Wind Theory Research Articles

ALMA view of the L1448-mm protostellar system on disk scales: CH3OH and H13CN as new disk wind tracers

Protostellar disks are known to accrete; however, the exact mechanism that extracts the angular momentum and drives accretion in the low-ionization “dead” region of the disk is under debate. In recent years, magnetohydrodynamic (MHD) disk winds have become a popular solution. Even so, observations of these winds require both high spatial resolution (~10 s au) and high sensitivity, which has resulted in only a handful of MHD disk wind candidates to date. In this work we present high angular resolution (~30 au) ALMA observations of the emblematic L1448-mm protostellar system and find suggestive evidence for an MHD disk wind. The disk seen in dust continuum (~0.9 mm) has a radius of ~23 au. Rotating infall signatures in H13CO+ indicate a central mass of 0.4 ± 0.1 M⊙ and a centrifugal radius similar to the dust disk radius. Above the disk, we identify rotation signatures in the outflow traced by H13CN, CH3OH, and SO lines and find a kinematical structure consistent with theoretical predictions for MHD disk winds. This is the first detection of an MHD disk wind candidate in H13CN and CH3OH. The wind launching region estimated from cold MHD wind theory extends out to the disk edge. The magnetic lever arm parameter would be λϕ ≃ 1.7, in line with recent non-ideal MHD disk models. The estimated mass-loss rate is approximately four times the protostellar accretion rate (Ṁacc ≃ 2 × 10−6M⊙ yr−1) and suggests that the rotating wind could carry enough angular momentum to drive disk accretion.

Research on general treatment principles and methods of bone fracture in Mongolian medicine

The Mongolian nomadic nation has created bone healing, or fracture healing, which is suitable for the extreme weather and territory, unique living conditions, and physical characteristics while struggling to fight diseases during a long historical period. Gradually, this treatment method has gradually developed into a more comprehensive theoretical system throughout history and has unique names due to the thinking scope of the Mongols, their cognition development, and thus their use of it in their everyday lives and continuing to enrich their knowledge. Mongols have rich experience healing bone fractures and injuries from ancient times. They are usually used to perform bone setting and massage therapy. On the other hand, they have experience using herbal and mineral medicines to heal bone fractures and injuries. During their practice, the knowledge of herbal and mineral medicines used for bone fractures and injuries became expansive. After Buddhism reemerged in the 16th century, Mongolian doctors and knowledgeable people wrote many medical books in Tibetan. One of the major representatives was Jambaldorj, who wrote Mongolian materia medica, called “The beautiful wondrous eye ornament,” based on “Four medical tantras.” In treating bone fracture and injury in traditional medicine, firstly, the four treatment methods mentioned in “Four medical tantras” are the main principles and methods, which are wind, bile and phlegm theory, dietary recommendations, advice on behavior, prescribing medicine, and accessory therapy. We concluded that the names of herbal and mineral medicines used to practice bone setting are the same, even though they are mentioned in various sources.

Analysis and Preliminary Design of Variable Flux Reluctance Machines: A Perspective from Working Field Harmonics

Variable flux reluctance machines (VFRMs) are increasingly attracting research interest due to their magnetless and robust brushless structure. Under the modulation effect of the airgap permeance, the VFRM operates with a series of field harmonics, distinguishing it from conventional AC synchronous machines. This paper deals with the analysis and preliminary design of the VFRM from the perspective of multiple working airgap field harmonics. Firstly, the spatial and temporal order of the working field harmonics are defined. The systematic winding theory, including the unified star of slots and winding factor calculation method, is established to consider all these working harmonics. Then, an average torque model is built and simplified. The key role of 1st-order rotor permeance, 1st- and 3rd-order polarized stator permeance is deduced. The relationship between key parameters and average torque is computed, providing a guideline for the preliminary design of the VFRM.

Revisiting electron-wind effect for electroplasticity: A critical interpretation

The interaction of moving electrons with dislocations during plastic deformation due to electroplasticity improves the mechanical behaviour. Despite being actively researched over the years, the governing mechanism of electroplasticity is still unclear. The complexity in understanding the controlling mechanism arises due to the involvement of multiple mechanisms and the difficulty in delineating their contributions. In the present work, one of the earliest proposed mechanisms, the electron-wind effect, is reviewed from different viewpoints, and an attempt is made to resolve the issues raised in the past literature. The criticisms levied upon the electron wind effect are specifically on the associated assumptions, rather than the effect itself. It is inferred from the present investigation that including changes in substructure and activation parameters allows the generalization of electron wind theory to accommodate a wide range of experimental observations.

Testing AGN outflow and accretion models with SDSS quasar demographics

AbstractOne commonly-invoked launching mechanism for AGN outflows is radiation line driving. This mechanism depends closely on the SED of the ionizing continuum, and so is inherently linked to the structure of the accretion flow. Theories of radiation line-driven winds therefore provide testable predictions as a function of black hole (BH) mass and accretion rate. In this work we confront these predictions using the ultraviolet emission line properties of 190,000 quasars from SDSS DR17. We quantify how the shape of CIV 1549Å and the equivalent width (EW) of HeII 1640Å depend on the BH mass and Eddington ratio inferred from MgII 2800Å. The blueshift of the CIV emission line is commonly interpreted as a tracer of quasar outflows, while the HeII EW traces the strength of the 10-100 eV continuum which photo-ionizes the ultraviolet emission line regions. Above L/LEdd > 0.2, there is a strong mass dependence in both CIV blueshift and HeII EW. Large CIV blueshifts are observed only in regions with both high BH mass and high accretion rate, consistent with predictions for radiation line driven winds. The observed trends in HeII and 2 keV X-ray strength are broadly consistent with theoretical models of AGN SEDs, where the ionizing SED depends on the accretion disc temperature and the strength of the soft excess. At L/LEdd < 0.2, we find a dramatic switch in behaviour: the ultraviolet emission properties show much weaker trends, and no longer agree with SED models, hinting at changes in the structure of the broad line region. Overall the observed emission line properties are generally consistent with the radiation line driving scenario, where quasar winds are governed by the SED, which itself results from the accretion flow and hence depends on both the SMBH mass and accretion rate.

Photoevaporation obfuscates the distinction between wind and viscous angular momentum transport in protoplanetary discs

ABSTRACT How protoplanetary discs evolve remains an unanswered question. Competing theories of viscosity and magnetohydrodynamic disc winds have been put forward as the drivers of angular momentum transport in protoplanetary discs. These two models predict distinct differences in the disc mass, radius, and accretion rates over time, that could be used to distinguish them. However that expectation is built on models that do not include another important process – photoevaporation, both internally by the host star and externally by neighbouring stars. In this work we produce numerical models of protoplanetary discs including viscosity, magnetohydrodynamic disc winds, and internal and external photoevaporation. We find that even weak levels of external photoevaporation can significantly affect the evolution of protoplanetary discs, influencing the observable features such as disc radii, that might otherwise distinguish between viscous and wind driven discs. Including internal photoevaporation further suppresses differences in evolution between viscous and wind driven discs. This makes it much more difficult than previously anticipated, to use observations of nearby star forming regions to determine whether discs are viscous or wind driven. Interestingly we find that evolved protoplanetary discs in intermediate FUV environments may be the best cases for differentiating whether they evolve through viscosity or magnetohydrodynamic disc winds. Ultimately this work demonstrates the importance of understanding what are the key evolutionary processes and including as many of those as possible when exploring the evolution of protoplanetary discs.

Simulation of Illumination and Wind Conditions for Green and Fed Cities Using CFD Software

To avoid ecological catastrophe, most cities are moving toward green building. The critical component is greening – conventional and green structures. Urban agriculture is a very prospective direction. Green roofs, terraces, and rooftop greenhouses are the most promising places for growing. This solves multiple tasks: heat loss recovery for planting (for rooftop greenhouses), additional thermal insulation, optimized logistics, increasing pollinator populations, avoiding pests, etc. In different-height districts, there are problems with natural illumination and winds. No good urban wind theory has been developed. The winds can be simulated in CFD software using a 3D model of a district. Most of the software can simulate solar radiation for thermotechnical calculations only. It should be simulated in other special software. The approach to calculating solar radiation is proposed using CFD software without additional needs. The unique "integrator" material should be added to the engineering database. Its thermotechnical properties can be set to obtain a temperature numerically equal to the exciting parameter. Application is shown in an example of a different-height building with a green roof. The results show areas most favorable for growing photophilous and shade-tolerant plants and placing cleaning and phytoncidal plants for maximum air quality in stagnation zones.

The wind of rotating B supergiants – II. The δ-slow hydrodynamic regime

ABSTRACT The theory of line-driven winds can explain many observed spectral features in early-type stars, though our understanding the winds of B supergiants remains incomplete. The hydrodynamic equations for slowly rotating stellar winds predict two regimes based on the line-force parameter δ: the fast and the δ-slow solution. In this paper, we aim to explore the capability of the latter to explain the observed properties of B supergiant winds. We calculate Hα line profiles, the most sensitive wind diagnostics in the optical, for both fast and δ-slow wind models. We fit them to observed data from a well-studied sample of B supergiants, by adapting the line-force parameters (k, α, and δ) of the hydrodynamic model. Unexpectedly, the observed Hα spectra can be reproduced by both hydrodynamic wind regimes with similar precision. We argue that this similarity results from the similar shape of the normalized velocity law produced by both regimes in the lower, Hα-forming wind region. Our findings raise a dichotomy, because mass-loss rates and terminal velocities (v∞) for each solution are quite different. The δ-slow solution predicts maximum values for v∞ that are systematically lower than those measured in the ultraviolet, whereas the v∞ values of the fast solution are closer, and probably more appropriate. However, our results also indicate that the δ-slow solution might better describe the dense winds of B hypergiants. Multiwavelength analyses and a larger sample of stars are needed to reach a definitive conclusion.

Variations in the intermediate wind region of the blue supergiant 55 Cygni

Context. The quantitative near-infrared (NIR) spectroscopic synthesis is an important technique for determining wind properties of massive stars. The Brα line is an excellent mass-loss tracer and provides valuable information on the physical conditions of intermediate-wind regions. The knowledge of the wind properties gained by studying the NIR lines could provide extra ingredients to the theory of line-driven winds, mainly because the standard theory does not predict observed properties of blue supergiants, such as high values for the β parameter (β> 2), low terminal velocities, and mass-loss variability. Aims. We seek to enhance our understanding of the wind properties of B supergiants. To this end, we propose analysing their NIR spectra over different epochs to study wind variability and its connection with phenomena arising from regions close to the photosphere. Methods. We present the first sets of multi-epoch high-resolution K- and L-band spectra of 55 Cyg acquired with the Gemini Near-InfraRed Spectrograph (GNIRS). We measured line equivalent widths and modelled the Brα line to derive (unclumped) mass-loss rates. Synthetic line profiles were computed for a homogeneous spherical wind by solving the radiative transfer equations in the co-moving frame for a multi-level atom in non-local thermodynamic equilibrium (NLTE). Results. We observe variations in the spectral lines originating in the upper photosphere and the wind. The perturbations, on average, have periods of ~13 and ~23 days; the latter is similar to that found previously from optical data (22.5 days). The NIR lines observed in 2013 are described with the same wind structure used to model a quasi-simultaneous observation in Hα. By contrast, from observations taken in 2015, we derived a higher mean mass-loss rate. Variations in the mass-loss rate are also detected within a few weeks. Interestingly, we find that the profile shape of the Hu14 line sets constraints on the mass loss. Moreover, we find the Mg II doublet in emission, which suggests a tenuous circumstellar gas ring or shell. Conclusions. The variability detected in the NIR H emission lines of 55 Cyg is related to changes in the mass-loss rate, which doubled its value between 2013 and 2015. Furthermore, the short-term variability (within three weeks) in the spectral lines and mass loss supports the hypothesis of strange-mode oscillations. This pilot project demonstrates the importance of comprehensive monitoring of blue supergiants’ variability to deeply understand the physical properties of their stellar winds and the role of pulsations in recurrently enhancing mass loss.

Dynamics of offshore wind turbine and its seabed foundation under combined wind-wave loading

Over the past two decades, a great number of offshore wind turbines (OWTs) have been built in offshore areas worldwide to harvest clean wind energy resources. The dynamic response and stability of OWTs under environmental loads, e.g., wind and wave, is a key technical problem that engineers are most concerned about. In this study, a wave-structure-foundation integrated numerical model OlaFlow–ABAQUS, which was independently developed through the secondary development, is used to study the dynamics characteristics of a thin-walled steel monopile offshore wind turbine and its seabed foundation under extreme wave and wind loads that would occur in typhoon weather. The wave-induced load imposed on the cylindrical tower of the OWT is determined by solving the VARANS (Volume Average Reynolds Average Navier-Stokes) hydrodynamic equation, the wind load on the turbine blades is estimated by applying the pulsating wind theory, and the mechanical behavior of seabed foundation soil is described by the ideal elastoplastic Mohr-Coulomb model. The computational results show that the OWT and its seabed foundation have a strong dynamic response under the combined action of extreme wind and wave, and there is intensive interaction between them. There is a transient liquefaction zone in the seabed foundation, and the maximum liquefaction depth, in this case, is approximately 2 m. Residual horizontal displacement with a magnitude of approximately 0.4 m occurs at the top of the cylindrical tower of the OWT, resulting in the overall tilting of the OWT. The maximum inclination angle of the cylindrical tower is approximately 0.51°. This angle of inclination may cause significant bending moment and stress concentration in some mechanical components such as the drive shafts and gearboxes that connect to the turbine blades. It reduces the service life of the OWT significantly and also is detrimental to the long-term service performance of the OWT.

Variations in global zonal wind from 18 to 100 km due to solar activity and the quasi-biennial oscillation and El Niño–Southern Oscillation during 2002–2019

Abstract. Variations of global wind are important in changing the atmospheric structure and circulation, in coupling of atmospheric layers, and in influencing the wave propagations. Due to the difficulty of directly measuring zonal wind from the stratosphere to the lower thermosphere, we derived a global balance wind (BU) dataset from 50∘ S to 50∘ N and during 2002–2019 using the gradient wind theory and SABER temperatures and modified by meteor radar observations at the Equator. The dataset captures the main feature of global monthly mean zonal wind and can be used to study the variations (i.e., annual, semi-annual, ter-annual, and linear) of zonal wind and the responses of zonal wind to quasi-biennial oscillation (QBO), El Niño–Southern Oscillation (ENSO), and solar activity (F10.7). The same procedure is performed on the MERRA-2 zonal wind (MerU) to validate BU and its responses below 70 km. The annual, semi-annual, and ter-annual oscillations of BU and MerU have similar amplitudes and phases. The semi-annual oscillation of BU has peaks around 80 km, which are stronger in the southern tropical region and coincide with previous satellite observations. As the increasing of the values representing QBO wind, both values of representing BU and MerU (short for BU and MerU) change from increasing to decreasing with the increasing height and extend from the Equator to higher latitudes. Both BU and MerU increase with the increasing of the values of multivariate ENSO index (MEI) and decrease with increasing F10.7​​​​​​​ in the southern stratospheric polar jet region below 70 km. The responses of winds to ENSO and F10.7 exhibit hemispheric asymmetry and are more significant in the southern polar jet region. While above 70 km, BU increases with the increasing of MEI and F10.7. The negative linear changes of BU at 50∘ N are absent in MerU during October–January. The discussions on the possible influences of the temporal intervals and sudden stratospheric warmings (SSWs) on the variations and responses of BU illustrate the following: (1) the seasonal variations and the responses to QBO are almost independent on the temporal intervals selected; (2) the responses to ENSO and F10.7 are robust but slightly depend on the temporal intervals; (3) the linear changes of both BU and MerU depend strongly on the temporal intervals; (4) SSWs affect the magnitudes but do not affect the hemispheric asymmetry of the variations and responses of BU at least in the monthly mean sense. The variations and responses of global zonal wind to various factors are based on BU, which is derived from observations, and thus provide a good complement to model studies and ground-based observations.

Extreme broad He ii emission at high and low redshifts: the dominant role of VMS in NGC 3125-A1 and CDFS131717

ABSTRACT Super star cluster (SSC) A1 ($3.1\times 10^5\, \mathrm{M}_\odot$) in NGC 3125 has one of the strongest ($EW=4.6\pm 0.5\,$ Å) broad ($FWHM=1131\pm 40\,$ km s−1) He ii λ1640 emission lines in the nearby universe and constitutes an important template for interpreting observations of extreme He ii emitters out to redshifts of z ∼ 2 – 3. We use Cosmic Origins Spectrograph (COS) observations of A1 to show that there is no significant contamination of the He ii line with nebular emission and that the line is redshifted by 121 ± 17 km s−1 relative to ISM lines. We compare the COS G130M + G160M observations of A1 to recent binary BPASS and single-star Charlot & Bruzual (C&B) simple stellar population (SSP) models with very massive stars (VMS) of up to $300\, \mathrm{M}_\odot$. On the other hand, we suggest why BPASS models fail to reproduce A1’s He ii emission. On the other hand, a C&B model with Z = 0.008, age = 2.2 Myr, and VMS approaching the Eddington limit provides an excellent fit to the He ii emission and fits reasonably well C iii λ1175, N v λλ1238, 1241, and C iv λλ1548, 1551. We present O v λ1371 line-profile predictions showing that this line constitutes an important tracer of youth and VMS in galaxies. Finally, we discuss the presence of VMS in CDFS131717, a highly star-forming low-metallicity galaxy located at z = 3.071, which has a tentative detection of O v absorption and strong broad He ii emission. These features are rare and hint to the presence of short-lived VMS in the galaxy. Our results show the effect of the latest developments of stellar wind theory and the importance of accounting for VMS in models.

Homogenization of Observed Surface Wind Speed Based on Geostrophic Wind Theory over China from 1970 to 2017

Abstract The observed surface wind speed (SWS) over China has declined in the past four decades, and recently, the trend has reversed, which is known as SWS stilling and recovery. The observed SWS is vulnerable to changes in nonclimatic factors, i.e., inhomogeneity. Unfortunately, most of the existing studies on the long-term trend of SWS were based on raw datasets without homogenization. In this study, by means of geostrophic wind speed and penalized maximal t test, we conduct a systematic homogeneity test and exploration of the homogenization impact for SWS at over 2000 stations in China from 1970 to 2017. The results show that the inhomogeneity in the observed SWS over China is detectable at 59% of national weather stations. The breakpoint years are mainly concentrated in the late 1970s, mid-1990s, and early 2000s. Overall, 18% of breakpoints are caused by station relocations, and the remaining breakpoints are likely related to anemometer replacement and measurement environment changes that occurred during the mid-1990s and early 2000s. After homogenization, the decreasing trend in SWS during 1970–2017 decreased from −0.15 to −0.05 m s−1 decade−1. The homogenized SWS recovery period advanced from the early twenty-first century to the early 1990s, which is consistent with the SWS variations, excluding the impact of urbanization around weather stations. The phase change in the Western Hemisphere warm pool (WHWP) might be one of the causes of homogenized SWS recovery.

Introducing ω and O′ nanodomains in Ti-6Al-4V: The mechanism of accelerating α → β transformation kinetics via electropulsing

Conventional kinetics theory for diffusion-controlled phase transformation shows that the reverse transition should lag behind the temperature rise through rapid heating, i.e., overheating is required. In this work, we found that the β-transus temperature decreased by ∼50 °C during studying the α → β transformation in Ti-6Al-4V alloy via electropulsing treatment (EPT). The calculation suggests that the acceleration of transformation kinetics cannot be fully explained by Joule heat and athermal effects of the electromigration effect and electron wind theory. The microstructural evolution during EPT was systematically investigated utilizing scanning electron microscope (SEM), electron backscattered diffraction (EBSD), X-ray diffraction (XRD), transmission Kikuchi diffraction (TKD), and transmission electron microscope (TEM). Microscopic analysis shows that the nano-sized ω and O′ phases formed in the β phase, which causes large numbers of lattice distortion regions. The defects are conducive to accelerating the bulk diffusion of alloying elements in β. Moreover, the nanodomains limited the growth of martensite, therefore nanocrystalline martensite formed after quenching. These findings develop the understanding of the destructive effect of current on metallic crystal, which will help to guide microstructural regulation in titanium and other alloys.

Radiation-Driven Wind Hydrodynamics of Massive Stars: A Review

Mass loss from massive stars plays a determining role in their evolution through the upper Hertzsprung–Russell diagram. The hydrodynamic theory that describes their steady-state winds is the line-driven wind theory (m-CAK). From this theory, the mass loss rate and the velocity profile of the wind can be derived, and estimating these properly will have a profound impact on quantitative spectroscopy analyses from the spectra of these objects. Currently, the so-called β law, which is an approximation for the fast solution, is widely used instead of m-CAK hydrodynamics, and when the derived value is β≳1.2, there is no hydrodynamic justification for these values. This review focuses on (1) a detailed topological analysis of the equation of motion (EoM), (2) solving the EoM numerically for all three different (fast and two slow) wind solutions, (3) deriving analytical approximations for the velocity profile via the LambertW function and (4) presenting a discussion of the applicability of the slow solutions.

Mantle-driven north–south dichotomy in geomagnetic polar minima

The geomagnetic field on the core-mantle boundary (CMB) is characterized by weak or even reversed field in the polar regions and intense flux patches at the edges of the intersection of the inner-core tangent cylinder (TC) with the CMB. This high-latitude field morphology is in agreement with thermal wind theory inside the TC in which polar upwellings disperse magnetic field lines. Furthermore, inferences from the geomagnetic secular variation hint to the presence of a westward jet at high latitudes of the northern hemisphere, also in agreement with the TC dynamical theory, but not in the southern hemisphere. Here we study polar minima in an ensemble of geomagnetic field models that span the historical era and in a set of numerical dynamo simulations with a heterogeneous outer boundary heat flux inferred from a tomographic model of lowermost mantle seismic anomalies. We quantified the polar minima using a previously-proposed expression as well as a new measure which may better capture this phenomenon. We found that throughout the historical era the geomagnetic field is characterized by stronger polar minima and more reversed flux inside the northern TC than inside the southern TC. Likewise, almost all dynamo models exhibit on average stronger polar minima in the northern hemisphere. This north/south dichotomy is explained in terms of the pattern of lowermost mantle seismic anomalies, in particular the southern centers of the two Large Low Shear-wave Velocity Provinces below Africa and the Pacific. We also investigated polar minima in planets where magnetic field models at the top of the dynamo region are available. We speculate that the absence of polar minima in Mercury’s field is likely due to the thick stratified layer at the top of its core, while the strong polar minima in Jupiter’s field might have a different dynamical origin than the geomagnetic polar minima.

Discovery of a New Molecular Bubble–Outflow Structure in the Taurus B18 Cloud

Star formation can produce bubbles and outflows, as a result of stellar feedback. Outflows and bubbles inject momentum and energy into the surrounding interstellar medium, and so are related to the overall energy balance of the molecular cloud. Molecular bubbles can be resolved by higher-resolution radio telescopes to quantify the effect of star formation on molecular clouds. We report here the identification of a new molecular bubble with an outflow, and a Herbig–Haro object, HH 319, located at the bubble center. Multiwavelength data have been utilized to study its spatial structure, energy injection, and dynamical timescale. This bubble has a kinetic energy of 5.8 × 1043 erg within the smallest radius of a bubble in Taurus, 0.077 pc. The bubble formed ∼70,000 yr ago. According to the proper-motion velocities of protostars from Gaia EDR3, the T Tauri binary stars (FY Tau and FZ Tau) at the southwest edge of the bubble may have produced the outflow–bubble structure. This is an unusual new structure found in low- and intermediate-mass star formation regions. Only a bubble in Orion A, driven by V380 Ori, has a similar structure. The bubble–outflow structure provides additional observational evidence for the theory of stellar wind from T Tauri stars. It enhances our understanding of how stellar feedback acts on molecular clouds.

A Novel Three-Layer Symmetry Winding Configuration for Five-Phase Motor

This paper presents a new three-layer, five-phase winding configuration theory of unconventional slot-pole combinations by each layer of winding for a phase vector correction, three layers of winding superimposed together to achieve the results of three-phase symmetry. Since the single-layer unconventional winding has to have an empty slot to meet its symmetry, based on the characteristics of single-layer winding, the unconventional winding design is carried out. Based on the simulation comparison between the single-layer unconventional winding and double-layer unconventional winding, a three-layer, nine-phase unconventional winding is proposed, which is based on the theory of single-layer unconventional winding, and three layers are staggered and stacked to realize nine-phase winding, which not only increases the utilization rate of the winding slot but also improves the fault tolerance performance. In addition, a 105-slot, 20-pole, three-layer, five-phase motor is proposed for a winding configuration and performance analysis to achieve both low torque pulsation and high fault tolerance.

Dynamical gravastars

We combine the ideas of a Weyl scaling invariant dark energy action, which eliminates black hole horizons, with the ``gravastar'' idea of a jump in the hole interior from a normal matter equation of state to an equation of state where pressure plus density approximately sum to zero. Using the Tolman-Oppenheimer-Volkoff equation, which requires continuous pressure, we present Mathematica notebooks in which the structure of the gravastar is entirely governed by the action and the equation of state, with the radii where structural changes occur emerging from the dynamics, rather than being specified in advance. The notebooks work even with zero cosmological constant, but when the cosmological constant is nonzero, there is a very small black hole ``wind'' that we calculate by a relativistic extension of standard pressure driven isothermal stellar wind theory.

Dynamics of offshore wind turbine-seabed foundation under hydrodynamic and aerodynamic loads: A coupled numerical way

The offshore wind power industry has significantly contributed to the production of green energy in China and Europe etc. and made significant contributions to the reduction of carbon emissions. However, the extreme wave and wind loads in typhoon weather bring a great threat to the stability of offshore wind turbines (OWT). It is crucial to understand the dynamic characteristics of OWT and develop reliable methods of stability evaluation to guarantee the stability of OWT. In this study, taking the software FssiCAS as the computational platform, and taking the open-source solver OlaFlow to determine the wave impact on OWT and its seabed foundation, as well as the fluctuating wind theory is applied to estimate the wind load on the turbine blades and tower cylinder, the dynamic characteristics and stability of a monopile OWT with a capacity of 1500 kW in typhoon weather are investigated adopting a coupled way for the first time worldwide. The influence of the complex geometric shape and mass distribution of OWT is considered, and the generalized elastoplastic constitutive model, Pastor-Zienkiewicz-Mark III, is used to describe the complex dynamic behavior of the seabed foundation. The computational results show that the seabed soil within 4–5 m below the seafloor surface becomes liquefied under extreme wind and wave loads, resulting in the horizontal bearing capacity of the seabed foundation being weakened. As a result, the tower cylinder of OWT tilts aside by 0.5°, which exceeds the limit specified in some design codes. Through comparative analysis, it is found that the wind load contributes up to 50% to the lateral displacement of the OWT, and the maximum bending moment in the tower cylinder. It is indicated that wind loads can significantly affect the stability of OWTs. Additionally, this study proves that the software FssiCAS is applicable to evaluate the dynamics and the stability of OWTs under a complex marine dynamic environment. FssiCAS could hopefully become a computational platform for the design of OWTs.