Journal articles on the topic 'Circular caustic'

The shadow optical method of caustics has been applied to the measurement of the bulging out of the surface of aluminum alloy 7075-T6 in the vicinity of a blunt notch in a single edge notch tensile sample after a compression overload and during compression fatigue. The size and shape of the caustic were found to be sensitive functions of the amount of elastic and plastic strain in the vicinity of the notch. Examination of the caustic during application and after release of the overload shows the elastic zone to be larger and more circular than the plastic zone, as predicted. A crack was propagated through the plastic zone using only far-field cyclic compression loading: the crack was self-arresting at the edge of the elasticplastic boundary created by the initial compression overload. The size of the plastic zone as measured by the caustic was found to agree with the maximum length of the crack. The actual surface profile in the vicinity of the notch was measured and its shape was used along with geometrical arguments to develop a model for interpretation of the caustics results. These results indicate that the caustics technique can be used to detect the presence of a plastic zone at the tip of a notch after a compressive overload, and that the size of this zone as measured by caustics is approximately equal to the size as determined by subsequent fatigue crack propagation.

We consider the amplification factor for the luminosity of an extended source near the fold caustic of the gravitational lens. It is assumed that the source has elliptical shape, and the brightness distribution along the radial directions is Gaussian. During the microlensing event the total brightness of all microimages is observed, which changes when the source moves relative to the caustic. The main contribution to the variable component is given by the so-called critical images that arise/disappear at the intersection of the caustic by the source. In the present paper we obtained an analogous formula for elliptical Gaussian source. The formula involves a dependence on the coordinates of the source centre, its geometric dimensions, and its orientation relative to the caustic. We show that in the linear caustic approximation the amplification of the circular and elliptical sources is described by the same (rescaled) formula. However, in the next approximations the differences are significant. We compare analytical calculations of the amplification curves for different orientations of an elliptical source and for a circular source with the same luminosity for the model example.

The high frequency field expressions are analyzed for perfect electromagnetic conducting (PEMC) elliptical reflector embedded in isotropic, homogeneous and reciprocal chiral medium. Geometric optics (GO) method is used to find the caustic region field for the PEMC elliptical reflector. However, GO fields are not valid around the caustic region due to the occurrence of un-realistic singularity around the caustic region. Therefore, Maslov’s method is used to derive the high frequency fields which are also valid in the vicinity of the caustic region. The effect of admittanceM of the PEMC boundary and the chirality parameter kβ on the high frequency fields are illustrated by plotting the numerical results using MATLAB software. A special case of PEMC circular reflector is also discussed.

Acutes corrosive poisonings can cause serious chemical injuries of the upper gastrointestinal tract, and they are localized most frequently in the esophagus and the stomach because the poison remains there a long time. Treatment of the acute corrosive intoxications include: neutralization of corrosive agents, antibiotics, corticosteroids, anti-secretory therapy, nutritional support, collagen synthesis inhibitors, esophageal dilation and stent placement, and surgery.The damaged mucosa, submucosa and muscle layer regenerate with great difficulty because of the surrounding inflammation, necrosis and secondary complications. Tissue fibrosis, adhesions or circular stenosis appear, which greatly disturb the normal functioning (impeded peristaltic, impeded passage). All these complicate the entire general condition of the patient, including inadequate normal food intake, loss of body weight, prostration, cachexia. These patients are also into a severe general condition due to hypercatabolic state and negative alkali balance. Therefore, early nutritional support is of substantial importance in treatment of these patients. Nutritional support can be given by parenteral way in peripheral or central vein and by enteral way through specially designed tubes inserted in the stomach or intestines, prepyloric or postpyloric.The type of artificial nutritional support will depend on the grade of esophageal or gastric damage determined by endoscopy.

We consider the radiation of internal gravity waves from a spherical body oscillating vertically in a stratified incompressible fluid. A near-field solution (under the Boussinesq approximation) is obtained by separation of variables in an elliptic problem, followed by analytic continuation to the frequencies ω < N of internal wave radiation. Matched expansions are used to relate this solution to a far-field solution in which non-Boussinesq terms are retained. In the outer near field there are parallel conical wavefronts between characteristic cones tangent to the body, but with a wavelength found to be shorter than that for oscillations of a circular cylinder. It is also found that there are caustic pressure singularities above and below the body where the characteristics intersect. Far from the source, non-Boussinesq effects cause a diffraction of energy out of the cones. The far-field wave-fronts are hyperboloidal, with horizontal axes. The case of horizontal oscillations of the sphere is also examined and is shown to give rise to the same basic wave structure.The related problem of a pulsating sphere is then considered, and it is concluded that certain features of the wave pattern, including the caustic singularities near the source, are common to a more general class of oscillating sources.

The three-dimensional pattern of the hyperbolic umbilic diffraction catastrophe is computed from an integral representation. A detailed description is given of the geometrical arrangement of the wave dislocation lines (optical vortices) on which the diffraction pattern is based. From a crossed grid of nodal lines in the focal plane, two bundles of dislocation lines spring out symmetrically into the regions of 4-wave interference. Each dislocation line then follows a chain of curved segments which approximate successive steps along lattice vectors in the space group Fmmm . The result is a bundle of helices of non-circular cross-section that gradually straighten out until, far from the focal plane, they become the dislocations of the Pearcey diffraction pattern for the cusp catastrophe. A new phenomenon is the multiple puncturing of the caustic surface by a series of helical dislocations.

ABSTRACT We present a systematic analysis of the constraints σγ on the mass profile slope γ obtainable when fitting a singular power-law ellipsoid model to a typical strong lensing observation of an extended source. These results extend our previous analysis of circular systems, Paper I. We draw our results from 676 mock observations covering a range of image configurations, each created with a fixed signal to noise ratio S = 100 in the images. We analyse the results using a combination of theory and a simplified model which identifies the contribution to the constraints of the individual fluxes and positions in each of the lensed images. The main results are: 1. For any lens ellipticity, the constraints σγ for two image systems are well described by the results of Paper I, transformed to elliptical coordinates; 2. We derive an analytical expression for σγ for systems with the source aligned with the axis of the lens; 3. For both two-image systems and aligned systems, σγ is limited by the flux uncertainties; 4. The constraints for off-axis four-image systems are a factor of two to eight better, depending on source size, than for two-image systems, and improve with increasing lens ellipticity. We show that the constraints on γ in these systems derive from the complementary positional information of the images alone, without using flux. The complementarity improves as the offset of the source from the axis increases, such that the best constraints σγ &lt; 0.01, for S = 100, occur when the source approaches the caustic.

Aims. We aim at analytically modelling the solar wind proton trajectories during their interaction with a partially ionised cometary atmosphere, not in terms of bulk properties of the flow but in terms of single particle dynamics. Methods. We first derive a generalised gyromotion, in which the electric field is reduced to its motional component. Steady-state is assumed, and simplified models of the cometary density and of the electron fluid are used to express the force experienced by individual solar wind protons during the interaction. Results. A three-dimensional (3D) analytical expression of the gyration of two interacting plasma beams is obtained. Applying it to a comet case, the force on protons is always perpendicular to their velocity and has an amplitude proportional to 1/r2. The solar wind deflection is obtained at any point in space. The resulting picture presents a caustic of intersecting trajectories, and a circular region is found that is completely free of particles. The particles do not lose any kinetic energy and this absence of deceleration, together with the solar wind deflection pattern and the presence of a solar wind ion cavity, is in good agreement with the general results of the Rosetta mission. Conclusions. The qualitative match between the model and the in situ data highlights how dominant the motional electric field is throughout most of the interaction region for the solar wind proton dynamics. The model provides a simple general kinetic description of how momentum is transferred between these two collisionless plasmas. It also shows the potential of this semi-analytical model for a systematic quantitative comparison to the data.

Aims. Observations of solar protons near comet 67P/Churyumov–Gerasimenko (67P) by the Rosetta spacecraft can be modelled by the planar motion in an effective magnetic field proportional to 1/r2. We aim to provide a thorough study of such dynamics, with a clear description of the behaviour of an incoming flux of particles. We will be able, then, to calibrate the free parameters of the model to Rosetta observations. Methods. Basic tools of dynamical analysis are used. They lead to a definition of the relevant parameters for the system and a classification of the possible types of trajectories. Using the so-obtained formalism, the structures formed by a flux of particles coming from infinity can be studied. Results. All the trajectories are parametrised by two characteristic radii, rE and rC, derived from first integrals. There are three different types of motion possible divided by a separatrix corresponding to rE = rC. An analytical expression of the trajectories, defined by an integral, is developed. Using this formalism, the application to a flux of particles coming from infinity (modelling the incident solar wind) gives one free parameter only, the radius rE, which scales the problem. A circular cavity of radius 0.28 rE is created, as well as an overdensity curve (analogous to a caustic in optics). At each observation time, rE can be calibrated to Rosetta plasma measurements, giving a qualitative understanding of the solar particle dynamics (incoming direction, cavity and density map). We also deduce that, in order to properly capture the essence of the dynamics, numerical simulations of the solar wind around a comet must use simulation boxes much larger than rE and grids much finer than rE.

This paper determines the ray structure of a spinning acoustic mode propagating inside a semi-infinite circular cylindrical duct, and thereby determines the ray structure of the field radiated from the end of the duct. Inside the duct, but outside of a caustic cylindrical surface, the rays are piecewise linear helices; on striking the rim of the end-face of the duct, these rays produce ‘Keller cones’ of diffracted rays. The cones determine the structure of the radiated field: for example, no rays penetrate two cone-shaped far-field quiet zones centred on the duct axis; two rays pass through each point in a forward loud zone; and one ray passes through each point in a rearward loud zone. The two rays through each point in the forward loud zone interfere to produce an oscillatory directivity pattern. One quarter of the rays on each cone point back inside the duct and produce the reflected field. Thus the rim of the end-face of the duct acts as a ‘ring source’, in which the radiated and reflected fields have their origin. Every propagating duct mode determines a polar angle and an azimuthal angle; these are taken as parameters specifying the mode and are used to calculate the positions and angles of all the rays. The mathematical method on which the paper is based is Debye's approximation for the Bessel function which appears in the expression for the duct modes; the approximation shows also that the duct contains a region of smooth helical rays on which the field consists of inhomogeneous waves: this region is the inner cylinder, lying inside the annulus of piecewise linear helical rays. The results of the paper are very promising for the application of Keller's geometrical theory of diffraction to detailed calculations of the sound radiated from aeroengine ducts. An alternative description of the field, using Cargill's meridional rays, is summarized.

Using the caustics method and the experimental system of digital laser dynamic caustics, the model experiment of drop hammer impact loading was carried out, and the effect of the defect shape (circular and rectangular) and the filling material (air, epoxy, and silicone rubber) on the propagation behavior of the running crack was investigated. The experimental results show that, under the impact loading, the running crack initiates at the end of precrack and propagates toward the defect. After the running crack connects to the defect, it accumulates energy within a certain period before initiating again at the upper edge of the defect. Subsequently, only one running crack is formed at the upper edge of the circular defect, but two running cracks are formed at the upper edge of the rectangular defect. The defect shape and the filling material have a significant effect not only on the energy accumulation time of the running crack at the defect but also on the stress intensity factor when initiating at the defect. The effect degree of the defect shape on the running crack propagation behavior is in the following order: circular defect > rectangular defect, whereas the effect degree of the filling material on the running crack propagation behavior follows this order: air > silicone rubber > epoxy.

John Nye was an internationally renowned physicist who made fundamental contributions to the understanding of crystals, ice and light. He explored defects in crystal structures, in particular continuous distributions of dislocations. He explained the mechanics of the flow of glaciers: their advance and retreat, and how this depends on the underlying topography; and how water flows beneath and within them. He was a pioneer in the study of optical singularities on three levels: stable caustics in geometrical optics; phase singularities (wavefront dislocations) in scalar waves; and lines of circular and linear polarization in electromagnetic fields.

A complexidade do processo saúde-doença tem ensejado a proposição de uma diversidade de modelos explicativos. Fazemos uma breve revisão dessas propostas, confrontando três perspectivas: o modelo oriundo da Medicina do século XIX, a lógica da História Natural da Doença e o debate epidemiológico no contexto da Medicina Social latino-americana. Tomando-se como referência teórica a ideia de causalidade circular presente na teoria da auto-organização, propomos que os fatores causais privilegiados em cada um dos modelos explicativos acima não seriam conflitantes. Uma noção-chave para se pensar o processo de autoorganização biopsicossocial é o "efeito baldwiniano", que descreve uma relação dialética ou coevolutiva entre processos naturais e socioculturais.

This short communication presents a study of the use of an annular X-ray beam produced by an ellipsoidal single-bounce monocapillary (ESBC) to perform focal construct geometry (FCG) high-intensity angular-dispersive X-ray diffraction (ADXRD) in transmission mode. The ESBC optic effectively focused a large focal spot X-ray source into a smaller focal spot and produced a narrowed X-ray ring in the far-field pattern when combined with a beam stop. A CCD imaging detector was linearly translated along the principal axis of the ESBC-FCG and obtained the corresponding sequential images of diffraction concentric circular caustics and convergence points, which were formed by the constructive interference of a continuous set of Debye cones arising from the annular interrogation volume. Pixels from the central region of an approximately 0.6 mm2 area were interrogated on each sequential image; as a result, a one-dimensional diffractogram of an aluminium oxide sample was revealed. The presented ESBC-FCG ADXRD technique shows potential for increasing the diffracted intensity and streamlining the operation of crystallographic analysis.

The Orbital Angular Momentum (OAM) carried by light beams with helical phasefront (vortex beams) has been widely employed in many applications such as optical tweezers, optical drives of micro-machines, atom trapping, and optical communication. OAM provides an additional dimension (diversity) to multiplexing techniques, which can be utilized in addition to conventional multiplexing methods to achieve higher data rates in wireless communication. OAM beams have been thoroughly studied and used in the optical regime but in the mm-wave and THz-wave region, they are still under investigation. In these frequency bands, there are difficulties associated with beam-splitting and beam-combining processes as well as with the use of spiral phase plates and other methods for OAM generation, since the wavelength is much larger compared to those at optical frequencies, leading to higher diffraction losses. The present paper describes the natural generation of high-power OAM modes by gyro-type vacuum electron devices with cylindrical interaction circuit and axial output of the generated rotating higher-order transverse electric mode TEm,n, where m > 1 and n are the azimuthal and radial mode index, respectively. The ratio between the total angular momentum (TAM) JN and total energy WN of N photons is given by m/ω, where ω is the angular frequency of the operating mode, which in a gyrotron oscillator is close to the TEm,n-mode cutoff frequency in the cavity. Therefore, m/ω = Rc/c, where Rc is the caustic radius and c the velocity of light in vacuum. This means that the OAM is proportional to the caustic radius and at a given frequency the same for all modes with the same azimuthal index m. Right-hand rotation (co-rotation with the electrons) corresponds to a positive value of m and left-hand rotation to negative m. The corresponding OAM mode number (topological charge) is l = m – 1. Circularly polarized TE1n modes only possess a Spin Angular Momentum (SAM: s = ±1). TE0n modes have neither SAM nor OAM. This is the result of the photonic (quasi-optical) approach to derive the TAM of modes generated in gyrotrons. The same result follows from the electromagnetic (EM) wave approach for the TAM within a given waveguide volume per total energy of the EM wave in the same volume. Such high-power output beams with very pure higher-order OAM, generated by gyrotron oscillators or amplifiers (broadband) could be used for multiplexing in long-range wireless communications. The corresponding mode and helical wavefront sensitive detectors for selective OAM-mode sorting are available and described in the present paper.

A abordagem sistêmica surgiu, essencialmente, a partir da dificuldade em utilizar a abordagem analítica para explicar fenômenos complexos que eram influenciados pelo contexto e pelas inter-relações. Os sistemas complexos são caracterizados por situações dinâmicas nas quais os problemas mudam ao interagir com outros problemas. Representam uma situação problemática para a qual é difícil formular as causas e consequências, uma vez que apresentam características de interdependência e multi-causalidades contínuas, circulares. Certos aspectos, vistos como causas, viram efeitos e vice-versa. Os sintomas são confundidos com o problema e as soluções produzem consequências inesperadas. Essas características se aplicam à problemática da estiagem e da gestão de recursos hídricos. O artigo, assim, objetiva apresentar os primeiros esboços conceituais de uma análise sistêmica do problema da estiagem em Santa Catarina. Foram utilizados os dados coletados durante a pesquisa intitulada “Estiagem no Oeste Catarinense: Diagnóstico e Resiliência” como a base para este estudo sistêmico preliminar. Especificamente, são apresentados três exemplos de arquétipos, ou seja, “histórias clássicas dos sistemas” aplicados ao entendimento de uma situação e à identificação dos ciclos de reforço e equilíbrio no contexto de pesquisa; dois esboços de diagramas causais gerais e um diagrama de ciclo causal consolidado que representa o resultado inicial da análise. O estudo teve o desafio de atender aos limites inerentes às teorias sistêmicas, ao mesmo tempo em que foi limitado em seu acesso às informações. Como um sistema de aprendizado, cada análise traz novas informações e possibilita diferente interpretações dos problemas e soluções da estiagem.

Introduction: Bubbles and Sport The ephemeral materiality of bubbles – beautiful, spectacular, and distracting but ultimately fragile – when applied to protect or conserve in the interests of sport-media profit, creates conditions that exacerbate existing inequalities in sport and society. Bubbles are usually something to watch, admire, and chase after in their brief yet shiny lives. There is supposed to be, technically, nothing inside them other than one or more gasses, and yet we constantly refer to people and objects being inside bubbles. The metaphor of the bubble has been used to describe the life of celebrities, politicians in purpose-built capital cities like Canberra, and even leftist, environmentally activist urban dwellers. The metaphorical and material qualities of bubbles are aligned—they cannot be easily captured and are liable to change at any time. In this article we address the metaphorical sporting bubble, which is often evoked in describing life in professional sport. This is a vernacular term used to capture and condemn the conditions of life of elite sportspeople (usually men), most commonly after there has been a sport-related scandal, especially of a sexual nature (Rowe). It is frequently paired with connotatively loaded adjectives like pampered and indulged. The sporting bubble is rarely interrogated in academic literature, the concept largely being left to the media and moral entrepreneurs. It is represented as involving a highly privileged but also pressurised life for those who live inside it. A sporting bubble is a world constructed for its most prized inhabitants that enables them to be protected from insurgents and to set the terms of their encounters with others, especially sport fans and disciplinary agents of the state. The Covid-19 pandemic both reinforced and reconfigured the operational concept of the bubble, re-arranging tensions between safety (protecting athletes) and fragility (short careers, risks of injury, etc.) for those within, while safeguarding those without from bubble contagion. Privilege and Precarity Bubble-induced social isolation, critics argue, encourages a loss of perspective among those under its protection, an entitled disconnection from the usual rules and responsibilities of everyday life. For this reason, the denizens of the sporting bubble are seen as being at risk to themselves and, more troublingly, to those allowed temporarily to penetrate it, especially young women who are first exploited by and then ejected from it (Benedict). There are many well-documented cases of professional male athletes “behaving badly” and trying to rely on institutional status and various versions of the sporting bubble for shelter (Flood and Dyson; Reel and Crouch; Wade). In the age of mobile and social media, it is increasingly difficult to keep misbehaviour in-house, resulting in a slew of media stories about, for example, drunkenness and sexual misconduct, such as when then-Sydney Roosters co-captain Mitchell Pearce was suspended and fined in 2016 after being filmed trying to force an unwanted kiss on a woman and then simulating a lewd act with her dog while drunk. There is contestation between those who condemn such behaviour as aberrant and those who regard it as the conventional expression of youthful masculinity as part of the familiar “boys will be boys” dictum. The latter naturalise an inequitable gender order, frequently treating sportsmen as victims of predatory women, and ignoring asymmetries of power between men and women, especially in homosocial environments (Toffoletti). For those in the sporting bubble (predominantly elite sportsmen and highly paid executives, also mostly men, with an array of service staff of both sexes moving in and out of it), life is reflected for those being protected via an array of screens (small screens in homes and indoor places of entertainment, and even smaller screens on theirs and others’ phones, as well as huge screens at sport events). These male sport stars are paid handsomely to use their skill and strength to perform for the sporting codes, their every facial expression and bodily action watched by the media and relayed to audiences. This is often a precarious existence, the usually brief career of an athlete worker being dependent on health, luck, age, successful competition with rivals, networks, and club and coach preferences. There is a large, aspirational reserve army of athletes vying to play at the elite level, despite risks of injury and invasive, life-changing medical interventions. Responsibility for avoiding performance and image enhancing drugs (PIEDs) also weighs heavily on their shoulders (Connor). Professional sportspeople, in their more reflective moments, know that their time in the limelight will soon be up, meaning that getting a ticket to the sporting bubble, even for a short time, can make all the difference to their post-sport lives and those of their families. The most vulnerable of the small minority of participants in sport who make a good, short-term living from it are those for whom, in the absence of quality education and prior social status, it is their sole likely means of upward social mobility (Spaaij). Elite sport performers are surrounded by minders, doctors, fitness instructors, therapists, coaches, advisors and other service personnel, all supporting athletes to stay focussed on and maximise performance quality to satisfy co-present crowds, broadcasters, sponsors, sports bodies and mass media audiences. The shield offered by the sporting bubble supports the teleological win-at-all-costs mentality of professional sport. The stakes are high, with athlete and executive salaries, sponsorships and broadcasting deals entangled in a complex web of investments in keeping the “talent” pivotal to the “attention economy” (Davenport and Beck)—the players that provide the content for sale—in top form. Yet, the bubble cannot be entirely secured and poor behaviour or performance can have devastating effects, including permanent injury or disability, mental illness and loss of reputation (Rowe, “Scandals and Sport”). Given this fragile materiality of the sporting bubble, it is striking that, in response to the sudden shutdown following the economic and health crisis caused by the 2020 global pandemic, the leaders of professional sport decided to create more of them and seek to seal the metaphorical and material space with unprecedented efficiency. The outcome was a multi-sided tale of mobility, confinement, capital, labour, and the gendering of sport and society. The Covid-19 Gilded Cage Sociologists such as Zygmunt Bauman and John Urry have analysed the socio-politics of mobilities, whereby some people in the world, such as tourists, can traverse the globe at their leisure, while others remain fixed in geographical space because they lack the means to be mobile or, in contrast, are involuntarily displaced by war, so-called “ethnic cleansing”, famine, poverty or environmental degradation. The Covid-19 global pandemic re-framed these matters of mobilities (Rowe, “Subjecting Pandemic Sport”), with conventional moving around—between houses, businesses, cities, regions and countries—suddenly subjected to the imperative to be static and, in perniciously unreflective technocratic discourse, “socially distanced” (when what was actually meant was to be “physically distanced”). The late-twentieth century analysis of the “risk society” by Ulrich Beck, in which the mysterious consequences of humans’ predation on their environment are visited upon them with terrifying force, was dramatically realised with the coming of Covid-19. In another iteration of the metaphor, it burst the bubble of twenty-first century global sport. What we today call sport was formed through the process of sportisation (Maguire), whereby hyper-local, folk physical play was reconfigured as multi-spatial industrialised sport in modernity, becoming increasingly reliant on individual athletes and teams travelling across the landscape and well over the horizon. Co-present crowds were, in turn, overshadowed in the sport economy when sport events were taken to much larger, dispersed audiences via the media, especially in broadcast mode (Nicholson, Kerr, and Sherwood). This lucrative mediation of professional sport, though, came with an unforgiving obligation to generate an uninterrupted supply of spectacular live sport content. The pandemic closed down most sports events and those that did take place lacked the crucial participation of the co-present crowd to provide the requisite event atmosphere demanded by those viewers accustomed to a sense of occasion. Instead, they received a strange spectacle of sport performers operating in empty “cathedrals”, often with a “faked” crowd presence. The mediated sport spectacle under the pandemic involved cardboard cut-out and sex doll spectators, Zoom images of fans on large screens, and sampled sounds of the crowd recycled from sport video games. Confected co-presence produced simulacra of the “real” as Baudrillardian visions came to life. The sporting bubble had become even more remote. For elite sportspeople routinely isolated from the “common people”, the live sport encounter offered some sensory experience of the social – the sounds, sights and even smells of the crowd. Now the sporting bubble closed in on an already insulated and insular existence. It exposed the irony of the bubble as a sign of both privileged mobility and incarcerated athlete work, both refuge and prison. Its logic of contagion also turned a structure intended to protect those inside from those outside into, as already observed, a mechanism to manage the threat of insiders to outsiders. In Australia, as in many other countries, the populace was enjoined by governments and health authorities to help prevent the spread of Covid-19 through isolation and immobility. There were various exceptions, principally those classified as essential workers, a heterogeneous cohort ranging from supermarket shelf stackers to pharmacists. People in the cultural, leisure and sports industries, including musicians, actors, and athletes, were not counted among this crucial labour force. Indeed, the performing arts (including dance, theatre and music) were put on ice with quite devastating effects on the livelihoods and wellbeing of those involved. So, with all major sports shut down (the exception being horse racing, which received the benefit both of government subsidies and expanding online gambling revenue), sport organisations began to represent themselves as essential services that could help sustain collective mental and even spiritual wellbeing. This case was made most aggressively by Australian Rugby League Commission Chairman, Peter V’landys, in contending that “an Australia without rugby league is not Australia”. In similar vein, prominent sport and media figure Phil Gould insisted, when describing rugby league fans in Western Sydney’s Penrith, “they’re lost, because the football’s not on … . It holds their families together. People don’t understand that … . Their life begins in the second week of March, and it ends in October”. Despite misgivings about public safety and equality before the pandemic regime, sporting bubbles were allowed to form, re-form and circulate. The indefinite shutdown of the National Rugby League (NRL) on 23 March 2020 was followed after negotiation between multiple entities by its reopening on 28 May 2020. The competition included a team from another nation-state (the Warriors from Aotearoa/New Zealand) in creating an international sporting bubble on the Central Coast of New South Wales, separating them from their families and friends across the Tasman Sea. Appeals to the mental health of fans and the importance of the NRL to myths of “Australianness” notwithstanding, the league had not prudently maintained a financial reserve and so could not afford to shut down for long. Significant gambling revenue for leagues like the NRL and Australian Football League (AFL) also influenced the push to return to sport business as usual. Sport contests were needed in order to exploit the gambling opportunities – especially online and mobile – stimulated by home “confinement”. During the coronavirus lockdowns, Australians’ weekly spending on gambling went up by 142 per cent, and the NRL earned significantly more than usual from gambling revenue—potentially $10 million above forecasts for 2020. Despite the clear financial imperative at play, including heavy reliance on gambling, sporting bubble-making involved special licence. The state of Queensland, which had pursued a hard-line approach by closing its borders for most of those wishing to cross them for biographical landmark events like family funerals and even for medical treatment in border communities, became “the nation's sporting hub”. Queensland became the home of most teams of the men’s AFL (notably the women’s AFLW season having been cancelled) following a large Covid-19 second wave in Melbourne. The women’s National Netball League was based exclusively in Queensland. This state, which for the first time hosted the AFL Grand Final, deployed sport as a tool in both national sports tourism marketing and internal pre-election politics, sponsoring a documentary, The Sporting Bubble 2020, via its Tourism and Events arm. While Queensland became the larger bubble incorporating many other sporting bubbles, both the AFL and the NRL had versions of the “fly in, fly out” labour rhythms conventionally associated with the mining industry in remote and regional areas. In this instance, though, the bubble experience did not involve long stays in miners’ camps or even the one-night hotel stopovers familiar to the popular music and sport industries. Here, the bubble moved, usually by plane, to fulfil the requirements of a live sport “gig”, whereupon it was immediately returned to its more solid bubble hub or to domestic self-isolation. In the space created between disciplined expectation and deplored non-compliance, the sporting bubble inevitably became the scrutinised object and subject of scandal. Sporting Bubble Scandals While people with a very low risk of spreading Covid-19 (coming from areas with no active cases) were denied entry to Queensland for even the most serious of reasons (for example, the death of a child), images of AFL players and their families socialising and enjoying swimming at the Royal Pines Resort sporting bubble crossed our screens. Yet, despite their (players’, officials’ and families’) relative privilege and freedom of movement under the AFL Covid-Safe Plan, some players and others inside the bubble were involved in “scandals”. Most notable was the case of a drunken brawl outside a Gold Coast strip club which led to two Richmond players being “banished”, suspended for 10 matches, and the club fined $100,000. But it was not only players who breached Covid-19 bubble protocols: Collingwood coaches Nathan Buckley and Brenton Sanderson paid the $50,000 fine imposed on the club for playing tennis in Perth outside their bubble, while Richmond was fined $45,000 after Brooke Cotchin, wife of team captain Trent, posted an image to Instagram of a Gold Coast day spa that she had visited outside the “hub” (the institutionally preferred term for bubble). She was subsequently distressed after being trolled. Also of concern was the lack of physical distancing, and the range of people allowed into the sporting bubble, including babysitters, grandparents, and swimming coaches (for children). There were other cases of players being caught leaving the bubble to attend parties and sharing videos of their “antics” on social media. Biosecurity breaches of bubbles by players occurred relatively frequently, with stern words from both the AFL and NRL leaders (and their clubs) and fines accumulating in the thousands of dollars. Some people were also caught sneaking into bubbles, with Lekahni Pearce, the girlfriend of Swans player Elijah Taylor, stating that it was easy in Perth, “no security, I didn’t see a security guard” (in Barron, Stevens, and Zaczek) (a month later, outside the bubble, they had broken up and he pled guilty to unlawfully assaulting her; Ramsey). Flouting the rules, despite stern threats from government, did not lead to any bubble being popped. The sport-media machine powering sporting bubbles continued to run, the attendant emotional or health risks accepted in the name of national cultural therapy, while sponsorship, advertising and gambling revenue continued to accumulate mostly for the benefit of men. Gendering Sporting Bubbles Designed as biosecurity structures to maintain the supply of media-sport content, keep players and other vital cogs of the machine running smoothly, and to exclude Covid-19, sporting bubbles were, in their most advanced form, exclusive luxury camps that illuminated the elevated socio-cultural status of sportsmen. The ongoing inequalities between men’s and women’s sport in Australia and around the world were clearly in evidence, as well as the politics of gender whereby women are obliged to “care” and men are enabled to be “careless” – or at least to manage carefully their “duty of care”. In Australia, the only sport for women that continued during the height of the Covid-19 lockdown was netball, which operated in a bubble that was one of sacrifice rather than privilege. With minimum salaries of only $30,000 – significantly less than the lowest-paid “rookies” in the AFL – and some being mothers of small children and/or with professional jobs juggled alongside their netball careers, these elite sportswomen wanted to continue to play despite the personal inconvenience or cost (Pavlidis). Not one breach of the netballers out of the bubble was reported, indicating that they took their responsibilities with appropriate seriousness and, perhaps, were subjected to less scrutiny than the sportsmen accustomed to attracting front-page headlines. National Netball League (also known after its Queensland-based naming rights sponsor as Suncorp Super Netball) players could be regarded as fortunate to have the opportunity to be in a bubble and to participate in their competition. The NRL Women’s (NRLW) Premiership season was also completed, but only involved four teams subject to fly in, fly out and bubble arrangements, and being played in so-called curtain-raiser games for the NRL. As noted earlier, the AFLW season was truncated, despite all the prior training and sacrifice required of its players. Similarly, because of their resource advantages, the UK men’s and boy’s top six tiers of association football were allowed to continue during lockdown, compared to only two for women and girls. In the United States, inequalities between men’s and women’s sports were clearly demonstrated by the conditions afforded to those elite sportswomen inside the Women’s National Basketball Association (WNBA) sport bubble in the IMG Academy in Florida. Players shared photos of rodent traps in their rooms, insect traps under their mattresses, inedible food and blocked plumbing in their bubble accommodation. These conditions were a far cry from the luxury usually afforded elite sportsmen, including in Florida’s Walt Disney World for the men’s NBA, and is just one of the many instances of how gendered inequality was both reproduced and exacerbated by Covid-19. Bursting the Bubble As we have seen, governments and corporate leaders in sport were able to create material and metaphorical bubbles during the Covid-19 lockdown in order to transmit stadium sport contests into home spaces. The rationale was the importance of sport to national identity, belonging and the routines and rhythms of life. But for whom? Many women, who still carry the major responsibilities of “care”, found that Covid-19 intensified the affective relations and gendered inequities of “home” as a leisure site (Fullagar and Pavlidis). Rates of domestic violence surged, and many women experienced significant anxiety and depression related to the stress of home confinement and home schooling. During the pandemic, women were also more likely to experience the stress and trauma of being first responders, witnessing virus-related sickness and death as the majority of nurses and care workers. They also bore the brunt of much of the economic and employment loss during this time. Also, as noted above, livelihoods in the arts and cultural sector did not receive the benefits of the “bubble”, despite having a comparable claim to sport in contributing significantly to societal wellbeing. This sector’s workforce is substantially female, although men dominate its senior roles. Despite these inequalities, after the late March to May hiatus, many elite male sportsmen – and some sportswomen - operated in a bubble. Moving in and out of them was not easy. Life inside could be mentally stressful (especially in long stays of up to 150 days in sports like cricket), and tabloid and social media troll punishment awaited those who were caught going “over the fence”. But, life in the sporting bubble was generally preferable to the daily realities of those afflicted by the trauma arising from forced home confinement, and for whom watching moving sports images was scant compensation for compulsory immobility. The ethical foundation of the sparkly, ephemeral fantasy of the sporting bubble is questionable when it is placed in the service of a voracious “media sports cultural complex” (Rowe, Global Media Sport) that consumes sport labour power and rolls back progress in gender relations as a default response to a global pandemic. Covid-19 dramatically highlighted social inequalities in many areas of life, including medical care, work, and sport. For the small minority of people involved in sport who are elite professionals, the only thing worse than being in a sporting bubble during the pandemic was not being in one, as being outside precluded their participation. Being inside the bubble was a privilege, albeit a dubious one. But, as in wider society, not all sporting bubbles are created equal. Some are more opulent than others, and the experiences of the supporting and the supported can be very different. The surface of the sporting bubble may be impermanent, but when its interior is opened up to scrutiny, it reveals some very durable structures of inequality. Bubbles are made to burst. They are, by nature, temporary, translucent structures created as spectacles. As a form of luminosity, bubbles “allow a thing or object to exist only as a flash, sparkle or shimmer” (Deleuze, 52). In echoing Deleuze, Angela McRobbie (54) argues that luminosity “softens and disguises the regulative dynamics of neoliberal society”. The sporting bubble was designed to discharge that function for those millions rendered immobile by home confinement legislation in Australia and around the world, who were having to deal with the associated trauma, risk and disadvantage. 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