Axisymmetric Structures Research Articles

A Climatology of Summer‐Time Arctic Cyclones Using a Modified Phase Space

AbstractWe perform a climatological analysis of summer‐time Arctic cyclone structure in reanalysis data using a phase space approach. A classification scheme for Arctic cyclones is proposed, dependent on whether vorticity structure during development is low‐level‐dominant (LLD) or upper‐level‐dominant (ULD). During growth, LLD cyclones (65.5%) exhibit warm‐core asymmetric structures, whereas ULD cyclones (34.5%) have cold‐core asymmetric structures. LLD cyclones typically have greater thermal asymmetry during growth. However, a transition to a persistent cold‐core axisymmetric structure after maturity is characteristic of summer‐time Arctic cyclones, regardless of structure during growth. LLD cyclones are typically stronger and preferentially track on the Russian coastline where there is high baroclinicity, whereas ULD cyclones tend to be longer‐lived and preferentially track in the Pacific sector, where they can interact with tropopause polar vortices. This study provides a platform for further research into different classes of Arctic cyclones and associated hazardous weather, and ultimately for developing conceptual models.

Experiment and Simulation Study of the Laser-Induced Cavitation Bubble Technique for Forming a Microgroove in Aluminum Foil.

The present work introduces a laser-induced cavitation bubble technique for forming an axisymmetric structure (i.e., microgroove) and the dynamics of a cavitation bubble from initial expansion to the collapse stages that were also simulated. Furthermore, the shock wave signals and dynamic properties of the cavitation bubble were recorded using a hydrophone and a high-speed camera. The experiments on microgrooves formed by laser-induced cavitation bubble stamping were carried out, and the effects of laser energy, the initial position of the bubble, and the number of impacts on the microformability of aluminum sheets are discussed. The depth of the microgroove was investigated using experiments, and it was found that the process can serve as a rapid technique for impressing microfeatures on thin-sheet metals. The experimental results showed that as the initial position of the bubble increased, the deformation depth decreased. As the laser energy and number of impacts increased, the deformation depth increased. The results of the response surface experiments showed that a laser energy of 27 mJ, 3 impacts, and a bubble position of 3 mm were optimal for the process. By using the optimal parameters, flat and smooth microgrooves with a forming depth of 102.54 µm were successfully fabricated. Furthermore, the maximum thickness thinning of the microgroove section occurred at the entrance areas, and this area had the greatest hardness. This also indicated that the greatest amount of plastic deformation of the material and grain refinement occurred in this area. On the other hand, the aluminum foil did not undergo oxidation during the plastic deformation process. These results demonstrated that laser-induced bubble stamping is an advanced micromachining method with promising applications.

Multi-Objective Optimization of Thin-Walled Composite Axisymmetric Structures Using Neural Surrogate Models and Genetic Algorithms.

Composite shells find diverse applications across industries due to their high strength-to-weight ratio and tailored properties. Optimizing parameters such as matrix-reinforcement ratio and orientation of the reinforcement is crucial for achieving the desired performance metrics. Stochastic optimization, specifically genetic algorithms, offer solutions, yet their computational intensity hinders widespread use. Surrogate models, employing neural networks, emerge as efficient alternatives by approximating objective functions and bypassing costly computations. This study investigates surrogate models in multi-objective optimization of composite shells. It incorporates deep neural networks to approximate relationships between input parameters and key metrics, enabling exploration of design possibilities. Incorporating mode shape identification enhances accuracy, especially in multi-criteria optimization. Employing network ensembles strengthens reliability by mitigating model weaknesses. Efficiency analysis assesses required computations, managing the trade-off between cost and accuracy. Considering complex input parameters and comparing against the Monte Carlo approach further demonstrates the methodology's efficacy. This work showcases the successful integration of network ensembles employed as surrogate models and mode shape identification, enhancing multi-objective optimization in engineering applications. The approach's efficiency in handling intricate designs and enhancing accuracy has broad implications for optimization methodologies.

(Re-)exploring the normal modes of axisymmetric structures: An English church bell case study

The normal modes of axisymmetric structures are of interest to structural engineers, physicists and musical acousticians. Previously, some of the present authors have made studies of church bells, hand bells, elephant bells, various gongs and rings. Group theoretical arguments have been used, with considerable success, in classifying the normal modes of these structures and in understanding how “beats” arise from split degenerate doublets. It is now pointed out that further information can be obtained from group theory using a variety of additional arguments. In particular, it infers a basic distinction between “in-extensional” and “extensional” types of modes. In the present work, we concentrate on the case of an English church bell, as an example axisymmetric structure, whose normal modes were previously measured in a frequency range of up to about 10 kHz. In that earlier work, the results were analyzed with what was then considered a state-of-the-art finite-element package. We now repeat this exercise with a modern finite-element package to explore the differences between the types of modes and validate the Group theory observations. The agreement with experiment is much improved and some new level of understanding of the spectrum of the bell is achieved.

Efficient post-processing of electromagnetic plane wave simulations to model arbitrary structured beams incident on axisymmetric structures

The study of an optical beam interacting with material structures is a fundamental of nanophotonics. Computational electromagnetic solvers facilitate the rapid calculation of the scattering from material structures with arbitrary geometry and complexity, but have limited efficiency when employing structured excitation fields. We have developed a post-processing method and package that can efficiently calculate the full three-dimensional electric and magnetic fields for any optical beam incident on a particle or structure with at least one axis of continuous rotational symmetry, called an axisymmetric body (such as a sphere, cylinder, cone, torus or surface). Provided an initial batch of plane wave simulations is computed, this open-source package combines data from computational electromagnetic solvers in a post-processing fashion using the angular spectrum representation to create arbitrarily structured beams, including vector vortex beams. Any and all possible incident beams can be generated from the initial batch of PWSs, without the need for further simulations. This allows for efficiently performing parameter sweeps such as changing the angle of illumination or translating the particle position relative to the beam, all in post-processing, with no need for additional time-consuming simulations. We demonstrate some applications by numerically calculating optical force and torque maps for a spherical plasmonic nanoparticle in a tightly focused Gaussian beam, a plasmonic nanocone in an azimuthally polarised beam and compute the fields of a non-paraxial Laguerre–Gaussian vortex beam reflecting on a multilayered surface. We believe this package, called BEAMS, is a valuable tool for rapidly quantifying electromagnetic systems that are beyond traditional analytical methods.

Effects of AC electric fields applied to radially on co-flow Bunsen flame

We investigated the impact of AC electric fields on a nonpremixed coflow-jet flame. To eliminate the azimuthal component of the ionic wind, we created a radially applied electric field using an axisymmetric electrode structure consisting of a nozzle and a cylindrical mesh surrounding the co-flow burner. By applying various voltages and frequencies, we identified four distinct flame behaviors: oscillating flame with applied frequency, fluctuating flame, instability-induced extinction, and blowout. Each behavior was analyzed and discussed using phase analysis, flame length variation over time synchronized with the polarity change of the applied voltage, and FFT analysis. When an AC voltage (VAC) of 2 kV was applied, the oscillating flame with applied frequency was observed regardless of the AC frequency (fAC). Notably, a double-peak oscillation was observed due to the asymmetric bidirectional ionic wind resulting from the polarity change. The fluctuating flame was exclusively observed at VDC = 5 kV with fAC = 1 Hz. In addition to the double-peak oscillation, an overlapping counter-rotating vortex-induced oscillation was observed, which was confirmed to be caused by the positive ions directed towards the nozzle in the negative voltage section. At VAC = 5 and 7 kV with fAC = 10 Hz, the oscillation frequency of the counter-rotating vortex induced oscillation (≈ 10 Hz) was almost identical to fAC, resulting in constructive interference, ultimately leading to the instability-induced extinction. Blowout occurred at VAC = 7 kV with fAC = 1 Hz, where the strong bi-directional ionic wind caused necking of the fuel stream and resulted in flame extinction. Finally, we derived a critical frequency for observing a stable flame regardless of the AC voltage by comparing and analyzing the collision reaction time with the applied frequency.

Gravity-induced virtual clocking effect in large-capacity/low-head pumped hydro energy storage system with horizontal shaft

Significant gravity effects in a large-capacity/low-head pumped hydro energy storage system with horizontal shaft can destroy the axisymmetric inner flow structures in pump mode compared with its hydraulic model. For the stationary guide-vane region, this makes the inflow condition of each vane change with its circumferential installation position and thus causes a virtual clocking effect between the visible guide-vanes and the invisible gravity. The virtual clocking effect may change the hydraulic performance and induce instability risks, but its specific influence is still unclear. In this article, for a low-head pumped hydro energy storage prototype system with horizontal shaft, four virtual clocking schemes, namely the top guide-vane inlet edge and the gravity direction staggering 0/4, 1/4, 2/4 and 3/4 passage interval angle, were established, and a comparative investigation on hydraulic performance in the optimal pump mode was carried out. Firstly, the pressure polarization oscillation is observed in the impeller region under different schemes. The differences in the polarization degree do not exceed 1%, but the circumferential distributions of the peak-to-peak values of pressure fluctuations at the impeller outlet show a phase difference, which should be considered in the circumferential support structures. Secondly, the partial flow separation is observed in the guide-vane region under different schemes, and the flow deviation ratio between the left and right sides at the guide-vane outlet exhibits differences of up to 10%, which cannot be ignored for a huge system. The scheme with staggering 1/4 passage interval angle exhibits the least flow deviation ratio while the scheme with staggering 3/4 passage interval angle exhibits the greatest flow deviation ratio. Overall, to ensure the hydraulic stability of the large-capacity/low-head pumped hydro energy storage system with horizontal shaft, the virtual clocking scheme with staggering 1/4 passage interval angle is recommended for the energy engineering.

Modeling Wind‐Blown Umbrella Clouds in Lagrangian Dispersion Models

AbstractThe ash and gas released by large explosive volcanic eruptions rises to its neutral buoyancy level in the atmosphere, then spreads laterally to form an umbrella cloud. Density stratification of the atmosphere generates buoyancy forces in the cloud, which drive the outward spread. Although umbrella clouds are often modeled as circular axisymmetric structures, in practice they are usually influenced quite strongly by the meteorological wind, with spread in the upwind direction halted by the oncoming wind, and different rates of spreading in the downwind and crosswind directions. In this work, we derive a simple parametrization of non‐axisymmetric umbrella cloud spreading from a much more complex physically based shallow‐layer intrusion model. The new parametrization is quick to evaluate and so is suitable for use in operational Volcanic Ash Transport and Dispersion Models (VATDMs). In contrast to previous parametrizations, in which there is assumed to be no interaction between a circular umbrella cloud and the meteorological wind, here the umbrella cloud is influenced by the wind and adopts a shape determined by the balance of buoyant spreading and downwind drag forces. We apply the new scheme to four historical case studies of eruptions at Puyehue 2011, Pinatubo 1991, Ulawun 2019, and Calbuco 2015. The results are compared with VATDM simulations using a conventional circular umbrella cloud parametrization. Using the new scheme, good descriptions of cloud spread are recovered and the prediction of horizontal ash distribution is improved relative to the axisymmetric parametrization.

A MATLAB finite element toolbox for the efficient nonlinear analysis of axisymmetric shells

AbstractShells of revolution under axisymmetric conditions exhibit a circumferentially uniform pre‐buckling stress state and are important fundamental systems which often serve as reference systems for those under more complex conditions. Given this status, work is continuing on a careful and complete characterization of their buckling response with the aid of the Reference Resistance Design (RRD) framework for the ultimate benefit of the EN 1993‐1‐6 Eurocode on the strength of stability of metal shells. The situation is greatly complicated by the fact that while modern finite element software packages offer axisymmetric shell elements in an efficient 2D modelling plane, these are not capable of detecting bifurcation buckling into non‐axisymmetric modes which are often critical for slender systems. Reverting to a full 3D plane is possible, but grossly inefficient and the explicitly modelled circumferential direction is parasitic and detrimental to the overall solution quality. AQUINAS is an accessible and intuitive toolbox developed by the Authors in MATLAB for the efficient analysis of axisymmetric shell structures, aiming to reintroduce a modelling capability that was once standard in the field. Data input is entirely object‐oriented and matrix assembly is parallelized with pre‐compiled C++ routines, with users being able to take direct advantage of MATLAB's visualization properties. The software natively supports the LA, LBA, MNA, GMNIA etc. Eurocode analysis taxonomy. This paper demonstrates the current capabilities of the toolbox, describes the extensive programme of verification against existing established solutions that has been performed, and illustrates its ability to efficiently compute very detailed capacity curves using the EN 1993‐1‐6 capacity curve framework.

Exploring the polarization of axially symmetric supernovae with unsupervised deep learning

ABSTRACT The measurement of non-zero polarization can be used to infer the presence of departures from spherical symmetry in supernovae (SNe). The origin of the majority of the intrinsic polarization observed in SNe is in electron scattering, which induces a wavelength-independent continuum polarization that is generally observed to be low ($\lesssim\!\! 1{{\ \rm per\, cent}}$) for all SN types. The key indicator of asymmetry in SNe is the polarization observed across spectral lines, in particular the characteristic ‘inverse P Cygni’ profile. The results of a suite of 900 Monte Carlo radiative transfer simulations are presented here. These simulations cover a range of possible axisymmetric structures (including unipolar, bipolar, and equatorial enhancements) for the line-forming region of the Ca ii infrared triplet. Using a variational auto-encoder, seven key latent parameters are learned that describe the relationship between Stokes I and q, under the assumption of an axially symmetric line-forming region and resonant scattering. Likelihood-free inference techniques are used to invert the Stokes I and q line profiles, in the latent space, to derive the underlying geometries. For axially symmetric structures that yield an observable ‘dominant axis’ on the Stokes q–u plane, we propose the existence of a geometry ‘conjugate’ (which is indistinguishable under a rotation of π/2). Using this machine learning infrastructure, we attempt to identify possible geometries associated with spectropolarimetric observations of the Type Ib SN 2017gax.

Highly efficient droplet generation device based on a three-dimensional fractal structure

In this paper, a three-dimensional axisymmetric fractal structure device was proposed for massive production of monodisperse droplets. Its channel number could increase to nm for an m-stage fractal device with n-channel distributors. A fractal device with 36 channels was constructed, and the droplet generation experiment was carried out. The experiment showed that the coefficient of variations (CVs) of the generated droplets were all lower than 4.0% at four different flow rates. Additionally, the relationship between the mass flow rate and fractal structure variation was examined through theoretical and data regression analysis. To elaborate the overall structure deviation, the accumulated deviation was introduced, the formula of accumulated deviation and droplet size was given. The results showed that the droplet products were highly monodisperse. The droplet size deviation was within 2% when the accumulated deviation of dispersed- and continuous-phase distributors was less than 4% and 10%, respectively.

Quantitative polarimetry for the transition disk in RX J1604.3-213010

Context. The characterization of the dust in protoplanetary disks is important for a better understanding of the resulting composition of forming planets and the dust particle evolution in these systems. Aims. We aim to accurately characterize the properties of the dust in the face-on transition disk around RX J1604.3–213010 (RX J1604) by analyzing the multiwavelength scattered light intensity and polarization images obtained with the ZIMPOL and IRDIS subinstruments of VLT/SPHERE. Methods. We used archival data of RX J1604 from the ESO archive and carefully corrected the polarization signal for instrumental effects, also taking the interstellar polarization into account. We measured the radial profiles of the disk for the azimuthal polarization, Qφ(r), in the R, J, and H bands and describe variations in our data due to the seeing and other effects. We derived the intrinsic polarization profiles of the disk, Q^φ(r), by comparing the data with rotationally symmetric models convolved with the point spread functions of the observations. We also measured the disk intensity, Idisk(r), with reference star differential imaging for the J and H bands. This provides the disk-integrated polarized intensity, Q^φ/I⋆, for the R, J, and H bands and the averaged fractional polarization, 〈p^φ〉, for the J and H bands. We investigated the azimuthal dependence of the scattered light and the shadows produced by hot dust near the star. The derived results were finally compared with model calculations to constrain the scattering properties of the reflecting dust in RX J1604. Results. RX J1604 is a dipper source, and the data show different kinds of variability. However, a detailed analysis of repeated measurements shows that the results are not affected by dipping events or atmospheric seeing variations. We derive accurate radial disk profiles for the intrinsic polarized intensity, Q^φ(r)/I⋆, and measure different profile peak radii for different bands because of the wavelength dependence of the dust opacity. The disk-integrated polarization is Q^φ/I⋆ = 0.92 ± 0.04% for the R band and 1.51 ± 0.11% for the J band, indicating a red color for the polarized reflectivity of the disk. The intensity of the disk is Idisk|I* = 3.9 ± 0.5% in the J band, and the fractional polarization is 〈p^φ〉 = 38 ± 4% for the J band and 42 ± 2% for the H band. The comparison with the IR excess for RX J1604 yields an apparent disk albedo of about ΛΙ ≈ 0.16 ± 0.08. We also find that previously described shadows seen in the R band data are likely affected by calibration errors. We derive, using dust scattering models for transition disks, approximate J band values for the scattering albedo ω ≈ 0.5, scattering asymmetry g ≈ 0.5, and scattering polarization pmax ≈ 0.7 for the dust. Conclusions. The bright disk of RX J1604 has a very simple axisymmetric structure and is therefore well suited as a benchmark object for accurate photo-polarimetric measurements. We derive values for the disk polarization, 〈p^φ〉, and the apparent disk albedo, ΛΙ, for the J band. Because 〈p^φ〉 and ΛΙ depend predominantly on dust scattering parameters and only weakly on the disk geometry, these parameters define tight relations for the dust scattering parameters between ω and pmax and between ω and g. The positive R to J band color for the polarized reflectivity, (Q^/I⋆)J ≈ 1.64 ⋅ (Q^/I⋆)R, is mainly a result of the wavelength dependence of dust parameters because the scattering geometry is expected to be very similar for different colors. This work demonstrates the potential of accurate photo-polarimetric measurements of the circumstellar disk RX J1604 for the determination of dust scattering parameters that strongly constrain the physical properties of the dust.

The role of boundary layer processes in summer-time Arctic cyclones

Abstract. Arctic cyclones are the most energetic weather systems in the Arctic, producing strong winds and precipitation that present major weather hazards. In summer, when the sea ice cover is reduced and more mobile, Arctic cyclones can have large impacts on ocean waves and sea ice. While the development of mid-latitude cyclones is known to be dependent on boundary layer (BL) turbulent fluxes, the dynamics of summer-time Arctic cyclones and their dependence on surface exchange processes have not been investigated. The purpose of this study is to characterise the BL processes acting in summer-time Arctic cyclones and understand their influence on cyclone evolution. The study focuses on two cyclone case studies, each characterised by a different structure during growth in the Arctic: (A) low-level-dominant vorticity (warm-core) structure and (B) upper-level-dominant vorticity (cold-core) structure, linked with a tropopause polar vortex. A potential vorticity (PV) framework is used to diagnose the BL processes in model runs from the ECMWF Integrated Forecasting System model. Both cyclones are associated with frictional Ekman pumping and downward sensible heat fluxes over sea ice. However, a third process, the frictional baroclinic generation of PV, acts differently in A and B due to differences in their low-level temperature structures. Positive PV is generated in Cyclone A near the bent-back warm front, like in typical mid-latitude cyclones. However, the same process produces negative PV tendencies in B, shown to be a consequence of the vertically aligned axisymmetric cold-core structure. This frictional process also acts to cool the lower troposphere, reducing the warm-core anomaly in A and amplifying the cold-core anomaly in B. Both cyclones attain a vertically aligned cold-core structure that persists for several days after maximum intensity, which is consistent with cooling from frictional Ekman pumping, frictional baroclinic PV generation, and downward sensible heat fluxes. This may help to explain the longevity of isolated cold-core Arctic cyclones with columnar vorticity structure.

Characteristics of a tip-vortex generated by a single rotor used in agricultural spraying drone

A better understanding of downwash flow is required to increase the efficiency of unmanned aerial vehicle sprayers. The tip vortex rolled up by the rotor blade tip rotating at high speed produces a complex induced velocity field, which has an important impact on the downwash flow in the wake of the rotor. Usually, a symmetrical experimental setup with a central rotor support perpendicular to the rotation plane is used in studies on rotating blade wake and vortices, potentially leading to differences in observed wake and vortices in real situations. whereas in reality, the rotor is typically supported by a parallel arm extending below the rotor in the rotation plane. It is crucial to consider these differences for accurate results in analyzing blade rotation. The behavior of the tip vortices, dynamic characteristics, and velocity field of the rotor wake in agricultural drone single-rotor downwash flow was experimentally investigated using particle image velocimetry (PIV) combined with high-speed camera imaging. The dynamics of blade tip vortices at different wake ages and rotational speeds of the rotor, 1000–3000 rpm, were measured and analyzed. The results indicate that in the early stages of a vortex's life, tip vortices generated by rotors do not have an axisymmetric structure, and the swirl velocity in the core decreases logarithmically as the wake age increases. Vortex models were validated by examining the swirl velocity structure of the tip of the vortex. Vortices within the vortex core exhibit a comparable self-similar velocity profile to the Iverson model's laminar profile, despite the transition flow outside the vortex core. With these measurements, the behavior of vortices in the rotor’s wake could be described with generalized semi-empirical models.

Diagonal and Vertical B ← N Lewis Pair Functionalized Perylenes.

Two novel multiple B ← N Lewis pair functionalized perylenes are reported. While OBN-Pery shows a centrosymmetric and planar architecture, PBN-Pery displays an axisymmetric and twist structure. B ← N functionalization in both of them results in a large decrease in the HOMO-LUMO energy gap. PBN-Pery in particular has a low LUMO energy level (-3.00 eV) and red emission at the NIR I region with high fluorescence quantum yield.

Partial flow separation in guide-vane region of large-capacity/low-head pumped hydro energy storage system with horizontal shaft

The hydraulic performance of a large-capacity/low-head pumped hydro energy storage system is usually assumed to be consistent with that of its hydraulic model system, that is, the energy parameters and the inner flow fields conform to the conventional similarity law. However, this expected hydraulic consistency may not be realized in actual engineering projects. In a prototype system with horizontal shaft, head change and vibration enhancement have been observed, but the origin of this inconsistency is still unclear. This article investigates the inner flow characteristics in the guide-vane region of a prototype system with horizontal shaft in the optimal pump mode. A new phenomenon, partial flow separation, is discovered. The most intuitive feature of partial flow separation is that large-scale separation vortices in the guide-vane region are concentrated in the top passages of the antigravity part, while the bottom passages demonstrate good through-flow capacity. This is significantly different from the axisymmetric inner flow structures in the model system. Further in-depth analysis shows that this new phenomenon directly stems from the constant circumferential imbalance of inflow attack angles, and is further attributed to the blade loading polarization in the impeller region under pronounced gravity effects. More importantly, partial flow separation can adversely affect energy performance and operation stability, including the aggravation of energy loss in the guide-vane region and severe flow deviation in the outflow passage. Particular attention should be paid in the future to the design and operation of large-capacity/low-head pumped hydro energy storage systems with horizontal shaft.

Residual stresses in austenitic thin-walled pipe girth welds: Manufacture and measurements

Determining residual stresses in thin-walled pipes is challenging. They are potentially difficult targets for simulation, because they may not behave as simple axisymmetric structures during welding. Thin-walled pipes are more sensitive to changes in the welding heat input than thick-walled pipes. They are also under-represented in the existing population of residual stress measurements used to generate upper bound residual stress profiles for structural integrity assessments. In this paper, residual stress characterisation of two thin-walled austenitic girth welded pipes is presented. The overall geometries of the two mock-up designs were the same; they differed in the linear heat input per pass and the total number of weld passes. The residual stress characterisation was carried out using two independent measurement techniques; the contour method and neutron diffraction. The multiple-cut contour strategy was implemented to measure the cross-sectional maps of hoop and axial stresses on axial-radial and hoop-radial planes respectively. The contour method results are compared with stresses measured using neutron diffraction and specific residual stress distribution signatures observed are discussed.

Jetted and Turbulent Stellar Deaths: New LVK-detectable Gravitational-wave Sources

Upcoming LIGO–Virgo–KAGRA (LVK) observing runs are expected to detect a variety of inspiralling gravitational-wave (GW) events that come from black hole and neutron star binary mergers. Detection of noninspiral GW sources is also anticipated. We report the discovery of a new class of noninspiral GW sources—the end states of massive stars—that can produce the brightest simulated stochastic GW burst signal in the LVK bands known to date, and could be detectable in LVK run A+. Some dying massive stars launch bipolar relativistic jets, which inflate a turbulent energetic bubble—cocoon—inside of the star. We simulate such a system using state-of-the-art 3D general relativistic magnetohydrodynamic simulations and show that these cocoons emit quasi-isotropic GW emission in the LVK band, ∼10–100 Hz, over a characteristic jet activity timescale ∼10–100 s. Our first-principles simulations show that jets exhibit a wobbling behavior, in which case cocoon-powered GWs might be detected already in LVK run A+, but it is more likely that these GWs will be detected by the third-generation GW detectors with an estimated rate of ∼10 events yr−1. The detection rate drops to ∼1% of that value if all jets were to feature a traditional axisymmetric structure instead of a wobble. Accompanied by electromagnetic emission from the energetic core-collapse supernova and the cocoon, we predict that collapsars are powerful multimessenger events.

A body-of-revolution discontinuous Galerkin time domain method based on curved mesh for Maxwell equations

ABSTRACT Numerical simulation of body-of-revolution (BoR) or axisymmetric structures for scattering and radiation problems has a broad spectrum of technology applications in microwave and optical engineering. In this work, we propose a high-order BoR discontinuous Galerkin time-domain method (BoR-DGTD) for solving Maxwell equations in the cylindrical coordinate system. The presented approach is based on or (m is the mode number and φ is the azimuth) expansions for different field components and thus yields a real-valued final system of equations. It saves half of the unknowns as compared to the existing method in which all the field components are assumed to have the same φ variation, i.e. . In contrast to the common practice of deriving variational formulation for the BoR Maxwell equations on two-dimensional grids in the meridian plane, we build it on three-dimensional coaxial toroidal subdomains. As a result, the singularity difficulty induced by the cylindrical coordinates is eliminated naturally. In addition, for BoR with curved material interfaces in the angular cross-section, a solution using curved grids in conjunction with the low-storage weight-adjusted approximation scheme is provided, which significantly enhances the simulation quality. Particularly, to achieve a set of optimized interpolation shape functions for the isoparametric transformation, an essential assistant in calculating the coefficient matrices, a heuristic procedure is developed to properly position the geometric control points on the curved grids. Some numerical experiments are conducted to demonstrate the accuracy and performance of our proposed BoR-DGTD method.

Critical strain method incorporating calculation of equivalent H-B strength parameters for back analysis during tunnel excavation

A comprehensive method is proposed for the continuous update of the design rockmass parameters during tunnel excavation coupled to novel calculation of the Hoek-Brown strength parameters for given Mohr-Coulomb ones. The method starts with the strength parameters of Mohr-Coulomb or Hoek-Brown criterion used at the design stage of tunnels, and then updates them by using the displacements measured during the excavation of tunnels. The update is performed based on a well established back analysis procedure that determines both cohesion C and internal friction angle φ of the Mohr-Coulomb criterion. Then, these parameters either directly update or are converted to equivalent Hoek-Brown parameters that update the original design parameters of the tunnel. The need arising for conversion of parameters during the back analysis is thus addressed: A method is developed for the evaluation of the equivalent Hoek-Brown parameters for an axisymmetric structure subjected to major principal initial stress p0 and supported by internal pressure pi. Four characteristic cases are analysed theoretically and numerically with a finite differences code and found to be in excellent agreement. The equivalent parameters solution is developed in Matlab source code under a creative commons license and greatly enables the automation of the update procedure.Based on the updated parameters, it is possible to continuously modify the original design of underground support structures, according to the results of back analysis of measured displacements. The modified strength parameters of the H-B criterion can also be used for assessing the stability of the tunnels for the next excavation stage of the tunnels.