Instability Model Research Articles

Millihertz oscillations near the innermost orbit of a supermassive black hole.

Recent discoveries from time-domain surveys are defying our expectations for how matter accretes onto supermassive black holes (SMBHs). The increased rate of short-timescale, repetitive events around SMBHs, including the recently discovered quasi-periodic eruptions1-5, are garnering further interest in stellar-mass companions around SMBHs and the progenitors to millihertz-frequency gravitational-wave events. Here we report the discovery of a highly significant millihertz quasi-periodic oscillation (QPO) in an actively accreting SMBH, 1ES 1927+654, which underwent a major optical, ultraviolet and X-ray outburst beginning in 20186,7. The QPO was detected in 2022 with a roughly 18-minute period, corresponding to coherent motion on a scale of less than 10 gravitational radii, much closer to the SMBH than typical quasi-periodic eruptions. The period decreased to 7.1 minutes over 2 years with a decelerating period evolution ( greater than zero). To our knowledge, this evolution has never been seen in SMBH QPOs or high-frequency QPOs in stellar-mass black holes. Models invoking orbital decay of a stellar-mass companion struggle to explain the period evolution without stable mass transfer to offset angular-momentum losses, and the lack of a direct analogue to stellar-mass black-hole QPOs means that many instability models cannot explain all of the observed properties of the QPO in 1ES 1927+654. Future X-ray monitoring will test these models, and if it is a stellar-mass orbiter, the Laser Interferometer Space Antenna (LISA) should detect its low-frequency gravitational-wave emission.

Time-resolved Hubble Space Telescope UV Observations of an X-Ray Quasiperiodic Eruption Source

Abstract X-ray quasiperiodic eruptions (QPEs) are a novel mode of variability in nearby galactic nuclei whose origin remains unknown. Their multiwavelength properties are poorly constrained, as studies have focused almost entirely on the X-ray band. Here, we report on time-resolved, coordinated Hubble Space Telescope far-ultraviolet (FUV) and XMM-Newton X-ray observations of the shortest period X-ray QPE source currently known, eRO-QPE2. We detect a bright UV point source (L FUV ≈ few × 1041 erg s−1) that does not show statistically significant variability between the X-ray eruption and quiescent phases. This emission is unlikely to be powered by a young stellar population in a nuclear stellar cluster. The X-ray-to-UV spectral energy distribution can be described by a compact accretion disk ( R out = 34 3 − 138 + 202 R g ). Such compact disks are incompatible with typical disks in active galactic nuclei, but form naturally following the tidal disruption of a star. Our results rule out models (for eRO-QPE2) invoking (i) a classic active galactic nucleus accretion disk and (ii) no accretion disk at all. For orbiter models, the expected radius derived from the timing properties would naturally lead to disk-orbiter interactions for both quasi-spherical and eccentric trajectories. We infer a black hole mass of log10(M BH) = 5.9 ± 0.3 M ⊙ and an Eddington ratio of 0.13 − 0.07 + 0.18 ; in combination with the compact outer radius, this is inconsistent with existing disk instability models. After accounting for the quiescent disk emission, we constrain the ratio of X-ray to FUV luminosity of the eruption component to be L X/L FUV > 16−85 (depending on the intrinsic extinction).

Instability model of water–steam–liquid metal three-phase jet flow during steam generator tube rupture accident in a fast reactor

The steam generator tube rupture (SGTR) accident in a lead-cooled fast reactor (LFR) results in an injection of high-pressure subcooled water from the secondary circuit into the high-temperature liquid lead-bismuth eutectic (LBE) pool in the primary loop. Rapid depressurization and phase-change heat transfer generate the steam between the water jet and liquid LBE. Based on jet instability theory, this study develops a temporal instability model focusing on the water–steam–liquid LBE three-phase flow in a cylindrical coordinate to investigate the breakup characteristics of water jet. By introducing velocity and pressure disturbances and adopting a linear assumption to the hydrodynamic governing equations, a dispersion equation is developed, and jet characteristic parameters are then defined. The effects of various operating parameters and key dimensionless numbers are further studied. By solving the dispersion equation, it is found that smaller steam film thickness and higher steam velocity enhance jet instability. Increasing jet velocity and reducing jet radius accelerate jet breakup and promote droplet refinement, while at higher jet velocities, the influence of jet radius diminishes. Additionally, the co-flow of LBE with the jet and the viscosity effect of LBE both stabilize the water jet. This model enables quantitative prediction of the breakup behavior of water jets in liquid LBE during the initial stage of SGTR accident, aiming to reveal the fundamental mechanisms of the physical process and provide theoretical guidance for safety analysis of LFR.

The morphologies of outburst light curves of black hole X-ray transients as telltale signs of disc instability evolution

Abstract We present a comprehensive spectral and timing analysis of 15 outbursts and 18 mini-outbursts from nine dynamically confirmed black hole X-ray transients with light curve and spectral data from RXTE, MAXI, and NuSTAR obtained from 1996 to 2024. Departed from the canonical fast-rise exponential decay (FRED) morphology, the most common morphology within our sample is triangular with similar rise and decay timescale. In most outbursts, the spectral evolutions indicate the presence of limit-cycle instability, as predicted by the disc instability model (DIM). Even though almost all of the outbursts showed a similar canonical pattern, unique transition patterns are found in FRED outbursts. On the other hand, no spectral transition is found in any mini-outburst, which was observed in either hard or thermal-dominant (TD) state only. The Fe K-α emission line is the most prominent feature in the hard state of the rising phase but none is found in the decay phase. Triangular outbursts are always in transition to the TD state, following a standard accretion disc, before the peak proceeds to match DIM prediction. This is unlike the FRED outburst which directly transitioned to the steep power-law (SPL) state or high Eddington ratio TD state, resembling a slim accretion disc. Non-canonical spectral evolution as well as the rarity of FRED outburst in our sample, seem to add more challenges for DIM. Studying the morphology of outburst light curve may reveal more clues on the evolution of the disc instability at least during the time relevant to the burst.

Influencing Factors of Shear Instability Characteristics of Rock Joints: Experimental and Theoretical Study

To investigate the influencing factors of the shear failure behavior of rock joints, especially the shear instability characteristics, direct shear tests were performed on marble joints with various grain sizes under different constant normal loads (CNLs). The experimental results show that the grain size and CNL have significant effects on the shear mechanical properties of rock joints. The peak shear strength (τp), peak shear displacement (up), post-peak modulus (S), and stress drop (Δτ) of rock joints all increase first and then decrease with the increase in grain size, but they increase with the increase in CNL. The mineral composition and microstructure also have a certain influence on the shear mechanical properties of rock joints. In addition, the post-peak soften modulus (Sp) was proposed to describe the shear instability characteristics of rock joints, and its relationship with grain size and CNL was established. The mechanical model of the shear instability of rock joints was established, and the shear instability criterion of rock joints was proposed based on the stiffness criterion and the proposed post-peak soften modulus (Sp). This paper further reveals the shear instability mechanism of rock joints, which can provide a reference for the stability analysis of jointed rockmass.

Incidence of cardiac arrest following implementation of a predictive analytics display in a pediatric intensive care unit.

More than 90% of in-hospital cardiac arrests involving children occur in an intensive care unit (ICU) with less than half surviving to discharge. We sought to assess the association of the display of risk scores of cardiovascular and respiratory instability with the incidence of cardiac arrest in a pediatric ICU. Employing supervised machine learning, we previously developed predictive models of cardiovascular and respiratory instability, incorporating real-time physiologic and laboratory data, to display risk scores for potentially catastrophic clinical events in the subsequent 12h. Clinical implementation with risk scores displayed on large screen monitors in multiple areas throughout the ICU was finalized in July 2022. We compared the incidence of cardiac arrest events in the 18-months pre- and post-implementation. The cardiac arrest incidence rate dropped from 3.0 events (95% CI 2.0-4.4) to 2.4 events (95% CI 1.6-3.5) per 1000 patient days following implementation. We observed a 50% increase in the rate of cardiac arrest events where return of spontaneous circulation (ROSC) was achieved (p=0.025). The incidence rate of cardiac arrest without ROSC dropped from 1.4 events (95% CI 0.7-2.4) to 0.4 events (95% CI 0.1-0.9) per 1000 patient days (incidence rate difference=1.0 (95% CI 0.13-1.87), p=0.01). We observed a non-significant decrease in the rates of cardiac arrest events and an increase in the rate of cardiac arrests events where ROSC was achieved following the implementation of a predictive analytics display of risk scores.

Dorsoradial ligament reconstruction versus imbrication for restoring trapeziometacarpal joint stability: a comparative biomechanical study

The unique saddle articulation of the trapeziometacarpal joint allows for a wide range of motion necessary for routine function of the thumb. Inherently unstable characteristics of the joint can lead painful instability. In this study, we modified a surgical dorsal ligament reconstruction technique for restoring trapeziometacarpal joint stability. We evaluated and compared the biomechanical efficacy of our reconstruction technique with that of dorsoradial capsulodesis by creating a cadaveric model of rotational instability. Twenty-four specimens were subjected to dorsoradial capsulodesis (n = 12) or dorsoradial ligament reconstruction using the abductor pollicis longus (APL) (n = 12). The modified dorsoradial ligament reconstruction entailed detaching one distally based slip of the APL. The harvested tendon’s proximal end was passed through a bone tunnel created at the dorsoradial ridge of the trapezium. A suture anchor was inserted at the dorsal base of the metacarpal bone. The tendon stump was sutured to the metacarpal bone using fiber wire in figure-of-eight configuration. The load to failure of the trapeziometacarpal joint under compression was higher in the reconstruction group (p = 0.003). The improvement in the rotational arc (observed in all specimens) was significantly greater in the reconstruction group than the capsulodesis group (p = 0.003). Our technique reconstructs only the necessary ligament, requires a smaller incision and relatively simpler surgical procedure, and enables precise determination of the insertion and exit sites of the tendon, making it a promising treatment for trapeziometacarpal joint instability.

On aerobreakup in the stagnation region of high-Mach-number flow over a bluff body

In this paper, aerobreakup in the stagnation region of high-Mach-number flow over a bluff body is studied with experiments and computations. Water drops of diameter 0.51–2.30 mm were acoustically levitated at sea level along the flight path of a rectangular $100\ {\rm mm} \times 150\ {\rm mm}$ rail-gun launched projectile. This enabled the study of aerobreakup at high Mach (3.03–5.12), post-shock Mach (1.5–1.9), Weber $(5 \times 10^4\unicode{x2013}4 \times 10^5)$ and Reynolds $(6 \times 10^4\unicode{x2013}3 \times 10^5)$ numbers. High-speed backlit shadowgraphy is used to record the flow structure. Computations are made for two cases, and it was found that the drop behaviour is not dominated by viscous or surface-tension effects and can be adequately captured by treating the gas as calorically perfect with the ratio of specific heats set to 1.3 to account for thermochemical effects. To assess drop surface stability at early breakup times, results from Newton's inclination method are used to determine the flow along the drop surface and input to a linear-stability analysis; from this, it was found that viscosity and surface tension can be neglected. Moreover, the acceleration term dominates the shear term at the stagnation point, a point accentuated as a drop flattens; this relation inverts closer to the drop equator. Linear-stability analysis was insufficient for modelling late-stage aerobreakup because the predicted wavelengths were too small and the expected aerobreakup times were non-physically short. To address this discrepancy, a nonlinear instability model with constant-rate growth is used that treats the accelerated drop surface as analogous to bubbles rising through a liquid; agreement with computations is good.

Double “acct”: A Distinct Double-peaked Supernova Matching Pulsational Pair Instability Models

Abstract We present multiwavelength data of SN 2020acct, a double-peaked stripped-envelope supernova (SN) in NGC 2981 at ∼150 Mpc. The two peaks are temporally distinct, with maxima separated by 58 rest-frame days and a factor of 20 reduction in flux between. The first is luminous (M r = −18.00 ± 0.02 mag) and blue (g − r = 0.27 ± 0.03 mag) and displays spectroscopic signatures of interaction with hydrogen-free circumstellar material. The second peak is fainter (M r = −17.29 ± 0.03 mag) and has some spectroscopic similarities to an evolved stripped-envelope SN, with strong forbidden [Ca ii] and [O ii] features. No other known double-peaked SN exhibits a light curve similar to that of SN 2020acct. We find the likelihood of two individual SNe occurring in the same star-forming region within that time to be highly improbable, while an implausibly fine-tuned configuration would be required to produce two SNe from a single binary system. We find that the peculiar properties of SN 2020acct match models of pulsational pair instability (PPI), in which the initial peak is produced by collisions of shells of ejected material, shortly followed by core collapse. Pulsations from a star with a 72 M ⊙ helium core provide an excellent match to the double-peaked light curve. The local galactic environment has a metallicity of 0.4 Z ⊙, a level where massive single stars are not expected to retain enough mass to encounter the PPI. However, late binary mergers or a low-metallicity pocket may allow the required core mass. We measure the rate of SN 2020acct–like events to be <3.3 × 10−8 Mpc−3 yr−1 at z = 0.07, or <0.1% of the total core-collapse SN rate.

Characterizing the negative triangularity reactor core operating space with integrated modeling

Abstract Negative triangularity (NT) has received renewed interest as a fusion reactor regime due to its beneficial power-handling properties, including low scrape-off layer power and a larger divertor wetted area that facilitates simple divertor integration. NT experiments have also demonstrated core performance on par with positive triangularity (PT) H-mode without edge-localized modes (ELMs), encouraging further study of an NT reactor core. In this work, we use integrated modeling to scope the operating space around two NT reactor strategies. The first is the high-field, compact fusion pilot plant concept MANTA (The MANTA Collaboration et al 2024 Plasma Phys. Control. Fusion 66 105006) and the second is a low field, high aspect ratio concept based on work by Medvedev et al (Medvedev et al 2015 Nucl. Fusion 55 063013). By integrating equilibrium, core transport, and edge ballooning instability models, we establish a range of operating points with less than 50 MW scrape-off layer power and fusion power comparable to positive triangularity (PT) H-mode reactor concepts. Heating and seeded impurities are leveraged to accomplish the same fusion performance and scrape-off layer exhaust power for various pressure edge boundary conditions. Scans over these pressure edge conditions accommodate any current uncertainty of the properties of the NT edge and show that the performance of an NT reactor will be extremely dependent on the edge pressure. The high-field case is found to enable lower scrape-off layer power because it is capable of reaching high fusion powers at a relatively compact size, which allows increased separatrix density without exceeding the Greenwald density limit. Adjustments in NT shaping exhibit small changes in fusion power, with an increase in fusion power density seen at weaker NT. Infinite-n ballooning instability models indicate that an NT reactor core can reach fusion powers comparable to leading PT H-mode reactor concepts while remaining ballooning-stable. Seeded krypton is leveraged to further lower scrape-off layer power since NT does not have a requirement to remain in H-mode while still maintaining high confinement. We contextualize the NT reactor operating space by comparing to popular PT H-mode reactor concepts, and find that NT exhibits competitive ELM-free performance with these concepts for a variety of edge conditions while maintaining relatively low scrape-off layer power.

Physics-Assisted Machine Learning Models for Predicting Pool Boiling Critical Heat Flux for Cryogenic Fluids

Abstract Cryogenic fluid management is highly crucial for NASA?s space missions and one challenge identified by NASA is the tank fill process for pure cryogenic fluids. To date, no predictive tool can accurately estimate the pool boiling curve during this process. We aim to address this gap by first accurately predicting critical heat flux. We use both traditional machine learning and physics-assisted machine learning methods to predict critical heat flux on a large dataset of 1322 datapoints from 53 published studies with a wide range of operational conditions and surface properties. While the traditional machine learning approach used no prior knowledge in modeling, the physics-assisted machine learning approach assumes the correlation form of the Zuber instability model [1,2] and predicts the multiplier for the hydrodynamic instability term to estimate the critical heat flux. Two groups of input features are compared including one with fluid-only properties and another with both fluid and solid surface properties. Various feature selection methods are employed to reduce the redundant features, and multiple machine learning models are used for modeling the dataset. Physics-assisted machine learning methods predict much better than traditional machine learning methods. The inclusion of solid properties further improves the predictions of critical heat flux. The best predictions are obtained using the extreme gradient boosting model based on the physics-assisted machine learning framework resulting in a mean absolute percentage error of 8.88% which is far better than the semi-empirical correlations.

The markers and risk stratification model of intracranial aneurysm instability based on large Chinese cohort

The markers and risk stratification model of intracranial aneurysm instability based on large Chinese cohort

Instability of bubbly jets subjected to unrelaxed axial elastic tension

Injection of bubbly jets is a critical process in various fields, such as fuel atomization and petrochemicals. However, existing instability models for bubbly jets have predominantly focused on density variations due to bubble compressibility, largely neglecting the impact of bubbles on the macroscopic rheological properties of the mixture. In this study, we have integrated compressibility with non-Newtonian properties induced by bubbles to explore the evaluation of jet perturbations. Additionally, considering bubble pre-deformation before injection, we particularly examine the role of unrelaxed axial elastic tension in the bubbly jets. Both linear stability analysis and energy budget methods are used to illustrate the contributions of viscosity, elasticity, and compressibility. The results indicate that the viscoelastic effects induced by bubbles can significantly outweigh the effects of compressibility during the jet destabilization process. Notably, a slight unrelaxed tension can markedly increase both the perturbation growth rate and the cutoff wavenumber, potentially making it a more dominant driver of jet instability than the classical surface tension.

Unveiling the rebrightening mechanism of GRS 1915+105: Insights from a change in the quasi-periodic oscillations and from a wind analysis

We report a significant rebrightening event in the microquasar GRS 1915+105 that was observed in July 2021 with NICER and NuSTAR. This event was characterized by quasi-periodic oscillations (QPOs) in the soft state, but is typically free of these oscillations. It was also marked by an increase in the disk wind ionization degree. By employing the Hilbert-Huang transform (HHT), we decomposed the stable low-frequency QPO from the light curves using data from NICER and NuSTAR. Our spectral analysis shows a weak change in the Fe XXV absorption lines and a strong change in the Fe XXV absorption edge with QPO phase. Other spectral parameters, including the photon index and the seed photon temperature, correlate positively with the QPO phase, but the electron temperature is inversely correlated. Based on our findings we propose that the observed QPOs were caused by magnetic activity and not by precession. The magnetic field drove a failed disk wind of high-ionization low-velocity material. These results support the accretion ejection instability model and provide deeper insights into the dynamics of accretion-ejection processes that are magnetized by a black hole.

Study on dynamic response distribution of excavated highway slope under dynamic action

In order to study the dynamic response distribution law of highway foundation pit slope under seismic dynamics, the dynamic response distribution law of cutting slope at different grading heights was compared and studied, and the dynamic instability model under gravity instability and seismic disturbance was established by using UDEC700 software, and the simulation calculation was carried out. The difference between static instability and dynamic instability of fractured rock slope is compared and analyzed, and the post-earthquake stress is greater than that before the earthquake. Under the action of power, the velocity at the top of the slope is greater than the velocity at the bottom of the slope, the velocity outside the upper platform is greater than the velocity inside, and the velocity inside the lower platform is greater than the velocity outside. This provides a new perspective for understanding the dynamic response of highway foundation pit slope under seismic dynamics.

Axis screw parallel to the sagittal plane versus traditional pedicle screw in the treatment of atlantoaxial fixation: a finite element study.

This study aims to conduct a finite element analysis (FEA) to assess the bio-mechanical properties of C2 sagittal-parallel pedicle screw (PPS) in fixation for atlantoaxial instability, thereby providing a theoretical foundation for its clinical application. A total of 5 intact C1-2 finite element models were established. Based on this, instability models were developed and two different fixation methods were applied for each model: C1 lateral mass screw (LMS) combined with C2 sagittal-parallel pedicle screw (C1LMS + C2PPS), and C1 lateral mass screw combined with C2 traditional pedicle screw (C1LMS + C2PS). Under a physiological load of 40N, a pure moment of 1.5 Nm was used to simulate movements of the cervical spine in flexion, extension, lateral bending, and axial rotation. The von Mises stress of implants and the segment range of motion (ROM) were analyzed and compared statistically. The intact model was validated and showed good consistency with other studies in terms of range of motion (ROM). In flexion and extension, the C1LMS + C2PPS resulted in lower segment ROM (12.4% and 6.3% decrease) and stress concentration (15.9% decrease in flexion) compared to C1LMS + C2PS. However, in lateral bending and axial rotation, the C1LMS + C2PPS exhibited higher segment ROM (42.9% and 5.9% increase) and stress concentration (8.7% and 21.4% increase) compared to C1LMS + C2PS. Both methods were safe and stable for the fixation of atlantoaxial instability. Compared to C1LMS + C2PS, the use of C1LMS + C2PPS may provide better stability and a lower risk of implant failure in flexion and extension. Clinically, it is feasible to utilize the C2 sagittal-parallel pedicle screw in fixing atlantoaxial instability.

Weakly nonlinear analysis of minimal models for Turing patterns

The simplest particle-based mass-action models for Turing instability – i.e. those with only two component species undergoing instantaneous interactions of at most two particles, with the smallest number of distinct interactions – fall into a surprisingly small number of classes of reaction schemes. In previous work we have computed this classification, with different schemes distinguished by the structure of the interactions. Within a given class the reaction stoichiometry and rates remain as parameters that determine the linear and nonlinear evolution of the system.Adopting the usual weakly nonlinear scalings and analysis reveals that, under suitable choices of reaction stoichiometry, and in nine of the 11 classes of minimal scheme exhibiting a spatially in-phase (“true activator-inhibitor”) Turing instability, stable patterns are indeed generated in open regions of parameter space via a generically supercritical bifurcation from the spatially uniform state. In three of these classes the instability is always supercritical while in six there is an open region in which it is subcritical. Intriguingly, however, in the remaining two classes of minimal scheme we require different weakly nonlinear scalings, since the coefficient in the usual cubic normal form unexpectedly vanishes identically. In these cases, a different set of asymptotic scalings is required.We present a complete analysis through deriving the normal form for these two cases also, which involves quintic terms. This fifth-order normal form also captures the behaviour along the boundaries between the supercritical and subcritical cases of the cubic normal form. The details of these calculations reveal the distinct roles played by reaction rate parameters as compared to stoichiometric parameters.We quantitatively validate our analysis via numerical simulations and confirm the two different scalings for the amplitude of predicted stable patterned states.

A probabilistic coral rubble mechanical instability model applied with field observations from the Great Barrier reef

Unstable coral rubble hinders coral recruitment and recovery of coral reefs after damage from cyclones and bleaching events. If coral rubble remains unstable under typical everyday environmental conditions, areas of coral rubble will not be able to recover. Evaluating the probability of rubble instability over regional scale reef systems can assist the optimization of coral reef restoration efforts. Currently, robust and verified models for such applications do not exist. This paper presents a comprehensive assessment method to predict the probability of coral rubble instability, which combines a fluid-structural interaction approach with a statistical regional wave climate model. The hydrodynamic model employs non-linear wave theory to determine near-bed velocity, pressure gradients, and the corresponding drag and inertia forces acting on the coral rubble. The instability model assesses when overturning or sliding forces exceed resisting forces, considering thousands of combinations of different coral sizes and densities to calculate the proportion of instability under a given wave forcing. The model was calibrated and validated using prior laboratory experiments as reported by Kenyon et al. (2023b). The hydrodynamic and instability models use an extensive dataset of non-cyclonic wave climates (hindcast from over 30 years of wind measurements) specific to the region around Heron Reef, Great Barrier Reef, Australia, enabling a comprehensive evaluation of the probability of rubble instability in this area. Results indicate that the overall probability of rubble instability (Pr3) reaches 0.74 in water depths less than 2 m (typical of reef crests or reef flats), while it declines to below 0.21 at a depth of 12 m (typical deeper parts of the fore reef). Coral rubble on reef crests near Heron Reef, which are sheltered by surrounding formations, demonstrates low probability of instability. Thus, coral rubble instability is influenced by both its specific location within the reef and the position of the reef relative to other nearby reefs. By integrating the rubble instability model with non-cyclonic wave climate data, a map of the probability of rubble instability was generated for eight reefs in the Capricorn and Bunker Group (CBG). This map provides valuable guidance for coral reef restoration efforts, significantly reducing the need for extensive field-based data.

Probing trade-off between critical size and velocity in cold-pray: An atomistic simulation

The detailed mechanism of bonding in the cold spray process has remained elusive for both experimental and theoretical parties. Adiabatic shear instability and hydrodynamic plasticity models have been so far the most popular explanations. Here, using molecular dynamics simulation, we investigate their validity at the nanoscale. The present study has potential applications in the fabrication of ultrathin layers in the electronics industry. For this aim, we considered Ti nanoparticles of different diameters and Si substrates of different orientations. It is shown that very high spray velocities are required for a jet to be observed at the nanoscale. We propose a method for thermostating the substrate that enables utilizing high spray velocities. For the first time, we demonstrate an oscillatory behavior in both the normal and radial stress components within the substrate that can propagate into the particle. We have shown that neither the adiabatic shear instability model nor the hydrodynamic plasticity model can be ignored at the nanoscale. In addition, the formation of a low-resistance titanium silicide proper for electronic application is illustrated.

Current-vortex-sheet model of the magnetic Rayleigh-Taylor instability.

This study investigates the Rayleigh-Taylor instability in the magnetic field applied parallel to the interface. The motion of the interface is described using a current-vortex-sheet model. The growth rate of the interface is obtained from a linear stability analysis of the model. The interface of a single mode k=1 is linearly stable for R_{A}≤1, where R_{A} denotes the Alfvén number. Further, we conduct numerical computations for the evolution of the interface from the model for both regimes of R_{A}≤1 and R_{A}>1. For R_{A}≤1, the interface oscillates vertically but does not intrude into the opposite phase. The amplitude of the interface and the oscillation period decrease with decrease in R_{A}. For 1<R_{A}≲1.5, the interface undergoes some growth at early times and then decreases. This oscillation is repeated, and no roll-ups are observed at the interface. Therefore, the nonlinear growth of the Rayleigh-Taylor instability is stabilized by a sufficiently strong magnetic field. For R_{A}≳3 the interface is unstable and the pattern of the interface evolution differs from the density ratio. In addition, the magnetic field is greatly amplified as R_{A} increases.