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Understand the interaction between ocean waves and oscillating systems with this useful new edition. With a focus on linear analysis of low-amplitude waves, you are provided with a thorough understanding of wave interactions, presented to be easily accessible to non-specialist readers. Topics covered include the background mathematics of oscillations, gravity waves on water, the dynamics of wave-body interactions, and the absorption of wave energy by oscillating bodies and oscillating water columns. Featuring new content throughout, including three new chapters on oscillating-body wave energy converters, oscillating water columns and other types of wave energy converters, and wave energy converter arrays, this book is an excellent resource for students, researchers, and engineers who are new to the subject of wave energy conversion, as well as those with more experience.
We present results of our zoom-in cosmological hydrodynamic simulations of direct collapse (DC) to supermassive black hole (SMBH) seeds with radiative transfer (RT). The DC has been modeled in dark matter halos of ∼108M⊙, using adaptive mesh refinement (AMR) code Enzo. For the first time, the baryonic collapse has been followed down to 10−7 pc (∼0.01 AU) with on-the-fly RT and the flux-limited diffusion (FLD) approximation. We find a complex behavior involving accretion flow and associated outflows driven by the radiation force. The resulting gas dynamics around the central density peak differs profoundly from that in previous works which adopted adiabatic approximation in the core. The core forms with a photosphere at ∼1 AU, and its growth starts to saturate at ∼100M⊙. The unrelaxed core radiates intermittently near the Eddington luminosity, correlated with strong anisotropic outflows.
Current state-of-the-art computational modeling makes it possible to build realistic models of stellar convection zones and atmospheres that take into account chemical composition, radiative effects, ionization, and turbulence. The standard 1D mixing-length-based evolutionary models are not able to capture many physical processes of the stellar interior dynamics. Mixing-length models provide an initial approximation of stellar structure that can be used to initialize 3D radiative hydrodynamics simulations which include realistic modeling of turbulence, radiation, and other phenomena.
In this paper, we present 3D radiative hydrodynamic simulations of an F-type main-sequence star with 1.47 solar mass. The computational domain includes the upper layers of the radiation zone, the entire convection zone, and the photosphere. The effects of stellar rotation is modeled in the f-plane approximation. These simulations provide new insight into the properties of the convective overshoot region, the dynamics of the near-surface, highly turbulent layer, and the structure and dynamics of granulation. They reveal solar-type differential rotation and latitudinal dependence of the tachocline location.
Recent observations have successfully detected UV or infrared flux from galaxies at the epoch of reionization. However, the origin of their radiative properties has not been fully understood yet. Combining cosmological hydrodynamic simulations and radiative transfer calculations, we present theoretical predictions of multi-wavelength radiative properties of the first galaxies at z = 6–15. We find that most of the gas and dust are ejected from star-forming regions due to supernova (SN) feedback, which allows UV photons to escape. We show that the peak of SED rapidly shifts between UV and infrared wavelengths on a timescale of 100 Myr due to intermittent star formation and feedback. When dusty gas covers the star-forming regions, the galaxies become bright in the observed-frame sub-millimeter wavelengths. In addition, we find that the escape fraction of ionizing photons also changes between 1–40% at z > 10. The mass fraction of H ii region changes with star formation history, resulting in fluctuations of metal lines and Lyman-α line luminosities. In the starbursting phase of galaxies with a halo mass ∼1011Mȯ (1012Mȯ), the simulated galaxy has L[OIII] ∼ 1042 (1043) erg s−1, which is consistent with the observed star-forming galaxies at z > 7. Our simulations suggest that deep [Cii] observation with ALMA can trace the distribution of neutral gas extending over ∼20 physical kpc. We also find that the luminosity ratio L[OIII]/L[CII] decreases with bolometric luminosity due to metal enrichment. Our simulations show that the combination of multi-wavelength observations by ALMA and JWST will be able to reveal the multi-phase ISM structure and the transition from starbursting to outflowing phases of high-z galaxies.
Stars in globular clusters lose mass through slow stellar winds that are retained by the stellar cluster and should contribute to build up a non-negligible intracluster medium over time. However, all the observations so far found only a negligible amount of gas in GCs. We propose here to test different mechanisms such as ram-pressure stripping by the motion of the GC in the Galactic halo medium and the inclusion of ionising sources to explain the lack of gas in GCs. We use full 3D hydrodynamical simulations taking into account stellar winds, ionising radiation, radiative heating and radiative pressure. We find that the combined effect of ram-pressure and ionisation are able to explain the negligible amount of gas observed in the core of intermediate-mass and massive GCs.
I will present results obtained by means of three-dimensional hydrodynamic simulations of the formation of second generation (SG) stars in a young globular cluster (GC). Our setup includes the mass return from Asymptotic Giant branch (AGB) stars, the accretion of pristine gas as well as star formation of SG stars, three ingredients which have never been simultaneously taken into account in previous 3D numerical studies of GC formation. The cluster is set in motion with respect to a distribution of gas and allowed to accrete mass from it. Formation of SG stars occurs out of the gas shed by AGB stars and from the gas accreted during the motion of the cluster. We consider two models characterised by different densities of the external gas. In both cases, we find that a very compact SG subsystem with central density > 105M⊙/pc3 forms in the innermost regions of the cluster.
We present results of full general relativistic (GR), three-dimensional (3D) core-collapse simulation of a massive star with multi-energy neutrino transport. Using a 70Mȯ zero-metallicity star, we show that the black-hole (BH) formation occurs at ∼ 300 ms after bounce. At a few ∼ 10 ms before the BH formation, we find that the stalled bounce shock is revived by neutrino heating from the forming hot proto-neutron star (PNS), which is aided by vigorous convection behind the shock. Our numerical results present the first evidence to validate the BH formation by the so-called fallback scenario. Furthermore we present results from a rapidly rotating core-collapse model of a 27Mȯ star that is trending towards an explosion. We point out that the correlated neutrino and gravitational-wave signatures, if detected, could provide a smoking-gun evidence of rapid rotation of the newly-born PNS.
We present examples of nonrelativistic field theories, starting with the nonrelativistic limit of a scalar field with canonical kinetic term. Then we present hydrodynamics, the study of fluids, with the goal of describing water waves. We derive the KdV equation and its soliton from the description of water waves. The KS equation is also described. Finally, we describe surface growth and the KPZ equation.
Stars of 8–10 M⊙ form a strongly electron-degenerate oxygen–neon–magnesium core which is more massive than ∼1.1 M⊙, and become super-Asymptotic Giant Branch stars. The oxygen–neon–magnesium core increases its mass through H and He shell burning. The core contracts accordingly and the central density increases. In the high density core, electron capture takes place and further boosts the core contraction. When electron capture on 20Ne starts, it induces oxygen–neon deflagration. It remains a theoretical question whether neutron star can be formed after the deflagration has started. If the star collapses, the following explosion is known as an electron capture supernova. In this article, we give a brief overview on the development of idea in the presupernova evolution and the hydrodynamics behaviour of electron capture supernovae. Using standard stellar evolutionary models that show rather high ignition density, we show that the collapse can occur in a wide range of model parameter. However, future study remains important. We also review the possible observables of electron capture supernovae and discuss their applications to the light curve model for the Crab supernova 1054.
This chapter provides fundamentals on protein chromatography. Different chromatographic media are described in terms of the solute-surface interactions that can be exploited to achieve the desired separation. Then, mechanistic models are presented to describe the three key physical phenomena involved in protein chromatography, namely the thermodynamics of fluid-solid equilibrium, the hydrodynamics and the kinetics of mass transfer. Simple methods to estimate model parameters are introduced as well as short-cut methods to design chromatographic processes. Although the main goal of this chapter is to bring theoretical basics about the modelling of protein chromatography, it is complemented by numerous experimental results for illustrative and pedagogical purposes.
Hot star winds are driven by the radiative force due to light absorption in lines of heavier elements. Therefore, the amount of mass lost by the star per unit of time, i.e., the mass-loss rate, is sensitive to metallicity. We provide mass-loss rate predictions for O stars with mass fraction of heavier elements 0.2 <Z/Z⊙ ≤ 1. Our predictions are based on global model atmospheres. The models allow us to predict wind terminal velocity and the mass-loss rate just from basic global stellar parameters. We provide a formula that fits the mass-loss rate predicted by our models as a function of stellar luminosity and metallicity. On average, the mass-loss rate scales with metallicity as (Z/Z⊙)0.59. The predicted mass-loss rates agree with mass-loss rates derived from ultraviolet wind line profiles. At low metallicity, the rotational mixing affects the wind mass-loss rates. We study the influence of magnetic line blanketing.
We present results from a non-cosmological, three-dimensional hydrodynamic simulation of an outflow from an intermediate-mass black hole in Dwarf Spheroidal Galaxies. Assuming an initial baryonic-to-dark-matter ratio derived from the CMB radiation and a cored, static dark matter potential, we evolved the galactic gas distribution over 3 Gyr, taking into account the outflow of a black hole. Our results indicate that in a homogeneous medium the outflow propagates freely in both directions with the same velocity and its capable of removing a fraction of the gas from the galaxy (it depends on the initial conditions of the outflow). When the SNe are taken into account, the effect of the outflow is substantially reduced. It is necessary an initial velocity around 1000 km/s and a density larger than 0.003 particles.cm−3 for the outflow to propagate. In these conditions, the removal of gas from the galaxy is almost negligible at the end of the 3 Gyr of the simulation.
Planets form in protoplanetary accretion discs around young protostars. These discs are driven by internal turbulence and the gas flow is not laminar but has stochastic components. For weakly ionised discs the turbulence can be generated purely hydrodynamically through the vertical shear instability (VSI). Embedded particles (dust/pebbles) experience a hydrodynamic drag and drift inward radially and are stirred up vertically by the turbulent motion of the disc. We study the accretion of particles onto a forming planet embedded in a VSI turbulent protoplanetary disc through a series of 3D hydrodynamical simulations for locally isothermal discs with embedded planets in the mass range from 5 to 100 Earth masses (M2295).
During the early stages of planet formation accretion of small bodies add mass to the planet and deposit their energy kinetic energy. Caused by frictional heating and/or large stagnation pressures within the dense and extended atmospheres most of the in-falling bodies get destroyed by melting or break-up before they impact on the planet’s surface. The energy is added to the atmospheric layers rather than heating the planet directly. These processes can significantly alter the physical properties of protoplanets before they are exposed with their primordial atmospheres to the early stellar source when the protoplanetary disk becomes evaporated.
Dwarf spheroidal galaxies of the Local Group share a similar characteristic nowadays: a low amount of gas in their interiors. In this work, we present results from a three-dimensional hydrodynamical simulation of the gas inside an object with similar characteristics of the Ursa Minor galaxy. We evolved the initial gas distribution over 3 Gyr, considering the effects of the types Ia and II supernovae. The instantaneous supernovae rates were derived from a chemical evolution model applied to spectroscopic data of the Ursa Minor galaxy. Our simulation shows that the amount of gas that is lost varies with time and galactocentric radius. The highest gas-loss rates occurred during the first 600 Myr of evolution. Our results also indicate that types Ia and II supernovae must be essential drivers of the gas loss in Ursa Minor galaxy (and probably in other similar dwarf galaxies).
The discovery via gravitational waves of binary black hole systems with total masses greater than 60Mʘ has raised interesting questions for stellar evolution theory. Among the most promising formation channels for these systems is one involving a common envelope binary containing a low metallicity, core helium burning star with mass ⁓30 – 40Mʘ and a black hole with mass ⁓30 – 40Mʘ. For this channel to be viable, the common envelope binary must eject more than half the giant star’s mass and reduce its orbital separation by as much as a factor of 80. We discuss issues faced in numerically simulating the common envelope evolution of such systems and present a 3D AMR simulation of the dynamical inspiral of a low-metallicity red supergiant with a massive black hole companion.
Eta Carinae is the most massive active binary within 10,000 light-years. While famous for the largest non-terminal stellar explosion ever recorded, observations reveal a supermassive (∼120 M⊙) binary consisting of an LBV and either a WR or extreme O star in a very eccentric orbit (e=0.9) with a 5.54-year period. Dramatic changes across multiple wavelengths are routinely observed as the stars move about in their highly elliptical orbits, especially around periastron when the hot (∼40 kK) companion star delves deep into the denser and much cooler (∼15 kK) extended wind photosphere of the LBV primary. Many of these changes are due to a dynamic wind-wind collision region (WWCR) that forms between the stars, plus expanding radiation-illuminated fossil WWCRs formed one, two, and three 5.54-year orbital cycles ago. These fossil WWCRs have been spatially and spectrally resolved by the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS) at multiple epochs, resulting in data cubes that spatially map Eta Carinae’s innermost WWCRs and follow temporal changes in several forbidden emission lines (e.g. [Fe iii] 4659 Å, [Fe ii] 4815 Å) across the 5.54-year cycle. We present initial results of 3D time-dependent hydrodynamical and radiative-transfer simulations of the Eta Carinae binary and its WWCRs with the goal of producing synthetic data cubes of forbidden emission lines for comparison to the available HST/STIS observations. Comparison of the theoretical models to the observations reveals important details about the binary’s orbital motion, photoionization properties, and recent (5–15year) mass loss history. Such an analysis also provides a baseline for following future changes in Eta Carinae, essential for understanding the late-stage evolution of a nearby supernova progenitor. Our modeling methods can also be adapted to a number of other colliding wind binary systems (e.g. WR 140) that are scheduled to be studied with future observatories (e.g. the James Webb Space Telescope).
We use 3D radiative-hydrodynamics simulations of convection with CO5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the Gaia G band [325–1030 nm]. We calculate the intensity-weighted mean of all emitting points tiling the visible stellar surface (i.e., the photo-center) and evaluate its motion as a function of time. We show that the convection-related variability accounts for a substantial part to the Gaia DR2 parallax error of our sample of semiregular variables. Finally, we denote that Gaia parallax variations could be exploited quantitatively to extract stellar parameters using appropriate RHD simulations corresponding to the observed star.
In recent years dedicated observations have uncovered star formation at extremely low rates in dwarf galaxies, tidal tails, ram-pressure stripped gas clouds, and the outskirts of galactic disks. At the same time, numerical simulations of galaxy evolution have advanced to higher spatial and mass resolutions, but have yet to account for the underfilling of the uppermost mass bins of stellar initial mass function (IMF) at low star-formation rates. In such situations, simulations may simply scale down the IMF, without realizing that this unrealistically results in fractions of massive stars, along with fractions of massive star feedback energy (e.g., radiation and SNII explosions). Not properly accounting for such parameters has consequences for the self-regulation of star formation, the energetics of galaxies, as well as for the evolution of chemical abundances. Here we present numerical simulations of dwarf galaxies with low star-formation rates allowing for two extreme cases of the IMF: a “filled” case with fractional massive stars vs. a truncated IMF, at which the IMF is built bottom-up until the gas reservoir allows the formation of a last single star at an uppermost mass. The aim of the study is to demonstrate the different effects on galaxy evolution with respect to self-regulation, feedback, and chemistry. The case of a stochastic sampled IMF is situated somewhere in between these extremes.
Meteoritic evidence shows that the Solar system at birth contained significant quantities of short-lived radioisotopes (SLRs) such as 60Fe and 26Al produced in supernova explosions and in the Wolf-Rayet winds. Explaining how they travelled from these origin sites to the primitive Solar system before decaying is an outstanding problem. In this paper, we present a chemo-hydrodynamical simulation of the entire Milky Way to measure for the distribution of 60Fe/56Fe and 26Al/27Al ratios over all stars in the Galaxy. We show that the Solar abundance ratios are well within the normal range. We find that SLRs are abundant in newborn stars because star formation is correlated on Galactic scales, so that ejecta preferentially enrich atomic gas that will subsequently be accreted onto existing GMCs or will form new ones. Thus new generations of stars preferentially form in patches of the Galaxy contaminated by previous generations of stellar feedback.