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Energy forecasting models deployed in industrial applications face uncertainty w.r.t. data availability, due to network latency, equipment malfunctions or data-integrity attacks. In particular, the case when a subset of features that has been used for model training becomes unavailable when the model is used operationally poses a major challenge to forecasting performance. Ad-hoc solutions, e.g., retraining without the missing features, may work for a small number of features, but they soon become impractical, as the number of models grows exponentially with the number of features. In this work, we present a principled approach to introducing resilience against missing features in energy forecasting applications via robust optimization. Specifically, we formulate a robust regression model that is optimally resilient against missing features at test time, considering both point and probabilistic forecasting. We develop three solution methods for the proposed robust formulation, all leading to Linear Programming problems, with varying degrees of tractability and conservativeness. We provide an extensive empirical validation of the proposed methods in prevalent applications, namely, electricity price, load, wind production, and solar production, forecasting, and we further compare against well-established benchmark models and methods of dealing with missing features, i.e., imputation and retraining. Our results demonstrate that the proposed robust optimization approach outperforms imputation-based models and exhibits similar performance to retraining without the missing features, while also maintaining computational practicality. To the best of our knowledge, this is the first work that introduces resilience against missing features into energy forecasting.

Although flux variability is one of the defining properties of accretion flows onto supermassive black holes, its dependence on physical parameters such as the mass of the compact object and the Eddington ratio remain under discussion. In this paper we address this issue using the structure function statistic to measure the variability at X-ray wavelengths of a sample of optically selected QSOs with available black hole masses and Eddington ratios. We present a new Bayesian methodology for estimating the structure function tailored to the Poisson nature of the X-ray data. This is applied to 15,548 SDSS DRQ16 QSOs with repeat observations in the XMM-Newton archive and/or the SRG/eROSITA All Sky Survey. The X-ray structure function monotonically increases to time intervals of about 10-15 years, suggesting a preference for scenarios in which instabilities of the accretion disk contribute to the X-ray variability on long timescales. Additionally, there is evidence that the amplitude of the stochastic X-ray flux variations rises with decreasing black hole mass and Eddington ratio. This finding imposes stringent constraints on empirical models of Active Galactic Nuclei variability derived from local samples, emphasizing the significance of high-redshift population studies for comprehending the stochastic flux variations in active black holes., Comment: 12 pages, 11 figure, MNRAS submitted, the code used in this paper is available at https://github.com/ageorgakakis/StructureFunction

XMM-Newton, a European Space Agency observatory, has been observing the X-ray, ultra-violet and optical sky for 23 years. During this time, astronomy has evolved from mainly studying single sources to populations and from a single wavelength, to multi-wavelength or messenger data. We are also moving into an era of time domain astronomy. New software and methods are required to accompany evolving astronomy and prepare for the next generation X-ray observatory, Athena. Here we present XMM2ATHENA, a programme funded by the European Union's Horizon 2020 research and innovation programme. XMM2ATHENA builds on foundations laid by the XMM-Newton Survey Science Centre (XMM-SSC), including key members of this consortium and the Athena Science ground segment, along with members of the X-ray community. The project is developing and testing new methods and software to allow the community to follow the X-ray transient sky in quasi-real time, identify multi-wavelength or messenger counterparts of XMM-Newton sources and determine their nature using machine learning. We detail here the first milestone delivery of the project, a new online, sensitivity estimator. We also outline other products, including the forthcoming innovative stacking procedure and detection algorithms to detect the faintest sources. These tools will then be adapted for Athena and the newly detected or identified sources will enhance preparation for observing the Athena X-ray sky., Comment: 7 pages, 1 figure, accepted for publication in Astronomische Nachrichten

XMM-Newton, a European Space Agency observatory, has been observing the X-ray, ultra-violet, and optical sky for 23 years. During this time, astronomy has evolved from mainly studying single sources to populations and from a single wavelength, to multi-wavelength/messenger data. We are also moving into an era of time domain astronomy. New software and methods are required to accompany evolving astronomy and prepare for the next-generation X-ray observatory, Athena. Here we present XMM2ATHENA, a program funded by the European Union's Horizon 2020 research and innovation program. XMM2ATHENA builds on foundations laid by the XMM-Newton Survey Science Centre (XMM-SSC), including key members of this consortium and the Athena Science ground segment, along with members of the X-ray community. The project is developing and testing new methods and software to allow the community to follow the X-ray transient sky in quasi-real time, identify multi-wavelength/messenger counterparts of XMM-Newton sources and determine their nature using machine learning. We detail here the first milestone delivery of the project, a new online, sensitivity estimator. We also outline other products, including the forthcoming innovative stacking procedure and detection algorithms, to detect the faintest sources. These tools will then be adapted for Athena and the newly detected/identified sources will enhance preparation for observing the Athena X-ray sky.

The black hole mass MBH is crucial in constraining the growth of supermassive BHs within their host galaxies. Since direct measurements of MBH with dynamical methods are restricted to a limited number of nearly quiescent nearby galaxies and a small minority of active galactic nuclei (AGN), we must rely on indirect methods. In this work, we utilize an unbiased, volume-limited, hard X-ray selected sample of AGN to compare the reliability of some commonly used indirect methods, emphasising those that can be applied to obscured AGN. Based on a subsample of AGN with MBH determined via dynamical methods, our study suggests that X-ray based techniques, such as the scaling method and the one based on the variability measured through the excess variance, are in good agreement with the dynamical methods. On the other hand, the M-sigma correlation based on inactive galaxies tends to systematically overestimate MBH, regardless of the level of obscuration. We provide a correcting factor that produces an acceptable agreement with dynamical values and can be used to quickly correct the MBH computed with this method. We also derive an alternative M-sigma correlation based on this unbiased sample of AGN with a slope considerably shallower than the ones obtained using inactive galaxies, suggesting that the latter correlation may not be appropriate to compute the MBH in AGN. Finally, we find that no quick fix can be applied to correct the MBH obtained from the fundamental plane of black hole activity, casting doubts on the reliability of this method., Comment: 15 pages, 9 figures, 3 tables, Accepted for publication in MNRAS

The recent serendipitous discovery of a new population of short duration X-ray transients, thought to be associated with collisions of compact objects or stellar explosions in distant galaxies, has motivated efforts to build up statistical samples by mining X-ray telescope archives. Most searches to date however, do not fully exploit recent developments in the signal and imaging processing research domains to optimise searches for short X-ray flashes. This paper addresses this issue by presenting a new source detection pipeline, STATiX (Space and Time Algorithm for Transients in X-rays), which directly operates on 3-dimensional X-ray data cubes consisting of two spatial and one temporal dimension. The algorithm leverages wavelet transforms and the principles of sparsity to denoise X-ray observations and then detect source candidates on the denoised data cubes. The light curves of the detected sources are then characterised using the Bayesian blocks algorithm to identify flaring periods. We describe the implementation of STATiX in the case of XMM-Newton data, present extensive validation and performance verification tests based on simulations and also apply the pipeline to a small subset of seven XMM-Newton observations, which are known to contain transients sources. In addition to known flares in the selected fields we report a previously unknown short duration transient found by our algorithm that is likely associated with a flaring Galactic star. This discovery demonstrates the potential of applying STATiX to the full XMM-Newton archive., Comment: 18 pages, accepted for publication in MNRAS

Algorithms that involve both forecasting and optimization are at the core of solutions to many difficult real-world problems, such as in supply chains (inventory optimization), traffic, and in the transition towards carbon-free energy generation in battery/load/production scheduling in sustainable energy systems. Typically, in these scenarios we want to solve an optimization problem that depends on unknown future values, which therefore need to be forecast. As both forecasting and optimization are difficult problems in their own right, relatively few research has been done in this area. This paper presents the findings of the ``IEEE-CIS Technical Challenge on Predict+Optimize for Renewable Energy Scheduling," held in 2021. We present a comparison and evaluation of the seven highest-ranked solutions in the competition, to provide researchers with a benchmark problem and to establish the state of the art for this benchmark, with the aim to foster and facilitate research in this area. The competition used data from the Monash Microgrid, as well as weather data and energy market data. It then focused on two main challenges: forecasting renewable energy production and demand, and obtaining an optimal schedule for the activities (lectures) and on-site batteries that lead to the lowest cost of energy. The most accurate forecasts were obtained by gradient-boosted tree and random forest models, and optimization was mostly performed using mixed integer linear and quadratic programming. The winning method predicted different scenarios and optimized over all scenarios jointly using a sample average approximation method.

Our objective is to critically assess the X-ray flux variability as a tool for measuring the black hole (BH) mass in active galactic nuclei (AGN). We aim to establish a prescription for estimating BH masses based on measurements of the normalised excess variance from X-ray data. We discuss the minimum requirements in terms of the light-curve duration and X-ray signal-to-noise ratio (S/N) to enable a reliable determination that is comparable to what can be derived from the continuum and emission line reverberation studies. We used the light curves of local Seyfert from the Nuclear Spectroscopic Telescope Array hard X-ray mission (NuSTAR), to compute the normalised excess variance (NXV) in the 3-10 and 10-20 keV bands, thus extending the analysis to an energy band higher than 10 keV. The excess variance measurements were then combined with independent BH mass estimates from the literature to establish the MBH versus NXV relation for different samples and weigh its accuracy in terms of the light-curve duration and X-ray S/N. We find that it is possible to accurately measure the BH mass in AGN using excess variance measurements in the 3-10 and the 10-20 keV bands, however, strong quality requirements should be applied. The minimum necessary S/N and duration of the light curves used to compute the excess variance ought to be 3 and approximately 100 ks, respectively. We provide a linear relationship between the normalised excess variance and the black hole mass that can be used to estimate the latter, with an average uncertainty of the order of 0.4 to 0.25 dex (depending on the adopted light-curve segment duration)., Comment: 20 pages, 8 figures

© 2020 BMJ Publishing Group. All rights reserved. The mean flow induced by a three-dimensional propagating internal gravity wave beam in a uniformly stratified fluid is studied experimentally and theoretically. Previous related work concentrated on the early stage of mean-flow generation, dominated by the phenomenon of streaming - a horizontal mean flow that grows linearly in time - due to resonant production of mean potential vorticity in the vicinity of the beam. The focus here, by contrast, is on the long-time mean-flow evolution. Experimental observations in a stratified fluid tank for times up to, where is the beam period, reveal that the induced mean flow undergoes three distinct stages: (i) resonant growth of streaming in the beam vicinity; (ii) saturation of streaming and onset of horizontal advection; and (iii) establishment of a quasi-steady state where the mean flow is highly elongated and stretches in the along-tank horizontal direction. To capture (i)-(iii), the theoretical model of Fan et al. (J. Fluid Mech., vol. 838, 2018, R1) is extended by accounting for the effects of horizontal advection and viscous diffusion of mean potential vorticity. The predictions of the proposed model, over the entire mean-flow evolution, are in excellent agreement with the experimental observations as well as numerical simulations based on the full Navier-Stokes equations.

The Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable ene

The Active Galactic Nuclei (AGN) produce copious amounts of X-rays through the corona that is the hot gas that lies close to the accretion disk. The temperature of the corona can be accurately determined by the cut-off signature in the X-ray spectrum. Owing to the large temperatures of the corona, observations well above 10 keV are necessary. Here, we explore the NuSTAR observations of 118 Gehrels/Swift selected Seyfert 1 AGN. We model the spectrum using a single power-law with an exponential cut-off modified by neutral and ionised absorption as well as a reflection component. We find secure spectral cut-off estimates in 62 sources while for the remaining ones we derive only lower limits. The mean value is 103 keV with a skewed distribution towards large energies with large dispersion. When we consider the lower limits using survival analysis techniques, the mean cut-off energy becomes significantly larger, about 200 keV. Because of various limitations (e.g. limited spectral passband, photon statistics, model degeneracies) we perform extensive simulations to explore the underlying spectral cut-off distribution. We find that an intrinsic spectral cut-off distribution which has a Maxwell-Boltzmann shape with a mean value in the range of 160 - 200 keV can reproduce sufficiently well the observations. Finally, our spectral analysis places very stringent constraints on both the photon index (Gamma=1.77+/-0.01) as well as on the reflection component (R=0.69+/-0.04) of the Seyfert 1 population. From the values of the spectral cut-off and the photon-index we deduce that the mean optical depth of the AGN corona is approximately tau=1.82+/-0.14 and its mean temperature approximately kT=65+/-10 keV., Comment: Accepted for publication in A&A

This paper presents the construction of the RapidXMM database that is available through the XMM-Newton Science Archive and offers access to upper limits and aperture photometry across the field of view of the XMM-Newton Pointed and Slew Survey observations. The feature of RapidXMM is speed. It enables the fast retrieval of X-ray upper limits and photometry products in three energy bands (0.2-2, 2-12, 0.2-12 keV) for large numbers of input sky positions. This is accomplished using the Hierarchical Equal Area Iso Latitude pixelation of the sphere (HEALPix). The pre-calculated upper-limits and associated X-ray photometry products are reprojected into the HEALPix grid of cells before being ingested into the RapidXMM database. This results in tables of upper limits and aperture photometry within HEALPix cells of size ~3 arcsec (Pointed Observations) and ~6 arcsec (Slew Survey). The database tables are indexed by the unique integer number of the HEALPix cells. This reduces spatial nearest-neighbor queries by sky position to an integer-matching exercise and significantly accelerates the retrieval of results. We describe in detail the processing steps that lead from the science products available in the XMM-Newton archive to a database optimised for sky queries. We also present two simple show-case applications of RapidXMM for scientific studies: searching for variable X-ray sources, and stacking analysis of X-ray faint populations, Comment: 20 pages, 20 figures. This article has been accepted for publication in MNRAS. Published by Oxford University Press on behalf of the Royal Astronomical Society

Author Posting. © American Meteorological Society, 2021. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 102(1), (2021): E99-E122, https://doi.org/10.1175/BAMS-D-19-0005.1., The Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable ene, The development of the Red Sea modeling system is being supported by the Virtual Red Sea Initiative and the Competitive Research Grants (CRG) program from the Office of Sponsored Research at KAUST, Saudi Aramco Company through the Saudi ARAMCO Marine Environmental Center at KAUST, and by funds from KAEC, NEOM, and RSP through Beacon Development Company at KAUST.

Author Posting. © American Meteorological Society, 2021. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 102(1), (2021): E99-E122, https://doi.org/10.1175/BAMS-D-19-0005.1., The Red Sea, home to the second-longest coral reef system in the world, is a vital resource for the Kingdom of Saudi Arabia. The Red Sea provides 90% of the Kingdom’s potable water by desalinization, supporting tourism, shipping, aquaculture, and fishing industries, which together contribute about 10%–20% of the country’s GDP. All these activities, and those elsewhere in the Red Sea region, critically depend on oceanic and atmospheric conditions. At a time of mega-development projects along the Red Sea coast, and global warming, authorities are working on optimizing the harnessing of environmental resources, including renewable energy and rainwater harvesting. All these require high-resolution weather and climate information. Toward this end, we have undertaken a multipronged research and development activity in which we are developing an integrated data-driven regional coupled modeling system. The telescopically nested components include 5-km- to 600-m-resolution atmospheric models to address weather and climate challenges, 4-km- to 50-m-resolution ocean models with regional and coastal configurations to simulate and predict the general and mesoscale circulation, 4-km- to 100-m-resolution ecosystem models to simulate the biogeochemistry, and 1-km- to 50-m-resolution wave models. In addition, a complementary probabilistic transport modeling system predicts dispersion of contaminant plumes, oil spill, and marine ecosystem connectivity. Advanced ensemble data assimilation capabilities have also been implemented for accurate forecasting. Resulting achievements include significant advancement in our understanding of the regional circulation and its connection to the global climate, development, and validation of long-term Red Sea regional atmospheric–oceanic–wave reanalyses and forecasting capacities. These products are being extensively used by academia, government, and industry in various weather and marine studies and operations, environmental policies, renewable ene, The development of the Red Sea modeling system is being supported by the Virtual Red Sea Initiative and the Competitive Research Grants (CRG) program from the Office of Sponsored Research at KAUST, Saudi Aramco Company through the Saudi ARAMCO Marine Environmental Center at KAUST, and by funds from KAEC, NEOM, and RSP through Beacon Development Company at KAUST.

Motivated by the question of whether and how wave–wave interactions should be implemented into atmospheric gravity-wave parametrizations, the modulation of triadic gravity-wave interactions by a slowly varying and vertically sheared mean flow is considered for a non-rotating Boussinesq fluid with constant stratification. An analysis using a multiple-scale WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) expansion identifies two distinct scaling regimes, a linear off-resonance regime, and a nonlinear near-resonance regime. Simplifying the near-resonance interaction equations allows for the construction of a parametrization for the triadic energy exchange which has been implemented into a one-dimensional WKBJ ray-tracing code. Theory and numerical implementation are validated for test cases where two wave trains generate a third wave train while spectrally passing through resonance. In various settings, of interacting vertical wavenumbers, mean-flow shear, and initial wave amplitudes, the WKBJ simulations are generally in good agreement with wave-resolving simulations. Both stronger mean-flow shear and smaller wave amplitudes suppress the energy exchange among a resonantly interacting triad. Experiments with mean-flow shear as strong as in the vicinity of atmospheric jets suggest that internal gravity-wave dynamics are dominated in such regions by wave modulation. However, triadic gravity-wave interactions are likely to be relevant in weakly sheared regions of the atmosphere., NSF (AC 71/8-2), NSF (AC 71/9-2), NSF (AC 71/10-2), NSF (AC 71/11-2), NSF (AC 71/12-2), NSF (BO 5071/1-2), NSF (631 DMS-1512925)

© 2020 BMJ Publishing Group. All rights reserved. The mean flow induced by a three-dimensional propagating internal gravity wave beam in a uniformly stratified fluid is studied experimentally and theoretically. Previous related work concentrated on the early stage of mean-flow generation, dominated by the phenomenon of streaming - a horizontal mean flow that grows linearly in time - due to resonant production of mean potential vorticity in the vicinity of the beam. The focus here, by contrast, is on the long-time mean-flow evolution. Experimental observations in a stratified fluid tank for times up to, where is the beam period, reveal that the induced mean flow undergoes three distinct stages: (i) resonant growth of streaming in the beam vicinity; (ii) saturation of streaming and onset of horizontal advection; and (iii) establishment of a quasi-steady state where the mean flow is highly elongated and stretches in the along-tank horizontal direction. To capture (i)-(iii), the theoretical model of Fan et al. (J. Fluid Mech., vol. 838, 2018, R1) is extended by accounting for the effects of horizontal advection and viscous diffusion of mean potential vorticity. The predictions of the proposed model, over the entire mean-flow evolution, are in excellent agreement with the experimental observations as well as numerical simulations based on the full Navier-Stokes equations.

The Active Galactic Nuclei (AGN) produce copious amounts of X-rays through the corona that is the hot gas that lies close to the accretion disk. The temperature of the corona can be accurately determined by the cut-off signature in the X-ray spectrum. Owing to the large temperatures of the corona, observations well above 10 keV are necessary. Here, we explore the NuSTAR observations of 118 Gehrels/Swift selected Seyfert 1 AGN. We model the spectrum using a single power-law with an exponential cut-off modified by neutral and ionised absorption as well as a reflection component. We find secure spectral cut-off estimates in 62 sources while for the remaining ones we derive only lower limits. The mean value is 103 keV with a skewed distribution towards large energies with large dispersion. When we consider the lower limits using survival analysis techniques, the mean cut-off energy becomes significantly larger, about 200 keV. Because of various limitations (e.g. limited spectral passband, photon statistics, model degeneracies) we perform extensive simulations to explore the underlying spectral cut-off distribution. We find that an intrinsic spectral cut-off distribution which has a Maxwell-Boltzmann shape with a mean value in the range of 160 - 200 keV can reproduce sufficiently well the observations. Finally, our spectral analysis places very stringent constraints on both the photon index (Gamma=1.77+/-0.01) as well as on the reflection component (R=0.69+/-0.04) of the Seyfert 1 population. From the values of the spectral cut-off and the photon-index we deduce that the mean optical depth of the AGN corona is approximately tau=1.82+/-0.14 and its mean temperature approximately kT=65+/-10 keV., Comment: Accepted for publication in A&A

This paper presents the construction of the RapidXMM database that is available through the XMM-Newton Science Archive and offers access to upper limits and aperture photometry across the field of view of the XMM-Newton Pointed and Slew Survey observations. The feature of RapidXMM is speed. It enables the fast retrieval of X-ray upper limits and photometry products in three energy bands (0.2-2, 2-12, 0.2-12 keV) for large numbers of input sky positions. This is accomplished using the Hierarchical Equal Area Iso Latitude pixelation of the sphere (HEALPix). The pre-calculated upper-limits and associated X-ray photometry products are reprojected into the HEALPix grid of cells before being ingested into the RapidXMM database. This results in tables of upper limits and aperture photometry within HEALPix cells of size ~3 arcsec (Pointed Observations) and ~6 arcsec (Slew Survey). The database tables are indexed by the unique integer number of the HEALPix cells. This reduces spatial nearest-neighbor queries by sky position to an integer-matching exercise and significantly accelerates the retrieval of results. We describe in detail the processing steps that lead from the science products available in the XMM-Newton archive to a database optimised for sky queries. We also present two simple show-case applications of RapidXMM for scientific studies: searching for variable X-ray sources, and stacking analysis of X-ray faint populations, Comment: 20 pages, 20 figures. This article has been accepted for publication in MNRAS. Published by Oxford University Press on behalf of the Royal Astronomical Society

Motivated by the question of whether and how wave–wave interactions should be implemented into atmospheric gravity-wave parametrizations, the modulation of triadic gravity-wave interactions by a slowly varying and vertically sheared mean flow is considered for a non-rotating Boussinesq fluid with constant stratification. An analysis using a multiple-scale WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) expansion identifies two distinct scaling regimes, a linear off-resonance regime, and a nonlinear near-resonance regime. Simplifying the near-resonance interaction equations allows for the construction of a parametrization for the triadic energy exchange which has been implemented into a one-dimensional WKBJ ray-tracing code. Theory and numerical implementation are validated for test cases where two wave trains generate a third wave train while spectrally passing through resonance. In various settings, of interacting vertical wavenumbers, mean-flow shear, and initial wave amplitudes, the WKBJ simulations are generally in good agreement with wave-resolving simulations. Both stronger mean-flow shear and smaller wave amplitudes suppress the energy exchange among a resonantly interacting triad. Experiments with mean-flow shear as strong as in the vicinity of atmospheric jets suggest that internal gravity-wave dynamics are dominated in such regions by wave modulation. However, triadic gravity-wave interactions are likely to be relevant in weakly sheared regions of the atmosphere.

Motivated by the laboratory experiments of Rodenborn et al. [Phys. Fluids 23, 026601 (2011)PHFLE61070-663110.1063/1.3553294], a weakly nonlinear model is developed that accounts for viscous dissipation in the reflection of a finite-width internal wave beam from a uniform slope. Asymptotically, at high Reynolds number, viscous effects come into play predominantly in the immediate vicinity of the critical slope angle equal to the propagation angle to the horizontal of the incident wave beam. However, in the experiments of Rodenborn et al. where the Reynolds number is moderately large, it turns out that viscosity is important throughout the slope range considered, which explains the overall poor agreement of their observations with earlier inviscid models. The predictions of the proposed model, by contrast, are in good qualitative, and in some respects quantitative, agreement with these experiments, and they also compare favorably against numerical Navier-Stokes simulations., NSF under Grant No. DMS-1512925

Internal gravity wavetrains in continuously stratified fluids are generally unstable as a result of resonant triad interactions that amplify short-scale perturbations with frequency equal to one half of that ofthe underlying wave. This so-called parametric subharmonic instability (PSI) has been studied extensively for spatially and temporally monochromatic waves, as a potential mechanism for transferring energy from large-scale internal waves to small-scale mixing in oceans. However, the PSI found in stability analyses ofpurely monochromatic wavetrains may not be entirely relevant to ocean internal waves, as such highly idealized disturbances are not encountered in the field. Instead, tidally generated ocean internal waves are often in the form of beams—time-harmonic plane waves with general spatial profile—that propagate along a direction to the vertical determined by the wave frequency. Here, we present an asymptotic analysis of PSI of internal wave beams in an effort to understand how these more realistic disturbances differ, in regard to PSI, from monochromatic waves.

We present the X-ray spectroscopic study of the Compton-thick (CT) active galactic nuclei (AGN) population within the $\textit{Chandra}$ Deep Field South (CDF-S) by using the deepest X-ray observation to date, the $\textit{Chandra}$ 7 Ms observation of the CDF-S. We combined an opimized version of our automated selection technique and a Bayesian Monte Carlo Markov Chains (MCMC) spectral fitting procedure, to develop a method to pinpoint and then characterize candidate CT AGN as less model dependent and/or data-quality dependent as possible. To obtain reliable automated spectral fits, we only considered the sources detected in the hard (2-8 keV) band from the CDF-S 2 Ms catalog with either spectroscopic or photometric redshifts available for 259 sources. Instead of using our spectral analysis to decide if an AGN is CT, we derived the posterior probability for the column density, and then we used it to assign a probability of a source being CT. We also tested how the model-dependence of the spectral analysis, and the spectral data quality, could affect our results by using simulations. We finally derived the number density of CT AGN by taking into account the probabilities of our sources being CT and the results from the simulations. Our results are in agreement with X-ray background synthesis models, which postulate a moderate fraction (25%) of CT objects among the obscured AGN population., Comment: 7 pages, 5 figures, accepted for publication in A&A

The hard X-ray sky at energies above 10 keV, has been extensively explored by the Swift and the NuSTAR missions in the 14-195 keV and the 3-24 keV bands respectively. The major population of the hard X-ray detected sources are AGN. We compare the number count distributions derived from the swift 105-month catalogue with those from the serendipitous NuSTAR source catalogue. In the 14-195 keV band, the Swift/BAT counts follow a Euclidean slope with alpha=1.51+/-0.10 (90% confidence level). The NuSTAR counts in the 8-24 keV band present a steeper slope with alpha = 1.71+/- 0.2$, because of an upturn at fluxes below ~2x10^{-13} erg/cm2/s. The same upturn is observed in the soft (3-8 keV) NuSTAR number counts, which in overall also present a steep slope with alpha = 1.82+/- 0.15. Only the bright part of the NuSTAR 3-8 keV counts agrees with the chandra number counts in the 2-10 keV band while the fainter part (<7x10^{-13} erg/cm2/s ) of the soft NuSTAR counts is in marked disagreement with the chandra counts. Next, we compare the derived number counts in the different bands using our X-ray AGN population synthesis models. The comparison between the Chandra and the Swift/BAT number counts shows a very good agreement for the 'standard' AGN spectrum with a power-law slope Gamma=1.9, a high energy cut-off at ~130 keV and a 2-10 keV reflection component of 3%. On the other hand, using the above standard AGN spectral model, only the bright part of the NuSTAR 8-24 keV and 3-8 keV number counts, agree with the model predictions. Then it is most likely that the disagreement between the X-ray number counts in the different bands is because of the faint NuSTAR number counts. We discuss various possibilities for the origin of this disagreement., Comment: To appear in Astronomy & Astrophysics

The hard X-ray sky at energies above 10 keV, has been extensively explored by the Swift and the NuSTAR missions in the 14-195 keV and the 3-24 keV bands respectively. The major population of the hard X-ray detected sources are AGN. We compare the number count distributions derived from the swift 105-month catalogue with those from the serendipitous NuSTAR source catalogue. In the 14-195 keV band, the Swift/BAT counts follow a Euclidean slope with alpha=1.51+/-0.10 (90% confidence level). The NuSTAR counts in the 8-24 keV band present a steeper slope with alpha = 1.71+/- 0.2$, because of an upturn at fluxes below ~2x10^{-13} erg/cm2/s. The same upturn is observed in the soft (3-8 keV) NuSTAR number counts, which in overall also present a steep slope with alpha = 1.82+/- 0.15. Only the bright part of the NuSTAR 3-8 keV counts agrees with the chandra number counts in the 2-10 keV band while the fainter part (<7x10^{-13} erg/cm2/s ) of the soft NuSTAR counts is in marked disagreement with the chandra counts. Next, we compare the derived number counts in the different bands using our X-ray AGN population synthesis models. The comparison between the Chandra and the Swift/BAT number counts shows a very good agreement for the 'standard' AGN spectrum with a power-law slope Gamma=1.9, a high energy cut-off at ~130 keV and a 2-10 keV reflection component of 3%. On the other hand, using the above standard AGN spectral model, only the bright part of the NuSTAR 8-24 keV and 3-8 keV number counts, agree with the model predictions. Then it is most likely that the disagreement between the X-ray number counts in the different bands is because of the faint NuSTAR number counts. We discuss various possibilities for the origin of this disagreement., Comment: To appear in Astronomy & Astrophysics

We present the X-ray spectroscopic study of the Compton-thick (CT) active galactic nuclei (AGN) population within the $\textit{Chandra}$ Deep Field South (CDF-S) by using the deepest X-ray observation to date, the $\textit{Chandra}$ 7 Ms observation of the CDF-S. We combined an opimized version of our automated selection technique and a Bayesian Monte Carlo Markov Chains (MCMC) spectral fitting procedure, to develop a method to pinpoint and then characterize candidate CT AGN as less model dependent and/or data-quality dependent as possible. To obtain reliable automated spectral fits, we only considered the sources detected in the hard (2-8 keV) band from the CDF-S 2 Ms catalog with either spectroscopic or photometric redshifts available for 259 sources. Instead of using our spectral analysis to decide if an AGN is CT, we derived the posterior probability for the column density, and then we used it to assign a probability of a source being CT. We also tested how the model-dependence of the spectral analysis, and the spectral data quality, could affect our results by using simulations. We finally derived the number density of CT AGN by taking into account the probabilities of our sources being CT and the results from the simulations. Our results are in agreement with X-ray background synthesis models, which postulate a moderate fraction (25%) of CT objects among the obscured AGN population., Comment: 7 pages, 5 figures, accepted for publication in A&A

As present weather forecast codes and increasingly many atmospheric climate models resolve at least part of the mesoscale flow, and hence also internal gravity waves (GWs), it is natural to ask whether even in such configurations subgrid-scale GWs might impact the resolved flow and how their effect could be taken into account. This motivates a theoretical and numerical investigation of the interactions between unresolved submesoscale and resolved mesoscale GWs, using Boussinesq dynamics for simplicity. By scaling arguments, first a subset of submesoscale GWs that can indeed influence the dynamics of mesoscale GWs is identified. Therein, hydrostatic GWs with wavelengths corresponding to the largest unresolved scales of present-day limited-area weather forecast models are an interesting example. A large-amplitude WKB theory, allowing for a mesoscale unbalanced flow, is then formulated, based on multiscale asymptotic analysis utilizing a proper scale-separation parameter. Purely vertical propagation of submesoscale GWs is found to be most important, implying inter alia that the resolved flow is only affected by the vertical flux convergence of submesoscale horizontal momentum at leading order. In turn, submesoscale GWs are refracted by mesoscale vertical wind shear while conserving their wave-action density. An efficient numerical implementation of the theory uses a phase-space ray tracer, thus handling the frequent appearance of caustics. The WKB approach and its numerical implementation are validated successfully against submesoscale-resolving simulations of the resonant radiation of mesoscale inertia GWs by a horizontally as well as vertically confined submesoscale GW packet. Keywords: Dynamics; Gravity waves; Internal waves; Subgrid-scale processes; Resonance; Parameterization

The all-sky hard X-ray survey performed by Swift/BAT allowed the detection of many heavily obscured Compton-thick AGN. In our previous work, we have identified more than 50 candidate Compton-thick AGN in the local Universe, corresponding to an observed fraction of about 7% of the total AGN population. This number can be converted to the intrinsic Compton-thick AGN number density, only if we know the form of the Compton-thick AGN spectrum, that is the energy of their absorption turnover, photon-index and its cut-off energy at high energies, as well as the strength of the reflection component on the matter surrounding the nucleus. In order to constrain their number density, we analyse the spectra of 19 Compton-thick AGN which have been detected with Swift/BAT and have been subsequently observed with NuSTAR in the 3-80 keV band. We analyse their X-ray spectra using the MYTORUS models of Murphy and Yaqoob which properly take into account the Compton scattering effects. These are combined with physically motivated Comptonisation models which accurately describe the primary coronal X-ray emission. We derive absorbing column densities which are consistent with those derived by the previous Swift/BAT analyses. We estimate the coronal temperatures to be roughly between 25 and 80 keV corresponding to high energy cut-offs roughly between 75 and 250 keV. We find that the majority of our AGN lacks a strong reflection component in the 20-40 keV band placing tighter constraints on the intrinsic Compton-thick AGN fraction. Combining these results with our X-ray background synthesis models, we estimate a Compton-thick AGN fraction in the local Universe of ~20 +/-3 % relative to the type-II AGN population., Comment: Accepted for publication in Astronomy and Astrophysics

The all-sky hard X-ray survey performed by Swift/BAT allowed the detection of many heavily obscured Compton-thick AGN. In our previous work, we have identified more than 50 candidate Compton-thick AGN in the local Universe, corresponding to an observed fraction of about 7% of the total AGN population. This number can be converted to the intrinsic Compton-thick AGN number density, only if we know the form of the Compton-thick AGN spectrum, that is the energy of their absorption turnover, photon-index and its cut-off energy at high energies, as well as the strength of the reflection component on the matter surrounding the nucleus. In order to constrain their number density, we analyse the spectra of 19 Compton-thick AGN which have been detected with Swift/BAT and have been subsequently observed with NuSTAR in the 3-80 keV band. We analyse their X-ray spectra using the MYTORUS models of Murphy and Yaqoob which properly take into account the Compton scattering effects. These are combined with physically motivated Comptonisation models which accurately describe the primary coronal X-ray emission. We derive absorbing column densities which are consistent with those derived by the previous Swift/BAT analyses. We estimate the coronal temperatures to be roughly between 25 and 80 keV corresponding to high energy cut-offs roughly between 75 and 250 keV. We find that the majority of our AGN lacks a strong reflection component in the 20-40 keV band placing tighter constraints on the intrinsic Compton-thick AGN fraction. Combining these results with our X-ray background synthesis models, we estimate a Compton-thick AGN fraction in the local Universe of ~20 +/-3 % relative to the type-II AGN population., Comment: Accepted for publication in Astronomy and Astrophysics

Parametric subharmonic instability (PSI) of internal wave beams in a uniformly stratified fluid is discussed, for the case where the beam frequency is nearly twice the inertial frequency due to background rotation. Compared with generic PSI, beams of finite width are expected on physical grounds to be more vulnerable to subharmonic perturbations of near-inertial frequency, as these disturbances have small group velocity and stay in contact with the underlying beam longer, thus extracting more energy. A weakly nonlinear theory for such near-inertial PSI is developed in the "distinguished limit" where the effects of triad nonlinear interactions, dispersion, and viscous dissipation are equally important. This model is used to examine the linear stability of a uniform beam to infinitesimal perturbations under a "pump-wave" approximation, as well as the nonlinear development of PSI that takes into account the effect of the growing perturbations on the beam evolution. Near-inertial PSI is possible for beams of general locally confined profile, in sharp contrast to generic PSI which can arise only for quasimonochromatic beams whose profile comprises a sinusoidal carrier modulated by a locally confined envelope. The theoretical predictions are consistent with earlier numerical simulations of semidiurnal internal tide beams generated over the continental shelf break at latitudes above and below the critical value 28.8âN, at which the subharmonic semidiurnal frequency matches the local inertial frequency., National Science Foundation (U.S.) (Grant DMS-1107335), National Science Foundation (U.S.) (Grant DMS-1512925)

The wave pattern generated by a pressure source moving over the free surface of deep water at speeds, U, below the minimum phase speed for linear gravity–capillary waves, cmin, was investigated experimentally using a combination of photographic measurement techniques. In similar experiments, using a single pressure amplitude, Diorio et al. (Phys. Rev. Lett., vol. 103, 2009, 214502) pointed out that the resulting surface response pattern exhibits remarkable nonlinear features as U approaches cmin, and three distinct response states were identified. Here, we present a set of measurements for four surface-pressure amplitudes and provide a detailed quantitative examination of the various behaviours. At low speeds, the pattern resembles the stationary state (U = 0), essentially a circular dimple located directly under the pressure source (called a state I response). At a critical speed, but still below cmin, there is an abrupt transition to a wave-like state (state II) that features a marked increase in the response amplitude and the formation of a localized solitary depression downstream of the pressure source. This solitary depression is steady, elongated in the cross-stream relative to the streamwise direction, and resembles freely propagating gravity–capillary ‘lump’ solutions of potential flow theory on deep water. Detailed measurements of the shape of this depression are presented and compared with computed lump profiles from the literature. The amplitude of the solitary depression decreases with increasing U (another known feature of lumps) and is independent of the surface pressure magnitude. The speed at which the transition from states I to II occurs decreases with increasing surface pressure. For speeds very close to the transition point, time-dependent oscillations are observed and their dependence on speed and pressure magnitude are reported. As the speed approaches cmin, a second transition is observed. Here, the steady solitary depression gives way to an u, National Science Foundation (U.S.) (NSF grant DMS-0604416), National Science Foundation (U.S.) (NSF grant DMS-098122), National Science Foundation (U.S.) (NSF grant OCE-751853), United States. Air Force Office of Scientific Research (AFSOR (grant FA9550-07-0005)), ARCS Foundation

Modern cosmological simulations rely heavily on feedback from active galactic nuclei (AGN) in order to stave off overcooling in massive galaxies and galaxy groups and clusters. An important independent test is whether or not the simulations capture the broad demographics of the observed AGN population. Here, we have used the cosmo-OWLS suite of cosmological hydrodynamical simulations to produce realistic synthetic catalogs of X-ray AGN out to $z$=3, with the aim of comparing the catalogs to the observed X-ray AGN population in the XXL survey and other recent surveys. We focused on the unabsorbed X-ray luminosity function (XLF), the Eddington ratio distribution, the black hole mass function, and the projected clustering of X-ray AGN. To compute the unabsorbed XLF of the simulated AGN, we used recent empirically-determined bolometric corrections. We show that the simulated AGN sample accurately reproduces the observed XLF over 3 orders of magnitude in X-ray luminosity in all redshift bins. To compare to the observed Eddington ratio distribution and the clustering of AGN, we produced detailed 'XMM-Newton-detected' catalogs of the simulated AGN. This requires the production of synthetic X-ray images extracted from light cones of the simulations that fold in the relevant instrumental effects of XMM-Newton. We apply a luminosity- and redshift-dependent obscuration function for the AGN and employ the same AGN detection algorithm as used for the real XXL survey. We demonstrate that the detected population of simulated AGN reproduces the observed Eddington ratio distribution and projected clustering from XXL quite well. We conclude that the simulations have a broadly realistic population of AGN and that our synthetic X-ray AGN catalogs should be useful for interpreting additional trends and as a helpful tool for quantifying AGN contamination in galaxy group and cluster X-ray surveys., Comment: 14 pages, accepted for publication in A&A

Mid-IR colour selection techniques have proved to be very efficient in finding AGN. This is because the AGN heats the surrounding dust producing warm mid-IR colours. Using the WISE 3.6, 4.5 and 12 $\mu m$ colours, the largest sample of IR selected AGN has already been produced containing 1.4 million AGN over the whole sky. Here, we explore the X-ray properties of this AGN sample by cross-correlating it with the subsample of the 3XMM X-ray catalogue that has available X-ray spectra and at the same time optical spectroscopy from SDSS. Our goal is to find rare luminous obscured AGN. Our final sample contains 65 QSOs with $\rm{log}\,\nu L_\nu \ge 46.2$\,erg\,s$^{-1}$. This IR luminosity cut corresponds to $\rm{log}\,L_X \approx 45$\,erg\,s$^{-1}$, at the median redshift of our sample ($z=2.3$), that lies at the bright end of the X-ray luminosity function at $z>2$. The X-ray spectroscopic analysis reveals seven obscured AGN having a column density $\rm N_H>10^{22} cm^{-2}$. Six of them show evidence for broad [CIV] absorption lines and five are classified as BALQSOs. We fit the optical spectra of our X-ray absorbed sources to estimate the optical reddening. We find that none of these show any obscuration according to the optical continuum. These sources add to the growing evidence for populations of luminous QSOs with evidence for substantial absorption by outflowing ionised material, similar to those expected to be emerging from their absorbing cocoons in the framework of AGN/galaxy co-evolution., Comment: 10 pages, 5 figures, 3 Tables, MNRAS accepted

This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media.

This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media.

Modern cosmological simulations rely heavily on feedback from active galactic nuclei (AGN) in order to stave off overcooling in massive galaxies and galaxy groups and clusters. An important independent test is whether or not the simulations capture the broad demographics of the observed AGN population. Here, we have used the cosmo-OWLS suite of cosmological hydrodynamical simulations to produce realistic synthetic catalogs of X-ray AGN out to $z$=3, with the aim of comparing the catalogs to the observed X-ray AGN population in the XXL survey and other recent surveys. We focused on the unabsorbed X-ray luminosity function (XLF), the Eddington ratio distribution, the black hole mass function, and the projected clustering of X-ray AGN. To compute the unabsorbed XLF of the simulated AGN, we used recent empirically-determined bolometric corrections. We show that the simulated AGN sample accurately reproduces the observed XLF over 3 orders of magnitude in X-ray luminosity in all redshift bins. To compare to the observed Eddington ratio distribution and the clustering of AGN, we produced detailed 'XMM-Newton-detected' catalogs of the simulated AGN. This requires the production of synthetic X-ray images extracted from light cones of the simulations that fold in the relevant instrumental effects of XMM-Newton. We apply a luminosity- and redshift-dependent obscuration function for the AGN and employ the same AGN detection algorithm as used for the real XXL survey. We demonstrate that the detected population of simulated AGN reproduces the observed Eddington ratio distribution and projected clustering from XXL quite well. We conclude that the simulations have a broadly realistic population of AGN and that our synthetic X-ray AGN catalogs should be useful for interpreting additional trends and as a helpful tool for quantifying AGN contamination in galaxy group and cluster X-ray surveys., Comment: 14 pages, accepted for publication in A&A

Mid-IR colour selection techniques have proved to be very efficient in finding AGN. This is because the AGN heats the surrounding dust producing warm mid-IR colours. Using the WISE 3.6, 4.5 and 12 $\mu m$ colours, the largest sample of IR selected AGN has already been produced containing 1.4 million AGN over the whole sky. Here, we explore the X-ray properties of this AGN sample by cross-correlating it with the subsample of the 3XMM X-ray catalogue that has available X-ray spectra and at the same time optical spectroscopy from SDSS. Our goal is to find rare luminous obscured AGN. Our final sample contains 65 QSOs with $\rm{log}\,\nu L_\nu \ge 46.2$\,erg\,s$^{-1}$. This IR luminosity cut corresponds to $\rm{log}\,L_X \approx 45$\,erg\,s$^{-1}$, at the median redshift of our sample ($z=2.3$), that lies at the bright end of the X-ray luminosity function at $z>2$. The X-ray spectroscopic analysis reveals seven obscured AGN having a column density $\rm N_H>10^{22} cm^{-2}$. Six of them show evidence for broad [CIV] absorption lines and five are classified as BALQSOs. We fit the optical spectra of our X-ray absorbed sources to estimate the optical reddening. We find that none of these show any obscuration according to the optical continuum. These sources add to the growing evidence for populations of luminous QSOs with evidence for substantial absorption by outflowing ionised material, similar to those expected to be emerging from their absorbing cocoons in the framework of AGN/galaxy co-evolution., Comment: 10 pages, 5 figures, 3 Tables, MNRAS accepted

This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media.

This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media.

This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media.

We consider a model consisting of two subsystems with crossing linear dispersion curves that describes, for example, light propagation in binary waveguide arrays. This model admits bright-dark gap solitons in both the discrete and the continuous (long-wavelength) limits, in spite of the absence of a gap in the linear (i.e., plane-wave) spectrum. We find that these solitons are always modulationally unstable in the continuous limit, whereas they can be stable in the discrete system if the amplitude of the background component exceeds a certain threshold., Fondazione Cariplo (Grant number 2008-2290), Fondazione Cariplo (Grant number 2010-0595), United States. Army (Grant Number W911NF-11-1-0285), National Science Foundation (U.S.). (Grant number ECCS-1128593)

We present the properties of X-ray detected dust obscured galaxies (DOGs) in the Chandra Deep Field South. In recent years, it has been proposed that a significant percentage of the elusive Compton-thick (CT) active galactic nuclei (AGN) could be hidden among DOGs. In a previous work, we presented the properties of X-ray detected DOGs by making use of the deepest X-ray observations available at that time, the 2Ms observations of the Chandra deep fields. In that work, we only found a moderate percentage ($<$ 50%) of CT AGN among the DOGs sample, but we were limited by poor photon statistics. In this paper, we use not only a deeper 6 Ms Chandra survey of the Chandra Deep Field South (CDF-S), but combine these data with the 3 Ms XMM-Newton survey of the CDF-S. We also take advantage of the great coverage of the CDF-S region from the UV to the far-IR to fit the spectral energy distributions (SEDs) of our sources. Out of the 14 AGN composing our sample, 9 are highly absorbed (but only 3 could be CT AGN), whereas 2 look unabsorbed, and the other 3 are only moderately absorbed. In only one of the CT AGN, we detect a strong Fe K$\alpha$ emission line; the source is already classified as a CT AGN with Chandra data in a previous work. For the other two CT candidates, the non-detection of the line could be because of the low number of counts in their X-ray spectra, but their location in the L$_{\rm 2-10\,keV}$/L$_{12\mu m}$ plot supports their CT classification. Although a higher number of CT sources could be hidden among the X-ray undetected DOGs, our results indicate that DOGs could be as well composed of only a fraction of CT AGN plus a number of moderate to highly absorbed AGN, as previously suggested. From our study of the X-ray undetected DOGs in the CDF-S, we estimate a percentage between 13 and 44% of CT AGN among the whole population of DOGs., Comment: 12 pages, 5 figues, accepted for publication in A&A

The 70-month Swift/BAT catalogue provides a sensitive view of the extragalactic X-ray sky at hard energies (>10 keV) containing about 800 Active Galactic Nuclei. We explore its content in heavily obscured, Compton-thick AGN by combining the BAT (14-195 keV) with the lower energy XRT (0.3-10 keV) data. We apply a Bayesian methodology using Markov chains to estimate the exact probability distribution of the column density for each source. We find 53 possible Compton-thick sources (with probability 3 to 100%) translating to a ~7% fraction of the AGN in our sample. We derive the first parametric luminosity function of Compton-thick AGN. The unabsorbed luminosity function can be represented by a double power-law with a break at $L_{\star} 2 \times 10^{42}$ $\rm ergs~s^{-1}$ in the 20-40 keV band., Comment: 13 pages, 9 figures

The angular correlation function is a powerful tool for deriving the clustering properties of AGN and hence the mass of the corresponding dark matter halos in which they reside. However, studies based on the application of the angular correlation function on X-ray samples, yield results apparently inconsistent with those based on the direct estimation of the spatial correlation function. The goal of the present paper is to attempt to investigate this issue by analysing a well defined sample. To this end we use the hard-band (2-10 keV) X-ray selected sources of the Chandra AEGIS fields, chosen because of the availability of accurately derived flux sensitivity maps. In particular we use the 186 hard-band sources with spectroscopic redshifts in the range z=0.3-1.3, a range selected in order to contain the bulk of the AGN while minimizing the contribution of unknown clustering and luminosity evolution from very high redshifts. Using the projected spatial auto-correlation function, we derive a clustering comoving length of 5.4+-1.0 Mpc (for gamma=1.8), consistent with results in the literature. We further derive the angular correlation function and the corresponding spatial clustering length using the Limber's inversion equation and a novel parametrization of the clustering evolution model that also takes into account the bias evolution of the host dark matter halo. The Limber's inverted spatial comoving clustering length of 5.5+-1.2 Mpc at a median redshift of z~0.75, matches the directly measured one, from the spatial correlation function analysis, but for a significant non-linear contribution to the growing mode of perturbations, estimated independently from literature results of x_0 at different redshifts. Therefore, using this sample of X-ray AGN and our clustering evolution parametrization we have found an excellent consistency between the angular and spatial clustering analysis., Comment: A&A in press, 9 pages, 6 figures

The propagation of wave disturbances in water of uniform depth is discussed, accounting for both gravity and compressibility effects. In the linear theory, free-surface (gravity) waves are virtually decoupled from acoustic (compression) waves, because the speed of sound in water far exceeds the maximum phase speed of gravity waves. However, these two types of wave motion could exchange energy via resonant triad nonlinear interactions. This scenario is analysed for triads comprising a long-crested acoustic mode and two oppositely propagating subharmonic gravity waves. Owing to the disparity of the gravity and acoustic length scales, the interaction time scale is longer than that of a standard resonant triad, and the appropriate amplitude evolution equations, apart from the usual quadratic interaction terms, also involve certain cubic terms. Nevertheless, it is still possible for monochromatic wavetrains to form finely tuned triads, such that nearly all the energy initially in the gravity waves is transferred to the acoustic mode. This coupling mechanism, however, is far less effective for locally confined wavepackets., MIT-Technion Fellowship