities region of the phytoplankton population. By using the phytoplankton-taxis sensitivity coefficient as the Turing instability threshold, one shows that the model exhibits Turing instability only when repulsive phytoplankton-taxis is added into the system, while the attractive-type phytoplankton-taxis cannot induce Turing instability of the system. In addition, the system does not exhibit Turing instability when the phytoplankton-taxis disappears. Numerically, we display the complex patterns in 1D, 2D domains and on spherical and zebra surfaces, respectively. In summary, our results indicate that the phytoplankton-taxis plays a pivotal role in giving rise to the Turing pattern formation of the model. Additionally, these theoretical and numerical results contribute to our understanding of the complex interaction dynamics between zooplankton and phytoplankton populations.

Investigating the impact of unstable network connections on the cluster running a consensus algorithm

This study explores the effects of unstable network connections on the operational efficiency of a computing cluster executing a consensus algorithm. Consensus algorithms are critical for maintaining the integrity and consistency of distributed systems, particularly in blockchain technologies and distributed databases. However, the reliability of these systems is often challenged by network instability, which can lead to delays, decreased throughput, and, in severe cases, loss of consensus. Research employs simulation experiments to quantify the impact of network disruptions such as latency variability on cluster running consensus algorithm. By systematically varying network conditions and observing the resultant effects on a cluster running a representative consensus algorithm, we identify critical thresholds of instability that significantly impair system performance. The findings contribute to a deeper understanding of the dynamics between network stability and distributed system, offering valuable insights for developers and engineers tasked with designing and maintaining robust distributed systems in the face of network unreliability.

Transition to plastic regime for Rayleigh-Taylor instability in soft solids.

Rayleigh-Taylor instability (RTI) is observed in soft materials that have significant resistance to yield. Estimating the instability threshold is critical to several engineering applications and has been the topic of several studies in past decades. However, limited attention has been given to the elastic-to-plastic (EP) transition threshold, where material properties vary significantly. This study explores the phase transition between the pure elastic and stable plastic regimes in RTI in a soft solid (mayonnaise) using a rotating wheel experimental setup with a time-varying acceleration profile. The material properties of the soft solid are characterized using rheological techniques. Different initial perturbation wavelength and amplitude combinations are used to analyze their role in the EP transition threshold and the subsequent maximum fully recoverable elastic strain. The effects of the initial perturbation dimensions, the steepness of the perturbation, and the mass of the perturbation on the stability of the samples, the EP transition thresholds, and the maximum fully recoverable elastic strains are analyzed. The samples with the largest full elastic recovery potentials and the parameters governing this phenomenon are identified, and the physics behind it is discussed. It is observed that increasing the initial perturbation wavelength decreases the required phase transition acceleration while increasing the maximum fully recoverable elastic strain. Finally, nondimensional parameters that involve the perturbation dimensions, as well as the mechanical properties of the material, are introduced to provide a generalized approach to the problem.

Vibration behavior prediction of submerged nanobeams with axially traveling supports: numerical, analytical, and machine learning approaches

This work surveyed the vibration behavior and stability analysis of an underwater moving flexible nanosize beam, implementing numerical and analytical methods as well as tree-based machine learning (ML) algorithms. Dynamic modeling is performed based on the nonlocal stress-strain gradient theory (NSSGT), incorporating variable environmental conditions, surface energy, and rotational inertia effects. The natural frequencies and instability threshold are computed numerically. The exact closed-form mathematical expression for the critical towing velocity of the nanosize beam is determined analytically. Also, decision tree regression and least-squares boosting tree (LSBT) regression algorithms are exploited to predict stability boundaries and the fundamental vibration frequency, and their efficiency is surveyed accordingly. Comparative studies and parametric investigations are conducted. The impressions of geometry, added mass coefficient, scale ratio parameter, surface layer characteristics, fluid mass ratio, humidity, temperature rise, and external magnetic field intensity on the nanosystem dynamics are examined and illuminated. It is detected that the results of the analytical method and ML-based approaches are consistent with those reported by the numerical technique and literature. The results asserted that the proposed ML algorithms have acceptable performance and excellent effectiveness in computational time and cost. It is comprehended that the dynamic features of submerged traveling nanobeams drastically depend on the rotational inertia effects and thickness-dependent scale effects. The stability of the immersed movable nanoscale beams is perceived to improve by increasing the scale ratio parameter and the added mass coefficient. From the perspective of the optimal design of engineering instrumentation tools, the outcomes of the current article can be applied as an inclusive benchmark.

Abnormal Static Sagittal Cervical Curvatures following Motor Vehicle Collisions: A Retrospective Case Series of 41 Patients before and after a Crash Exposure.

Three spine clinic records were reviewed over a 2-year period, looking for patients where both an initial lateral cervical X-ray and an examination were performed prior to the patient being exposed to a MVC; afterwards, an additional exam and radiographic analysis were obtained. A total of 41 patients met the inclusion criteria. Examination records of pain intensity on numerical pain rating scores (NPRS) and neck disability index (NDI), if available, were analyzed. The CLRs were digitized and modeled in the sagittal plane using curve fitting and the least squares error approach. Radiographic variables included total cervical curve (ARA C2-C7), Chamberlain's line to horizontal (skull flexion), horizontal translation of C2 relative to C7, segmental translations (retrolisthesis and anterolisthesis), and circular modelling radii. There were 15 males and 26 females with an age range of 8-65 years. Most participants were drivers (28) involved in rear-end impacts (30). The pre-injury NPRS was 2.7 while the post injury was 5.0; p < 0.001. The NDI was available on 24/41 (58.5%) patients and increased after the MVC from 15.7% to 32.8%, p < 0.001. An altered cervical curvature was identified following exposure to MVC, characterized by an increase in the mean radius of curvature (265.5 vs. 555.5, p < 0.001) and an approximate 8° reduction of lordosis from C2-C7; p < 0.001. The mid-cervical spine (C3-C5) showed the greatest curve reduction with an averaged localized mild kyphosis at these levels. Four participants (10%) developed segmental translations that were just below the threshold of instability, segmental translations < 3.5 mm. The post-exposure MVC cervical curvature was characterized by an increase in radius of curvature, an approximate 8° reduction in C2-C7 lordosis, a mild kyphosis of the mid-cervical spine, and a slight increase in anterior translation of C2-C7 sagittal balance. The modelling result indicates that the post-MVC cervical sagittal alignment approximates a second-order buckling alignment, indicating a significant alteration in curve geometry. Future biomechanics experiments and clinical investigations are needed to confirm these findings.

Divergent patterns of landslide activity and triggering factors at a local scale of a single mountain massif (Island Beskid Mts., Western Carpathians, Poland)

Landslide protection and mitigation are critical issues in many regions worldwide, where lives and livelihoods depend on correctly determining landslide hazards. However, local differences in the response of landslide slopes to meteorological or seismic triggering factors can decrease the performance of landslide models and forecasts. Thus, recognising and understanding spatial patterns of landslide activity at a local scale should be one of the priorities of landslide research. In this study, we analyse the activity and triggering factors of two landslides in one mountain massif, <2 km apart, in the Western Carpathians, Poland. We analysed 61-year-long (1959–2019) records of the activity of study landslides, i.e. dendrochronological reconstruction based on ring eccentricity and compression wood dated in 65 specimens of European silver fir (Abies alba). We compared the dendrochronological proxy of landslide activity at two study slopes with precipitation and earthquakes in the study area. Based on statistical correlations with 560 precipitation indicators, we found that the similarities between the two study landslides include only the direct triggers in June–July and March. The Wiśnia landslide, unlike Hajdowska, can also be triggered by precipitation in October. However, the main difference between the study landslides lies in the preparatory precipitation. Hajdowska shows significant dependence from precipitation of the previous December and current February, while at the Wiśnia study site, the preparatory precipitation is less important and covers the previous October–November and current January. Our results show that although study landslides could be reactivated at one time by similar direct triggers of spring or summer, such simultaneous reactivation would require preconditions of antecedent precipitation of the previous winter half-year (October–March) different for each landslide. Suppose, the requirements of antecedent precipitation are fulfilled only for one of the landslides during the winter half-year. In that case, the other will remain inactive despite the later occurrence of a shared direct trigger in spring or summer. The example of Hajdowska and Wiśnia shows that significant differences in landslide activity, hazard and triggering factors can exist even at the local scale. We argue that omitting even such subtle, unevident differences in the conditions of landslide activity leads to errors in landslide modelling and forecasting. For example, linking Hajdowska and Wiśnia landslides with one precipitation threshold or model of slope instability based on their adjacent location would not be effective in predicting reactivations. The precision of landslide modelling and forecasting depends on the accuracy of preceding analyses of landslide activity and triggering factors. We argue that in the case of the two adjacent landslides studied the divergent patterns of their activity and triggers would not be revealed without analysing long-term (> 60 years long) data sets.

Impact of thermal lensing on the TMI threshold powers in rod-type Yb-doped fiber amplifiers

The impact of thermal lensing (TL) on the transverse mode instability (TMI) threshold power in rod-type fiber amplifiers is investigated. Simulations are conducted with a 3D coupled mode analysis on a set of five scaled large pitch fiber (LPF) amplifiers. The LPF fibers are represented by surrogate step-index fibers (SIFs) with scaled cladding diameters, core diameters, and numerical apertures for a fixed normalized frequency V equal to 3.0 and scaled modal field overlap integrals with the core and cladding. It is found that thermal lensing decreases the TMI threshold powers due to increases in the TMI nonlinear gain. This gain increase is attributed to an increase in the nonlinear gain overlap integrals that occurs with the reduction in the fundamental mode effective area. Estimates for the TMI threshold power are in good agreement with measurements; however, the simulations overestimate the mode shrinkage factor. This discrepancy is tentatively attributed to the representation of the LPF by an effective SIF. These results may offer opportunities for fiber designs that increase the TMI threshold powers.

Experimental investigation of the oscillation threshold to limit state operation of a single branch pulsating heat pipe

The study investigates the characteristics of oscillations and associated thermo-hydrodynamic phenomena for startup, limit state, and intermediate transitional behavior of a pulsating heat pipe (PHP) with the help of its single branch. Experiments are performed on a transparent single branch PHP (SBPHP) at different orientations, evaporator and condenser section temperatures using n-pentane as the working fluid. The entire two-phase flow behavior is recorded with the help of shadowgraph based high speed imaging synchronized in real-time domain with pressure data acquisition at evaporator end. Instability threshold is determined in terms of evaporator temperature at different tube orientations and condenser temperatures. The oscillation startup mechanism along with the associated intermittency is studied in detail. The SBPHP is found to have characteristic variations in oscillation amplitude and frequency as it undergoes a gradual transition from its oscillation threshold to limit state. The mechanism by which the limit state creeps-in and intumesces further is an intrinsic function of liquid-vapor distribution in SBPHP, which in turn depends on the applied boundary conditions. The operational limit is governed by evaporator dryout exceeding permissible limits marked by the steep rise in the dry length of evaporator. As SBPHP approaches or operates at its limit state, evaporator is found to have different regimes across its length, viz., mild convective evaporation combined with subcooled nucleate boiling, saturated nucleate boiling, forced convective boiling, film breakdown and permanent dryout. The liquid film distribution, pressure fluctuations, and heat transfer components in evaporator at the limit state have also been studied.

On viscous stratified Darcy–Forchheimer flow in a horizontal porous layer with thermal anisotropy and variable permeability

This study analyzes the effect of anisotropy and the internal heat source in a Darcy–Forchheimer porous layer. It is well known that the variations in viscosity can be attributed to the temperature. Therefore, in the present problem, we consider a linear variation in viscosity with temperature for simplicity. We first derived the linear instability theory and then established global stability using the energy functional approach. In the global stability analysis, we show that working with the L2 norm fails to give a sufficient condition for global stability by exhibiting that the associated maximization problem is unbounded in the underlying stability measure space. Then, we show that a conditional stability bound can be achieved by restricting the internal heat source parameter Q with higher-order norms. The eigenvalue problems obtained in linear and nonlinear theories were integrated numerically. The linear and nonlinear instability thresholds are then compared to identify the potential regions of sub-critical instabilities. It is observed that the system is stabilized when the horizontal component of thermal diffusivity dominates and is unstable when the vertical component of thermal diffusivity dominates. We also found that increasing the variable permeability parameter λ destabilized the system. It is observed that increasing viscosity stabilizes the system, and decreasing viscosity encourages the start of convection. It is also interesting that, in the presence of an internal heat source, the region of subcritical instability increases with increasing viscosity effect but reduces with increasing vertical permeability λ.

Nonlinear stability analysis of Rayleigh-Bénard problem for a Navier-Stokes-Voigt fluid

The linear and nonlinear stability analyses of thermosolutal convection in a non-Newtonian Navier-Stokes-Voigt fluid, considering Soret and Ekman damping effects, are conducted analytically. Instability thresholds are determined for thermosolutal convection within a viscoelastic fluid of the Kelvin-Voigt type, wherein a dissolved salt field exists. Two scenarios are examined: one where the fluid layer is heated from the bottom and concurrently salted from the bottom, and the other where the fluid layer is heated from the bottom and concurrently salted from the top. The governing partial differential equations system includes conservation laws of mass, momentum, energy, and salt concentration. Using the energy method, the disturbances to the fluid system are shown to decay exponentially. Analytical expressions are developed for the eigenvalue as a function of Soret, Lewis, Prandtl, Kelvin-Voigt, and Rayleigh friction numbers. The study illustrates the shift from a stationary mode of convection to an oscillatory mode and provides thresholds that indicate these transitions. It is found that the viscoelastic property of the fluid acts as a stabilizing agent for oscillatory mode convection. Rayleigh friction substantially controls the convection threshold. Upon comparing threshold values between linear and nonlinear theories, a subcritical instability region is observed in the heating bottom-salting bottom case (case-1), whereas such a region is absent in the heating bottom-salting top case (case-2).

The First Photometric Analysis of Two Low-mass-ratio Contact Binary Systems in TESS Survey

Low-mass-ratio (q) contact binary systems are progenitors of stellar mergers such as blue stragglers or fast-rotating FK Com stars. In this study, we present the first light curve analysis of two newly identified low mass-ratio contact binary systems, TIC 55007847 and TIC 63597006, that are identified from TESS. Both stars are classified as A-subtype contact binaries. We obtained the precise orbit periods for the two objects by using the O − C method, i.e., P = 0.6117108 day for TIC 55007847 and P = 0.7008995 day for TIC 63597006, and found an obvious periodic signal in the O − C curve of TIC 63597006. We suggest that the periodic signal comes from a third body. We further use the Markov chain Monte Carlo method with PHOEBE to derive the photometric solutions for the two binaries. The photometric solution for this object shows that the contribution of the third body is about 6%. Our analysis revealed that TIC 55007847 has an extremely low mass ratio of q = 0.08. By calculating the ratio of spin angular momentum to the orbital angular momentum J s/J o, we found that TIC 55007847 is very close to the instability threshold with J s/J o = 0.31, indicating that it may merge into a single, fast-rotating star in the future. For TIC 63597006, q = 0.14 and J s/J o = 0.15. This object is in a relatively stable evolutionary status at present.

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

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

Terahertz scale microbunching instability driven by high resistivity nonevaporable getter coating resistive-wall impedance

Nonevaporable getter (NEG) coating is widely required in the new generation of light sources and circular e+e− colliders for small vacuum pipes to improve the vacuum level, which, however, also enhances the high-frequency resistive-wall impedance and often generates a resonator-like peak in the terahertz frequency region. In this paper, we will use the parameters of the planned Hefei Advanced Light Facility storage ring to study the impact of NEG-coating resistive-wall impedance on the longitudinal microwave instability via particle tracking simulation. Using different NEG-coating parameters (resistivity and thickness) as examples, we find that the impedance with a narrow and strong peak in the terahertz frequency region can cause terahertz scale microbunching instability, which has a low instability threshold current and contributes to a large energy spread widening above the threshold. In order to obtain a convergent simulation of the beam dynamics, one must properly resolve such a peak. The coating with a lower resistivity has a less sharp peak in its impedance spectrum, and there is a regime that it is helpful to suppress the terahertz scale microbunching instability and in return contributes to a higher instability threshold current. Published by the American Physical Society 2024

Stability and instability of thermosolutal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with couple stress effect

In this article, the phenomenon of thermosolutal convection within a fluid characterized by the Brinkman–Darcy–Kelvin–Voigt (BDKV) model is delved into, while the impact of couple stresses on this process is considered. Both linear instability and nonlinear stability analyses are encompassed in our investigation. Several noteworthy observations have been made. When the fluid layer is heated from below and salt is introduced from above, it is found that the points at which stability and instability thresholds are reached coincide. This alignment is supported by the validity of the linear theory in predicting the initiation of convection under these conditions. However, the scenario changes when the layer is salted from the bottom while being heated. In this case, the stability thresholds remain constant, regardless of variations in the salt Rayleigh number. This discrepancy between the thresholds of linear instability and nonlinear stability is deemed significant. To gain a deeper understanding, numerical computations were conducted to identify and thoroughly discuss the thresholds of linear instability. These findings offer valuable insights into the behavior of the system under study. It is indicated by our results that parameters such as Brinkman, couple stresses, and Kelvin–Voigt contribute to stabilizing the system. Additionally, it was noted that the salt Rayleigh number has a stabilizing effect when the layer is salted from below, whereas it has a destabilizing effect when salt is introduced from above.

Linear Theory Analysis and One‐Dimensional Hybrid Simulations of High‐Frequency EMIC Waves in a Dipole Magnetic Field

AbstractNarrowband (Δf ≲ 0.1fcp), high‐frequency (0.9fcp ≲ f &lt; fcp) electromagnetic ion cyclotron (EMIC) waves, or HFEMIC waves for short, are a relatively new type of EMIC waves, where fcp is the proton cyclotron frequency. Here, we investigate the instability threshold conditions and the nonlinear evolution of HFEMIC waves at parallel propagation. First, linear theory analysis is extended to a regime relevant to HFEMIC waves (parallel proton beta β‖p &lt; 0.01). The instability threshold follows a similar anisotropy‐β‖p relation and requires a large value of anisotropy (T⊥p/T‖p ≳ 10) for wave growth. As a result of decreasing group velocity, the convective growth rate at a fixed threshold exhibits a similar inverse relation with β‖p. Heavy ions affect the instability only weakly, primarily through the introduction of stop bands. Second, we carry out one‐dimensional hybrid simulations in a parabolic background magnetic field, with initial parameters constrained by observation. Despite the narrow source region (within about ±3° latitude), HFEMIC waves can grow well above the thermal noise level due in large part to a small group velocity of HFEMIC waves. The saturation level is well within the range of observational amplitudes, and the quasilinear process primarily determines the wave evolution. Finally, we demonstrate that the present results compare favorably to the recent statistical results, thereby supporting anisotropic low‐energy protons as free energy source for HFEMIC waves.

Effect of depth ratio on Faraday instability in a binary liquid system

The response of two incompressible and immiscible liquids of comparable densities at different depth ratios in a rectangular container subject to parametric sinusoidal forcing, similar to Faraday waves, has been considered in the present study. The effect of various depth ratios on the instability threshold and the flow field are investigated for (0, 2) and (0, 4) modes. Numerical simulation has been performed using OpenFOAM to solve Navier-Stokes equations. A source term is added in the interFoam module of OpenFOAM to take the effect of the oscillating container without using any dynamic mesh function. The threshold amplitude and wavenumbers are validated following the linear Floquet analysis of Kumar and Tuckerman (1994 J. Fluid Mech. 279 49–68). The Floquet analysis showed a substantial shift in natural frequency (reduction) and an increase in threshold amplitude when the interface is in close proximity to the wall. The response amplitude follows a square law with the forcing amplitude for all the depth ratios considered in the present study. The wave amplitude response above the threshold curve is found to be an exponential function of liquid depths and forcing parameters.