Disk Theory Research Articles

A rotating disk study of the photocatalytic oxidation of p-nitrophenol on phosphorus-modified TiO2 photocatalyst

After discussing the general aspects of photocatalytic oxidation of organic compounds in aqueous solutions and the application of the rotating disk theory to (photo)catalytic phenomena, we report the oxidation of p-nitrophenol (PNP) on illuminated phosphorus modified TiO2 (P-TiO2) and TiO2 photocatalysts under controlled hydrodynamic conditions. We found that the performance of the oxygen transfer reaction can be described considering mass transport in solution and surface reaction according to Langmuir–Hinshelwood kinetics. From analysis of the dependence of the reaction rate on the rotation rate, we obtained the apparent organic–photocatalyst adduct interaction constant K, the rate constant k of the surface reaction between adsorbed PNP and hydroxyl radicals, and the diffusion coefficient D of PNP in solution. The results showed that degradation of PNP using P-TiO2 and UV light was readily possible, with reaction half-lives significantly lower than those obtained using pristine TiO2 photocatalyst.

Simultaneous optical and near-IR photometry of 4U1957+115 - a missing secondary star

We report the results of quasi-simultaneous optical and NIR photometry of the low-mass X-ray binary, 4U 1957+115. Our observations cover B, V, R, I, J, H and K-bands and additional time-series NIR photometry. We measure a spectral energy distribution, which can be modelled using a standard multi-temperature accretion disc, where the disc temperature and radius follow a power-law relation. Standard accretion disc theory predicts the power law exponent to be -3/4, and this yields, perhaps surprisingly, acceptable fits to our SED. Given that the source is a persistent X-ray source, it is however likely that the accretion disc temperature distribution is produced by X-ray heating, regardless of its radial dependence. Furthermore, we find no evidence for any emission from the secondary star at any wavelength. However, adding a secondary component to our model allows us to derive a 99\% lower limit of 14 or 15 kpc based on Monte Carlo simulations and using either an evolved K2 or G2V secondary star respectively. In $>$60\% of cases the distance is $>$80kpc. Such large distances favor models with a massive ($>$15 M$_{\odot}$) black hole primary. Our quasi-simultaneous J and V-band time-series photometry, together with the SED, reveals that the optical/NIR emission must originate in the same region i.e. the accretion disc. The likely extreme mass ratio supports suggestions that the accretion disc must be precessing which, depending on the length of the precession period, could play a major part in explaining the variety of optical light curve shapes obtained over the last two decades.

On the high-frequency spectrum of a classical accretion disc

Abstract We derive simple and explicit expressions for the high-frequency spectrum of a classical accretion disc. Both stress-free and finite stress inner boundaries are considered. A classical accretion disc spectrum with a stress-free inner boundary departs from a Wien spectrum at large ν, scaling as ν2.5 (as opposed to ν3) times the usual exponential cut-off. If there is finite stress at the inner disc boundary, the maximum disc temperature generally occurs at this edge, even at relatively modest values of the stress. In this case, the high-frequency spectrum is proportional to ν2 times the exponential cut-off. If the temperature maximum is a local hotspot, instead of an axisymmetric ring, then an interior maximum produces a ν2 prefactor while an edge maximum yields ν1.5. Because of beaming effects, these latter findings should pertain to a classical relativistic disc. The asymptotics are in general robust and independent of the detailed temperature profile, provided only that the liberated free energy of differential rotation is dissipated locally, and may prove useful beyond the strict domain of classical disc theory. As observations continue to improve with time, our findings suggest the possibility of using the high-energy spectral component of black hole candidates as a signature prediction of classical theory, as well as a diagnostic of the stress at the inner regions of an accretion disc.

Observational Appearance of Black Holes in X-Ray Binaries and AGN

Accretion onto black holes powers most luminous compact sources in the Universe. Black holes are found with masses extending over an extraordinary broad dynamic range, from several to a few billion times the mass of the Sun. Depending on their position on the mass scale, they may manifest themselves as X-ray binaries or active galactic nuclei. X-ray binaries harbor stellar mass black holes—endpoints of the evolution of massive stars. They have been studied by X-ray astronomy since its inception in the early 60-ies, however, the enigma of the most luminous of them—ultra-luminous X-ray sources, still remains unsolved. Supermassive black holes, lurking at the centers of galaxies, are up to hundreds of millions times more massive and give rise to the wide variety of different phenomena collectively termed “Active Galactic Nuclei”. The most luminous of them reach the Eddington luminosity limit for a few billions solar masses object and are found at redshifts as high as z≥5–7. Accretion onto supermassive black holes in AGN and stellar- and (possibly) intermediate mass black holes in X-ray binaries and ultra-luminous X-ray sources in star-forming galaxies can explain most, if not all, of the observed brightness of the cosmic X-ray background radiation. Despite the vast difference in the mass scale, accretion in X-ray binaries and AGN is governed by the same physical laws, so a degree of quantitative analogy among them is expected. Indeed, all luminous black holes are successfully described by the standard Shakura-Sunyaev theory of accretion disks, while the output of low-luminosity accreting black holes in the form of mechanical and radiative power of the associated jets obeys to a unified scaling relation, termed as the “fundamental plane of black holes”. From that standpoint, in this review we discuss formation of radiation in X-ray binaries and AGN, emphasizing their main similarities and differences, and examine our current knowledge of the demographics of stellar mass and supermassive black holes.

Limit cases for rotor theories with Betz optimization

A complete analytical formulation of the vortex approach for the rotor with an ideal load distribution under Betz optimal condition needs some additional assumption about a correct choice of the helical pitch for vortex sheets in the rotor wake. An examination of the three evident assumptions (the pitch is independent from velocities induced by the wake; the pitch depends on the induced velocities in the far wake; the pitch depends on the induced velocities in the rotor plane) was considered by a comparison with the main restriction of the actuator disk theory – the Betz-Joukowsky limit. In the present investigation an analytical solution for the limit case of an infinite number of blades was used to re-examine the choice of the wake pitch.

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Magnetic fields of laboratory, planetary, stellar, and galactic plasmas commonly exhibit significant order on large temporal or spatial scales compared to the otherwise random motions within the hosting system. Such ordered fields can be measured in the case of planets, stars, and galaxies, or inferred indirectly by the action of their dynamical influence, such as jets. Whether large scale fields are amplified in situ or a remnant from previous stages of an object’s history is often debated for objects without a definitive magnetic activity cycle. Magnetic helicity, a measure of twist and linkage of magnetic field lines, is a unifying tool for understanding large scale field evolution for both mechanisms of origin. Its importance stems from its two basic properties: (1) magnetic helicity is typically better conserved than magnetic energy; and (2) the magnetic energy associated with a fixed amount of magnetic helicity is minimized when the system relaxes this helical structure to the largest scale available. Here I discuss how magnetic helicity has come to help us understand the saturation of and sustenance of large scale dynamos, the need for either local or global helicity fluxes to avoid dynamo quenching, and the associated observational consequences. I also discuss how magnetic helicity acts as a hindrance to turbulent diffusion of large scale fields, and thus a helper for fossil remnant large scale field origin models in some contexts. I briefly discuss the connection between large scale fields and accretion disk theory as well. The goal here is to provide a conceptual primer to help the reader efficiently penetrate the literature.

THERMAL STABILITY OF A THIN DISK WITH MAGNETICALLY DRIVEN WINDS

The absence of thermal instability in the high/soft state of black hole X-ray binaries, in disagreement with the standard thin disk theory, is a long-standing riddle for theoretical astronomers. We have tried to resolve this question by studying the thermal stability of a thin disk with magnetically driven winds in the $\dot{M}- \Sigma$ plane. It is found that disk winds can greatly decrease the disk temperature and thus help the disk become more stable at a given accretion rate. The critical accretion rate $\dot{M}_{\rm crit}$ corresponding to the thermal instability threshold is increased significantly in the presence of disk winds. For $\alpha=0.01$ and $B_{\rm \phi}=10B_{\rm _p}$, the disk is quite stable even for a very weak initial poloidal magnetic field [$\beta_{\rm p,0}\sim 2000, \beta_{\rm p}=(P_{\rm {gas}}+P_{\rm rad})/(B_{\rm p}^2/8\pi)$]. But when $B_{\rm \phi}=B_{\rm _p}$ or $B_{\rm \phi}=0.1B_{\rm _p}$, a somewhat stronger (but still weak) field ($\beta_{\rm p,0}\sim 200$ or $\beta_{\rm p,0}\sim 20$) is required to make the disk stable. Nevertheless, despite the great increase of $\dot{M}_{\rm crit}$, the luminosity threshold corresponding to instability remains almost constant or even decreases slowly with increasing $\dot{M}_{\rm crit}$ due to the decrease of gas temperature. The advection and diffusion timescales of the large-scale magnetic field threading the disk are also investigated in this work. We find that the advection timescale can be smaller than the diffusion timescale in a disk with winds, because the disk winds take away most of the gravitational energy released in the disk, resulting in the decrease of the magnetic diffusivity $\eta$ and the increase of the diffusion timescale.

On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor

An analytical treatment to quantify the losses captured in the induced power factor, k, is provided for flapping wings in normal hover, including the effects of non-uniform downwash, tip losses and finite flapping amplitude. The method is based on a novel combination of actuator disc and lifting line blade theories that also takes into account the effect of advance ratio. The model has been evaluated against experimental results from the literature and qualitative agreement obtained for the effect of advance ratio on the lift coefficient of revolving wings. Comparison with quantitative experimental data for the circulation as a function of span for a fruitfly wing shows that the model is able to correctly predict the circulation shape of variation, including both the magnitude of the peak circulation and the rate of decay in circulation towards zero. An evaluation of the contributions to induced power factor in normal hover for eight insects is provided. It is also shown how Reynolds number can be accounted for in the induced power factor, and good agreement is obtained between predicted span efficiency as a function of Reynolds number and numerical results from the literature. Lastly, it is shown that for a flapping wing in hover k owing to the non-uniform downwash effect can be reduced to 1.02 using an arcsech chord distribution. For morphologically realistic wing shapes based on beta distributions, it is shown that a value of 1.07 can be achieved for a radius of first moment of wing area at 40% of wing length.

Actuator Disk Theory—Steady and Unsteady Models

In this paper, the classical work on steady actuator disk theory is recalled and the interpretation of the flow as the continuous shedding of vortex rings of constant strength that causes the slip stream is shown to be consistent with the classical model, yet offers a different approach that provides more flexibility for the extension to unsteady flow. The ring model is in agreement with the conservation law theorems which indicate that the axial inductance inside the streamtube, far downstream, is twice that at the rotor disk. The actuator disk relationship between the power and the axial inductance at the rotor plane has been used previously to construct the prescribed wake in the 3D vortex line model (VLM) of the author. The local pitch of the vortex sheet helices is based on the axial inductance along the streamtube, therefore, it is important to be able to calculate the axial inductance in all cases. In unsteady flow, the strength of the shed rings varies with power absorbed by the rotor and a new relationship between the two is derived to first-order, using the unsteady Bernoulli equation, which allows to calculate the inductance at the rotor and in the wake with the Biot-Savart law, even in cases where the Betz limit is exceeded. This more rigorous model can replace the semi empirical models such as dynamic stall and dynamic inflow used in the blade element method (BEM). The proposed new model has been incorporated in the VLM and applied to two sets of experiments, the Tjaereborg in-field tests and the NREL wind tunnel campaign, for which test data has been collected and serves for the comparison. The simulations show an overall good agreement with the experimental data. In some tests, the power coefficient exceeds the Betz limit, in which cases there are no solutions to the steady actuator disk theory, but the new model provides a solution for the inductance even in this case.

Bipartite bound entanglement in continuous variables through degaussification

We introduce a class of bipartite entangled continuous variable states that are positive under partial transposition operation, i.e., PPT bound entangled. These states are based on realistic preparation procedures in optical systems, being thus a feasible option to generate and observe genuinely bipartite bound entanglement in high precision experiments. One fundamental step in our scheme is to perform a non-Gaussian operation over a single-mode Gaussian state; this deGaussification procedure is achieved through a modified single-photon addition, which is a procedure that has currently being investigated in diverse optical setups. Although dependent on a single-photon detection in a idler channel, the preparation can be made unconditional after a calibration of the apparatus. The detection and proof of bound entanglement is made by means of the Range Criterion, theory of Hankel operators and Gerschgorin Disk s perturbation theorems.

THE AVERAGE SIZE AND TEMPERATURE PROFILE OF QUASAR ACCRETION DISKS

We use multi-wavelength microlensing measurements of a sample of 10 image pairs from 8 lensed quasars to study the structure of their accretion disks. By using spectroscopy or narrow band photometry we have been able to remove contamination from the weakly microlensed broad emission lines, extinction and any uncertainties in the large-scale macro magnification of the lens model. We determine a maximum likelihood estimate for the exponent of the size versus wavelength scaling ($r_s\propto \lambda^p$ corresponding to a disk temperature profile of $T\propto r^{-1/p}$) of $p=0.75^{+0.2}_{-0.2}$, and a Bayesian estimate of $p=0.8\pm0.2$, which are significantly smaller than the prediction of thin disk theory ($p=4/3$). We have also obtained a maximum likelihood estimate for the average quasar accretion disk size of $r_s=4.5^{+1.5}_{-1.2} $ lt-day at a rest frame wavelength of $\lambda = 1026~{\mathrm \AA}$ for microlenses with a mean mass of $M=1 M_\sun$, in agreement with previous results, and larger than expected from thin disk theory.

Centred and staggered arrangements of tidal turbines

AbstractIn this paper we extend linear momentum actuator disc theory to consider two rows of tidal turbines placed in a centred or staggered arrangement. The extensions assume a streamwise spacing between rows that is sufficient for pressure equalization, but is not too large for significant mixing of the upstream turbine wake before the second row. We first consider a given number of turbines in a tidal channel; in this case the average power for a staggered arrangement over two rows is found to be higher than that for a centred arrangement, but lower than can be obtained by placing all turbines side-by-side in one row (if all turbines have the same local resistance). Furthermore, staggered arrangements extract power more efficiently than centred arrangements, but less efficiently than a single row with the same number of turbines, and this has implications for ranking different arrangements of tidal turbines. We also use the extended actuator disc models (together with an argument of scale separation) to consider some example arrangements of tidal turbines in laterally unconfined flow. Specifically, it is shown that locally staggering a fixed number of turbines in an array to form a tidal farm generates less power than placing the same number of turbines side-by-side. However, if more than one row of turbines is adopted (perhaps to keep the farm spatially compact) then the optimum turbine spacing within a row increases significantly with addition of a second row. This trend suggests that multi-row tidal turbine farms would require wide turbine spacing within each row to maximize the power per turbine, similarly to existing offshore wind farms.

The effects of array configuration on the hydro-environmental impacts of tidal turbines

The economic viability of tidal turbines will require the deployment of multiple devices in array formations in a manner analogous to wind farms. This research investigates the effects of the configuration of a tidal turbine array, specifically the turbine spacing and capacity, on the hydro-environmental impacts of the array. The hydrodynamic regime of the Shannon Estuary, a highly energetic estuary on the west coast of Ireland, was simulated using a depth integrated 2D hydro-environmental model. The numerical model was modified to incorporate the mechanics of energy extraction using linear momentum actuator disc theory and the impacts of a multiple device array were simulated. Three different array configurations were examined with turbine spacings of 0.5, 2 and 5 rotor diameters. The model results demonstrate that flows are attenuated inside the array and accelerated around the array. Water levels are also affected with a reduction in tidal range within, and upstream of, the array and a delay in high and low tides upstream of the array. The magnitude and extent of the observed impacts are found to reduce as the density and capacity are increased and that the impacts of large-scale arrays can be acceptable if deployed using a low density spacing of 5 rotor diameters.

Tidal stream energy resource assessment of the Anglesey Skerries

Many candidate sites for tidal stream power devices can be classified as headlands. This paper analyses one such site, off Anglesey. In order to investigate the disturbance to the local flow field due to the operation of tidal arrays and evaluate the extractable power at the site, a two-dimensional depth-averaged shallow water model of the naturally occurring tidal dynamics of the south-west UK and Irish Sea has been developed and validated. In the model, the effect of tidal arrays is represented by line discontinuities where upstream and downstream heads are related by Linear Momentum Actuator Disk Theory. A parametric study to investigate the importance of array locations, the connectivity of the arrays and local blockage effects on the available power has been undertaken. General conclusions from this analysis are that it is usually advantageous to arrange tidal turbines in long rows rather than as a number of rows in series, and that arrays with higher local blockage outperform arrays with lower blockage.

The available power from tidal stream turbines in the Pentland Firth

This paper assesses an upper bound for the tidal stream power resource of the Pentland Firth. A depth-averaged numerical model of the tidal dynamics in the region is set-up and validated against field measurements. Actuator disc theory is used to model the effect of turbines on the flow, and to estimate the power available for generation after accounting for losses owing to mixing downstream of the turbines. It is found that three rows of turbines extending across the entire width of the Pentland Firth and blocking a large fraction of the channel can theoretically generate 1.9 GW, averaged over the spring–neap cycle. However, generation of significantly more power than this is unlikely to be feasible as the available power per additional swept area of turbine is too small to be viable. Our results differ from those obtained using simplified tidal channel models of the type used commonly in the literature. We also use our numerical model to investigate the available power from rows of turbines placed across various subchannels within the Pentland Firth, together with practical considerations such as the variation in power over the spring–neap tidal cycle and the changes to natural tidal flows which result from power extraction.

Vane-Turbine as an Energy Conversion in the Propeller Slipstream of Single Screw Ship

The screw propeller of a ship generates thrust to make it moving. As a propeller rotates, it draws fluid into itself from the surrounding area (slipstream). The propeller produces two types of flow behind it, accelerated and circulated flows. Some of the energy from the ship engine is lost in the accelerated flow behind ship as a jet wash.The kinetic energy losses in the slipstream propeller captured by a turbine called the propeller-turbine system. This composed screw propeller of a vessel (the main propeller) and a vane turbine that is the area of vanes located inside the wake of the main propeller. It recovers the energy generated by the main propeller pushing water back out (which would be otherwise wasted behind the main propeller) and hopefully enhancing the efficiency of the main propeller.The influence of vane turbine on the performance breakdown of single screw ships were analyzed by using 5 (five) ships . Ship powering was calculated by using DESP Code 10 software. Thrust and power of vane turbine were calculated by applying actuator disc theory. Although the vane turbine affected speed loss of the ship, the power efficiency gained to be found always positive. Vane turbine is suitable as an energy saving device of the single screw ship.

Rotating Disks Made from Materials with Negative Poisson's Ratio

Auxetic materials are those that exhibit negative Poissons ratio. In spite of their rarity, auxetic materials have been artificially produced and also found to exist are known to exist naturally. Arising from their anomalous behavior, research on auxetic materials has been carried out for possible applications in fields as diverse as biomechanics and aero-structures. This paper investigates the effect of auxeticity on the maximum stress in thin and thick rotating disks. The obtained results show that maximum stresses are lower in rotating thin disks that are made from negative Poissons ratio materials. It is also revealed that the maximum stresses in thick rotating disks can be reasonably approximated by rotating thin disk theory if the thick disk material possesses negative Poissons ratio.

A CHANGE IN THE QUIESCENT X-RAY SPECTRUM OF THE NEUTRON STAR LOW-MASS X-RAY BINARY MXB 1659–29

The quasi-persistent neutron star low-mass X-ray binary MXB 1659-29 went into quiescence in 2001, and we have followed its quiescent X-ray evolution since. Observations over the first 4 years showed a rapid drop in flux and temperature of the neutron star atmosphere, interpreted as cooling of the neutron star crust which had been heated during the 2.5 year outburst. However, observations taken approximately 1400 and 2400 days into quiescence were consistent with each other, suggesting the crust had reached thermal equilibrium with the core. Here we present a new Chandra observation of MXB 1659-29 taken 11 years into quiescence and 4 years since the last Chandra observation. This new observation shows an unexpected factor of ~3 drop in count rate and change in spectral shape since the last observation, which cannot be explained simply by continued cooling. Two possible scenarios are that either the neutron star temperature has remained unchanged and there has been an increase in the column density, or, alternatively the neutron star temperature has dropped precipitously and the spectrum is now dominated by a power-law component. The first scenario may be possible given that MXB 1659-29 is a near edge-on system, and an increase in column density could be due to build-up of material in, and a thickening of, a truncated accretion disk during quiescence. But, a large change in disk height may not be plausible if standard accretion disk theory holds during quiescence. Alternatively, the disk may be precessing, leading to a higher column density during this latest observation.

TIME DELAY AND ACCRETION DISK SIZE MEASUREMENTS IN THE LENSED QUASAR SBS 0909+532 FROM MULTIWAVELENGTH MICROLENSING ANALYSIS

We present three complete seasons and two half-seasons of SDSS r-band photometry of the gravitationally lensed quasar SBS 0909+532 from the U.S. Naval Observatory, as well as two seasons each of SDSS g-band and r-band monitoring from the Liverpool Robotic Telescope. Using Monte Carlo simulations to simultaneously measure the system's time delay and model the r-band microlensing variability, we confirm and significantly refine the precision of the system's time delay to \Delta t_{AB} = 50^{+2}_{-4} days, where the stated uncertainties represent the bounds of the formal 1\sigma\ confidence interval. There may be a conflict between the time delay measurement and a lens consisting of a single galaxy. While models based on the Hubble Space Telescope astrometry and a relatively compact stellar distribution can reproduce the observed delay, the models have somewhat less dark matter than we would typically expect. We also carry out a joint analysis of the microlensing variability in the r- and g-bands to constrain the size of the quasar's continuum source at these wavelengths, obtaining log[(r_{s,r}/cm) [cos{i}/0.5]^{1/2}] = 15.3 \pm 0.3 and log[(r_{s,g}/cm) [cos{i}/0.5]^{1/2}] = 14.8 \pm 0.9, respectively. Our current results do not formally constrain the temperature profile of the accretion disk but are consistent with the expectations of standard thin disk theory.

The local stability of accretion disk models with considering the role of various viscosity and cooling mechanisms

The standard thin accretion disk model can explain the soft X-ray spectra of Galactic black hole systems and AGN successfully. However, there are still a few observational documents for Radiation pressure theory in X-ray novae in black hole binary systems and AGN. The luminosity in accretion onto black holes is corresponds to L>0.01L E . According to standard thin disk model, when the accretion rate is over a small fraction of the Eddington rate, L>0.01L E , the inner region of the disk is radiation-pressure-dominated and thermally unstable. However, observations of the high/soft state of black hole X-ray binaries with luminosity within (0.01L E <L<0.5L E ) show that the disk is quite stable. Thus, this contradiction shows the objection of this model and maybe it is essential to change the standard viscosity law or one of the other basic assumptions in order to get a stable disk models. In this paper, we revisit and recalculate the thermal instability with a different models of viscosity and cooling functions and show that the choosing of an arbitrary cooling and viscosity functions can affect on the stability of a general disk model and hence maybe answer to a this problem in accretion disk theory. We choose an arbitrary functions of surface density Σ and half thickness of disk H for cooling and viscosity. Also, we discuss a general disk with thermal conduction, radial force and advection. Then, we solve the equations numerically. We obtain a fourth degree dispersions relation and discuss solutions and instability modes. This analysis shows the great sensitivity of stability of disk to the form of viscosity, so there are various effective factors to stabilize the disk. For example the exist of advection and thermal conduction can effect to stability of disks also.