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The measure of partial mutual information from mixed embedding (PMIME) is an information theory-based measure to accurately identify the direct and directional coupling, termed Granger causality or simply causality, between the observed variables or subsystems of a high-dimensional dynamical and complex system, without any a priori assumptions about the nature of the coupling relationship. In its core, it is a forward selection procedure that aims to iteratively identify the lag-dependence structure of a given observed variable (response) to all the other observed variables (candidate drivers). This model-free approach is capable of detecting nonlinear interactions, abundantly present in real-world complex systems, and it was shown to perform well on multivariate time series of moderately high dimension. However, the PMIME presents some inefficiencies in its performance mainly when applied on strongly stochastic (linear or nonlinear) systems as it may falsely detect non-existent relationships. Moreover, and by construction, the measure cannot extract purely synergetic relationships present in a system. In the current work, the issue of false detections is addressed by introducing an improved resampling significance test and a procedure of rechecking the identified drivers (backward revision). Regarding the inability to detect synergetic relationships, the PMIME is further enhanced by checking pairs as candidate drivers for the response variable after having considered all drivers individually. The effects of these modifications are investigated in a systematic simulation study on properly designed systems involving strong stochasticity, regressor terms with synergetic effects, and a system dimension ranging from 3 to 30. The overall results of the simulations indicate that these modifications indeed improve the performance of PMIME and alleviate to a significant degree the issues of the original algorithm. Guidelines for balancing between accuracy and computational efficiency are also given, particularly relevant for real-world applications. Finally, the measure performance is investigated in the study of futures of various government bonds and stock market indices in the period around COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point detection may not be sensitive to it. In this article, we present a novel scheme for detecting structural breaks through the occurrence or vanishing of nonlinear causal relationships in a complex system. A significance resampling test was developed for the null hypothesis (H0) of no nonlinear causal relationships using (a) an appropriate Gaussian instantaneous transform and vector autoregressive (VAR) process to generate the resampled multivariate time series consistent with H0; (b) the modelfree Granger causality measure of partial mutual information from mixed embedding (PMIME) to estimate all causal relationships; and (c) a characteristic of the network formed by PMIME as test statistic. The significance test was applied to sliding windows on the observed multivariate time series, and the change from rejection to no-rejection of H0, or the opposite, signaled a non-trivial change of the underlying dynamics of the observed complex system. Different network indices that capture different characteristics of the PMIME networks were used as test statistics. The test was evaluated on multiple synthetic complex and chaotic systems, as well as on linear and nonlinear stochastic systems, demonstrating that the proposed methodology is capable of detecting nonlinear causality. Furthermore, the scheme was applied to different records of financial indices regarding the global financial crisis of 2008, the two commodity crises of 2014 and 2020, the Brexit referendum of 2016, and the outbreak of COVID-19, accurately identifying the structural breaks at the identified times. [ABSTRACT FROM AUTHOR]

Deriving decisions from data typically involves a sequential process with two components, forecasting and optimization. Forecasting models learn by minimizing a loss function that stands as a proxy for task-specific costs (e.g., trading, scheduling) without considering the downstream optimization, which in practice creates a performance bottleneck and obscures the impact of data on decisions. This work proposes a single data-driven module that leverages the structure of the optimization component and directly learns a policy conditioned on explanatory data. For this purpose, we describe an algorithm to train ensembles of decision trees by directly minimizing task-specific costs, and prescribe decisions via a weighted Sample Average Approximation of the original problem. We then develop a generic framework to assess the impact of explanatory data on prescriptive performance. To illustrate the efficacy of the proposed modeling approach, we consider two case studies related to trading renewable energy. First, we examine trading in a day-ahead market and propose strategies that balance optimal trading decisions and predictive accuracy. Next, we append a storage device and co-optimize the day-ahead offers and the operational policy, based on a tractable approximation using the linear decision rule approach. The empirical results demonstrate improved prescriptive performance compared to solutions derived under the standard stochastic optimization framework. Further, we provide valuable insights on how explanatory data impact optimization performance and how this impact evolves under different market designs. [ABSTRACT FROM AUTHOR]

Streptococcal infection remains the leading cause of neonatal sepsis and death. Systematic use of antibiotic prophylaxis and advanced neonatal care guidelines aiming in the restriction and elimination of adverse effects on neonatal Group B Streptococcus disease neither eliminated it nor restricted it. Maternal immunisation with a Group B Streptococcus vaccine is considered the best strategy for the prevention of both early and late-onset invasive Group B Streptococcus disease. However, such an effective vaccine has yet to be fully licensed, although various attempts through the years have been made. At present, a hexavalent Ia, Ib, II, III, IV and V glyco-conjugate vaccine has completed Phase I clinical trials, showed promising results among healthy adults and was allowed to undergo Phase II trials. The early observations are promising allowing larger studies for determining the factors of optimal efficacy, such as timing of administration. The specific timing of administering a Group B Streptococcus vaccine during pregnancy has yet to be determined, although evidence show that for maximum levels of anti Group B Streptococcus antibodies to be transferred to the fetus, the best time of administration is during the second half of pregnancy or early on the third trimester. Furthermore, it remains uncertain if the vaccine should be recommended to all pregnant women, only those at higher risk or those testing positive, nor are specified the benefits of a second dose. In addition, a large Phase III clinical trial is required in order to evaluate possible adverse effects, including neuro-developmental assessments of the infants born to vaccinated mothers prior to licensing any vaccine candidate. [ABSTRACT FROM AUTHOR]

A simple method is presented for estimating the specific storage of a confined aquifer from an overdamped slug test in a fully penetrating well. This method is based on the quasi-steady flow model developed previously by the authors, simplified to decoupled algebraic equations upon using Hvorslev's estimate of the hydraulic conductivity. The model equations are solved efficiently on a spreadsheet sequentially. The ability of the algebraic method to estimate the specific storage of a confined aquifer is assessed against slug test data from three field cases and against sets of synthetic data generated with the rigorous Cooper-Bredehoeft-Papadopulos method, which is used as reference. The algebraic method estimates the order of magnitude of the specific storage correctly in all three field cases, with two of them arithmetically very close to the Cooper-Bredehoeft-Papadopulos solution, while the hydraulic parameters computed with the numerical quasi-steady solution nearly match the reference values. In the cases of synthetic data, the algebraic method estimates the specific storage reliably when the storage parameter α equals 10−4 and within an order of magnitude when α equals 10−5. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A notable feature of Kelvin surface-wave patterns due to submerged sources at small Froude numbers (F ≪ 1) is that the wave amplitudes are exponentially small with respect to F. Moreover, as F → 0 the assumption of linearization is not appropriate. Thus, the role of nonlinear effects in Kelvin wake patterns at small F hinges on exponential ('beyond-all-orders') asymptotics. This outstanding theoretical issue is addressed here in the context of a simple partial differential equation with a quadratic nonlinear term, controlled by a parameter ɛ , and a locally confined forcing term in two spatial dimensions. The linear far-field wave response of this model equation is akin to a Kelvin wake whose wave amplitudes are exponentially small with respect to a parameter μ , analogous to F in water waves. To understand how nonlinearity affects this Kelvin-like pattern for ɛ , μ ≪ 1 , we develop an exponential asymptotics technique motivated by our earlier analysis in the wavenumber domain of the fKdV equation. Results are presented for three forcing terms that mimic a submerged source, a submerged doublet and a surface pressure. While the linear wave-crest geometry remains intact, the wave amplitudes in the Kelvin wake are significantly enhanced/suppressed by nonlinearity, depending on the type, strength and sign (polarity) of the forcing term. The asymptotic predictions generally are supported by direct numerical computations for various ɛ and μ. [Display omitted] [ABSTRACT FROM AUTHOR]

David J. Benney (1930–2015) was an applied mathematician and fluid dynamicist whose highly original work has shaped our understanding of nonlinear wave and instability processes in fluid flows. This article discusses the new paradigm he pioneered in the study of nonlinear phenomena, which transcends fluid mechanics, and it highlights the common threads of his research contributions, namely, resonant nonlinear wave interactions; the derivation of nonlinear evolution equations, including the celebrated nonlinear Schrödinger equation for modulated wave trains; and the significance of three-dimensional disturbances in shear flow instability and transition. [ABSTRACT FROM AUTHOR]

The black hole mass M BH is crucial in constraining the growth of supermassive black holes within their host galaxies. Since direct measurements of M BH 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, emphasizing those that can be applied to obscured AGN. Based on a subsample of AGN with M BH 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 –σ⋆ correlation based on inactive galaxies tends to systematically overestimate M BH, 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 M BH computed with this method. We also derive an alternative M –σ⋆ correlation based on this unbiased sample of AGN with a slope considerably shallower than the ones obtained using inactive galaxies, suggesting that the latter may not be appropriate to compute the M BH in AGN. Finally, we find that no quick fix can be applied to correct the M BH obtained from the fundamental plane of black hole activity, casting doubts on the reliability of this method. [ABSTRACT FROM AUTHOR]

The hard X-ray sky at energies above 10 keV has been extensively explored by the Swift/Gehrels and the NuSTAR missions in the 14−195 keV and the 3−24 keV bands. respectively. The main population of the hard X-ray detected sources are active galactic nuclei (AGN). A discrepancy has been reported between the number count distributions of the two missions in the sense that the extrapolation of the Swift/Gehrels number counts in the flux regime sampled by NuSTAR lies significantly below the NuSTAR counts. We explore this aspect anew by comparing the number count distributions derived from the Swift/Gehrels 105-month catalogue with those from the serendipitous NuSTAR source catalogue. We use a novel number count distribution estimator that makes use of the C-statistic on the unbinned data. In the 14−195 keV band, the Swift/BAT counts follow a Euclidean slope with α = 1.51 ± 0.10 (90% confidence level). The NuSTAR counts in the 8−24 keV band present a steeper slope with α = 1.71 ± 0.20 because of an upturn at fluxes below ∼2 × 10−13 erg cm−2 s−1. The same upturn is observed in the soft (3−8 keV) NuSTAR number counts, which generally also present a steep slope with α = 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 (below ∼7 × 10−13 erg cm−2 s−1) 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 Γ = 1.9, a high-energy cut-off at ∼130 keV and a 2−10 keV reflection component of 3%. On the other hand, using this standard AGN spectral model, only the bright part of the NuSTAR 8−24 keV and 3−8 keV number counts agrees with the model predictions. It is therefore most likely that the disagreement between the X-ray number counts in the different bands is caused by the faint NuSTAR number counts. We discuss various possibilities for the origin of this disagreement. [ABSTRACT FROM AUTHOR]

Small‐amplitude expansions are utilized to discuss the mean flow induced by the reflection of a weakly nonlinear internal gravity wave beam at a uniform rigid slope, in the case where the beam planes of constant phase meet the slope at an arbitrary direction, not necessarily parallel to the isobaths, and the flow cannot be taken as two dimensional. Along the vertical, the Eulerian mean flow, due to such an oblique reflection, is equal and opposite to the Stokes drift so the Lagrangian mean flow vanishes, similar to a two‐dimensional reflection. The horizontal Eulerian mean flow, however, is controlled by the mean potential vorticity (PV) and the corresponding Lagrangian mean flow is generally nonzero, in contrast to two‐dimensional flow where PV identically vanishes. For an oblique reflection, furthermore, viscous dissipation can trigger generation of horizontal mean flow via irreversible production of mean PV, a phenomenon akin to streaming. [ABSTRACT FROM AUTHOR]

The evolution of the accretion history of the Universe has been studied in unprecedented detail owing to recent X-ray surveys performed by Chandra and XMM-Newton. A focus on the most heavily obscured or Compton-thick active galactic nuclei (AGNs) is missing in these studies. These AGNs evade detection even in X-ray surveys owing to their extreme hydrogen column densities, which exceed 1024 cm−2. Recently, the all-sky hard X-ray survey performed by Swift/BAT brought a breakthrough, allowing the detection of many of these AGNs. This is because of the very high energy bandpass (14–195 keV) of this instrument, which helps to minimise attenuation effects. In our previous work, we identified more than 50 candidate Compton-thick AGNs in the local Universe, corresponding to an observed fraction of about 7% of the total AGNs population. This number can only be converted to the intrinsic Compton-thick AGNs number density if we know their exact selection function. This function sensitively depends on 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, and the strength of the reflection component on the matter surrounding the nucleus. For example, the reflection component at hard energies 20–40 keV antagonises the number density of missing Compton-thick AGNs in the sense that the stronger the reflection the easier these sources are detected in the BAT band. In order to constrain their number density, we analysed the spectra of 19 Compton-thick AGNs that have been detected with Swift/BAT and have been subsequently observed with NuSTAR in the 3–80 keV band. We analysed their X-ray spectra using the MYTORUS models which properly take into account the Compton scattering effects. These were combined with physically motivated Comptonisation models, which accurately describe the primary coronal X-ray emission. We derived absorbing column densities that 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. Furthermore, we find that the majority of our AGNs lack a strong reflection component in the 20–40 keV band placing tighter constraints on the intrinsic fraction of Compton-thick AGNs. Combining these results with our X-ray background synthesis models, we estimate a percentage of Compton-thick AGNs in the local Universe of ≈20 ± 3 % relative to the type-II AGNs population. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is known that standard multiple-scale perturbation techniques fail to pinpoint the soliton solution branches that bifurcate at edges of bandgaps in periodic media, owing to the appearance of exponentially small growing wave tails when the soliton's envelope is not properly positioned. When the bifurcation is from a single wave mode of a band edge, this difficulty has been handled in recent work by computing these tails via an exponential asymptotics technique in the wave number domain. However, the same approach is not directly applicable to the bifurcation of solitons near the opening of a bandgap, where wave modes from two nearby band edges interact with each other. Here, we discuss two nontrivial extensions of the exponential asymptotics technique that enable resolving this issue. For simplicity, the analysis focuses on two model problems, namely, a steady-state forced Korteweg-de Vries equation and a steady-state forced nonlinear Schrödinger equation, with the precise form of forcing and balance between nonlinear and dispersive terms chosen so as to mimic the situation encountered in the bifurcation of solitons near a bandgap opening. Our analysis exhibits a number of new features that are significantly different from previous exponential asymptotics procedures, such as the treatments when the nonlinearity dominates dispersion and when the decay rates of the Fourier-transformed solution are asymmetric. In addition, the analysis reveals new, and in some cases rather unexpected, functional forms for exponentially small wave tails, which are also confirmed by numerical results. [ABSTRACT FROM AUTHOR]

An asymptotic study is made of nonlinear effects in steady radiating waves due to moving sources in dispersive media. The focus is on problems where the radiated waves have exponentially small amplitude with respect to a parameter μ ≪ 1 , as for instance free-surface waves due to a submerged body in the limit of low Froude number. In such settings, weakly nonlinear effects (controlled by the source strength ɛ) can be as important as linear propagation effects (controlled by μ), and computing the wave response for μ , ɛ ≪ 1 may require exponential (beyond-all-orders) asymptotics. This issue is discussed here using a simple model, namely, the forced Korteweg–de Vries (fKdV) equation where μ is the dispersion and ɛ is the nonlinearity parameter. The forcing term f (x) is assumed to be even and its Fourier transform f ˆ (k) to decay for k ≫ 1 like A k α exp (− β k) , where A , α and β > 0 are free parameters. For this class of forcing profiles, the wave response hinges on beyond-all-orders asymptotics only if α > − 1 , and nonlinear effects differ fundamentally depending on whether α > 0 , α = 0 or − 1 < α < 0. Furthermore, the sign of the forcing amplitude parameter A is an important controlling factor of the nonlinear wave response. The asymptotic results compare favorably against direct numerical solutions of the fKdV equation for a wide range of μ and ɛ , in contrast to the linear wave response whose validity is rather limited. [Display omitted] • Steady wavetrains due to localized forcing in the fKdV equation are studied. • Exponential asymptotics is utilized for small dispersion and nonlinearity. • Nonlinear effects hinge on the profile and the sign of forcing. • Asymptotic results are supported by direct numerical solutions. • Linear wave solutions have limited validity. [ABSTRACT FROM AUTHOR]

Within the framework of the European Life+-funded project PhotoPAQ (Demonstration of Photocatalytic remediation Processes on Air Quality) , which was aimed at demonstrating the effectiveness of photocatalytic coating materials on a realistic scale, a photocatalytic de-polluting field site was set up in the Leopold II tunnel in Brussels, Belgium. For that purpose, photocatalytic cementitious materials were applied on the side walls and ceiling of selected test sections inside a one-way tunnel tube. This article presents the configuration of the test sections used and the preparation and implementation of the measuring campaigns inside the Leopold II tunnel. While emphasizing on how to implement measuring campaigns under such conditions, difficulties encountered during these extensive field campaigns are presented and discussed. This included the severe de-activation observed for the investigated material under the polluted tunnel conditions, which was revealed by additional laboratory experiments on photocatalytic samples that were exposed to tunnel air. Finally, recommendations for future applications of photocatalytic building materials inside tunnels are given. [ABSTRACT FROM AUTHOR]

Slug tests offer an efficient method for estimating the hydraulic parameters of an aquifer without water pumping. Two inverse methods are typically used to assess the slug test data and derive parameter estimates of a confined aquifer. The first method provides estimates of both hydraulic conductivity and specific storage, is visual (hence difficult to automate), and is based on the transient-flow analytical solution of Cooperet al.The second method, proposed by Hvorslev, is very straightforward, but provides only hydraulic conductivity estimates. In this study, we are testing the recently proposed quasi-steady method of Koussis and Akylas, which enables the estimation of both hydraulic parameters and, furthermore, can be easily implemented in computer code or an electronic spreadsheet. This quasi-steady method was coupled with the shuffled complex evolution optimization method to fully automate parameter estimation. This coupling is tested using data from field observations, synthetic data produced from the transient-flow analytical solution, and synthetic data with noise. The results show the usefulness and the limitations of the proposed method.Editor Z.W. Kundzewicz [ABSTRACT FROM AUTHOR]

We generalize Batchelor's parameterization of the autocorrelation functions of isotropic turbulence in a form involving a product expansion with multiple small scales. The richer small scale structure acquired this way, compared to the usual Batchelor function, is necessary so that the associated energy spectrum approximate well actual spectra in the universal equilibrium range. We propose that the generalized function provides an approximation of arbitrary accuracy for actual spectra of isotropic turbulence over the universal equilibrium range. The degree of accuracy depends on the number of higher moments which are determinable and it is reflected in the number of small scales involved. The energy spectrum of the generalized function is derived, and for the case of two small scales is compared with data from high-resolution direct numerical simulations. We show that the compensated spectra (which illustrate the bottleneck effect) and dissipation spectra are encapsulated excellently, in accordance with our proposal. [ABSTRACT FROM AUTHOR]

As a first step toward a fully two-dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in general two-dimensional periodic potentials. For this two-dimensional problem, it is no longer viable to rely on a certain recurrence relation for going beyond all orders of the usual multiscale perturbation expansion, a key step of the exponential asymptotics procedure previously used for solitons in one-dimensional problems. Instead, we propose a more direct treatment which not only overcomes the recurrence-relation limitation, but also simplifies the exponential asymptotics process. Using this modified technique, we show that line solitons with any rational line slopes bifurcate out from every Bloch-band edge; and for each rational slope, two line-soliton families exist. Furthermore, line solitons can bifurcate from interior points of Bloch bands as well, but such line solitons exist only for a couple of special line angles due to resonance with the Bloch bands. In addition, we show that a countable set of multiline-soliton bound states can be constructed analytically. The analytical predictions are compared with numerical results for both symmetric and asymmetric potentials, and good agreement is obtained. [ABSTRACT FROM AUTHOR]

Quality changes due to oven-baking of sardine for 20, 40, 50 and 60 min and due to deep frying of anchovy for 2, 3, 4 and 5 min in olive and sunflower oil were studied. Linear increase in total losses with the time of processing was observed. A linear inverse relationship was observed between moisture/lipid and moisture/protein due to time of baking of sardines and time of frying of anchovies (wet matter). However, no changes were detected in sardine samples due to time of baking (dry matter), while a reduction in proteins and ash followed by an increase in lipids was detected in fried anchovies due to time of frying (dry matter). The fatty acid profiles indicated that a rich in EPA + DHA (33.16%) and in ω-3/ω-6 ratio (9.40) baked sardines can be produced in 20 min at 200 °C. The fatty acid profiles of fried anchovies tremendously changed, indicating entirely different products. Olive oil is probably a better medium to fry fish products, since either the two beneficial fatty acids (EPA and DHA) detected at higher concentrations in anchovies fried in olive oil or the ω-3/ω-6 ratio remained at higher values (0.71–2.56). An increase of cholesterol and squalene content with increasing the time of baking was detected in sardine samples, probably due to decline of moisture content. On the contrary, cholesterol significantly reduced due to frying of anchovy in olive oil. Simultaneously squalene concentration significantly and linearly increased, from 3.87 mg/100 g in the unprocessed anchovies to 73.25 mg/100 g in the samples fried for 5 min, indicating its existence at beneficial levels, besides low cholesterol concentration detected in fried olive oil and squalene concentration gradually and linearly decreased, confirming the absorption from the anchovy samples. Similar was the changes of cholesterol and squalene in anchovies samples fried in sunflower oil. [ABSTRACT FROM PUBLISHER]

The authors discuss the complete form of the extended Boussinesq equation. They mention the mathematical foundations of subsurface flow on a sloping base based on the Dupuit-Forchheimer theory of unconfined flow. They also mention the analytical steady-state solution of the nonlinear extended Boussinesq equation of Henderson and Wooding in 1964 and its linearisation solutions.

In the great majority of slug tests performed in wells fully penetrating confined geologic formations, and for over-damped conditions, the response data are evaluated with the transient-flow model of Cooper et al. (1967) when the radial hydraulic conductivity Kr and the coefficient of specific storage Ss are to be estimated. That particular analytical solution, however, is computationally involved and awkward to use. Thus, groundwater professionals often use a few pre-prepared type-curves to fit the data by a rough matching procedure, visually or computationally. On the other hand, the method of Hvorslev (1951), which assumes the flow to be quasi-steady, is much simpler but yields only Kr estimates. In this work, we develop a complete quasi-steady flow model that includes a storage balance inside the aquifer and allows estimating Kr and Ss simultaneously, through matching of the well response data to a type-curve. The new model approximates the model of Cooper et al. closely and has the practical advantage that its solution type-curves are generated easily using an electronic spreadsheet, so that the optimal fit of data by a type-curve can be readily automated. [ABSTRACT FROM AUTHOR]

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schrödinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, which span a large number of lattice periods. In this limit, the allowed positions of solitary waves relative to the lattice, as well as their linear stability properties, hinge upon a certain recurrence relation which contains information beyond all orders of the usual two-scale perturbation expansion. It follows that only two such positions are permissible, and of those two solitary waves, one is linearly stable and the other unstable. For a cosine lattice, in particular, the two possible solitary waves are centered at a maximum or minimum of the lattice, with the former being stable, and the analytical predictions for the associated linear stability eigenvalues are in excellent agreement with numerical results. Furthermore, a countable set of multi-solitary-wave bound states are constructed analytically. In spite of rather different physical settings, the exponential asymptotics approach followed here is strikingly similar to that taken in earlier studies of solitary wavepackets involving a periodic carrier and a slowly varying envelope, which underscores the general value of this procedure for treating multiscale solitary-wave problems. [ABSTRACT FROM AUTHOR]

Solitary waves in one-dimensional periodic media are discussed by employing the nonlinear Schrödinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become non-local owing to the presence of growing tails of exponentially small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such non-local solitary waves, high-order locally confined gap solitons, or bound states, are constructed. Details are worked out for bound states comprising two non-local solitary waves in the presence of a sinusoidal potential. A countable set of bound-state families, characterized by the separation distance of the two solitary waves, is found, and each family features three distinct solution branches that bifurcate near Bloch-band edges at small, but finite, amplitude. Power curves associated with these solution branches are computed asymptotically for large solitary-wave separation, and the theoretical predictions are consistent with numerical results. [ABSTRACT FROM AUTHOR]

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the "linear forcing," which amounts to a force term that is linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence toward a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS, the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to rewrite the problem as one of decaying turbulence with a decreasing viscosity. Its late-time behavior can then be studied by scaling symmetry considerations. The evolution of the system in the description of "decaying" turbulence can be understood as the gradual symmetry breaking of a larger approximate symmetry to a smaller symmetry that is exact at late times. The latter symmetry implies a stationary state: In the original description all correlators are constant in time, while, in the "decaying" turbulence description, that state possesses constant Reynolds number and integral length scale. The finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times: In linear forcing there is no other large scale than the domain size, therefore, it is the only scale available to set the magnitude of the necessarily constant integral length scale in the stationary state. A high degree of local isotropy is implied by the late-time exact symmetry, the symmetries of the domain itself, and the solenoidal nature of the velocity field. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy that is necessarily broken at the large scale by the finiteness of the domain. Indeed, to strengthen this conclusion somewhat, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view. Simultaneously, the naturalness of the Taylor microscale as a self-similarity scale in this system is emphasized. In this context the stationary state emerges as a stable fixed point. We also note that self-preservation seems to be the reason behind a noted similarity of the third-order structure function between the linearly forced and freely decaying turbulence, where, again, the finiteness of the domain plays a significant role. [ABSTRACT FROM AUTHOR]

Abstract: An analytical theory utilizing exponential asymptotics is presented for one-dimensional gap solitons that bifurcate from edges of Bloch bands in the presence of a general periodic potential. It is shown that two soliton families bifurcate out from every Bloch-band edge under self-focusing or self-defocusing nonlinearity, and an asymptotic expression for the eigenvalues associated with the linear stability of these solitons is derived. The locations of these solitons relative to the underlying potential are determined from a certain recurrence relation, that contains information beyond all orders of the usual perturbation expansion in powers of the soliton amplitude. Moreover, this same recurrence relation decides which of the two soliton families is unstable. The analytical predictions for the stability eigenvalues are in excellent agreement with numerical results. [Copyright &y& Elsevier]

When a dispersive wave system is subject to forcing by a moving external disturbance, a maximum or minimum of the phase speed is associated with a critical forcing speed at which the linear response is resonant. Nonlinear effects can play an important part near such resonances, and the salient characteristics of the nonlinear response depend on whether the maximum or minimum of the phase speed is realized in the long-wave limit (zero wavenumber) or at a finite wavenumber. The focus here is on the latter case that, among other physical systems, applies to gravity–capillary waves on water of finite or infinite depth. The analysis, for simplicity, is based on a forced–damped fifth-order Korteweg–de Vries equation, a model problem that features a phase-speed minimum at a finite wavenumber. When damping is not too strong compared with forcing, multiple subcritical finite-amplitude steady-solution branches coexist with the small-amplitude response predicted by linear theory. For forcing speed well below critical, the transient response from rest approaches the small-amplitude state, but at speeds close to critical, jump phenomena can occur, and reaching a time-periodic state that involves shedding of wavepacket solitary waves is also possible. [ABSTRACT FROM AUTHOR]

In this work we apply superstatistics, in a rather novel way, to derive the blackbody radiation laws in the context of the kappa distribution. Superstatistics incorporates automatically an important aspect of the kappa distribution i.e. the correlations between non-interacting degrees of freedom; this is actually a feature of any stationary non-Boltzmannian distribution derived by superstatistics. The correlations between photons in the same state affect the modified Planck and Wien laws. The correlations between photons of different states affect the fluctuations of the radiated energy, inducing very large fluctuations unless the kappa index is fairly large (i.e. near to the Boltzmannian limit), thereby compromising the very notion of stationarity. It is also shown that the Einstein absorption/emission coefficients are left intact, under the plausible assumption that the system matter-radiation obeys the given non-Boltzmannian distribution. The first-order correction to the Planck's law near the Boltzmannian limit is deduced, and compared with the residual spectrum of the cosmic microwave background radiation from the FIRAS-COBE project data; the modified law cannot account for the residuals. No thermodynamic/entropic arguments are employed in this work. [ABSTRACT FROM AUTHOR]

In the classical water-wave problem, fully localized nonlinear waves of permanent form, commonly referred to as lumps, are possible only if both gravity and surface tension are present. While much attention has been paid to shallow-water lumps, which are generalizations of Korteweg–de Vries solitary waves, the present study is concerned with a distinct class of gravity–capillary lumps recently found on water of finite or infinite depth. In the near linear limit, these lumps resemble locally confined wave packets with envelope and wave crests moving at the same speed, and they can be approximated in terms of a particular steady solution (ground state) of an elliptic equation system of the Benney–Roskes–Davey–Stewartson (BRDS) type, which governs the coupled evolution of the envelope along with the induced mean flow. According to the BRDS equations, however, initial conditions above a certain threshold develop a singularity in finite time, known as wave collapse, due to nonlinear focusing; the ground state, in fact, being exactly at the threshold for collapse suggests that the newly discovered lumps are unstable. In an effort to understand the role of this singularity in the dynamics of lumps, here we consider the fifth-order Kadomtsev–Petviashvili equation, a model for weakly nonlinear gravity–capillary waves on water of finite depth when the Bond number is close to one-third, which also admits lumps of the wave packet type. It is found that an exchange of stability occurs at a certain finite wave steepness, lumps being unstable below but stable above this critical value. As a result, a small-amplitude lump, which is linearly unstable and according to the BRDS equations would be prone to wave collapse, depending on the perturbation, either decays into dispersive waves or evolves into an oscillatory state near a finite-amplitude stable lump. [ABSTRACT FROM AUTHOR]

Short-term electricity load forecasting is key to the safe, reliable, and economical operation of power systems. An important challenge that arises with high-frequency load series, e.g., hourly load, is how to deal with the complex seasonal patterns that are present. Standard approaches suggest either removing seasonality prior to modeling or applying time series decomposition. This work proposes a hybrid approach that combines Singular Spectrum Analysis (SSA)-based decomposition and Artificial Neural Networks (ANNs) for day-ahead hourly load forecasting. First, the trajectory matrix of the time series is constructed and decomposed into trend, oscillating, and noise components. Next, the extracted components are employed as exogenous regressors in a global forecasting model, comprising either a Multilayer Perceptron (MLP) or a Long Short-Term Memory (LSTM) predictive layer. The model is further extended to include exogenous features, e.g., weather forecasts, transformed via parallel dense layers. The predictive performance is evaluated on two real-world datasets, controlling for the effect of exogenous features on predictive accuracy. The results showcase that the decomposition step improves the relative performance for ANN models, with the combination of LSTM and SAA providing the best overall performance. [ABSTRACT FROM AUTHOR]

We apply inviscid rapid distortion theory to the generalized case of turbulent hyperbolic flow in a rotating frame and investigate the dependence of the evolution of the turbulent kinetic energy on the frame rotation rate. We derive an analytical two-dimensional solution which allows for an accurate approximation of the three-dimensional initially isotropic problem. From the analytical solutions we determine a new generalized stability criterion for the evolution of the turbulent kinetic energy in this class of flows. [ABSTRACT FROM AUTHOR]

There is evidence from balloon measurements that atmospheric buoyancy–frequency profiles, apart from a sharp increase (roughly by a factor of two) at the tropopause, often feature appreciable oscillations (typical wavelength 1–2 km) with altitude. It is argued here that such short-scale oscillatory variations of the background buoyancy frequency, which usually are ignored in theoretical models, can have a profound effect on the generation of mountain waves owing to a resonance mechanism that comes into play at certain wind speeds depending on the dominant oscillation wavelength. A simple linear model assuming small sinusoidal buoyancy–frequency oscillations suggests, and numerical solutions of the Euler equations for more realistic flow conditions confirm, that under resonant conditions the induced gravity-wave activity is significantly increased above and upstream of the mountain, similarly to resonant flow of finite depth over topography. [ABSTRACT FROM AUTHOR]

A theoretical study is made of finite-amplitude modulated internal wavetrains and the attendant nonlinear interaction with the mean flow induced by the modulations, in an unbounded uniformly stratified Boussinesq fluid rotating around the vertical axis. When the rotation is relatively weak, in particular, ‘flat’ wavetrains, that feature stronger vertical than horizontal modulations, are resonantly coupled with the mean flow in a manner analogous to the resonant long–short wave interaction between gravity and capillary waves on the surface of deep water. A coupled set of evolution equations for the vertical wavenumber, the wave amplitude, and the mean flow is derived under resonant conditions, and is used to examine the propagation of locally confined wavetrains with initially uniform wavenumber and no pre-existing mean flow. The resonant interaction causes radiation of energy away from a flat wavetrain by means of the induced mean flow which forms a trailing wake; this furnishes a possible mechanism for generating low-frequency inertial–gravity waves in the atmosphere, as suggested by field observations. Moreover, owing to refraction by the mean flow, a finite-amplitude wavetrain may experience rapid wavenumber variations in certain locations, consistent with prior numerical simulations. Eventually, in these regions, the wavenumber tends to become multi-valued, suggesting the formation of caustics. [ABSTRACT FROM AUTHOR]

We apply inviscid rapid distortion theory to the limiting hyperbolic case of turbulent plain strain flow in a rotating frame and investigate the dependence of the evolution of the turbulent kinetic energy on the frame rotation rate. We derive an analytical two-dimensional solution that, unlike previous oversimplified pressureless analyses, allows for an accurate approximation of the three-dimensional initially isotropic problem. From the analytical solutions, we determine the correct stability criterion for the evolution of the turbulent kinetic energy in this flow. Also, we calculate the asymptotic states of the turbulence, in terms of the normalized Reynolds stresses and structure dimensionality tensor components, which coincide with the exact three-dimensional numerical results. [ABSTRACT FROM AUTHOR]

Summary: We study the interaction of a stream with a sloping unconfined aquifer that the stream is assumed to fully penetrate. The analysis applies to flow in a vertical section, considers the existence of a low-conductivity streambed layer and the flow in the aquifer to be induced by variations of the stream stage. Invoking the Dupuit assumption yields the 1-D Boussinesq equation, extended for a sloping base. The Boussinesq equation is linearised, the derived flow model is critiqued and an objective procedure for determining the linearisation level is developed. We solve the linear governing equation by the method of Laplace transform, with analytical inversion; the horizontal-aquifer case is treated in the zero-slope limit. The system response function is derived for the general case (sloping aquifer, sediment bed layer) and for several specific cases, and solutions are verified against known analytical results. Responses are contrasted for aquifers on positive, negative and zero slopes to step changes in the stage of streams with and without a sediment bed layer. The solutions give the aquifer stage and flow rate, the flow exchange rate at the stream–aquifer interface and the exchanged water volumes (bank storage/release). [Copyright &y& Elsevier]

Summary: We convolve the system response functions of the linearised 1D equation of Boussinesq (extended for slope, Dupuit approximation) derived in the companion paper of Akylas and Koussis [Akylas, E., Koussis, A.D., (submitted for publication). Response of sloping unconfined aquifer to stage changes in adjacent stream: I. Theoretical analysis and derivation of system response functions, J. Hydrol] and develop solutions for the interaction of a fully penetrating stream with a sloping unconfined aquifer, taking also into account a low-conductivity streambed layer. These solutions give the aquifer stage and flow rate, the flow exchange rate at the stream–aquifer interface and the exchanged water volumes (bank storage/release). The solutions are analytical, when the flow-inducing stream stage variations are common functions; otherwise, the convolution integral is evaluated numerically. Responses are compared for aquifers on positive, negative and zero base slopes to a wave-like change in the stage of the stream. Analytical and numerical convolution-derived solutions are used to model the interaction of Cedar River and its adjacent unconfined aquifer near Cedar Rapids, Iowa. In the model, the aquifer base is taken to be horizontal or inclined and the streambed clogged by a low-conductivity sediment layer; the model is verified against data not used in the calibration and is found to perform very well. [Copyright &y& Elsevier]

Abstract: In the frame of this paper three widely used planetary boundary layer parameterisations are evaluated for their ability to forecast near-surface temperature and wind speed. The analysis is based on the operational forecasts produced by the Pennsylvania State University — National Center for Atmospheric Research MM5 model over the Athens Area (Greece) during the warm period of 2002. The near-surface temperature and wind forecasts at a grid increment of 8 and 2 km over the highly complex terrain of the Athens Area are statistically verified against the available surface station observations. The results of the analysis showed that the increase in horizontal resolution (from 8 to 2 km) increases the forecast accuracy especially for temperature. As it concerns the forecast skill of each scheme it seems that the MRF scheme produces the best forecasts as it concerns the near-surface temperature while for the near-surface wind the ETA scheme gives the best results. Blackadar schemes present a consistently good behaviour for both temperature and wind forecasts. [Copyright &y& Elsevier]

Rapid distortion theory is applied to stratified homogeneous turbulence that is sheared in a rotating frame. Insight into the stabilizing and destabilizing effects of the combined stratification and frame rotation is gained by considering initial fields that are two-dimensional, with the axis of independence aligned with the flow direction. For these conditions, we derive solutions for the Fourier components of the flow variables, and for one-point statistics in physical space. The analytical results are in qualitative agreement with the exact numerical solution for initially isotropic homogeneous turbulence, and they could be a reference point for the development of turbulence models. [ABSTRACT FROM AUTHOR]

In the present study, we investigate, using inviscid rapid distortion theory, the evolution of sheared turbulence in a rotating frame as a function of the rotation rate (including stable, transitional, and unstable regimes), and examine the sensitivity of the results for various nonisotropic initial conditions. Analytical solutions are derived for the evolution of the stresses and the structure dimensionality tensor components for three one-dimensional and three two-dimensional initializations. From these solutions, we calculate the asymptotic states of the turbulence, which are compared to the exact numerical solution of the three-dimensional initially isotropic case. From the investigation it is shown that the qualitative characteristics of the isotropic solution in the unstable regime are represented quite accurately when the initial turbulence is dependent at least on the axis of the rotation of the frame. For the transitional and the stable regimes, though, the initial dependence of the turbulence on the axis of the mean flow is also crucial. [ABSTRACT FROM AUTHOR]

In this study we apply rapid distortion theory to the case of nonstratified homogeneous turbulence that is sheared in a frame that counter-rotates at a rate that matches in magnitude the rotation associated with the mean shear. In the inviscid case, analytical solutions are worked out for the evolution of the components of the Reynolds stresses and the structure dimensionality tensor, and these are shown to equal each other. The results are compared to direct numerical simulations data with which they proved to be in good agreement, especially in terms of the Reynolds shear stress and of the dimensionless tensor components. Finally, the development of the structure of a passive scalar field with a constant mean gradient is investigated, and remarkable analogies are shown to exist between this case and the case of shear in a fixed frame. [ABSTRACT FROM AUTHOR]

In this study, profile functions for flux calculations during unstable conditions are proposed and examined. These functions are based on a direct interpolation for the dimensionless wind speed and temperature gradients between the standard Businger–Dyer formulae, $$\phi_{{\rm K}u} (\zeta) = (1 - \gamma _{u} \zeta)^{-1/4}$$, $$\phi_{{\rm K}t} (\zeta) = (1 - \gamma _{t} \zeta )^{-1/2}$$, and free convection forms, $$\phi _{{\rm C}u,t} (\zeta) = (1 - \alpha _{{\rm C}u,t} \zeta )^{-1/3}$$, $$\zeta$$ being the Monin–Obukhov stability parameter. A previously presented interpolation between the corresponding profile relationships, in attempting to provide a general relationship for the whole unstable regime, leads to serious restrictions for the values of $$\alpha _{{\rm C}u ,t}$$ in the free convection forms. These restrictions rendered available experimental data almost inapplicable, since the behaviour of the formulae in the near-neutral range controls the values of those parameters. The proposed interpolation provides functions that, firstly, fit the standard Businger–Dyer forms for near-neutral conditions and, secondly, satisfy the asymptotic behaviour as $$\zeta \rightarrow -\infty$$, permitting wider ranges of possible $$\alpha _{{\rm Cu},t}$$ values. This step is very important, taking into account the large spread of the experimental data. Thus, as further and more accurate observations at strong instability become available, this approach could prove very efficient in fitting these data while retaining correct near-neutral behaviour. [ABSTRACT FROM AUTHOR]

We explore the X-ray properties of optically selected quasi-stellar objects (QSOs) spectroscopically identified in the course of the 2dF QSO survey (2QZ). Our main goal is to expand to higher redshifts, previous findings suggesting the presence of a fraction of X-ray obscured sources among the low-redshift, optically selected, broad line active galactic nucleus (AGN) population. The X-ray data are from the wide field (∼2.5 deg2) shallow[] XMM–Newton/2dF survey. A total of 96 2QZ QSOs overlap with the area covered by our X-ray survey. 66 of them have X-ray counterparts while 30 remain undetected in our X-ray survey. The 66 X-ray detected QSOs have a mean photon index of≈2 suggesting little or no X-ray obscuration for most of these sources. Individual X-ray spectral fittings reveal only one source (intrinsicat) that is likely to be obscuredat the 90 per cent confidence level. Additionally, there are nine 2QZ sources that show evidence for moderate absorption (mean observedNH of). For the 30 QSOs that remain undetected in our X-ray survey, we use stacking analysis to estimate a mean hardness ratio (HR) ofsuggesting that the bulk of this population hasNH consistent with the Galactic value. However, we cannot exclude the possibility that some of these sources have enhanced photoelectric absorption that is not revealed in the mean stacked spectrum. We estimate a lower limit to the fraction of optically selected QSO with X-ray absorption of approximately 10 per cent (10 out of 96). [ABSTRACT FROM AUTHOR]

We revisit the classical problem of internal wave propagation in a stratified fluid layer bounded by rigid walls and point out a mechanism by which unsteady locally confined disturbances generate far-field shelves. Carrying the standard expansion procedure to fourth order in the wave amplitude reveals that weakly nonlinear long waves of a certain mode shed, in general, lower- and higher-mode shelves, which propagate upstream and downstream with the corresponding long-wave speeds. This phenomenon is brought about by the combined effect of nonlinear interactions and the presence of transience in the main disturbance. While the shelves accompanying small-amplitude waves are relatively weak, numerical solutions of the full Euler equations indicate that shelves induced by unsteady disturbances of finite amplitude close to breaking can be quite significant. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation with a third-order dispersive term is considered. Infinite families of embedded solitons, parameterized by the propagation velocity, are found through a gauge transformation. By applying this transformation, an embedded soliton can acquire any velocity above a certain threshold value. It is also shown that these families of embedded solitons are linearly stable, but nonlinearly semi-stable. [ABSTRACT FROM AUTHOR]

Symmetric solitary waves on the interface between two fluid layers are discussed for the case when the upper fluid is bounded above and the lower fluid is infinitely deep. In this flow geometry, under the conditions that the fluid densities are nearly equal and interfacial tension is relatively large, Benjamin [J. Fluid Mech. 245, 401 (1992)] derived a weakly nonlinear long-wave evolution equation which admits a new kind of elevation solitary wave that features decaying oscillatory tails. We present computations of solitary waves of this type and examine their stability to small perturbations on the basis of the full Euler equations using numerical methods. Computed solitary-wave profiles are found to be in good agreement with solutions of the Benjamin equation even for Weber and Froude numbers well outside the formal range of validity of weakly nonlinear long-wave analysis. Furthermore, our computations reveal that, unless the upper fluid is very light relative to the lower fluid, moderately steep interfacial solitary waves behave qualitatively as predicted by the Benjamin equation: elevation waves with a tall center crest, akin to those found by Benjamin, are stable and coexist with depression solitary waves (not reported by Benjamin) which are unstable. As expected, for low enough density ratio, these two solution branches exchange stabilities and computed profiles resemble those of free-surface gravity-capillary solitary waves on deep water. [ABSTRACT FROM AUTHOR]

We analyse 37 RXTE observations of the type 2 Seyfert galaxy Mrk 348 obtained over a period of 14 months. We confirm the spectral variability previously reported by Smith, Georgantopoulos & Warwick, in the sense that the column density decreases by a factor of ∼3 as the count rate increases. Column density variations could possibly originate either from the random drift of clouds within the absorption screen, or from photoionization processes. Our modelling of the observed variations implies that the first scenario is more likely. These clouds should lie within a distance of >2 light-years from the source, having a diameter of a few light-days and a density of >10[sup 7] cm[sup -3] , hence probably residing outside the broad-line region. [ABSTRACT FROM AUTHOR]

Reports on the research work of David J. Benney, managing editor of the 'Studies in Applied Mathematics' journal. Theory of hydrodynamic stability and transition to turbulence; Dynamics of nonlinear waves; Basis of the mathematical analysis used to study nonlinear interactions of unstable modes in shear flows.

We investigate the X-ray spectra of the type 2 Seyfert galaxies NGC 7172 and ESO 103-G35, using BeppoSAX observations, separated by approximately one year. We find that the X-ray spectra of both NGC 7172 and ESO 103-G35 can be well fitted using a power-law model with an Fe Kα emission line at 6.4 keV. We did not find any statistically significant evidence for the existence of a reflection component in the X-ray spectra of these two galaxies. The continuum flux has decreased by a factor of approximately 2 during this period, in both objects. However, the spectral index as well as the absorption column have remained constant. We find weak evidence for the decrease of the normalization of the Fe Kα emission line in a similar manner to the continuum in NGC 7172. We also report tentative evidence for a broad Fe Kα line in agreement with previous ASCA observations. In contrast, in the case of ESO 103-G35 the line flux does not change while its width remains unresolved. [ABSTRACT FROM AUTHOR]

We have derived the angular correlation function of a sample of 2096 sources detected in the ROSAT All-Sky Survey (RASS) Bright Source Catalogue, in order to investigate the clustering properties of active galactic nuclei (AGN) in the local Universe. Our sample is constructed by rejecting all known stars, as well as extended X-ray sources. Areas with |b|<30° and declination δ<-30° are also rejected owing to the high or uncertain neutral hydrogen absorption. Cross-correlation of our sample with the Hamburg/RASS optical identification catalogue suggests that the vast majority of our sources are indeed AGN. A 4.1σ correlation signal between 0° and 8° was detected with w(θ<8°)=2.5±0.6×10[sup -2]. Assuming a two-point correlation function of the form w(θ)=(θθ[sub 0])[sup -0.8], we find θ[sub 0]=0°062. Deprojection on three dimensions, using Limber's equation, yields a spatial correlation length of r[sub 0]≈6.0±1.6 h[sup -1] Mpc. This is consistent with the AGN clustering results derived at higher redshifts in optical surveys and suggests a comoving model for the clustering evolution. [ABSTRACT FROM AUTHOR]