Transition Layer Model Research Articles

Assessment on earthquake-induced liquefaction around a hybrid monopile foundation for offshore wind turbines with a transition layer model

Offshore wind turbines are currently being developed to have a large size. A hybrid monopile foundation, which is composed of a single pile and a wheel, is advantageous in terms of bearing capacity and liquefaction resistance in liquefiable soil. In this study, the seismic response of a hybrid monopile foundation was investigated using a verified numerical model. Earthquake-induced liquefaction around the foundation was assessed by considering the influence of the foundation dimensions. In the numerical model, a pile-soil contact element was proposed using a transition layer model that effectively buffered the pile-soil interactions. The soil characteristics were evaluated based on the distribution of excess pore water pressure. The liquefaction resistance of the shallow layer was improved by the wheel, and the pile length had a negligible influence on the seismic response. Larger wheel diameter and thickness demonstrated a more pronounced improvement in the anti-liquefaction ability. The influencing zone was determined based on the liquefiable area and had a conical shape under the wheel. This study quantitatively investigated the liquefaction characteristics of a hybrid monopile foundation and provided insights into the numerical calculation of dynamic pile-soil interactions.

Evolution mechanisms of microstructure and mechanical properties in a friction stir welded ultrahigh-strength quenching and partitioning steel

Ultrahigh-strength quenching and partitioning (Q&P) steels have attracted strong interests in the auto manufactory, while the comprehensive understanding in the microstructure and mechanical behavior of their welded joints is highly needed to enrich their applications. In the present work, it is designed to make an insight into these imperative conundrums. Equal strength Q&P 1180 steel joints to parent metal were successfully fabricated via friction stir welding (FSW) technique under different parameters. Apparent hardening and softening were observed in stir zone (SZ) and heat-affected zone (HAZ) respectively, whose microstructures strongly depended on the peak temperature and cooling rate during welding. The formation of fresh martensite was the main mechanism for the SZ hardening, while the decomposition of metastable phases played key roles in the microhardness drop of the HAZ. A heat source zone-isothermal phase transition layer model was proposed to clarify the impregnability of the joint strength under parameter variation. The dual-phase structure, nano-carbide particles, tempered initial martensite, and ultrafine-grained ferrite synergistically improved the strain hardening ability of the HAZ, which eventually resulted in the equal strength FSW joints.

A Surface Transition Layer Model for Size Effect in T2 Copper Micro-Compression

The effects of sample size and grain size on the surface morphology and flow stress of deformed samples were investigated by means of copper micro-cylinder compression experiments at room temperature. The results of SEM showed that when the grain size increased or the sample size decreased, the deformation non-uniformity of samples’ free surfaces increased. Meanwhile, the stress–strain curves showed that during the compression process, the flow stress of the sample also tended to decrease as the grain size increased or the sample size decreased. According to the experimental results of nanoindentation, a surface transition layer model was established on the basis of the surface layer model by considering the mutual constraint of grains and the existence of transition layer grains. The experimental results indicated that the stress–strain curve calculated by the surface transition layer model can more accurately reflect the actual deformation situation of the material compared to the surface layer model.

Large-scale altitude distribution profile of auroral parallel electric potentials: A statistical analysis of Cluster data

It is generally believed that the heart of the Auroral Acceleration Region (AAR) is located between 5000 and 8000 km altitude above the auroral oval. Various altitude distribution profiles are suggested by different theories, including the transition layer model, which predicts that the strongest electric fields can be found at about 1 RE, and can vary depending on the plasma and geomagnetic conditions. However, there have been no specific experimental results that cover regions both below and well above such altitude. This paper presents a method for obtaining such a profile from AAR satellite crossings, applies it to a data set gathered from 116 Cluster spacecraft encounters with acceleration potential structures, and discusses the results. The crossings cover an altitude range between 0.63 RE and 2.9 RE. The outcome is the first empirical altitude distribution profile of the auroral acceleration potentials. The results suggest that the region within the altitude range of 0.9245 RE and 1.158 RE statistically contains 30% of the total potential, which is the largest fraction of the parallel potentials among all altitude segments of the same size. The altitude which equally divides the distribution of acceleration potentials was found at 1.076 RE (6863 km). The obtained parallel potential distribution is in agreement with both the magnetic mirror force theory and the transition layer model, and can hence provide a proper baseline for future missions to the AAR.

Synthesis of BaSO4 nanoparticles in a water-tetrahydrofuran system

A highly nonequilibrium system of two miscible liquids is proposed as a generator of barium sulfate nanoparticles. A dynamic transition layer model developed in this work is used to explain the obtained results; according to this model, the smallest diameter of the resulting particles is determined by the size of the prephase associates formed in rotating Benard cells. It is hypothesized that the Benard cell-ambient solution interface has certain barrier properties, at least with respect to the new phase precursor’s particles penetrating from outside. The effect of the H2O/tetrahydrofuran ratio on the size of particles and the shape of associates and nanocrystallites is studied. The dependence of the size of nanocrystalline particles on the above ratio is derived. A possible explanation is proposed for the dependence of the size of nanoparticles on the viscosity of a solvent.

On Experience in using the remote acoustic method of partial reflections in studies of the lower troposphere

Using the phenomenon of the partial reflection of acoustic waves from anisotropic wind-velocity and temperature inhomogeneities in the lower troposphere is justified in determining the structure of these inhomogeneities. The data (obtained with the method of bistatic acoustic sounding) on signals reflected from stratified inhomogeneities in the lower 600-m layer of the troposphere are given. A detonation-type pulsed acoustic source was used. The methods of isolating a small (in amplitude) reflected signal against the background of noise and determining the reflecting-layer height and the partial-reflection coefficient from the measured parameters (time delay and amplitude) of a reflected signal are presented. The method of estimating the vertical gradients of the effective sound speed and the squared acoustic refractive index from the partial-reflection coefficient previously calculated is described on the basis of an Epstein transition-layer model. The indicated parameters are experimentally estimated for concrete cases of recording reflected signals. A comparison of our estimates with independent analogous data simultaneously obtained for the same parameters with monitoring instruments (a sodar and a temperature profiler) has yielded satisfactory results.

Interface tension in binary systems with curved boundaries (including the sphere of a nanosize)

Within the framework of finite thick method the equation of the interfacial tension isotherm for a disperse particle of radius r (including the sphere of nanosize) immersed in a dispersive medium is obtained with taking into account the particle interactions in binary system. The account of particle interactions in condensed phases far from a critical condition has been conducted with use of a rigid transition layer model when the value of molar partial surface does not vary with change of an interfacial tension. Cases when the pressure in the dispersive medium and a dispersive particle are independent on temperature are considered. The known formulas received earlier by other authors follow from obtained equation of the interfacial tension isotherm at corresponding assumptions, including expressions for one-component system, flat boundary between two solutions in a binary system, condensed phase at the boundary of vapor and others.

Semi-analytical method of wedge-shaped interface transition layer model in laminated composites

The wedge-shaped interface transition layer model is proposed for determining the crack growing directions in laminated composites. The Navier equations are given with the material parameters varying with the angle in the polar coordinate system. The singularity of the order of −1/2 is proved. An effective solver of the ordinary differential equations is adopted, and the continuous eigenfunctions of the stress, strain and displacement fields near the crack tip are obtained. The crack growing directions can be determined rapidly and accurately based on the obtained results and the relevant fracture criterion. Therefore, a highly effective approach is provided for solving the complicated problem of crack growing directions in the laminated composites.

Spectral Index and Quasi‐Periodic Oscillation Frequency Correlation in Black Hole Sources: Observational Evidence of Two Phases and Phase Transition in Black Holes

Recent studies have shown that strong correlations are observed between the low frequencies (1-10 Hz) of quasi-periodic oscillations (QPOs) and the spectral power law index of several black hole (BH) candidate sources, in low (hard) states, steep power law (soft) states, and transitions between these states. The observations indicate that the X-ray spectra of such state (phases) show the presence of a power-law component and are sometimes related to simultaneous radio emission, indicating the probable presence of a jet. Strong QPOs (>20% rms) are present in the power density spectrum in the spectral range where the power-law component is dominant (i.e., 60%90%). This evidence contradicts the dominant, long-standing interpretation of QPOs as a signature of the thermal accretion disk. We present the data from the literature and our own data to illustrate the dominance of power-law index-QPO frequency correlations. We provide a model that identifies and explains the origin of the QPOs and how they are imprinted on the properties of the power-law flux component. We argue for the existence of a bounded compact coronal region that is a natural consequence of the adjustment of the Keplerian disk flow to the innermost sub-Keplerian boundary conditions near the central object and that ultimately leads to the formation of a transition layer (TL) between the adjustment radius and the innermost boundary. The model predicts two phases or states dictated by the photon upscattering produced in the TL: (1) a hard state, in which the TL is optically thin and very hot (kT approximately greater than 50 keV), producing photon upscattering via thermal Comptonization (the photon spectrum index Gamma approximates 1.7 for this state is dictated by gravitational energy release and Compton cooling in an optically thin shock near the adjustment radius), and (2) a soft state that is optically thick and relatively cold (kT approximately less than 5 keV the index for this state, Gamma approximates 2.8, is determined by soft-photon upscattering and photon trapping in a converging flow into the BH). In the TL model for the corona, the QPO frequency V(sub high) is related to the gravitational (close to Keplerian) frequency V(sub K) at the outer (adjustment) radius and v(sub low) is related to the TL's normal mode (magnetoacoustic) oscillation frequency v(sub MA) . The observed correlations between index and low and high QPO frequencies are readily explained in terms of this model. We also suggest a new method for evaluation of the BH mass using the index-frequency correlation.

The Atoll Source States of 4U 1608−52

We have studied the atoll source 4U 1608-52 using a large data set obtained with the Rossi X-ray Timing Explorer. We find that the timing properties of 4U 1608-52 are almost exactly identical to those of the atoll sources 4U 0614+09 and 4U 1728-34 despite the fact that contrary to these sources 4U 1608-52 is a transient covering two orders of magnitude in luminosity. The frequencies of the variability components of these three sources follow a universal scheme when plotted versus the frequency of the upper kilohertz QPO, suggesting a very similar accretion flow configuration. If we plot the Z sources on this scheme only the lower kilohertz QPO and HBO follow identical relations. Using the mutual relations between the frequencies of the variability components we tested several models; the transition layer model, the sonic point beat frequency model, and the relativistic precession model. None of these models described the data satisfactory. Recently, it has been suggested that the atoll sources (among them 4U 1608-52) trace out similar three-branch patterns as the Z sources in the color-color diagram. We have studied the relation between the power spectral properties and the position of 4U 1608-52 in the color-color diagram and conclude that the timing behavior is not consistent with the idea that 4U 1608-52 traces out a three-branched Z shape in the color-color diagram along which the timing properties vary gradually, as Z sources do.

Effects of Resonance in Quasi-periodic Oscillators of Neutron Star Binaries

Using a large quantity of Rossi X-Ray Timing Explorer data presented in the literature, I offer a detailed investigation into the accuracy of the quasi-periodic oscillation (QPO) frequency determination. The QPO phenomenon seen in X-ray binaries is possibly a result of the resonance of the intrinsic (eigen) oscillations and harmonic driving forces of the system. I show that the resonances, in the presence of the damping of oscillations, occur at frequencies that are systematically and randomly shifted with respect to the eigenfrequencies of the system. The shift value strongly depends on the damping rate that is measured by the half-width of the QPO feature. Taking into account this effect, I analyze the QPO data for four Z sources, Scorpius X-I, GX 340+0, GX 5-1, and GX 17+2, and two atoll sources, 4U 1728-34 and 4U 0614+09. The transition-layer model (TLM) predicts the existence of the invariant quantity delta, an inclination angle of the magnetospheric axis with respect to the normal to the disk. I calculate delta and the error bars of delta using the resonance shift, and I find that the inferred delta-values are consistent with constants for these four Z sources, in which horizontal-branch oscillation and kilohertz frequencies have been detected and correctly identified. It is shown that the inferred delta are in the range between 5.5 deg and 6.5 deg. I conclude that the TLM seems to be compatible with the data.

On the Low and High Frequency Correlation in Quasi-periodic Oscillations among White Dwarf, Neutron Star, and Black Hole Binaries

We interpret the correlation over 5 orders of magnitude between high frequency νhigh and low frequency νlow in quasi-periodic oscillations (QPOs) found by Psaltis, Belloni, & van der Klis for black hole (BH) and neutron star (NS) systems and then extended by Mauche to white dwarf (WD) binaries. The observed correlation strongly constrains theoretical models and provides clues to understanding the nature of the QPO phenomena at large. We argue that the observed correlation is a natural consequence of the Keplerian disk flow adjustment to the innermost sub-Keplerian boundary conditions near the central object that ultimately leads to the formation of the sub-Keplerian transition layer (TL) between the adjustment radius and the innermost boundary (the star surface for the NS and WD and the horizon for the BH). In the frameworks of the TL model, νhigh is related to the Keplerian frequency at the outer (adjustment) radius νK, and νlow is related to the magnetoacoustic oscillation frequency νMA. Using a relation between νMA, the magnetic and gas pressure, and the density and the hydrostatic equilibrium condition in the disk, we infer a linear correlation between νK and νMA. Identification of νhigh, νlow with νK, νMA, respectively, leads us to the determination of H/rout = 1.5 × 10-2 and β = 0.1 (where H is the half-width of the disk and β is a ratio of magnetic pressure to gas pressure). We estimate the magnetic field strength near the TL outer radius for BHs, NSs, and WDs. The fact that the observed high-low frequency correlation over 5 orders of magnitude is valid for BHs, NSs, and down to WDs strongly rules out relativistic models for QPO phenomena. We come to the conclusion that the QPO observations indicate the adjustment of the geometrically thin disk to sub-Keplerian motion near the central object. This effect is a common feature for a wide class of systems, starting from WD binaries up to BH binaries.

Quasi-periodic X-ray oscillations in the source Cygnus X-2

The RXTE observations of Scorpius X-1 in 1996–1999 are presented. The properties of its quasi-periodic X-ray oscillations are studied in detail. The results obtained are used for analysis in terms of the transition-layer model (TLM) and the relativistic-precession model (RPM) for a slowly rotating neutron star. Theoretical predictions of the two models are compared and their self-consistency is verified. The tilt of the magnetosphere to the accretion-disk plane, the neutron-star mass, and its angular momentum are determined in terms of the models.

Normal-Branch Quasi-periodic Oscillations in Scorpius X-1: Viscous Oscillations of a Spherical Shell Near the Neutron Star

We present a comprehensive classification of all observed quasi-periodic oscillations (QPOs) within the framework of the transition layer model using a large set of Rossi X-Ray Timing Explorer data for Scorpius X-1. The model assumes an optically thin material along the observer's line of sight in the horizontal branch and an increasingly optically thick material while in the other two branches that is consistent with X-ray and radio observations and the disk transition layer model of QPOs. We identify the ~6 Hz frequencies in the normal branch as acoustic oscillations of a spherical shell around the neutron star (NS) that is formed after radiation pressure near the Eddington accretion rate destroys the disk. The size of the shell is on the order of one NS radius from the NS. We also estimate the upper limit of Sco X-1's magnetic field to be 0.7 × 106 G at about one NS radius above the NS surface while in the horizontal X-ray branch.

Classification of Power Density Spectrum Features and Estimation of the δ-invariant Value for the Z Source GX 340+0

We present a theoretical analysis of Rossi X-Ray Timing Explorer data of Z source GX 340+0 obtained by Jonker et al. In the frameworks of the recently formulated transition layer model, the δ-angle is an angle between the neutron star (NS) magnetospheric axis and the disk (presumably NS rotational) axis. We determine the angle δ = 63 ± 03, which is a combination of the simultaneously observed kilohertz quasi-periodic and horizontal-branch oscillation frequencies. While these three frequencies change by a factor of 3 or more, their δ-combination stays almost constant. GX 340+0 is the fourth source (in addition to 4U 0614+09, Scorpius X-1, and 4U 1702-42) for which δ has been determined. With one (constrained) parameter, at most, we make a complete classification of six observed power spectral features, including the two kilohertz frequencies, the first and second harmonics of the horizontal-branch oscillation frequency, the low-frequency noise component, and the break frequencies. We demonstrate that a new component discovered by Jonker et al. in the GX 340+0 power spectrum is related to the viscous-frequency branch that has in fact been reported earlier in 4U 1728-34 by Ford & van der Klis. Finally, we reclassify several previously misidentified features in the power spectrum.

Testing the Transition Layer Model of Quasi‐periodic Oscillations in Neutron Star X‐Ray Binaries

We compare the theoretical predictions of the transition layer model with some observational features of quasi-periodic oscillations (QPOs) in neutron star X-ray binaries. We found that the correlation between horizontal branch oscillation (HBO) frequencies and kilohertz (kHz) QPO frequencies, the difference between the low-frequency QPOs in atoll sources and HBOs in Z sources, and the correlation between the frequencies of low-frequency QPOs and break frequencies can be well explained by the transition layer model, provided the neutron star mass is around 1.4 M☉ and the angle between magnetosphere equator and accretion disk plane is around 6°. The observed decrease of peak separation between the two kHz QPO frequencies with the increase of the kHz QPO frequencies and the increase of QPO frequencies with the increase of inferred mass accretion rate are also consistent with the theoretical predictions of the transition layer model. In addition, we derive a simple equation that can be adopted to estimate the angle (δ) between magnetosphere equator and accretion disk plane by use of the simultaneously observed QPO frequency data. We estimate this angle, in the range of 4°-8°, for five Z sources and two atoll sources. The nearly constant δ value for each source, derived from the different sets of simultaneously observed QPO frequency data, provides a strong test of the theoretical model. Finally, we suggest that similar transition layer oscillations may be responsible for the observed QPOs in accretion-powered millisecond X-ray pulsars and Galactic black hole candidates.

Parallel electric fields in discrete arcs

We present a large‐scale model of the parallel electric fields in the upward current region of the aurora. The model, called the “Transition Layer Model”, applies to intense, discrete arcs. It is based on 1‐D spatial, 2‐D velocity static Vlasov simulations and observations from the Fast Auroral Snapshot (FAST) satellite. The model depicts three regions along the magnetic field that are separated by two transition layers which contain parallel electric fields. The current‐voltage properties closely follow the Knight relation.

A multi-phase Mullins–Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem

We propose a generalisation of the Mullins–Sekerka problem to model phase separation in multi-component systems. The model includes equilibrium equations in bulk, the Gibbs–Thomson relation on the interfaces, Young's law at triple junctions, together with a dynamic law of Stefan type. Using formal asymptotic expansions, we establish the relationship to a transition layer model known as the Cahn-Hilliard system. We introduce a notion of weak solutions for this sharp interface model based on integration by parts on manifolds, together with measure theoretical tools. Through an implicit time discretisation, we construct approximate solutions by stepwise minimisation. Under the assumption that there is no loss of area as the time step tends to zero, we show the existence of a weak solution.

A transition layer model and its application to resonant tunneling in heterostructures

A transition layer model is proposed and used to calculate resonant tunneling in a double-barrier quantum well system. Compared with the ideal step of the potential at the interface, the studied system has transition layers that are composed by many thin rectangular barriers with a random height. It is found that these transition layers can improve the peak-to-valley ratio of the tunneling current and change the negative differential conductance.

Near surface transition layer model of MBE growth

Near surface transition layer model of MBE growth