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At least 55 records · Page 3

A streamline coordinate analysis of a turbulent boundary layer subject to pressure gradients and curvature on the windward side of a bump

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

42 ENGINEERING↗

Mechanical failure of fresh nuclear grade iron–chromium–aluminum (FeCrAl) cladding under simulated hot zero power reactivity initiated accident conditions

The reactivity initiated accident (RIA) is a postulated accident in light water reactors initiated by a rapid increase in reactivity which causes an increase in fission rate and fuel temperature. One potential mode of fuel system failure during RIA is pellet cladding mechanical interaction (PCMI) due to the rapid thermal expansion of the fuel pellet. Simulated PCMI experiments were performed by rapidly pressurizing iron-chromium-aluminum (FeCrAl) cladding tube samples using a hydraulic modified burst test system, causing the specimens to burst under a biaxial loading path. Deformation and rupture of the specimens were tracked with a telecentric lens and high-speed camera system. Outer surface strains were calculated using digital image correlation (DIC) on speckle patterns painted on the specimens’ outer surfaces. Experiments were conducted at approximately 275 °C, representative of hot zero power RIA conditions. The failure hoop strain was DIC-calculated between approximately 1.8–3.4%, corresponding to quasi-static energy depositions of approximately 110–260 calories per gram UO 2 assuming initial pellet-cladding contact. These conditions are very similar to the proposed energy deposition limit of 150 calories per gram UO 2 for unirradiated zirconium-based cladding in US Nuclear Regulatory Commission (NRC) Draft Regulatory Guide 1327. A very small strain rate dependence was observed in the data, with the magnitude of the failure hoop strain decreasing slightly with increasing strain rate. This observed dependence may be relevant because the FeCrAl cladding strain rate will be approximately 20% higher than in zirconium-based cladding due to the harder neutron spectrum and resultant shorter neutron generation time.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Preliminary research on overmoded high-power millimeter-wave Cerenkov generator with dual-cavity reflector in low guiding magnetic field

This paper presents preliminary research on a V-band overmoded Cerenkov generator with dual-cavity reflector operating in a low guiding magnetic field. It is found that the fluctuation of the electron envelope in the low guiding magnetic field can be predicted using an equivalent coaxial model of a foilless diode, and a dual-cavity reflector based on the model matching method can provide strong reflection at the front end of the overmoded structures so that any microwave power that leaks into the diode region can be effectively suppressed. Numerical simulations indicate that the control of the beam envelope and the use of the dual-cavity reflector ease generator operation in the low guiding magnetic field. In the experimental research, the fluctuation of the annular electron beam with the outer radius of 7.5 mm measures approximately 0.7 mm, which is in good agreement with the theoretical results. The disturbance caused by power leaking from the overmoded slow wave structure is eliminated by the dual-cavity reflector. With accurate fabrication and assembly processes, an operating frequency of 61.6 GHz is attained by the fifth harmonic heterodyne method, and the output power is measured to be approximately 123 MW by the far-field measurement method at a diode voltage of 445 kV, a beam current of 4.45 kA, and under a guiding magnetic field of 1.45 T. The output mode is measured using an array of neon flash bulbs, and the pulse shortening phenomenon is both observed and analyzed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermodynamic limits of energy harvesting from outgoing thermal radiation

Significance A large part of the research on renewable energy has focused on harvesting power from solar radiation. But, for the Earth to maintain its temperature, it must radiate to the outer space an amount of power approximately equal to that of the incoming solar radiation. However, far less is understood about the theoretical limits of harvesting power from such outgoing radiation. Here, we identify a duality relation between harvesting incoming and outgoing thermal radiation and use it to derive fundamental limits of harvesting outgoing thermal radiation. Our results indicate a theoretical limit that far exceeds what was previously thought to be possible and highlight the significant potential for harvesting outgoing thermal radiation for renewable energy applications.

42 ENGINEERING↗

Fast Neutron Spectrum Potassium Worth for Space Power Reactor Design Validation

A variety of critical experiments were constructed of enriched uranium metal (oralloy ) during the 1960s and 1970s at the Oak Ridge Critical Experiments Facility (ORCEF) in support of criticality safety operations at the Y-12 Plant. The purposes of these experiments included the evaluation of storage, casting, and handling limits for the Y-12 Plant and providing data for verification of calculation methods and cross-sections for nuclear criticality safety applications. These included solid cylinders of various diameters, annuli of various inner and outer diameters, two and three interacting cylinders of various diameters, and graphite and polyethylene reflected cylinders and annuli. Of the hundreds of delayed critical experiments, one was performed that consisted of uranium metal annuli surrounding a potassium-filled, stainless steel can. The outer diameter of the annuli was approximately 13 inches (33.02 cm) with an inner diameter of 7 inches (17.78 cm). The diameter of the stainless steel can was 7 inches (17.78 cm). The critical height of the configurations was approximately 5.6 inches (14.224 cm). The uranium annulus consisted of multiple stacked rings, each with radial thicknesses of 1 inch (2.54 cm) and varying heights. A companion measurement was performed using empty stainless steel cans; the primary purpose of these experiments was to test the fast neutron cross sections of potassium as it was a candidate for coolant in some early space power reactor designs.The experimental measurements were performed on July 11, 1963, by J. T. Mihalczo and M. S. Wyatt with additional information in its corresponding logbook. Unreflected and unmoderated experiments with the same set of highly enriched uranium metal parts were performed at the Oak Ridge Critical Experiments Facility in the 1960s and are evaluated in the International Handbook for Evaluated Criticality Safety Benchmark Experiments (ICSBEP Handbook) with the identifier HEU MET FAST 051. Thin graphite reflected (2 inches or less) experiments also using the same set of highly enriched uranium metal parts are evaluated in HEU MET FAST 071. Polyethylene-reflected configurations are evaluated in HEU-MET-FAST-076. A stack of highly enriched metal discs with a thick beryllium top reflector is evaluated in HEU-MET-FAST-069, and two additional highly enriched uranium annuli with beryllium cores are evaluated in HEU-MET-FAST-059. Both detailed and simplified model specifications are provided in this evaluation. Both of these fast neutron spectra assemblies were determined to be acceptable benchmark experiments. The calculated eigenvalues for both the detailed and the simple benchmark models are within ~0.26 % of the benchmark values for Configuration 1 (calculations performed using MCNP6 with ENDF/B-VII.1 neutron cross section data), but under-calculate the benchmark values by ~7s because the uncertainty in the benchmark is very small: ~0.0004 (1s); for Configuration 2, the under-calculation is ~0.31 % and ~8s. Comparison of detailed and simple model calculations for the potassium worth measurement and potassium mass coefficient yield results approximately 70 – 80 % lower (~6s to 10s) than the benchmark values for the various nuclear data libraries utilized. Both the potassium worth and mass coefficient are also deemed to be acceptable benchmark experiment measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

THE DYNAMICS OF THE OUTER PARTS OF {omega} CENTAURI

The multi-object fiber-fed spectrograph AAOmega at the Anglo-Australian Telescope has been used to establish and measure accurate ({<=}1 km s{sup -1}) radial velocities for a new sample of members in the outer parts of the stellar system {omega} Centauri. The new sample more than doubles the number of known members with precise velocities that lie between 25' and 45' from the cluster center. Combining this sample with earlier work confirms that the line-of-sight velocity dispersion of {omega} Cen remains approximately constant at {approx}6.5 km s{sup -1} in the outer parts of the cluster, which contain only a small fraction of the total cluster stellar mass. It is argued that the approximately constant velocity dispersion in the outer regions is most likely a consequence of external influences, such as the tidal shock heating that occurs each time {omega} Cen crosses the Galactic plane. There is therefore no requirement to invoke dark matter or non-standard gravitational theories.

79 ASTRONOMY AND ASTROPHYSICS↗

Analytic Expressions for the Inner-rim Structure of Passively Heated Protoplanetary Disks

We analytically derive the expressions for the structure of the inner region of protoplanetary disks based on the results from the recent hydrodynamical simulations. The inner part of a disk can be divided into four regions: a dust-free region with a gas temperature in the optically thin limit, an optically thin dust halo, an optically thick condensation front, and the classical, optically thick region, in order from the innermost to the outermost. We derive the dust-to-gas mass ratio profile in the dust halo using the fact that partial dust condensation regulates the temperature relative to the dust evaporation temperature. Beyond the dust halo, there is an optically thick condensation front where all the available silicate gas condenses out. The curvature of the condensation surface is determined by the condition that the surface temperature must be nearly equal to the characteristic temperature ∼1200 K. We derive the midplane temperature in the outer two regions using the two-layer approximation, with the additional heating by the condensation front for the outermost region. As a result, the overall temperature profile is step-like, with steep gradients at the borders between the outer three regions. The borders might act as planet traps where the inward migration of planets due to gravitational interaction with the gas disk stops. The temperature at the border between the two outermost regions coincides with the temperature needed to activate magnetorotational instability, suggesting that the inner edge of the dead zone must lie at this border. The radius of the dead zone inner edge predicted from our solution is ∼2–3 times larger than that expected from the classical optically thick temperature.

79 ASTRONOMY AND ASTROPHYSICS↗

New insights on divertor parallel flows,E × B drifts, and fluctuations from in situ, two-dimensional probe measurement in the Tokamak à Configuration Variable

Abstract In situ , two-dimensional (2D) Langmuir probe measurements across a large part of the TCV outer divertor are reported in L-mode discharges with and without divertor baffles. This provides detailed insights into time averaged profiles, particle fluxes, and fluctuation behavior in different divertor regimes. The presence of the baffles is shown to substantially increase the divertor neutral pressure for a given upstream density and to facilitate the access to detachment, an effect that increases with plasma current. The detailed, 2D probe measurements allow for a divertor particle balance, including ion flux contributions from parallel flows and E × B drifts. The poloidal flux contribution from the latter is often comparable or even larger than the former, and the divertor parallel flow direction reverses in some conditions, pointing away from the target. In most conditions, the integrated particle flux at the outer target can be predominantly ascribed to ionization along the outer divertor leg, consistent with a closed-box approximation of the divertor. The exception is a strongly detached divertor, achieved here only with baffles, where the total poloidal ion flux even decreases towards the outer target, indicative of significant plasma recombination. The most striking observation from relative density fluctuation measurements along the outer divertor leg is the transition from poloidally uniform fluctuation levels in attached conditions to fluctuations strongly peaking near the X-point when approaching detachment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Cool Cores in Clusters of Galaxies in the Dark Energy Survey

We search for the presence of cool cores in optically selected galaxy clusters from the Dark Energy Survey (DES) and investigate their prevalence as a function of redshift and cluster richness. Clusters were selected from the redMaPPer analysis of three years of DES observations that have archival Chandra X-ray observations, giving a sample of 99 clusters with a redshift range of 0.11 < z < 0.87 and a richness range of 25 < λ < 207. Using the X-ray data, the core temperature was compared to the outer temperature to identify clusters where the core temperature is a factor of 0.7 or less than the outer temperature. We found a cool core fraction of approximately 20% with no significant trend in the cool core fraction with either redshift or richness.

79 ASTRONOMY AND ASTROPHYSICS↗

Structural diversity and clustering of bacterial flagellar outer domains

Supercoiled flagellar filaments function as mechanical propellers within the bacterial flagellum complex, playing a crucial role in motility. Flagellin, the building block of the filament, features a conserved inner D0/D1 core domain across different bacterial species. In contrast, approximately half of the flagellins possess additional, highly divergent outer domain(s), suggesting varied functional potential. In this study, we report atomic structures of flagellar filaments from three distinct bacterial species: Cupriavidus gilardii , Stenotrophomonas maltophilia , and Geovibrio thiophilus . Our findings reveal that the flagella from the facultative anaerobic G. thiophilus possesses a significantly more negatively charged surface, potentially enabling adhesion to positively charged minerals. Furthermore, we analyze all AlphaFold predicted structures for annotated bacterial flagellins, categorizing the flagellin outer domains into 682 structural clusters. This classification provides insights into the prevalence and experimental verification of these outer domains. Remarkably, two of the flagellar structures reported herein belong to a distinct cluster, indicating additional opportunities on the study of the functional diversity of flagellar outer domains. Our findings underscore the complexity of bacterial flagellins and open up possibilities for future studies into their varied roles beyond motility.

Science & Technology - Other Topics↗

Characteristics of anomalous skin effect and evolution of power absorption regions in a cylindrical radio frequency inductively coupled plasma

In a low-pressure radio-frequency (13.56 MHz), inductively coupled argon plasma generated by a normal cylindrical rf coil, electric field, current density, and absorbed power density is calculated from magnetic field measured with a phase-resolved magnetic probe. The anomalous skin effect (ASE) for the cylindrical rf coil is compared to those previously reported for the planar and re-entrant cylindrical rf coils. Physical reasons for our observed characteristics of ASE are presented. With the increasing discharge power, the size and the number of negative and positive power absorption regions evolve into several distinct patterns. For the low discharge power (at 156.9 W), there is one area of positive and one area of negative power absorption in the radial direction. For the medium discharge power (279 W–683.5 W), there are two areas of negative and two areas of positive power absorption. For the even higher discharge power (above 803.5 W), the number of areas is the same as that of the medium discharge power, but the size of the inner positive and negative power absorption areas is approximately doubled and halved, respectively, while the outer positive and negative power absorption areas slightly shrinks. The evolution of positive and negative power absorption regions is explained as a result of electron thermal diffusion and the energy conversion between rf current and electric field. The spatial decays of electric field and current density are also elucidated by linking them with the positive and negative power absorption pattern.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

PROPERTIES OF THE MAGNETO-IONIC MEDIUM IN THE HALO OF M51 REVEALED BY WIDE-BAND POLARIMETRY

We present a study of the magneto-ionic medium in the Whirlpool galaxy (M51) using new wide-band multi-configuration polarization data at L band (1-2 GHz) obtained at the Karl G. Jansky Very Large Array. By fitting the observed diffuse complex polarization Q+iU as a function of wavelength directly to various depolarization models, we find that polarized emission from M51 at 1-2 GHz originates from the top of the synchrotron disk and then experiences Faraday rotation in the near-side thermal halo of the galaxy. Thus, the scale height of the thermal gas must exceed that of the synchrotron emitting gas at L band. The observed Faraday depth distribution at L band is consistent with a halo field that is comprised of a plane-parallel bisymmetric component and a vertical component that produces a Faraday rotation of ∼–9 rad m{sup –2}. The derived rotation measure (RM) structure functions indicate a characteristic scale of RM fluctuations of less than 560 pc in the disk and approximately 1 kpc in the halo. The outer scale of turbulence of 1 kpc found in the halo of M51 is consistent with superbubbles and the Parker instability being the main energy injection mechanisms in galactic halos.

79 ASTRONOMY AND ASTROPHYSICS↗

Demonstration of Microwave Cavity Transducer Performance in High Temperature Fluid Flow Sensing: Development of Microwave Cavity Flow Meter for Advanced Reactor High Temperature Fluids

We are investigating a microwave resonant cavity transducer for flow sensing in the vessel of a high temperature fluid advanced reactor (AR), such as a molten salt cooled reactor (MSCR) or a sodium fast reactor (SFR). This transducer is a hollow metallic cylindrical cavity, with one of the flat walls of the cylinder flexible enough to undergo microscopic deflection due to dynamic fluid pressure. Membrane deflection leads to a shift in the microwave resonant frequency, which can be detected with a spectrum analyzer. We have performed a preliminary proof-of-principle test of flow sensing in high temperature liquid sodium in environment, which is similar to that of an advanced reactor. The liquid sodium setup consists of a cylindrical vessel with a center feed line, where a transducer inserted through the top cap of the vessel measures velocity of the impinging liquid jet. For this test, we have developed a cylindrical resonator, which was machined from stainless steel 316 and electroplated with silver on the interior surfaces. Outer diameter of the cylindrical cavity is approximately 3cm, and the thin wall is approximately 200µm thick. We have also developed and insertion probe consisting of a 50cm WR-42 brass waveguide enclosed in a protective SS316 tube. The cavity was excited through a WR-42 waveguide through a subwavelength hole on the side of the wall of the cylinder in the TE 011 mode with resonant frequency f ≈ 17.8GHz. As a calibration experiment, we have assembled a water vessel with a center feed, and with dimensions similar to those of the liquid sodium setup. Frequency shift of the cavity spectral response was obtained at room temperature and ambient pressure by gradually increasing water flow rate from 0 to 25GPM (gallons per minute). Corresponding monotonic increase of resonant frequency by several hundred KHz was observed. Next, a sodium flow rate sensing study was performed in a liquid sodium vessel at 340° C temperature and ambient pressure. The flow rate was changed by varying sodium pump power, and a frequency shift of several hundred KHz was observed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

PDADMAC/PSS Oligoelectrolyte Multilayers: Internal Structure and Hydration Properties at Early Growth Stages from Atomistic Simulations

We analyze the internal structure and hydration properties of poly(diallyl dimethyl ammonium chloride)/poly(styrene sulfonate sodium salt) oligoelectrolyte multilayers at early stages of their layer-by-layer growth process. Our study is based on large-scale molecular dynamics simulations with atomistic resolution that we presented recently [Sánchez et al., Soft Matter 2019, 15, 9437], in which we produced the first four deposition cycles of a multilayer obtained by alternate exposure of a flat silica substrate to aqueous electrolyte solutions of such polymers at 0.1M of NaCl. In contrast to any previous work, here we perform a local structural analysis that allows us to determine the dependence of the multilayer properties on the distance to the substrate. We prove that the large accumulation of water and ions next to the substrate observed in previous overall measurements actually decreases the degree of intrinsic charge compensation, but this remains as the main mechanism within the interface region. We show that the range of influence of the substrate reaches approximately 3 nm, whereas the structure of the outer region is rather independent from the position. This detailed characterization is essential for the development of accurate mesoscale models able to reach length and time scales of technological interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hollow nanoparticles with hybrid double layers

The present invention discloses the morphology of hollow, double-shelled submicrometer particles generated through a rapid aerosol-based process. The inner shell is an essentially hydrophobic carbon layer of nanoscale dimension (5-20 nm), and the outer shell is a hydrophilic silica layer of approximately 5-40 nm, with the shell thickness being a function of the particle size. The particles are synthesized by exploiting concepts of salt bridging to lock in a surfactant (CTAB) and carbon precursors together with iron species in the interior of a droplet. This deliberate negation of surfactant templating allows a silica shell to form extremely rapidly, sealing in the organic species in the particle interior. Subsequent pyrolysis results in a buildup of internal pressure, forcing carbonaceous species against the silica wall to form an inner shell of carbon. The incorporation of magnetic iron oxide into the shells opens up applications in external stimuli-responsive nanomaterials.

John, Vijay T.↗

THE DESIGN OF RADIAL HONEYCOMB LATTICES FOR IMPACT ENERGY ABSORPTION IN RADIOACTIVE MATERIALS PACKAGES

In this research we present a variation on the corrugation technique of honeycomb lattices, for cylindrical honeycombs, making them much easier to design for impact energy absorption in radioactive materials packages. This variation, termed radial honeycomb lattices, eliminates the residual strain and saddle effect. The use of honeycomb lattices provides advantages over the typically used foams. While foams are effective at absorbing impact energy, they can burn, their material properties are difficult to control, they can degrade over time, and procurement of raw materials can be dependent on timing of manufacturer batch runs. While the weaknesses of foam are strengths for honeycomb lattices, lattices have a different set of problems. Typically, when cylindrical honeycomb lattices are manufactured, they are manufactured flat, wrapped around a mandrel of the desired radius, and then brazed. This approach introduces residual strains, resulting in the saddle effect, which limits both the radial thickness and cylinder length. The radial honeycomb lattice approach presented here makes the design of thicker and longer cylinder honeycombs possible. To address these issues, we propose a honeycomb lattice which changes in cross-section from the inner to the outer radius of the cylinder. This causes the lattice to automatically wrap into a cylinder as it exits the corrugating gears. The theoretically bounding case, of a square cross-section at the inner radius, transitioning through a hexagon, to a diamond cross-section at the outer radius, results in a maximum thickness of approximately 41% of the inner radius. Full mathematical derivations, implemented in computer code, allow for the design of an entire radial honeycomb lattice, including the corrugating gears. To accomplish this only the radial thickness, inner cross-section shape, cell size, and nominal gear radius need to be specified, making the design of these lattices very efficient. Radial honeycomb lattice prototypes have demonstrated that the honeycomb does indeed wrap into a cylinder as intended, without the saddle effect, and can therefore be used to create thick-walled cylinders of any length. These design improvements make cylindrical honeycomb lattices much more accessible as a design element for radioactive materials packages

Johnson, William R. [Savannah River National Labor↗

A CHEMICAL ABUNDANCE STUDY OF 10 OPEN CLUSTERS BASED ON WIYN -HYDRA SPECTROSCOPY

We present a detailed chemical abundance study of evolved stars in 10 open clusters based on Hydra multi-object echelle spectra obtained with the WIYN 3.5 m telescope. From an analysis of both equivalent widths and spectrum synthesis, abundances have been determined for the elements Fe, Na, O, Mg, Si, Ca, Ti, Ni, Zr, and for two of the 10 clusters, Al and Cr. To our knowledge, this is the first detailed abundance analysis for clusters NGC 1245, NGC 2194, NGC 2355, and NGC 2425. These 10 clusters were selected for analysis because they span a Galactocentric distance range R{sub gc} {approx} 9-13 kpc, the approximate location of the transition between the inner and outer disks. Combined with cluster samples from our previous work and those of other studies in the literature, we explore abundance trends as a function of cluster R{sub gc}, age, and [Fe/H]. As found previously by us and other studies, the [Fe/H] distribution appears to decrease with increasing R{sub gc} to a distance of {approx}12 kpc and then flattens to a roughly constant value in the outer disk. Cluster average element [X/Fe] ratios appear to be independent of R{sub gc}, although the picture for [O/Fe] is more complicated with a clear trend of [O/Fe] with [Fe/H] and sample incompleteness. Other than oxygen, no other element [X/Fe] exhibits a clear trend with [Fe/H]; likewise, there does not appear to be any strong correlation between abundance and cluster age. We divided clusters into different age bins to explore temporal variations in the radial element distributions. The radial metallicity gradient appears to have flattened slightly as a function of time, as found by other studies. There is also some indication that the transition from the inner disk metallicity gradient to the {approx}constant [Fe/H] distribution of the outer disk occurs at different Galactocentric radii for different age bins. However, interpretation of the time evolution of radial abundance distributions is complicated by the unequal R{sub gc} and [Fe/H] ranges spanned by clusters in different age bins.

79 ASTRONOMY AND ASTROPHYSICS↗

Light curves from supernova shock breakout through an extended wind

Recent observations suggest that some supernovae may be the result of an explosion into an optically thick circumstellar material, the product of pre-explosion mass loss (wind) by the progenitor star. This scenario has been studied previously both analytically and numerically. However, many previous studies base their analysis on the diffusion approximation for radiation transfer, which is inappropriate in the optically thin outer layers of the wind. Here we study the deviations from diffusion and calculate light curves more accurately using a Monte Carlo approach to photon transfer. We distinguish between 'compact' winds, for which the diffusion approximation is appropriate, and 'extended' winds, which require a more delicate treatment of the radiation. We show that this effect is more significant than that of the light-travel time difference to a distant observer, which has a secondary influence on the light curves of extended-wind systems. We also comment on the applicability of the widely used flux-limited diffusion approximation in this context: we find that it generally does not reproduce the Monte Carlo results. The flux-limited diffusion approximation leads to results that are not only quantitatively but also qualitatively wrong in the extended-wind regime.

79 ASTRONOMY AND ASTROPHYSICS↗