Disk Plane Research Articles

Sensors based on evanescent field perturbation of microresonators.

We consider a whispering gallery mode (WGM) sensor where a dielectric perturber extends into the evanescent tail of the microresonator. The position of the perturber rather than the morphology of the resonator is modified by a change in the measured property, inducing a shift in the WGM. This approach can be used for both three-dimensional (spheres, toroids) and planar (disks, rings) resonator geometries. We demonstrate, through analysis and experiments, the feasibility of this sensor approach for both geometries by using a sphere resonator and an on-chip ring resonator. Experiments show that the motion of the perturber across the evanescent tail on the resonator's outer surface leads to a measurable shift in the resonator WGM. In the latter experiment, a ferromagnetic structure is attached to the perturber stem so that the system acts as a magnetic field detector. The results show a consistent relationship between the mode shift and the magnetic field strength.

Elliptical Accretion Disk as a Model for Tidal Disruption Events

Abstract Elliptical accretion disk models for tidal disruption events (TDEs) have been recently proposed and independently developed by two groups. Although these two models are characterized by a similar geometry, their physical properties differ considerably. In this paper, we further investigate the properties of the elliptical accretion disk of the nearly uniform distribution of eccentricity within the disk plane. Our results show that the elliptical accretion disks have distinctive hydrodynamic structures and spectral energy distributions, associated with TDEs. The soft X-ray photons generated at pericenter and nearby are trapped in the disk and advected around the ellipse because of large electron scattering opacity. They are absorbed and reprocessed into emission lines and low-frequency continuum via recombination and bremsstrahlung emission. Because of the rapid increase of bound–free and free–free opacities with radius, the low-frequency continuum photons become trapped in the disk at large radius and are advected through apocenter and back to the photon-trapping radius. Elliptical accretion disks predict sub-Eddington luminosities and emit mainly at the photon-trapping radius of thousands of Schwarzschild radii with a blackbody spectrum of nearly single temperature of typically about 3 × 104 K. Because of the self-regulation, the photon-trapping radius expands and contracts following the rise and fall of accretion rate. The radiation temperature is nearly independent of BH mass and accretion rate and varies weakly with the stellar mass and the viscosity parameter. Our results are well consistent with the observations of optical/UV TDEs.

Justification of parameters of a four-row disk harrow using the experiment planning method

Disk harrows with individual installation of the disk on a separate stand are widely used in resource-saving technology of soil preparation for grain crops after late harvesting of row crops (corn, sunflower). Four-row disc harrows provide soil preparation for grain crops in one or two passes through the maize and sunflower predecessors. The main parameter of the disk harrow is the depth of processing, the value of which depends on the disk setting angle to the unit movement direction. An increase in the setting angle is accompanied by not only an increase in the depth of processing, but also the traction resistance and fuel costs for soil treatment increase. However, a number of disk parameters also affect the processing depth value – the diameter, the inclination angle of the disk in the vertical plane, the width of the chamfer cutting edge, the vertical load on the disk, the thickness of the disk and a number of others. Consideration of these factors during the adjustment to the required processing depth will reduce the disk setting angle to the direction of the unit movement, which will help to reduce disk harrow traction resistance and increase the fuel efficiency of preparing the soil for sowing grain on rowed predecessors.

Some Novel Cosine Similarity Measures Based on Complex Hesitant Fuzzy Sets and Their Applications

The theory of complex hesitant fuzzy set (CHFS) is a modification technique of the complex fuzzy set (CFS) to cope with awkward and unreliable information’s in daily life issues. CHFS contains the grade of truth in the form of complex number, whose real and imaginary parts are in the form of the finite subset of the unit interval. CHFS is the mixture of hesitant fuzzy set (HFS) and CFS, which handles the complex and uncertain information in real-world issues which is compared with fuzzy sets and complex fuzzy sets. The positive membership in CHFS is in the form a polar coordinate belonging to unit disc in the complex plane. The aims of this manuscript are to explore some similarity measures (SMs), weighted SMs (WSMs) such as cosine SMs, weighted cosine SMs, SMs based on cosine function, WSMs based on cosine function, SMs based on tangent function, and WSMs based on tangent function of CHFS. Some special cases of the presented measures are discussed in detail. Moreover, we use our described SMs and weighted SMs of CHFS in the environment of medical diagnosis and pattern recognition to assess the practicality and competence of the described SMs. Finally, to find the validity and proficiency of the investigated measures based on CHFSs, the comparison between explored measures with some already defined measures and their graphical representations are also discussed in detail.

Dynamical evolution of massive perturbers in realistic multicomponent galaxy models I: implementation and validation

ABSTRACT Galaxies are self-gravitating structures composed by several components encompassing spherical, axial, and triaxial symmetry. Although real systems feature heterogeneous components whose properties are intimately connected, semi-analytical approaches often exploit the linearity of the Poisson’s equation to represent the potential and mass distribution of a multicomponent galaxy as the sum of the individual components. In this work, we expand the semi-analytical framework developed in Bonetti et al. (2020) by including both a detailed implementation of the gravitational potential of exponential disc (modelled with a sech2 and an exponential vertical profile) and an accurate prescription for the dynamical friction experienced by massive perturbers (MP) in composite galaxy models featuring rotating disc structures. Such improvements allow us to evolve arbitrary orbits either within or outside the galactic disc plane. We validate the results obtained by our numerical model against public semi-analytical codes as well as full N-body simulations, finding that our model is in excellent agreement to the codes it is compared with. The ability to reproduce the relevant physical processes responsible for the evolution of MP orbits and its computational efficiency make our framework perfectly suited for large parameter-space exploration studies.

The Relative Contribution of Solutal Marangoni Convection to Thermal Marangoni Flow Instabilities in a Liquid Bridge of Smaller Aspect Ratios under Zero Gravity

The effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge with different aspect ratios As has been investigated by three-dimensional (3D) numerical simulations under zero gravity. We consider a half-zone model of a liquid bridge between a cold (top plane) and a hot (bottom plane) disks. The highest Si concentration is on the top of the liquid bridge. The aspect ratio (As) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (MaTAs≲1800)) has the same dependence on As as the critical thermal Marangoni number (under small solutal Marangoni numbers (400≲MaCAs≲800)), i.e., it decreases with increasing As. The azimuthal wavenumber of the traveling wave mode increases as decreasing As, i.e., larger azimuthal wavenumbers (m=6,7,11,12, and 13) appear for As=0.25, and only m=2 appears when As is one and larger. The oscillatory modes of the hydro waves have been extracted as the spatiotemporal structures by using dynamic mode decomposition (DMD). The present study suggests a proper parameter region of quiescent steady flow suitable for crystal growth for smaller aspect ratios of the liquid bridge.

Micromagnetic instabilities in spin-transfer switching of perpendicular magnetic tunnel junctions

Micromagnetic instabilities and non-uniform magnetization states play a significant role in spin transfer induced switching of nanometer scale magnetic elements. Here we model domain wall mediated switching dynamics in perpendicularly magnetized magnetic tunnel junction nanopillars. We show that domain wall surface tension always leads to magnetization oscillations and instabilities associated with the disk shape of the junction. A collective coordinate model is developed that captures aspects of these instabilities and illustrates their physical origin. Model results are compared to those of micromagnetic simulations. The switching dynamics is found to be very sensitive to the domain wall position and phase, which characterizes the angle of the magnetization in the disk plane. This sensitivity is reduced in the presence of spin torques and the spin current needed to displace a domain wall can be far less than the threshold current for switching from a uniformly magnetized state. A prediction of this model is conductance oscillations of increasing frequency during the switching process.

The influence of the blade tip shape on brownout by an approach based on computational fluid dynamics

In this study, a computational fluid dynamics approach based on solving the Reynolds-averaged Navier-Stokes equation and shear stress transport (SST) (Menter) k-ω turbulence model is used to solve the rotor in ground effect. A discrete element method based on solving the Hertz-Mindlin (no-slip) contact model and considering the real physical properties and collision is used to solve the motion and distribution of sediment particles in the field. By coupling the two approaches, the dust cloud development in the ground-effect flow field of a helicopter with rectangular-tip and slotted-tip blades is simulated for six seconds. The characteristics of the flow field are analyzed, and the influence of the flow field generated by the two types of blades on the movement and distribution of sediment particles on the ground and the subsequent dust cloud development over time are compared. The relatively long time of numerical results show that the sediment particles initially located on the ground are uplifted by the interaction between the blade tip vortex and the ground. Over time, the particles become more concentrated around the tip vortex core. The sediment particles in the dust cloud move primarily in the radial and axial directions of the rotation center, and the circumferential movement is not significant. The optimized slotted-tip blade provides better dissipation of the tip vortex core intensity near the ground than the rectangular-tip blade, thus weakening the entrainment effect of the sediment particles on the ground and reducing the dust cloud concentration around the disc plane.

Efficacy and Safety of the Atrial Septal Defect Closure for Patients with Absent or Malaligned Aortic Rim Using a Figulla Flex II Device Flared and Straddling Behind the Aorta

Background: Although transcatheter closure of atrial septal defect (ASD) is safe and effective for patients with sufficient rim, ASD patients with absent and/or malaligned aortic and/or superior rim have higher risks of device embolization and cardiac erosion. We have treated such high-risk patients using a Figulla Flex II (FFII) device shaped flared and straddling behind the aorta because this method would avoid such serious complications. However, its long-term efficacy and safety remain unclear. Therefore, the midterm efficacy and safety of this method were studied. Methods: We retrospectively evaluated the outcome of 47 consecutive patients with such rim (age 6–73 years, weight 17–75 kg, 31 females) treated with this method at our hospital between February 2016 and September 2019. To make the flared and straddling shape, we selected a FFII 4–6 mm larger than the balloon sizing diameter by stop-flow technique. We also studied the device shape, the disc pressure to the Valsalva wall and their changes over 6 months by transesophageal echocardiography. Results: All procedures were successful, and leakage disappeared within 1 year. During a mean follow up of 37 ± 12 months, complications included a transient sinus node dysfunction and one I° atrioventricular block within 3 months. Whole device shape changed from bulky to thin: the device waist and thickness significantly decreased by around 1.5 mm and 3.5 mm, respectively (p < 0.05), but the two discs remained flared and straddling behind the aorta over 6 months; therefore, the disc edges seldom pressed the Valsalva wall perpendicularly, even though the inner plane of either disc often slightly pressed the wall. Conclusions: ASD closure using a FFII shaped flared and straddling behind the aorta is probably effective and safe for patients with absent and/or malaligned aortic and/or superior rim although requiring care for conduction disorders.

Second Hankel determinant for certain subclass of bi-univalent functions

The main purpose of this paper is to obtain an upper bound for the second Hankel determinant for functions belonging to a subclass of bi-univalent functions in the open unit disk in the complex plane. Furthermore, the presented results in this work improve or generalize the recent works of other authors.

Clustering in a hyperbolic model of complex networks

In this paper we consider the clustering coefficient, and clustering function in a random graph model proposed by Krioukov et al. in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at most at a certain hyperbolic distance from each other. It has been previously shown that this model has various properties associated with complex networks, including a power-law degree distribution, “short distances” and a non-vanishing clustering coefficient. The model is specified using three parameters: the number of nodes $n$, which we think of as going to infinity, and $\alpha , \nu > 0$, which we think of as constant. Roughly speaking, the parameter $\alpha $ controls the power law exponent of the degree sequence and $\nu $ the average degree. Here we show that the clustering coefficient tends in probability to a constant $\gamma $ that we give explicitly as a closed form expression in terms of $\alpha , \nu $ and certain special functions. This improves earlier work by Gugelmann et al., who proved that the clustering coefficient remains bounded away from zero with high probability, but left open the issue of convergence to a limiting constant. Similarly, we are able to show that $c(k)$, the average clustering coefficient over all vertices of degree exactly $k$, tends in probability to a limit $\gamma (k)$ which we give explicitly as a closed form expression in terms of $\alpha , \nu $ and certain special functions. We are able to extend this last result also to sequences $(k_{n})_{n}$ where $k_{n}$ grows as a function of $n$. Our results show that $\gamma (k)$ scales differently, as $k$ grows, for different ranges of $\alpha $. More precisely, there exists constants $c_{\alpha ,\nu }$ depending on $\alpha $ and $\nu $, such that as $k \to \infty $, $\gamma (k) \sim c_{\alpha ,\nu } \cdot k^{2 - 4\alpha }$ if $\frac {1}{2} < \alpha < \frac {3}{4}$, $\gamma (k) \sim c_{\alpha ,\nu } \cdot \log (k) \cdot k^{-1}$ if $\alpha =\frac {3}{4}$ and $\gamma (k) \sim c_{\alpha ,\nu } \cdot k^{-1}$ when $\alpha > \frac {3}{4}$. These results contradict a claim of Krioukov et al., which stated that $\gamma (k)$ should always scale with $k^{-1}$ as we let $k$ grow.

Corona theorem for strictly pseudoconvex domains

Nearly 60 years have passed since Lennart Carleson gave his proof of Corona Theorem for unit disc in the complex plane. It was only recently that M. Kosiek and K. Rudol obtained the first positive result for Corona Theorem in multidimensional case. Using duality methods for uniform algebras the authors proved "abstract" Corona Theorem which allowed to solve Corona Problem for a wide class of regular domains. In this paper we expand Corona Theorem to strictly pseudoconvex domains with smooth boundaries.

Eccentric Black Hole Mergers in Active Galactic Nuclei

Abstract The astrophysical origin of gravitational wave transients is a timely open question in the wake of discoveries by the Laser Interferometer Gravitational-Wave Observatory (LIGO)/Virgo. In active galactic nuclei (AGNs), binaries form and evolve efficiently by interaction with a dense population of stars and the gaseous AGN disk. Previous studies have shown that stellar-mass black hole (BH) mergers in such environments can explain the merger rate and the number of suspected hierarchical mergers observed by LIGO/Virgo. The binary eccentricity distribution can provide further information to distinguish between astrophysical models. Here we derive the eccentricity distribution of BH mergers in AGN disks. We find that eccentricity is mainly due to binary–single (BS) interactions, which lead to most BH mergers in AGN disks having a significant eccentricity at 0.01 Hz, detectable by the Laser Interferometer Space Antenna. If BS interactions occur in isotropic-3D directions, then 8%–30% of the mergers in AGN disks will have eccentricities at 10 Hz above e 10 Hz ≳ 0.03, detectable by LIGO/Virgo/Kamioka Gravitational Wave Detector, while 5%–17% of mergers have e 10 Hz ≥ 0.3. On the other hand, if BS interactions are confined to the AGN–disk plane due to torques from the disk, with 1–20 intermediate binary states during each interaction, or if BHs can migrate to ≲ 10−3 pc from the central supermassive BH, then 10%–70% of the mergers will be highly eccentric (e 10 Hz ≥ 0.3), consistent with the possible high eccentricity in GW190521.

The twisted dark matter halo of the Milky Way

ABSTRACT We analyse systems analogous to the Milky Way (MW) in the eagle cosmological hydrodynamics simulation in order to deduce the likely structure of the MW’s dark matter (DM) halo. We identify MW mass haloes in the simulation whose satellite galaxies have similar kinematics and spatial distribution to those of the bright satellites of the MW, specifically systems in which the majority of the satellites (8 out of 11) have nearly coplanar orbits that are also perpendicular to the central stellar disc. We find that the normal to the common orbital plane of the coplanar satellites is well aligned with the minor axis of the host DM halo, with a median misalignment angle of only 17.3°. Based on this result, we infer that the minor axis of the Galactic DM halo points towards (l, b) = (182°, −2°), with an angular uncertainty at the 68 and 95 percentile confidence levels of 22° and 43°, respectively. Thus, the inferred minor axis of the MW halo lies in the plane of the stellar disc. The halo, however, is not homologous and its flattening and orientation vary with radius. The inner parts of the halo are rounder than the outer parts and well aligned with the stellar disc (that is the minor axis of the halo is perpendicular to the disc). Further out, the halo twists and the minor axis changes direction by 90°. This twist occurs over a very narrow radial range and reflects variations in the filamentary network along which mass was accreted into the MW.

Investigation of Different Groove Profile Effects on Torque Transmission in Shear Mode Magnetorheological Clutch: Numerical Simulation and Experimental Study

Abstract In this research paper, an attempt has been made to investigate the torque transmission characteristics in a radial magnetorheological (MR) clutch disc with different groove profiles. To estimate the transmitted torque, a numerical procedure is initiated by the implementation of the Bingham constitutive model into a magnetic field analysis followed by computational fluid dynamic (CFD) analysis. CFD results are presented for the analysis of transmitted torque between a plane driving disc and three different driven discs, i.e., plane, radial groove, and circular groove disc, under the conditions of different working radii, magnetic fields, and rotational speeds. The MR fluid (MRF) domain is modeled using a technique which can be applied for any wall texture of driving and driven disc. To verify the numerical findings, an MR clutch with three different discs and a MR transmission test bed have been built, and the influence of groove profile on the transmission torque of MRFs has been investigated on the test bed. The results are presented to obtain the relationships among torque performance, disc radius, rotational speed, and magnetic field. Numerical results show good agreement of torque transmission for different groove profiles with experiments. Finally, temperature distribution patterns in different three MR clutches and an optimization of the radial groove profile have been analyzed numerically.

First Detection of Orbital Motion for HD 106906 b: A Wide-separation Exoplanet on a Planet Nine–like Orbit

Abstract HD 106906 is a 15 Myr old short-period (49 days) spectroscopic binary that hosts a wide-separation (737 au) planetary-mass ( ) common proper motion companion, HD 106906 b. Additionally, a circumbinary debris disk is resolved at optical and near-infrared wavelengths that exhibits a significant asymmetry at wide separations that may be driven by gravitational perturbations from the planet. In this study we present the first detection of orbital motion of HD 106906 b using Hubble Space Telescope images spanning a 14 yr period. We achieve high astrometric precision by cross-registering the locations of background stars with the Gaia astrometric catalog, providing the subpixel location of HD 106906 that is either saturated or obscured by coronagraphic optical elements. We measure a statistically significant 31.8 ± 7.0 mas eastward motion of the planet between the two most constraining measurements taken in 2004 and 2017. This motion enables a measurement of the inclination between the orbit of the planet and the inner debris disk of either deg or deg, depending on the true orientation of the orbit of the planet. There is a strong negative correlation between periastron and mutual inclination; orbits with smaller periastra are more misaligned with the disk plane. With a periastron of au, HD 106906 b is likely detached from the planetary region within 100 au radius, showing that a Planet Nine–like architecture can be established very early in the evolution of a planetary system.

A note on some elementary properties and applications of certain operators to certain functions analytic in the unit disk

Abstract This scientific note relates to introducing certain elementary operators defined in the unit disk in the complex plane, then determining various applications (specified by those operators) to certain analytic functions, and also revealing a number of possible implications of them.

An off-centred bulge or a satellite? Hydrodynamical N-body simulations of the disc galaxy NGC 5474

ABSTRACT We present dynamical models of the star-forming galaxy NGC 5474 based on N-body hydrodynamical numerical simulations. We investigate the possible origin of the compact round stellar structure, generally interpreted as the bulge of the galaxy, but unusually off-set by ${\simeq} 1\, {\rm kpc}$ in projection from the visual and the kinematic centres of both the star and the gas discs. We argue that it is very unlikely that the putative bulge is in a coplanar orbit in the disc plane, showing that such a configuration would be hardly compatible with its smooth and regular spatial distribution, and, in case its mass is above $10^8\, \mathrm{ M}_{\odot }$, also with the regular ${\rm H\,{\small I}}$ velocity field of NGC 5474. Instead, if the putative bulge is in fact an early-type satellite galaxy orbiting around NGC 5474, not only the off-set can be easily produced by projection effects, but our simulations suggest that the gravitational interaction between the two systems can explain also the warped ${\rm H\,{\small I}}$ distribution of NGC 5474 and the formation of its loose spiral arms. As a by-product of the simulations, we find that the peculiar overdensity of old stars detected in the south-west region of NGC 5474 may be explained with the interaction between NGC 5474 and a smaller stellar system, unrelated to the putative bulge, accreted in the disc plane.

Jaccard and Dice Similarity Measures Based on Novel Complex Dual Hesitant Fuzzy Sets and Their Applications

Complex dual hesitant fuzzy set (CDHFS) is a combination of two modifications, called complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). CDHFS makes two degrees, called membership valued and nonmembership valued in the form of a finite subset of a unit disc in the complex plane, and is a capable method to solve uncertain and unpredictable information in real-life problems. The goal of this study is to describe the notion of CDHFS and its operational laws. The novel approach of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its fundamental laws are also described and defended with the help of an example. Further, the vector similarity measures (VSMs), weighted vector similarity measures (WVSMs), hybrid vector similarity measure, and weighted hybrid vector similarity measure are additionally explored. These similarity measures (SM) are applied to the environment of pattern recognition and medical diagnosis to assess the capability and feasibility of the interpreted measures. We additionally solved some numerical examples utilizing the established measures. We examine the dependability and validity of the proposed measures by comparing them with some existing measures. The advantages, comparative analysis, and graphical portrayal of the investigated interpreted measures and existing measures are additionally described in detail.

Exploring the origin of low-metallicity stars in Milky-Way-like galaxies with the NIHAO-UHD simulations

ABSTRACT The kinematics of the most metal-poor stars provide a window into the early formation and accretion history of the Milky Way (MW). Here, we use five high-resolution cosmological zoom-in simulations (∼ 5 × 106 star particles) of MW-like galaxies taken from the NIHAO-UHD project, to investigate the origin of low-metallicity stars ([Fe/H] ≤ −2.5). The simulations show a prominent population of low-metallicity stars confined to the disc plane, as recently discovered in the MW. The ubiquity of this finding suggests that the MW is not unique in this respect. Independently of the accretion history, we find that ≳90 per cent of the retrograde stars in this population are brought in during the initial build-up of the galaxies during the first few Gyr after the Big Bang. Our results therefore highlight the great potential of the retrograde population as a tracer of the early build-up of the MW. The prograde planar population, on the other hand, is accreted during the later assembly phase and samples the full galactic accretion history. In case of a quiet accretion history, this prograde population is mainly brought in during the first half of cosmic evolution (t ≲ 7 Gyr), while, in the case of an ongoing active accretion history, later mergers on prograde orbits are also able to contribute to this population. Finally, we note that the MW shows a rather large population of eccentric, very metal-poor planar stars. This is a feature not seen in most of our simulations, with the exception of one simulation with an exceptionally active early building phase.