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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.

The increased uncertainty due to the integration of stochastic renewable energy sources necessitates solving Optimal Power Flow (OPF) problems repeatedly and with greater granularity. Machine learning methods hold significant potential to reduce the computing time for OPF problems by learning a mapping from varying input loads to decisions, thus bypassing the need for an optimization solver during inference. However, current machine learning methods for OPF lack interpretability and may produce infeasible decisions, which impedes their adoption by industry stakeholders. To this end, we propose a novel approach for interpretable learning of OPF solutions with feasibility guarantees. Specifically, we develop prescriptive decision trees that learn a piecewise affine mapping from input data to the solutions of a constrained optimization problem, using robust optimization to ensure that decisions are feasible. One important contribution of our work is the development of a tree-based learning method that utilizes non-orthogonal splits informed by domain knowledge, including network congestion and the merit order curve. By incorporating this information, we enhance both the interpretability and performance of the model. We further present a surrogate learning algorithm to handle large-scale problems. The proposed approach is evaluated on several test networks, up to 300 buses, under different types of uncertainty and operating conditions, and is compared to neural network-based models, which do not guarantee feasibility. Notably, our results demonstrate that interpretable, shallow prescriptive trees perform comparably to neural network-based models, which are considered the current state of the art. To the best of our knowledge, this work is the first to introduce an interpretable machine learning approach for directly learning OPF solutions.

The radiation of steady surface gravity waves by a uniform stream U0over locally confined (width L) smooth topography is analyzed based on potential flow theory. The linear solution to this classical problem is readily found by Fourier transforms, and the nonlinear response has been studied extensively by numerical methods. Here, an asymptotic analysis is made for subcritical flow D/λ>1in the low-Froude-number (F2≡λ/L≪1) limit, where λ=U02/gis the lengthscale of radiating gravity waves and Dis the uniform water depth. In this regime, the downstream wave amplitude, although formally exponentially small with respect to F, is determined by a fully nonlinear mechanism even for small topography amplitude. It is argued that this mechanism controls the wave response for a broad range of flow conditions, in contrast to linear theory which has very limited validity.

Properly tuning the Fermi level position in topological insulators is of vital importance to tailor their spin-polarized electronic transport and to improve the efficiency of any functional device based on them. Here, we report the full in situ metal organic chemical vapor deposition (MOCVD) and study of a highly crystalline Bi2Te3/Sb2Te3topological insulator heterostructure on top of large area (4″) Si(111) substrates. The bottom Sb2Te3layer serves as an ideal seed layer for the growth of highly crystalline Bi2Te3on top, also inducing a remarkable shift of the Fermi level to place it very close to the Dirac point, as visualized by angle-resolved photoemission spectroscopy. To exploit such ideal topologically protected surface states, we fabricate the simple spin-charge converter Si(111)/Sb2Te3/Bi2Te3/Au/Co/Au and probe the spin-charge conversion (SCC) by spin pumping ferromagnetic resonance. A large SCC is measured at room temperature and is interpreted within the inverse Edelstein effect, thus resulting in a conversion efficiency of λIEEE∼ 0.44 nm. Our results demonstrate the successful tuning of the surface Fermi level of Bi2Te3when grown on top of Sb2Te3with a full in situ MOCVD process, which is highly interesting in view of its future technology transfer.

This study is the first attempt to characterize the quality status of El Fahs aquifer by combining graphical tools, multivariate statistical techniques and traditional geostatistical methods. Water samples are collected from thirty-six observation wells during April 2016 to characterize the physicochemical properties of the aquifer. Subsequently, these samples are partitioned into three hydrochemically distinct water classes (i.e., C1, C2, and C3) using the K-means clustering method. Principal Component Analysis is used to reduce the dimensionality of the dataset prior performing the clustering computations, resulting in clusters of higher quality than the non-reduced case in terms of Silhouette coefficient. Piper diagram is used to display the chemical composition of the samples, revealing the dominant role of Mg–Ca–Cl water type for all three classes, whereas Sodium and Sulfate were found to be the second most important cations and anions respectively. Indicator kriging (IK) is used to identify the probability of occurrence of the hydrochemical classes beyond the sampling locations. It is found that Class 1, associated with fresh groundwater component, is most probable to occur at the central part of the plain, mainly due to the presence of a dense hydrological network, whereas Classes 2 (agricultural activities) and 3 (dissolution of evaporate geological formations) are expected to occur at the southern and northern regions respectively. IK also identified the regions associated with high levels of uncertainty, mostly occurring in a large portion of the northern area due to the absence of available hydrochemical information. The results showed that integration of graphical methods, multivariate statistical techniques and geostatistical modeling, is an efficient approach for characterizing the hydrochemical status of the aquifer system, to spatially optimize the groundwater monitoring well networks and quantify the uncertainty levels of the water classes in a systematic way.

One of the most challenging aspects in the study of the complex dynamical systems is the estimation of their underlying, interdependence structure. Being in the era of Big Data, this problem gets even more complicated since more observed variables are available. To estimate direct causality effects in this setting, dimension reduction has to be employed in the Granger causality measure. The measure should also be capable to detect non-linear effects, persistently present in real-world complex systems. The model-free information-based measure of partial mutual information from mixed embedding (PMIME) has been developed to address these issues and it was found to perform well on multivariate time series of moderately high dimension. Here, the problem of forming complex networks from direct, possibly non-linear, high-dimensional time series at the order of hundreds is investigated. The performance of the measure PMIME is tested on two coupled dynamical systems in discrete time (coupled Hénon maps) and continuous time (coupled Mackey–Glass delay differential equations). It is concluded that the correct detection of the underlying causality network depends mainly on the network density rather than on its size (number of nodes). Finally, the effect of network size is investigated in the study of the British stock market in the period around Brexit.

We derive the early‐time solution of the Boussinesq equation for the horizontal unconfined aquifer in the buildup phase under constant recharge and zero inflow. The solution is expressed as a power series of a suitable similarity variable, which is constructed so that to satisfy the boundary conditions at both ends of the aquifer, that is, it is a polynomial approximation of the exact solution. The series turns out to be asymptotic and it is regularized by resummation techniques that are used to define divergent series. The outflow rate in this regime is linear in time, and the (dimensionless) coefficient is calculated to eight significant figures. The local error of the series is quantified by its deviation from satisfying the self‐similar Boussinesq equation at every point. The local error turns out to be everywhere positive, hence, so is the integrated error, which in turn quantifies the degree of convergence of the series to the exact solution. The initially dry, unconfined horizontal aquifer problem under constant recharge rate, is solved by power series for the early times regimeThe outflow rate is linear in time and the proportionality constant can be calculated with significant accuracyThe derived series are asymptotic, and they are treated by regularization techniques used in divergent series

Satellite observations recently revealed trains of internal solitary waves (ISWs) in the off‐shelf region between 16.0°N and 16.5°N in the southern Red Sea. The generation mechanism of these waves is not entirely clear, though, as the observed generation sites are far away (50 km) from the shelf break and tidal currents are considered relatively weak in the Red Sea. Upon closer examination of the tide properties in the Red Sea and the unique geometry of the basin, it is argued that the steep bathymetry and a relatively strong tidal current in the southern Red Sea provide favorable conditions for the generation of ISWs. To test this hypothesis and further explore the evolution of ISWs in the basin, 2‐D numerical simulations with the nonhydrostatic MIT general circulation model (MITgcm) were conducted. The results are consistent with the satellite observations in regard to the generation sites, peak amplitudes and the speeds of first‐mode ISWs. Moreover, our simulations suggest that the generation process of ISWs in the southern Red Sea is similar to the tide‐topography interaction mechanism seen in the South China Sea. Specifically, instead of ISWs arising in the immediate vicinity of the shelf break via a hydraulic lee wave mechanism, a broad, energetic internal tide is first generated, which subsequently travels away from the shelf break and eventually breaks down into ISWs. Sensitivity runs suggest that ISW generation may also be possible under summer stratification conditions, characterized by an intermediate water intrusion from the strait of Bab el Mandeb. First study to simulate the generation and evolution of internal solitary waves in the Red SeaTide background has been analyzed and properties of ISWs have been estimatedThe main generation mechanism is tide topography interaction, tidal beam affects little

We present X-ray spectral analysis of the brightest sources ($f_{2{-}10~{\rm keV}} > 10^{-15}$$\rm erg\,cm^{-2}\,s^{-1}$) in the Chandra Deep Field North. Our sample consists of 222 sources; for the vast majority (171) either a spectroscopic or a photometric redshift is available. Our goal is to discover the Compton-thick AGN in a direct way i.e. through their X-ray spectra. Compton-thick AGN give away their presence in X-rays either directly through the absorption turnover redshifted in the Chandra passband, or through a flat, reflection-dominated, spectrum. The above selection criteria yield 10 Compton-thick AGN candidates of which the nine are reflection dominated. The IR or sub-mm data where available, corroborate the presence of a heavily obscured nucleus in most cases. All the five candidate Compton-thick sources with available 24 μm data present very high values of the f24/fRflux ratio suggesting that they are dust obscured galaxies. The low fx/fIRratio also suggest the presence of obscured nuclei in many cases. Four of the candidate Compton-thick sources are associated with sub-mm galaxies at high redshifts $z \sim 2$. The number count vs. flux distribution of the candidate Compton-thick AGN as well as their distribution with redshift agree reasonably well with the predictions of the X-ray background synthesis models of Gilli et al.

We present XMM-Newtonspectral analysis of all 38 Seyfert galaxies from the Palomar spectroscopic sample of galaxies. These are found at distances of up to 67 Mpc and cover the absorbed 2–10 keV luminosity range ~1038–1043erg s-1. Our aim is to determine the distribution of the X-ray absorption in the local Universe. Three of these are Compton-thick with column densities just above 1024cm-2and high equivalent width FeKαlines (>700 eV). Five more sources have low values of the X-ray to [OIII] flux ratio suggesting that they could be associated with obscured nuclei. Their individual spectra show neither high absorbing columns nor flat spectral indices. However, their stacked spectrum reveals an absorbing column density of NH~ 1023cm-2. Therefore the fraction of absorbed sources (>1022cm-2) could be as high as 55±12%. A number of Seyfert-2 appear to host unabsorbed nuclei. These are associated with low-luminosity sources LX< 3$\times$1041erg s-1. Their stacked spectrum again shows no absorption while inspection of the Chandraimages, where available, shows that contamination from nearby sources does not affect the XMM-Newtonspectra in most cases. Nevertheless, such low luminosity sources are not contributing significantly to the X-ray background flux. When we consider only the brighter, >1041erg s-1, 21 sources, we find that the fraction of absorbed nuclei rises to 75±19% while that of Compton-thick sources to 15–20%. The fraction of Compton-thick AGN is lower than that predicted by the X-ray background synthesis model in the same luminosity and redshift range.

Chandraand XMM-Newtonsurveys show that the fraction of obscured AGN decreases rapidly with increasing luminosity. Although this is usually explained by assuming that the covering factor of the central engine is much smaller at luminous QSOs, the exact origin of this effect remains unknown. We perform toy simulations to test whether photo-ionisation of the obscuring screen in the presence of a strong radiation field can reproduce this effect. In particular, we create X-ray spectral simulations using a warm absorber model assuming a range of input column densities and ionisation parameters. We fit instead the simulated spectra with a simple cold absorption power-law model that is the standard practice in X-ray surveys. We find that the fraction of absorbed AGN should fall with luminosity as $L^{-0.16\pm0.03}$in rough agreement with the observations. Furthermore, this apparent decrease in the obscuring material is consistent with the dependence of the FeKαnarrow-line equivalent width on luminosity, i.e. the X-ray Baldwin effect.

We present Chandraand Spitzerdata for the 186, extragalactic, hard 2–10 keV X-ray selected sources, which lie in the central part of the Chandra Deep Field South (CDFS). For the vast majority of sources (99.5%), there is a spectroscopic or photometric redshift available. We classify 17 sources as X-ray obscured QSOs, strictly according to X-ray criteria, i.e. defined as having large hydrogen column densities ($N_{\rm H}>10^{22}$$\rm cm^{-2}$) and luminosities ($L_{\rm x}>10^{44}$$\rm erg~s^{-1}$). The surface density of X-ray obscured QSOs is ~210 $\rm deg^{-2}$. We find 18 candidate Compton-thick $N_{\rm H}>10^{24}$$\rm cm^{-2}$sources, of which three have QSO luminosities ($L_{\rm x}>10^{44}$$\rm erg~s^{-1}$). The X-ray obscured QSO comprise a mixed bag of objects, covering the redshift range $z=1.3{-}4.3$. Eight of these show narrow-line optical spectra, two show no obscuration in their optical spectra that present broad lines, while for the other seven there is only a photometric redshift available. About half of the X-ray obscured QSOs show high X-ray to optical flux ratios, ${\rm X/O}>1$, and red colours, $I-3.6~\mu{\rm m}>4$. Combining the X-ray with the mid-IR $8~\mu{\rm m}$or 24 $\mu{\rm m}$flux can be used as an additional diagnostic to sift out the heavily obscured AGN. All X-ray selected QSOs present red mid-IR colours and can be easily separated among mid-IR sources, demonstrating that mid-IR selection provides a powerful tool for detecting obscured QSOs.

We combine bright XMM-Newtondata with the ChandraDeep Field South observations to explore the behavior of the intrinsic AGN absorption, as a function of redshift and luminosity. Our sample consists of 359 sources selected in the hard 2–8 keV band, spanning the flux range 6 $\times$10-16–3 $\times$10-13$\rm erg~cm^{-2}~s^{-1}$with a high rate of spectroscopic or photometric redshift completeness (100 and 85 per cent respectively for the Chandraand XMM-Newtondata). We derive the column density values using X-ray spectral fits. We find that the fraction of obscured AGN falls with increasing luminosity in agreement with previous findings. The fraction of obscured AGN shows an apparent increase at high redshifts ($z>2$). Simulations show that this effect can most probably be attributed to the fact that at high redshifts the column densities are overestimated.

We study the XMM-Newton spectra of a sample of 32 soft X-ray selected QSOs. Our goal is to check, using the spectra of moderate redshift ($z\sim1.5$), faint ($f_{0.2-8~{\rm keV}}>5\times 10^{-15}$$\rm erg~cm^{-2}~s^{-1}$) broad-line QSOs, previous claims for either significant intrinsic absorption or spectral hardening at high energies. We derive hardness ratios for all sources and furthermore we perform spectral fits for the 11 brighter sources. The majority of sources have steep spectra $\Gamma>1.9$. We find a few QSOs with large amounts of intrinsic absorption, as high as $N_{\rm H}\sim10^{23}$$\rm cm^{-2}$. We find no strong evidence for spectral hardening above 2 keV. The coadded QSO spectrum is well described by a single power-law with photon index of ~1.9, demonstrating that, on average, any effects of absorption are not important. This suggests that the discrepancy between the X-ray background and the (soft X-ray selected) QSO spectrum holds well at the faint fluxes probed here.

We present BeppoSAXobservations of 6 “type-2” LINER and “transition” galaxies (NGC 3379, NGC 3627, NGC 4125, NGC 4374, NGC 5195 and NGC 5879) from the Ho et al. ([CITE]) spectroscopic sample of nearby galaxies. All objects are detected in the 2–10 keV band, having luminosities in the range $ L_{2-10\,\rm keV}\sim 1\times10^{39}{-}1\times10^{40}$$\rm erg~s^{-1}$. The PDS upper limits above 10 keV place constraints on the presence of a heavily obscured AGN in the case of NGC 3379 and NGC 4125. No significant variability is detected in any of the objects. The spectra are described in most cases by a simple power-law model with a spectral slope of $\Gamma \sim 1.7{-}2.5$while there is evidence neither for a significant absorption above the Galactic nor for an FeKαemission line. Therefore, based on the spectral properties alone, it is difficult to differentiate between a low-luminosity AGN or a star-forming galaxy scenario. However, imaging observations of NGC 3627 and NGC 5195 with ChandraACIS-S reveal very weak nuclear sources while most of the X-ray flux originates either in off-nuclear point sources or in diffuse emission. The above clearly argue in favour of a star-forming origin for the bulk of the X-ray emission, at least in the above two sources.

Mass conservation links the storage Sand the outflow Qof an aquifer. A relation between them (an S‐Qrelation) provides then a model governing the evolution of these quantities. In this work we construct an analytical quasi‐steady state model which exploits the properties of the exact S‐Qrelation associated with steady state solutions of the Boussinesq equation for the sloping aquifer (that is, the Henderson and Wooding[1964] solutions). The model is derived by matching the asymptotic forms of the exact S‐Qrelation which arise for small and large values of the Henderson and Wooding parameter λ. These asymptotic forms provide a novel rederivation of well‐known semiempirical S‐Qrelations of the form Q∝Sand Q∝S2, and they lead to soluble quasi‐steady state models. The quadratic asymptotic relation turns out to hold for surprisingly low values of λ. This characteristic and its formal properties allow smooth matching with the linear relation at λ=π2/4=2.47. The obtained model holds over the entire parameter space. An important characteristic of the model, stemming from its derivation, is that it involves only the geometric and hydraulic quantities present in the exact Boussinesq equation. The model is tested by best fitting four data sets from experiments simulating aquifer drainage. The derived curves for the drained volume are in excellent agreement with the data. The estimated values for kand nare also in overall very good agreement with their reference values. The quasi‐steady states of the nonlinear Boussinesq are an effective toolTheir small and large slope asymptotics lead to an effective analytical modelThe derived models contain only the standard parameters of the aquifer

The Data Interpolating Empirical Orthogonal Functions method is a special technique based on Empirical Orthogonal Functions and developed to reconstruct missing data from satellite images, which is especially useful for filling in missing data from geophysical fields. Successful experiments in the Western Mediterranean encouraged extension of the application eastwards using a similar experimental implementation. The present study summarizes the experimental work done, the implementation of the method and its ability to reconstruct the sea-surface temperature fields over the Eastern Mediterranean basin, and specifically in the Levantine Sea. L3 type Satellite Sea-surface Temperature data has been used and reprocessed in order to recover missing information from cloudy images. Data reconstruction with this method proved to be extremely effective, even when using a relatively small number of time steps, and markedly accelerated the procedure. A detailed comparison with the two oceanographic models proves the accuracy of the method and the validity of the reconstructed fields.

This study presents an integrated method for the estimation and analysis of potential wind-energy resources in Cyprus, which is applied at selected sites on the western side of the island. Firstly, a statistical analysis of wind speed and direction data was conducted at six meteorological stations in western Cyprus, establishing daily, monthly and annual variations of wind speed. Also examined were the Weibull distributions of the wind at each site. These wind statistics serve as the basis for estimating corrected statistical distributions over the extended study areas, which were calculated using the Wind Atlas Analysis and Application Program (WAsP) that modifies wind flow estimates based on local topographic effects. As a result, a geographic and wind-resource database was formulated around each station. Aggregation of this data using statistical weighting methods allows the extrapolation of observed results and the visualization for selected hours of the day over the western part of Cyprus. The results indicate the strong influence of the sea-breeze on the island’s wind potential, and identify a number of areas of higher wind-energy potential suitable for wind-resource exploitation. It is hoped that both the methodology applied and results obtained can be further used by potential investors and wind-energy developers.

The main goal of this study is the derivation of Carlson’s Trophic State Index (TSI) through the remote sensing of four different Case-2 waters in the Mediterranean region such as Cyprus and Greece. TSISDis derived through extensive field ground campaign of Secchi Disk Depth measurements for the Asprokremmos Dam, located in Paphos District in Cyprus; Alyki Salt Lake, located in Larnaca District in Cyprus; and in Karla Lake, located in Volos District in Greece; and finally to three coastal water areas in the Limassol coastal area. Several regression models have been applied in order to develop the best regression model between the TSISDand in-band reflectance values for Landsat TM/ETM derived from spectroradiometric measurements using a GER-1500 field spectroradiometer over the main case study area in Asprokremmos Dam in Cyprus. Finally, we apply several regression models for Asprokremmos Dam for retrieving the suitable Landsat TM/ETM band or band combinations (obtained from field spectroradiometric measurements) in which TSISDcan be determined. Indeed, the best regression model has been obtained by correlating ‘TSI Versus Band2/Band3’, with R2=0.89. All field TSISDand in-band reflectance values from the four different water bodies have been used to develop the best fitted model for the established TSISDVersus Band2/Band3 model. We find that the exponential regression model provides the best fitted equation over the four different water bodies.

An analytical solution of planar flow in a sloping soil layer described by the linearized extended Boussinesq equation is presented. The solution consists of the sum of steady-state and transient-series solutions, the latter in a separation-of-variables form, and can satisfy an arbitrary initial condition via collocation; this feature reduces the number of series terms, making the solution efficient. Key parameter is the dimensionless linearization depth ηo(R), R being the dimensionless recharge. The variable ηo(R), not the slope, characterizes the flow as kinematic or diffusive, and R ≈ 0.2 demarcates the two regimes. The transient series converges rapidly for large ηo (large R, near-diffusive flow) and slowly as ηo → 0 (kinematic flow). The quasi-steady (QS) state method of Verhoest & Troch is also analysed and it is shown that the QS depth profiles approximate the transient ones well, only if Δt exceeds a system-dependent transition time between flow states (possibly >>1 day). In an application example for a 30-day recharge series, the QS solution differs from the transient one by as much as 20% (RMSE = 15%), does not track recharge changes as well and fails to conserve mass.

The stability of steep gravity–capillary solitary waves in deep water is numerically investigated using the full nonlinear water-wave equations with surface tension. Out of the two solution branches that bifurcate at the minimum gravity–capillary phase speed, solitary waves of depression are found to be stable both in the small-amplitude limit when they are in the form of wavepackets and at finite steepness when they consist of a single trough, consistent with observations. The elevation-wave solution branch, on the other hand, is unstable close to the bifurcation point but becomes stable at finite steepness as a limit point is passed and the wave profile features two well-separated troughs. Motivated by the experiments of Longuet-Higgins & Zhang (1997), we also consider the forced problem of a localized pressure distribution applied to the free surface of a stream with speed below the minimum gravity–capillary phase speed. We find that the finite-amplitude forced solitary-wave solution branch computed by Vanden-Broeck & Dias (1992) is unstable but the branch corresponding to Rayleigh’s linearized solution is stable, in agreement also with a weakly nonlinear analysis based on a forced nonlinear Schrödinger equation. The significance of viscous effects is assessed using the approach proposed by Longuet-Higgins (1997): while for free elevation waves the instability predicted on the basis of potential-flow theory is relatively weak compared with viscous damping, the opposite turns out to be the case in the forced problem when the forcing is strong. In this régime, which is relevant to the experiments of Longuet-Higgins & Zhang (1997), the effects of instability can easily dominate viscous effects, and the results of the stability analysis are used to propose a theoretical explanation for the persistent unsteadiness of the forced wave profiles observed in the experiments.

Steady, finite-amplitude internal-wave disturbances, induced by nearly hydrostatic stratified flow over locally confined topography that is more elongated in the spanwise than the streamwise direction, are discussed. The nonlinear three-dimensional equations of motion are handled via a matched-asymptotics procedure: in an ‘inner’ region close to the topography, the flow is nonlinear but weakly three-dimensional, while far upstream and downstream the ‘outer’ flow is governed, to leading order, by the fully three-dimensional linear hydrostatic equations, subject to matching conditions from the inner flow. Based on this approach, non-resonant flow of general (stable) stratification over finite-amplitude topography in a channel of finite depth is analysed first. Three-dimensional effects are found to inhibit wave breaking in the nonlinear flow over the topography, and the downstream disturbance comprises multiple small-amplitude oblique wavetrains, forming supercritical wakes, akin to the supercritical free-surface wake induced by linear hydrostatic flow of a homogeneous fluid. Downstream wakes of a similar nature are also present when the flow is uniformly stratified and resonant (i.e. the flow speed is close to the long-wave speed of one of the modes in the channel), but, in this instance, they are induced by nonlinear interactions precipitated by three-dimensional effects in the inner flow and are significantly stronger than their linear counterparts. Finally, owing to this nonlinear-interaction mechanism, vertically unbounded uniformly stratified hydrostatic flow over finite-amplitude topography also features downstream wakes, in contrast to the corresponding linear disturbance that is entirely locally confined.

In dispersive wave systems with dispersion relations such that the phase speed attains an extremum at a finite wavenumber, a rich variety of solitary waves that feature decaying oscillatory tails is known to arise. Here we use the fifth–order Korteweg–de Vries (KdV) equation, a model for small–amplitude gravity–capillary waves on water of finite depth when the Bond number is close to to examine the stability of the two symmetric solitary–wave solution branches that bifurcate at the minimum phase speed. In the vicinity of the bifurcation point, these solitary waves take the form of modulated wave packets with envelopes that can be approximated by the same soliton solution of the nonlinear Schrodinger (NLS) equation, suggesting that both branches would be stable in the small–amplitude limit. It is shown, however, that the branch of the so–called elevation waves is unstable while the branch of depression waves is stable, consistent with numerical results. The coupling between the carrier oscillations and their envelope, an effect beyond all orders of the expansion underlying the NLS equation, is essential to this behaviour: the dimensionless growth rates of the instability modes found for elevation waves are exponentially small with respect to the solitary–wave steepness. The asymptotic procedure followed here would be useful in discussing the stability of solitary waves with decaying oscillatory tails in other settings as well, and details are worked out for a nonlinear beam equation and a modified fifth–order KdV equation.

In dispersive wave systems, when leading-order nonlinear and dispersive effects, are taken into account the envelope of a small-amplitude narrow-band wave pulse is known to satisfy the nonlinear Schrödinger (NLS) equation which, under certain conditions, admits envelope-soliton solutions. These solitons describe locally confined wave groups with envelopes of permanent form and find applications in various physical contexts. Here, is addressed the question of whether NLS envelope solitons survive when higher-order effects are taken into account. Based on a kinematic argument first, it is suggested that oscillatory tails are inevitably emitted, and this claim is further supported by numerical computations by use of a fifth-order Korteweg-deVries equation as a simple example. The radiation of tails is caused by a resonance mechanism that lies beyond all orders of the usual multiple-scale expansion leading to the NLS equation, and a procedure for calculating these tails by use of exponential asymptotics is outlined. Despite having exponentially small amplitude in the asymptotic sense, the radiated tails can be significant when pulses of relatively short duration are considered.

An analytical and numerical study is made of the propagation of waves whose wavenumbers are close to conditions for direct resonance. These waves emerge from the linear initial value problem as the dominant far field signal. The nonlinear evolution characteristics are investigated. It is found that weakly nonlinear waves at direct resonance may rapidly amplify and tend to become fully nonlinear in a finite time.

The phenomenon of shelf generation by long nonlinear internal waves in stratified flows is investigated. The problem of primary interest is the case of a uniformly stratified Boussinesq fluid of finite depth. In analysing the transient evolution of a finite-amplitude long-wave disturbance, the expansion procedure of Grimshaw & Yi (1991) breaks down far downstream, and it proves expedient to follow a matched-asymptotics procedure: the main disturbance is governed by the nonlinear theory of Grimshaw & Yi (1991) in the ‘inner’ region, while the ‘outer’ region comprises multiple small-amplitude fronts, or shelves, that propagate downstream and carry O(1) mass. This picture is consistent with numerical simulations of uniformly stratified flow past an obstacle (Lamb 1994). The case of weakly nonlinear long waves in a fluid layer with general stratification is also examined, where it is found that shelves of fourth order in wave amplitude are generated. Moreover, these shelves may extend both upstream and downstream in general, and could thus lead to an upstream influence of a type that has not been previously considered. In all cases, transience of the main nonlinear wave disturbance is a necessary condition for the formation of shelves.

Using the forced Korteweg‐de Vries equation as a simple model, a perturbation procedure is presented for calculating the amplitude of short‐scale oscillatory tails induced by steady long‐wave disturbances. In the limit of weak dispersion, these tails have exponentially small amplitude that lies beyond all orders of the usual long‐wave expansion. It is demonstrated that by working in the wavenumber domain, the tail amplitude can be determined quite simply, without the need for asymptotic matching in the complex plane. The induced short‐wave tail is sensitive to the details of the long‐wave profile. The proposed technique is applicable to nonlocal solitary waves and to other problems that require the use of exponential asymptotics.

A classical description of the atomic capture and cascade is used to calculate the muon spin precession. The binding energies and orbital angular momenta at which the total angular momentumj becomes a good quantum number are calculated. The depolarization in the quantall part of the cascade is also studied. Using this information, and assuming a statistical initial angular momentum distribution, we calculate the residual polarization of the muon in the 1s state. The results agree substantially better with the experimental data than the previously used theoretical predictions. Moreover, it is shown that the residual polarization does not depend very sensitively on the initial angular momentum distribution.

In certain wave systems it is possible for the amplitudes associated with special wave numbers to be larger than expected. Such may be the case if two frequencies are close together. Direct resonances of this type are studied and some possible applications are discussed.

A viscous boundary‐layer flow, first proposed by Lock as a model for the initiation of water waves by wind, is studied. A stability analysis of the flow indicates that the linear instability present is relatively weak. However, under certain conditions, the system can support coalescing normal modes, and thus, direct resonance between such modes is possible. A nonlinear perturbative analysis at direct resonance is performed, and the equation governing the slow temporal evolution of a finite‐amplitude oscillatory disturbance is derived. The appropriate evolution equation is of second order in time. The nonlinear effects are of crucial importance in the development of a resonant disturbance. Comparison of the theoretical predictions with experiments suggests that direct resonance may play a significant role in explaining the observed large initial growth rates of gravity water waves of wavelength longer than about 12 cm.

Sound radiation by instability wavepackets evolving from general initial conditionsin a low‐Mach‐number, slightly unstable boundary layer is studied. The formulation can be viewed as an exact instance of Lighthill's [13] acoustic analogy. The original disturbance may be line‐ or point‐centered with an infinitesimal amplitude. The sound field is confined within an expanding sphere. The directivity of sound is beamed and points upstream. This “superdirectivity” is slowly enhanced in time whereas the sound level is slowly attenuated. Nonlinear processes, once they come into play, reverse the temporal behavior of the sound level and sound directivity. For the boundary‐layer profiles studied, nonlinearity causes a “burst,” in a finite time, of the sound field in the form of a dipole.

A theoretical study is made of the free‐surface flow induced by a wavemaker, performing torsional oscillations about a vertical axis, in a shallow rectangular channel near a cut‐off frequency. Exactly at cut‐off, linearized water‐wave theory predicts a temporally unbounded response due to a resonance phenomenon. It is shown, through a perturbation analysis using characteristic variables, that the nonlinear response is governed by a forced Kadomtsev—Petviashvili (KP) equation with periodic boundary conditions across the channel. This nonlinear initial‐boundary‐value problem is investigated analytically and numerically. When surface‐tension effects are negligible, the nonlinear response reaches a steady state and exhibits jump phenomena. On the other hand, in the high‐surface‐tension regime, no steady state is obtained. These results are discussed in connection with similar forced wave phenomena studied previously in a deepwater channel and related laboratory experiments.

The excitation of surface waves on a viscous fluid by shear flows is studied. Turbulent and laminar air flows over oil of low and high viscosity are considered. It is found that the dominant wave-generation mechanism depends crucially on the shear-flow profile: for a turbulent flow, long surface waves are generated at low wind speeds due to the work done by the stress components in phase with the surface slope, while Kelvin-Helmholtz instability is responsible for the excitation of short waves at higher wind speeds. On the other hand, for a laminar shear flow, direct resonance between surface waves and Tollmien-Schlichting waves in the shear flow is the dominant wave-generation mechanism.