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We present an overview of both older and recent developments concerning scale separation in string theory. We focus on parametric scale separation obtained at the classical level in flux compactifications down to AdS vacua. We review the scenarios that have been proposed to achieve a hierarchy of scales between spacetime and the internal space, built from a low-dimensional perspective. We then discuss how they have been understood to arise from proper higher-dimensional descriptions. Eventually, limitations of these constructions as well as Swampland and holographic arguments addressing the question of scale separation in string theory are discussed. The purpose of the review is to draw an accurate picture of the state of the art of the subject at the moment. [ABSTRACT FROM AUTHOR]

The ERA5 global reanalysis has been compared against a high‐resolution regional reanalysis (COSMO‐REA6) by means of scale‐separation diagnostics based on 2d Haar discrete wavelet transforms. The presented method builds upon existing methods and enables the assessment of bias, error and skill for individual spatial scales, separately. A new skill score (evaluated against random chance) and the Symmetric Bounded Efficiency are introduced. These are compared to the Nash‐Sutcliffe and the Kling‐Gupta Efficiencies, evaluated on different scales, and the benefits of symmetric statistics are illustrated. As expected, the wavelet statistics show that the coarser resolution ERA5 products underestimate small‐to‐medium scale precipitation compared to COSMO‐REA6. The newly introduced skill score shows that the ERA5 control member (EA‐HRES), despite its higher variability, exhibits better skill in representing small‐to‐medium scales with respect to the smoother ensemble members. The Symmetric Bounded Efficiency is suitable for the inter‐comparison of reanalyses, since it is invariant with respect to the order of comparison. [ABSTRACT FROM AUTHOR]

In this paper, minimal supersymmetric AdS3 solutions on G2‐orientifolds of type IIA and IIB supergravity are studied. These are obtained by techniques of the bispinor formalism. A straightforward argument is derived against AdS3 solutions in massless type IIA string theory on such G2‐backgrounds. Furthermore, it is shown that some of the AdS3 solutions in massive type IIA do admit a separation of scales, whereas the same cannot be said for the type IIB vacua. Finally, a formula for the 3d superpotential in the bispinor language is given that is valid for both type IIA and type IIB configurations. It is shown that the supersymmetry conditions of this superpotential lead back to the bispinor equations. [ABSTRACT FROM AUTHOR]

Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant error estimates were formally described in our previous work Burghardt et al (2021 J. Phys. A: Math. Theor. 54 414002). Specifically, we consider a representative two-dimensional tunneling system where a double well and a harmonic coordinate are cubically coupled. The time-dependent Hartree approximation is compared with a fully correlated solution, for different parameter regimes. The impact of the coupling and the resulting correlations are quantitatively assessed in terms of a time-dependent reaction probability along the tunneling coordinate. We show that the numerical error is correctly predicted on moderate time scales by a theoretically derived error estimate. [ABSTRACT FROM AUTHOR]

An important epistemic issue in climate modelling concerns structural uncertainty: uncertainty about whether the mathematical structure of a model accurately represents its target. How does structural uncertainty affect our knowledge and predictions about the climate? How can we identify sources of structural uncertainty? Can we manage the effect of structural uncertainty on our knowledge claims? These are some of the questions that an epistemology of structural uncertainty faces, and these questions are also important for climate scientists and policymakers. I develop three desiderata for an epistemological account of structural uncertainty. In my view, an account of structural uncertainty should (1) identify sources of structural uncertainty, (2) explain how these sources limit the applicability of a model, and (3) show how the severity of structural uncertainty depends on the questions that can be asked of a model. I argue that analyzing structural uncertainty by paying attention to the details of model building can satisfy these desiderata. I focus on parametrizations, which are representations of important processes occurring at scales that are not resolved by climate models. Parametrizations are often thought to be ad-hoc, but I show that some important parametrizations are theoretically justified by explicit or implicit scale separation assumptions. These assumptions can also be supported empirically. Analyzing these theoretical and empirical justificatory roles of the scale separation assumptions can provide insights into how parametrizations contribute to structural uncertainty. I conclude by sketching how my approach can satisfy the desiderata I set out at the beginning, highlighting its importance for policy-relevant scientific statements about the climate. [ABSTRACT FROM AUTHOR]

Shot peening can be an effective solution for the prevention or retardation of scale formation, and subsequent exfoliation, upon exposure of the inner tube to steam in coal-fired power plants. In this study, specimens of T91 tubes were shot peened and then exposed to 1-bar steam for 100–1000 h at 650 °C, and were then analyzed using Vickers hardness test and microscopic techniques OM, SEM, TEM, etc. The analysis indicates that the oxide scales are typically Fe2O3 on the topmost layer, Fe3O4 below, and a FeCr2O4 spinel on the bottom in both shot peening treated and untreated specimens. However, the oxide scale thicknesses of shot peened specimens are thinner, indicating that shot peened specimens have better oxidation resistance. In addition, numerous defects, such as voids and micro-cracks, were found in the untreated specimens, which are believed to cause exfoliation of the uppermost Fe2O3 layers of the specimens exposed to steam for 800 and 1000 h. By contrast, the shot peened specimens maintained a dense contact oxide scale with fewer defects. [ABSTRACT FROM AUTHOR]

Hierarchical defects are defined as adjacent defects at different length scales. Involved are the two scales where the stress field distribution is interrelated. Based on the complex variable method and conformal mapping, a multiscale framework for solving the problems of hierarchical defects is formulated. The separated representations of mapping function, the governing equations of potentials, and the stress field are subsequently obtained. The proposed multiscale framework can be used to solve a variety of simplified engineering problems. The case in point is the analytical solution of a macroscopic elliptic hole with a microscopic circular edge defect. The results indicate that the microscopic defect aggregates the stress concentration on the macroscopic defect and likely leads to global propagation and rupture. Multiple micro-defects have interactive effects on the distribution of the stress field. The level of stress concentration may be reduced by the coalescence of micro-defects. This work provides a unified method to analytically investigate the influence of edge micro-defects within the scope of multiscale hierarchy. The formulated multiscale approach can also be potentially applied to materials with hierarchical defects, such as additive manufacturing and bio-inspired materials. [ABSTRACT FROM AUTHOR]

The standard formulation of 4D‐Var assumes random zero‐mean errors for all sources of information used in the analysis. This assumption is usually not well verified in real‐world applications. The performance of a weak‐constraint 4D‐Var formulation ("forcing" formulation) is studied in this paper in a simplified experimental setting using additive model errors of different length‐scales and observing systems of different coverage and accuracy. A set of twin experiments is carried out and results show that weak‐constraint 4D‐Var can accurately estimate the actual model errors and the initial state only when background and model errors have different spatial scales and when the observations are unbiased and spatially homogeneous. We also present preliminary results from a different weak‐constraint 4D‐Var formulation ("state" formulation) which could in principle overcome some of these limitations, but at the cost of a substantial increase of computational and memory requirements. These findings help identify the potential but also the intrinsic limitations of the weak‐constraint 4D‐Var approach. They also help to clarify the experimental results seen in the operational ECMWF analysis system where the analysis and first‐guess temperature bias is reduced by up to 50% in the stratosphere. [ABSTRACT FROM AUTHOR]

The standard, strong‐constraint formulation of 4D‐Var is designed to correct for random, zero‐mean errors from the model forecast and the observations. However, significant systematic errors are generated by the forecast models used in global numerical weather prediction (NWP), and the Integrated Forecast System (IFS) model of the European Centre for Medium‐Range Weather Forecasts (ECMWF) is no exception. To deal with this type of error, a modification of the standard 4D‐Var algorithm, weak‐constraint 4D‐Var, has long been proposed and was implemented in operations at ECMWF in 2009. In the original implementation, the model error corrections were only active in the upper stratosphere, as a full application of the algorithm would lead to unacceptable degradation of forecast scores. Thus the impact of weak‐constraint 4D‐Var on ECMWF analyses and forecasts has always been small heretofore. In a companion article, it was shown through theoretical considerations and experiments with a simplified model that weak‐constraint 4D‐Var can correct accurately for model errors and initial‐state errors only when background and model errors have different spatial scales and when the observing system has a component, sufficient in number, that is unbiased and spatially homogeneous. This article presents new diagnostics based on radio occultation (RO) temperature retrievals and shows how those assumptions are verified in the IFS model. A new model‐error covariance matrix is derived and reduces the analysis and first‐guess temperature bias in the stratosphere by up to 50%. We also present how the model error tendencies diagnosed by weak‐constraint 4D‐Var can be used to reduce mean errors in medium‐range forecasts and discuss how they can also be applied in a reanalysis context to improve the fidelity and continuity of climate reconstructions. [ABSTRACT FROM AUTHOR]

Shot peening can be an effective solution for the prevention or retardation of scale formation, and subsequent exfoliation, upon exposure of the inner tube to steam in coal-fired power plants. In this study, specimens of T91 tubes were shot peened and then exposed to 1-bar steam for 100–1000 h at 650 °C, and were then analyzed using Vickers hardness test and microscopic techniques OM, SEM, TEM, etc. The analysis indicates that the oxide scales are typically Fe2O3 on the topmost layer, Fe3O4 below, and a FeCr2O4 spinel on the bottom in both shot peening treated and untreated specimens. However, the oxide scale thicknesses of shot peened specimens are thinner, indicating that shot peened specimens have better oxidation resistance. In addition, numerous defects, such as voids and micro-cracks, were found in the untreated specimens, which are believed to cause exfoliation of the uppermost Fe2O3 layers of the specimens exposed to steam for 800 and 1000 h. By contrast, the shot peened specimens maintained a dense contact oxide scale with fewer defects.

In order to study the segregation of arsenic impurities at the metal/oxide interface during high temperature exposure, isothermal oxidation behavior of arsenic bearing steels with various Ce content was systematically investigated. The result showed that oxidation mass gain of arsenic bearing steel in the temperature range of 950–1150 °C was decreased as a whole with increasing Ce content from 0 to 0.035 wt.%. At 1100 and 1150 °C, the best results are obtained for 0.027 and 0.035 wt.% Ce. Moreover, Ce addition could prevent grain boundaries oxidation, which reduced or even eliminated the formation of visible oxide particles along grain boundaries at 1000 and 1050 °C. In case of oxidation at 1050 and 1100 °C, the arsenic enrichment amount at the scale/metal interface was firstly decreased with increasing Ce content from 0 to 0.027 wt.% and then slightly increased as Ce content increased from 0.027 to 0.035 wt.%. This variation was attributed to the separation behavior of oxide scale, the formation of a continuous solid Fe2SiO4 layer and the arsenious rare earth particles promoted by Ce addition. [ABSTRACT FROM AUTHOR]

Abstract Low cost sensors are becoming increasingly available for studying urban air quality. Here we show how such sensors, deployed as a network, provide unprecedented insights into the patterns of pollutant emissions, in this case at London Heathrow Airport (LHR). Measurements from the sensor network were used to unequivocally distinguish airport emissions from long range transport, and then to infer emission indices from the various airport activities. These were used to constrain an air quality model (ADMS-Airport), creating a powerful predictive tool for modelling pollutant concentrations. For nitrogen dioxide (NO 2), the results show that the non-airport component is the dominant fraction (∼75%) of annual NO 2 around the airport and that despite a predicted increase in airport related NO 2 with an additional runway, improvements in road traffic fleet emissions are likely to more than offset this increase. This work focusses on London Heathrow Airport, but the sensor network approach we demonstrate has general applicability for a wide range of environmental monitoring studies and air pollution interventions. Highlights • Network of low cost sensors for high spatio-temporal pollution measurements at LHR. • Unprecedented source apportionment information at LHR, including emission factors. • Show that majority of the local pollution was not from airport activities. • Network data used to constrain an air quality model. • Using the refined model prediction to show future impacts of developments at LHR. [ABSTRACT FROM AUTHOR]

Classical homogenization techniques are known to be effective for materials with large scale separation between the size and spacing of their underlying heterogeneities on the one hand and the structural problem dimensions on the other. For low scale separation, however, they generally become inaccurate. This paper assesses the scale separation limit of classical asymptotic homogenization applied to periodic linear elastic composite materials and demonstrates the effectiveness of higher-order homogenization in stretching this limit. A quantitative assessment is performed on a two-dimensional elastic two-phase composite consisting of stiff circular particles in a softer matrix material and subjected to anti-plane shear, as introduced by Smyshlyaev and Cherednichecko (J. Mech. Phys. Solids 48:1325–1358, 2000). Reference solutions are created rigorously using full-scale numerical simulations in which a family of translated microstructures is considered and the ensemble average of their solutions is defined as the homogenized solution. This solution is used as a reference, which is compared with the periodic homogenization solution for a range of scale ratios. It is shown that the zeroth-order classical homogenization solution significantly deviates from the exact solution below a certain scale ratio for a given microstructure. Below this limit, the higher-order solutions provide a clear improvement of the match. Further, the performance of classical and higher-order asymptotic homogenization solution are evaluated for varying stiffness contrast ratio between the two phases of the microstructure and error contours are presented by comparison with full-scale numerical simulations. [ABSTRACT FROM AUTHOR]

The pre-multiplied spanwise energy spectra of streamwise velocity fluctuations are investigated in this paper. Two distinct spectral peaks in the spanwise spectra are observed in low-Reynolds-number wall-bounded turbulence. The spectra are calculated from direct numerical simulation (DNS) of turbulent channel flows and zero-pressure-gradient boundary layer flows. These two peaks locate in the near-wall and outer regions and are referred to as the inner peak and the outer peak, respectively. This result implies that the streamwise velocity fluctuations can be separated into large and small scales in the spanwise direction even though the friction Reynolds number Reτ can be as low as 1000. The properties of the inner and outer peaks in the spanwise spectra are analyzed. The locations of the inner peak are invariant over a range of Reynolds numbers. However, the locations of the outer peak are associated with the Reynolds number, which are much higher than those of the outer peak of the pre-multiplied streamwise energy spectra of the streamwise velocity. [ABSTRACT FROM AUTHOR]

Daily composite Fourier coefficients of height, zonal, meridional and vertical velocity, temperature, vorticity and divergence for zonal wave numbers 0–4, during 7 days of pre‐ and 4 days of post‐depression, from 1000 to 200 hPa in the latitude belt 0–30°N are obtained for six monsoon depressions formed over the Bay of Bengal in the years 2006–2008. The planetary‐scale fields zonally averaged over the Indian region (75–96°E) are examined. Consistent with the quasi‐geostrophic approximation, in the northern sector (15–30°N) the monsoon trough, the low‐level westerlies and the vorticity are strongly intensified and progressively extended upward to 400 hPa preceding depressions. Wave number 1 is the dominant contributor towards the strengthening and vertical upward expansion of these entities linked to an increase of its amplitude in the lower‐ and a large westward phase shift in the mid‐troposphere, respectively. The cyclonic shear zone in the lower troposphere is developed to the north of 15°N due to the combined effect of intensification and sharp decrease of meridional scale of the westerlies. Different northward speeds of the zonal wind reversal and westerly maximum creates a strong cyclonic zone 2 days before depressions at 400 hPa. The planetary‐scale zonal flow in the troposphere satisfies the necessary condition for barotropic instability. The northward (westward) movement of wave number 1 at 400 hPa is 0.73° latitude (5.6° longitude) day−1. An intensification of direct thermal meridional circulation is associated with a southward and upward shift of the primary rising motion zone. The planetary waves have captured the main characteristics of observed vertical and latitudinal profiles of unstable background zonal flow, used earlier for instability studies. It is concluded that wave number 1 is the main contributor to genesis of a depression. The planetary fields weakened in the presence of depressions mainly due to wave numbers 3 and 4. [ABSTRACT FROM AUTHOR]

A reduced-order semi-analytic model of multiple zonal jets in the Southern Ocean is proposed based on the statistical approach and scale decomposition. By introducing two dominant scales in the vorticity equation, the model describes the large-scale and mesoscale dynamics using the explicit momentum dissipation in the horizontal and vertical directions. For validation and physical insights, the results of the reduced-order model are compared with solutions of two eddy-resolving ocean models: (i) a realistic primitive-equation HYCOM (HYbrid Coordinate Ocean Model) simulation of the Southern Ocean and (ii) an idealized quasi-geostrophic model of a shear-driven channel flow. • There is a scale separation in vorticity spectrum of the Southern Ocean. • The large- and small-scale components are described by a semi-analytical model. • The large-scale flow is derived by wind and dissipated via bottom friction. • Zonal jets result from balance of beta term, vertical stretching and dissipation. • Zonal jets are coupled to the background flow through eddy viscosity. [ABSTRACT FROM AUTHOR]

Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497−21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin−Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA.

This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed Lévy noise, which are invariant on the compact horizontal leaves of a foliated manifold subject to small transversal random perturbations. We extend a result for such diffusions with exponential moments and bounded, deterministic perturbations to diffusions with polynomial moments of order $p\geqslant 2$ , perturbed by deterministic and stochastic integrals with unbounded coefficients and polynomial moments. The main argument relies on a result of the dynamical system for each individual jump increments of the corresponding canonical Marcus equation. The example of Lévy rotations on the unit circle subject to perturbations by a planar Lévy-Ornstein-Uhlenbeck process is carried out in detail. [ABSTRACT FROM AUTHOR]

This paper quantifies the mixing effects on algal growth in loop photobioreactors using two-scale low-dimensional models derived through spatial averaging of the Convection–Diffusion–Reaction equation using Liapunov–Schmidt technique of the classical bifurcation theory. The local mixing in the reactor is captured in terms of the mixing time and the difference between the mixing-cup and the spatially averaged concentrations of the algae, which are representatives of the convection scale in the fluid phase and the reaction scale at the algal surface, respectively. We solve coupled unsteady-state low-dimensional partial differential equations (PDEs) to simulate the temporal dynamics of the algae ( Chlorella vulgaris ), carbon dioxide and oxygen along the reactor in laminar and turbulent mixing regimes. Analytical solutions are derived for the unsteady and pseudo-steady state cases in the turbulent regime. We show that while laminar mixing results in significant scale separation between the convection and reaction scales, turbulent mixing – propelled by the turbulent diffusivity – eliminates all scale separation and mass transfer limitations in the photobioreactor and maximizes algal growth. Increasing Reynolds number ( Re ) increases the dimensionless mixing time (and thus, the scale separation) in the laminar regime but has negligible effect on turbulent mixing. Thus, the system transitions from the mixing-limited asymptote in the laminar regime to the reaction-limited asymptote in the turbulent regime. For maximum algal growth per unit energy cost, we recommend operating loop photobioreactors at a low Re (>2300) in the turbulent flow regime so as to generate turbulent mixing for rapid mass transfer of the growth substrates and the algae between the convection (fluid) and the reaction (solid) phases, at optimal pressure drops. Our two-scale model would be an important design tool for quantifying mixing effects while scaling up photobioreactors. [ABSTRACT FROM AUTHOR]

Due to the emergence of new high-resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet transforms offer an effective framework to decompose spatial data into separate (and possibly orthogonal) scales and directions. Most wavelet-based spatial verification techniques have been developed or refined in the last decade and concentrate on assessing forecast performance (i.e. forecast skill or forecast error) on distinct physical scales. Particularly during the last 5 years, a significant growth in meteorological applications could be observed. However, a comparison with other scientific fields, such as feature detection, image fusion, texture analysis or facial and biometric recognition, shows that there is still a considerable, currently unused potential to derive useful diagnostic information. In order to tap the full potential of wavelet analysis, we review the state-of-the-art in one- and two-dimensional wavelet analysis and its application, with emphasis on spatial verification. We further use a technique developed for texture analysis in the context of high-resolution quantitative precipitation forecasts, which is able to assess the structural characteristics of the precipitation fields and allows efficient clustering of ensemble data. [ABSTRACT FROM AUTHOR]