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At least 307 records · Page 17

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DOE OSTI2018

Nanoscale mapping of hydrogen evolution on metallic and semiconducting MoS 2 nanosheets

Hydrogen evolution reaction (HER) on molybdenum disulfide (MoS 2 ) nanosheets is enhanced for the metallic (1T) phase relative to the thermodynamically stable semiconducting (2H) phase. To measure this difference, we employ scanning electrochemical microscopy (SECM) for high-resolution mapping (<20 nm spatial resolution) of surface reactivity for mixed-phase and pure 2H-only MoS 2 nanosheets. For mixed-phase MoS 2 nanosheets, we find major differences in reactivity of the two phases for electron transfer involving ferrocenemethanol, allowing us to locate 1T and 2H regions and directly map the corresponding HER activity. In our measurements, we find that HER is immeasurably slow on the 2H basal plane and much faster on edges, whereas 1T portions are highly reactive across the entire portion. We also use scanning transmission electron microscopy-electron energy loss spectroscopy and scanning Kelvin probe microscopy to corroborate the phase domains and local workfunctions (surface potentials) within the MoS 2 nanosheets; the mixed-phase MoS 2 has a shallower workfunction compared to 2H MoS 2 , which could enable a greater driving force for H 2 generation. As a result, this powerful combination of techniques for spatially mapping surface reactivity and correlated phase domains should be applicable to a broad range of materials for HER and other catalysis reactions.

36 MATERIALS SCIENCE↗

NASA NTRS2015

Variable-Domain Displacement Transfer Functions for Converting Surface Strains into Deflections for Structural Deformed Shape Predictions

Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions

displacement transfer functions↗

DOE OSTI2023

Geospatial mapping of distribution grid with machine learning and publicly-accessible multi-modal data

Abstract Detailed and location-aware distribution grid information is a prerequisite for various power system applications such as renewable energy integration, wildfire risk assessment, and infrastructure planning. However, a generalizable and scalable approach to obtain such information is still lacking. In this work, we develop a machine-learning-based framework to map both overhead and underground distribution grids using widely-available multi-modal data including street view images, road networks, and building maps. Benchmarked against the utility-owned distribution grid map in California, our framework achieves > 80% precision and recall on average in the geospatial mapping of grids. The framework developed with the California data can be transferred to Sub-Saharan Africa and maintain the same level of precision without fine-tuning, demonstrating its generalizability. Furthermore, our framework achieves a R 2 of 0.63 in measuring the fraction of underground power lines at the aggregate level for estimating grid exposure to wildfires. We offer the framework as an open tool for mapping and analyzing distribution grids solely based on publicly-accessible data to support the construction and maintenance of reliable and clean energy systems around the world.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2014

Time-bin state transfer to electron spin coherence in solids

We demonstrate that a coherent superposition state of two temporally separated optical pulses, called a time-bin state, can be transferred to that of up/down electron spins in a semiconductor by synchronizing the time separation to the precession period of either electrons or holes. The time-bin transfer scheme does not require polarization mode degeneracy and can map the time-bin state to the electron spin state that is not accessible directly using only polarization. The scheme offers a new approach for quantum interfaces between photons and electron spins.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Density functional theory study of the influence of segregation of S or Fe impurities on electromigration in nano-grained copper interconnects

The reliability of the circuits in the modern microelectronic devices remains, during last decades, one of the key topics in research and gains an attention for improving the promising candidates for conductors. Improvement of materials for such applications can be obtained by both electronic and compositional optimization. Ab initio calculations using full potential linearized augmented plane wave method in density functional theory are applied to explain the reduction in electromigration effect in the vicinity of grain boundaries (GB) in nano-structured Cu due to the segregation of some additives to the GB. Several possible mechanisms are considered. It is demonstrated that S atoms segregated to GB of nano-structured Cu lead to the growth of effective mass of the electrons. This decreases the mobility of electrons in external electric field, and, correspondingly, the momentum that they may transfer to atoms in collisions. Fe atoms segregated to GB of Cu create new empty states at the top of the valance band. These non-occupied states may stimulate the current of holes when external electric field is applied to the system, creating the “hole wind” in the direction opposite to the current of electrons. Such “hole wind” will compensate the forces generated by the electron current and therefore will reduce the total momentum transfer between charge carriers and atoms. The calculated electron density maps show that S and Fe segregating to Cu GB increases the strength of covalent bonds reducing the diffusion of Cu atoms in the vicinity of GB.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Weak-charge form-factor determination at the electron-ion collider

Determining the weak charge form factor, 𝐹 𝑊 ⁡(𝑄 2 ), of nuclei over a continuous range of momentum transfers, 0 ≲ 𝑄 2 ≲ 0.1 GeV 2 , is essential for mapping out the distribution of neutrons in nuclei. The neutron density distribution has significant implications for a broad range of areas, including studies of nuclear structure, neutron stars, and physics beyond the Standard Model. Currently, our knowledge of 𝐹 𝑊 ⁡(𝑄 2 ) comes primarily from fixed target experiments that measure the parity-violating asymmetry in coherent elastic electron-ion scattering. Fixed target experiments, such as CREX and PREX-1,2, have provided high-precision weak charge form factor extractions for the 48 Ca and 208 Pb nuclei, respectively. However, a major limitation of fixed target experiments is that they each provide data only at a single value of 𝑄 2 . With the proposed electron-ion collider (EIC) on the horizon, we explore its potential to impact the determination of the weak charge form factor. While it cannot compete with the precision of fixed target experiments, it can provide data over a wide and continuous range of 𝑄 2 values, and for a wide variety of nuclei. We show that with data corresponding to an integrated luminosity of ℒ ∼ 500/𝐴 fb −1 , where 𝐴 is the nucleus atomic weight, the EIC can significantly impact constraints by lifting degeneracies in theoretical models of the neutron density distribution. Ensuring EIC detector coverage at low 𝑄 2 and large negative pseudorapidities will be essential for such 𝐹 𝑊 ⁡(𝑄 2 ) measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2001

Application of Remote Sensing to Assess the Impact of Short Term Climate Variability on Coastal Sedimentation

The University of Wisconsin and Louisiana State University have teamed to study the forcing of winter season cold frontal wind systems on sediment distribution patterns and geomorphology in the Louisiana coastal zone. Wind systems associated with cold fronts have been shown to modify coastal circulation and resuspend sediments along the microtidal Louisiana coast. The assessment includes quantifying the influence of cumulative winter season atmospheric forcing (through surface wind observations) from year to year in response to short term climate variability, such as El Nino events. A correlation between winter cyclone frequency and the strength of El Nino events has been suggested. The atmospheric forcing data are being correlated to geomorphic measurements along western Louisiana's prograding muddy coast. Remote sensing data is being used to map and track sediment distribution patterns for various wind conditions. Transferring a suspended sediment concentration (SSC) algorithm to EOS MODIS observations will enable estimates of SSC in case 2 waters over the global domain. Progress in Year 1 of this study has included data collection and analysis of wind observations for atmospheric forcing characterization, a field activity (TX-2001) to collect in situ water samples with co-incident remote sensing measurements from the NASA ER-2 based MODIS Airborne Simulator (MAS) and the EOS Terra based MODerate resolution Imaging Spectroradiometer (MODIS) instruments, aerial photography and of sediment burial pipe field measurements along the prograding muddy Chenier Plain coast of western Louisiana for documenting coastal change in that dynamic region, and routine collection of MODIS 250 in resolution data for monitoring coastal sediment patterns. The data sets are being used in a process to transfer an SSC estimation algorithm to the MODIS platform. Work is underway on assessing coastal transport for the winter 2000-01 season. Water level data for use in a Geomorphic Impact Index, which relates wind energy, water level conditions, and geomorphic change along the microtidal western Louisiana coastline is being assembled.

Moeller, Christopher C.↗

NASA NTRS2001

[Limb Scattering Data Analysis]

The primary purpose of this grant was to support analysis of the limb scattering data taken during the 1997 flight of the SOLSE (Shuttle Ozone Limb Sounding Experiment) and LORE (Limb Ozone Retrieval Experiment) instruments. Work was done to assess the performance of the retrieval algorithms for cloudy and clear sky cases in preparation for a poster presentation. The nadir-viewing data were also compared to coincident GOME (Global Ozone Monitoring Experiment) data and to radiative transfer calculations. An algorithm similar to the TOMS (Total Ozone Mapping Spectrometer) ozone retrieval algorithm was developed to infer the ozone column amount from the SOLSE nadir data. Comparison with coincident TOMS ozone column data confirmed that column ozone could be derived successfully from SOLSE nadir radiances, and also revealed significant changes in the SOLSE wavelength resolution and absolute radiometric calibration that were subsequently confirmed by comparing the post-flight instrument characterization to the pre-flight characterization, indicating a potentially useful method for monitoring instrument behavior in-flight.

Loughman, Robert↗

NASA NTRS2003

A Systematic Global Mapping of the Radiation Field at Aviation Altitudes

This paper presents early results from aircraft measurements made by a Low-LET Radiation Spectrometer (LoLRS), as part of a long-range effort to study the complex dynamics of the atmospheric radiation field. For this purpose, a comprehensive data base is being generated to enable a multivariable global mapping (and eventually modeling) of doses and Linear-Energy-Transfer (LET) spectra at aviation altitudes. To accomplish this, a methodical collection of data from the LoLRS (and other instruments), is planned over extended periods of time, in a manner that complements some previous isolated and sporadic measurements by other workers, with the objective to generate a detailed long-range description of the cosmic-ray induced particle environment and to study its variability and dependence on atmospheric thickness, magnetic latitude, L-shell or rigidity, space weather, solar particle events, solar cycle effects, magnetic field variation, diurnal and seasonal effects, and atmospheric weather. Analysis of initial data indicates that the dose is rising with increasing altitude and increasing magnetic latitude. Comparison of total doses with predictions is in good agreement.

Stassinopoulos, E. G.↗

NASA NTRS2010

Measurement of the Isotopic Signatures of Water on Mars: Implications for Studying Methane

The recent discovery of methane on Mars has led to much discussion concerning its origin. On Earth, the isotopic signatures of methane vary with the nature of its production. Specifically, the ratios among 12CH4, 13CH4, and 12CH3D differ for biotic and abiotic origins. On Mars, measuring these ratios would provide insights into the origins of methane and measurements of water isotopologues co-released with methane would assist in testing their chemical relationship. Since 1997, we have been measuring HDO and H2O in Mars atmosphere and comparing their ratio to that in Earth s oceans. We recently incorporated a line-by-line radiative transfer model (LBLRTM) into our analysis. Here, we present a map for [HDO]/[H2O] along the central meridian (1541W) for Ls 501. From these results, we constructed models to determine the observational conditions needed to quantify the isotopic ratios of methane in Mars atmosphere. Current ground-based instruments lack the spectral resolution and sensitivity needed to make these measurements. Measurements of the isotopologues of methane will likely require in situ sampling.

Novak, R. E.↗

NASA NTRS2014

Gravity and Heater Size Effects on Pool Boiling Heat Transfer

The current work is based on observations of boiling heat transfer over a continuous range of gravity levels between 0g to 1.8g and varying heater sizes with a fluorinert as the test liquid (FC-72/n-perfluorohexane). Variable gravity pool boiling heat transfer measurements over a wide range of gravity levels were made during parabolic flight campaigns as well as onboard the International Space Station. For large heaters and-or higher gravity conditions, buoyancy dominated boiling and heat transfer results were heater size independent. The power law coefficient for gravity in the heat transfer equation was found to be a function of wall temperature under these conditions. Under low gravity conditions and-or for smaller heaters, surface tension forces dominated and heat transfer results were heater size dependent. A pool boiling regime map differentiating buoyancy and surface tension dominated regimes was developed along with a unified framework that allowed for scaling of pool boiling over a wide range of gravity levels and heater sizes. The scaling laws developed in this study are expected to allow performance quantification of phase change based technologies under variable gravity environments eventually leading to their implementation in space based applications.

Boiling↗

NASA NTRSDate not supplied

Development of a Consistent MODIS and VIIRS Cloud Detection Approach for CERES

A consistent cloud fraction record across various satellite platforms is essential for maintaining a long-term and stable climate data record of Earth's energy budget. With the Aqua satellite nearing the end of its operational lifetime, the continuation of this record relies on utilizing VIIRS observations from NOAA20 for cloud detection in NASA’s Clouds and Earth’s Radiant Energy System (CERES) project. However, integrating data from VIIRS and MODIS instruments poses challenges due to their distinct characteristics, such as varying spatial resolutions and different spectral channels. As a result, deriving consistent cloud properties from these two sensors without introducing artificial discontinuities in the time series remains a complex and challenging task. This paper will present progress toward developing a unified MODIS and VIIRS cloud mask using common channels to produce consistent cloud properties for CERES next edition (Ed5) Earth radiation budget data products. The fundamental approach taken in the CERES cloud mask is to compare the observed radiances to the expected background clear sky radiances. Therefore, one vital step is to compute clear sky radiances with a radiative transfer model that accurately accounts for satellite-specific, spectrally dependent surface reflectance, surface emission, and atmospheric absorption. Refined radiative transfer models and updated ancillary data inputs including surface emissivity maps, IGBP, snow and ice maps are incorporated into the processing framework to improve cloud detection consistency and accuracy. Pixel level cloud mask results and monthly global cloud fraction comparisons between MODIS and VIIRS will be presented to evaluate their consistency. Remaining challenges will be discussed. It is expected that this work will contribute consistent cloud properties for CERES that adequately bridges the MODIS and VIIRS imager data records.

CERES↗

DOE OSTI2018

Locality-aware and load-balanced static task scheduling for MapReduce

Task scheduling for MapReduce jobs has been an active area of research with the objective of decreasing the amount of data transferred during the shuffle phase via exploiting data locality. In the literature, generally only the scheduling of reduce tasks is considered with the assumption that scheduling of map tasks is already determined by the input data placement. However, in cloud or HPC deployments of MapReduce, the input data is located in a remote storage and scheduling map tasks gains importance. Here, we propose models for simultaneous scheduling of map and reduce tasks in order to improve data locality and balance the processors’ loads in both map and reduce phases. Our approach is based on graph and hypergraph models which correctly encode the interactions between map and reduce tasks. Partitions produced by these models are decoded to schedule map and reduce tasks. A two-constraint formulation utilized in these models enables balancing processors’ loads in both map and reduce phases. The partitioning objective in the hypergraph models correctly encapsulates the minimization of data transfer when a local combine step is performed prior to shuffle, whereas the partitioning objective in the graph models achieve the same feat when a local combine is not performed. Here, we show the validity of our scheduling on the MapReduce parallelizations of two important kernel operations – sparse matrix–vector multiplication (SpMV) and generalized sparse matrix–matrix multiplication (SpGEMM) – that are widely encountered in big data analytics and scientific computations. Compared to random scheduling, our models lead to tremendous savings in data transfer by reducing data traffic from several hundreds of megabytes to just a few megabytes in the shuffle phase and consequently leading up to 2.6x and 4.2x speedup for SpMV and SpGEMM, respectively.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2010

Advances in Landslide Hazard Forecasting: Evaluation of Global and Regional Modeling Approach

A prototype global satellite-based landslide hazard algorithm has been developed to identify areas that exhibit a high potential for landslide activity by combining a calculation of landslide susceptibility with satellite-derived rainfall estimates. A recent evaluation of this algorithm framework found that while this tool represents an important first step in larger-scale landslide forecasting efforts, it requires several modifications before it can be fully realized as an operational tool. The evaluation finds that the landslide forecasting may be more feasible at a regional scale. This study draws upon a prior work's recommendations to develop a new approach for considering landslide susceptibility and forecasting at the regional scale. This case study uses a database of landslides triggered by Hurricane Mitch in 1998 over four countries in Central America: Guatemala, Honduras, EI Salvador and Nicaragua. A regional susceptibility map is calculated from satellite and surface datasets using a statistical methodology. The susceptibility map is tested with a regional rainfall intensity-duration triggering relationship and results are compared to global algorithm framework for the Hurricane Mitch event. The statistical results suggest that this regional investigation provides one plausible way to approach some of the data and resolution issues identified in the global assessment, providing more realistic landslide forecasts for this case study. Evaluation of landslide hazards for this extreme event helps to identify several potential improvements of the algorithm framework, but also highlights several remaining challenges for the algorithm assessment, transferability and performance accuracy. Evaluation challenges include representation errors from comparing susceptibility maps of different spatial resolutions, biases in event-based landslide inventory data, and limited nonlandslide event data for more comprehensive evaluation. Additional factors that may improve algorithm performance accuracy include incorporating additional triggering factors such as tectonic activity, anthropogenic impacts and soil moisture into the algorithm calculation. Despite these limitations, the methodology presented in this regional evaluation is both straightforward to calculate and easy to interpret, making results transferable between regions and allowing findings to be placed within an inter-comparison framework. The regional algorithm scenario represents an important step in advancing regional and global-scale landslide hazard assessment and forecasting.

Kirschbaum, Dalia B.↗

NASA NTRS2000

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Gould, Dana C.↗

DOE OSTI2023

Mapping foliar photosynthetic capacity in sub-tropical and tropical forests with UAS-based imaging spectroscopy: Scaling from leaf to canopy

Accurate understanding of the variability in foliar physiological traits across landscapes is critical to improve parameterization and evaluation of terrestrial biosphere models (TBMs) that seek to represent the response of terrestrial ecosystems to a changing climate. Numerous studies suggest imaging spectroscopy can characterize foliar biochemical and morphological traits at the canopy scale, but there is only limited evidence for retrieving canopy photosynthetic capacity (e.g., maximum carboxylation rate, V c,max and maximum electron transport rate, J max ). Moreover, the effect of canopy structure within forest communities on scaling up spectra-trait relationships from leaf to canopy level is not well known. To advance the spectra-trait approach and enable the estimation of key traits using remote sensing, we collected imaging spectroscopy data from an Unoccupied Aerial System (UAS) platform over two forest sites in China (a subtropical forest in Mt. Dinghu and a tropical rainforest in Xishuangbanna). At these sites, we also collected ground measurements of leaf spectra and traits, including biochemical (leaf nitrogen, phosphorus, chlorophyll, and water content), morphological (leaf mass per area, LMA) and physiological (V c,max25 and J max25 ) traits (n=135 tree-crowns from 42 species across two sites). Using a partial least-squares regression (PLSR) approach, we built and tested spectra-trait models with repeated cross-validation. The spectral models developed with leaf spectra were directly transferred to canopy spectra to evaluate the effect of canopy structure. Here we further applied canopy spectral models to map these traits at individual tree-crown scale. The results demonstrate that (1) UAS-based canopy spectra can be used to estimate V c,max (R 2 =0.55, nRMSE=11.79%), Jmax (R 2 =0.54, nRMSE=12.34%), and five additional foliar traits (R 2 =0.38-0.60, nRMSE=10.11-13.56%) at the tree-crown scale with demonstrated generalizability across two sites; (2) canopy structure strongly affects the spectratrait relationships from leaf to canopy level, but the effects vary considerably across foliar traits and cannot be well captured by the 4SAIL canopy radiative transfer model. UAS-based imaging spectroscopy maps large variability in all foliar traits (including physiological traits) with spatially explicit information, reproducing the field-observed inter- and intra-specific variations. These results demonstrate the capability of using UAS-based imaging spectroscopy for characterizing the variability of foliar physiological traits at individual tree-crown scale over forest landscapes and highlight the similar generalizability but different biophysical mechanisms underlying spectra-trait relationships at leaf and canopy levels.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2013

A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction

We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1991

Studies of magnetopause structure

From the International Sun-Earth Explorers (ISEE) 1 magnetopause crossings on November 10, 1977, three-dimensional distribution functions for energetic ions were studied in the magnetosphere, through the magnetopause, and in the magnetosheath (Speiser and Williams, 1982). The particle distributions were particularly examined at and near the times that Russell and Elphic (1978) identified as flux transfer events (FTE). Using a simple, one-dimensional, quasi-static model, particle orbits were followed numerically, from the magnetosphere into the sheath. The inner, trapped, distribution initializes the distribution function. Liouville's theorem allows the inner distribution to be mapped into the sheath following the orbits. This mapping is shown for four mangetosheath ion flows (MIF's) corresponding to four flux transfer events. Results from the studies are discussed. A brief discussion of current sheet particle motion is presented.

Speiser, Theodore W.↗