Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “thermal & statistical models”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

Downscaling MODIS Land Surface Temperature for Urban Public Health Applications

This study is part of a project funded by the NASA Applied Sciences Public Health Program, which focuses on Earth science applications of remote sensing data for enhancing public health decision-making. Heat related death is currently the number one weather-related killer in the United States. Mortality from these events is expected to increase as a function of climate change. This activity sought to augment current Heat Watch/Warning Systems (HWWS) with NASA remotely sensed data, and models used in conjunction with socioeconomic and heatrelated mortality data. The current HWWS do not take into account intra-urban spatial variation in risk assessment. The purpose of this effort is to evaluate a potential method to improve spatial delineation of risk from extreme heat events in urban environments by integrating sociodemographic risk factors with estimates of land surface temperature (LST) derived from thermal remote sensing data. In order to further improve the consideration of intra-urban variations in risk from extreme heat, we also developed and evaluated a number of spatial statistical techniques for downscaling the 1-km daily MODerate-resolution Imaging Spectroradiometer (MODIS) LST data to 60 m using Landsat-derived LST data, which have finer spatial but coarser temporal resolution than MODIS. In this paper, we will present these techniques, which have been demonstrated and validated for Phoenix, AZ using data from the summers of 2000-2006.

Al-Hamdan, Mohammad↗

Characterisation of ion temperature and toroidal rotation on the ST40 tokamak

ST40 is a high field low-aspect ratio spherical tokamak built and operated by Tokamak Energy Ltd. Recent plasma operations were aimed at exploring operational scenarios to maximise the central plasma temperature and have culminated in the achievement of thermal ion temperatures of over 9 keV. Here this paper presents ion temperature and toroidal rotation measurements performed on ST40 during the 2021–22 campaign for a range of different scenarios. Several independent diagnostic systems are used, analysing their correlation and interpreting their differences using new diagnostic forward models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The thermal engine of Venus: Implications from the impact crater distribution

Questions concerning the state of Venus' volcanological activity are currently under investigation. These questions were raised by the imaging radar and altimetric data obtained by the Magellan spacecraft, which began mapping Venus in Sept. 1990. Clues about the answers to these questions are provided by the nature and distribution of impact craters on the surface of Venus. Statistical tests show that the distribution of craters on Venus cannot be distinguished from a completely spatially random population. Further, the majority of craters look relatively pristine; only about 5 percent of the observed craters appear to be embayed or flooded by lavas. The simplest interpretation of these observations is a model in which the impact craters lie on a surface that has been undisturbed by volcanological and tectonic processes since the time the surface was formed. Counting up the number of craters and estimating the rate at which meteoroids strike the surface then gives an age for the venusian surface of 500 million years; in this model the volcanic activity since that time has been essentially nil. This scenario is described as a 'production' model, or perhaps more appropriately, a 'catastrophic' model.

Phillips, Roger J.↗

Soft matter roadmap

Soft materials are usually defined as materials made of mesoscopic entities, often self-organised, sensitive to thermal fluctuations and to weak perturbations. Archetypal examples are colloids, polymers, amphiphiles, liquid crystals, foams. The importance of soft materials in everyday commodity products, as well as in technological applications, is enormous, and controlling or improving their properties is the focus of many efforts. From a fundamental perspective, the possibility of manipulating soft material properties, by tuning interactions between constituents and by applying external perturbations, gives rise to an almost unlimited variety in physical properties. Together with the relative ease to observe and characterise them, this renders soft matter systems powerful model systems to investigate statistical physics phenomena, many of them relevant as well to hard condensed matter systems. Understanding the emerging properties from mesoscale constituents still poses enormous challenges, which have stimulated a wealth of new experimental approaches, including the synthesis of new systems with, e.g. tailored self-assembling properties, or novel experimental techniques in imaging, scattering or rheology. Theoretical and numerical methods, and coarse-grained models, have become central to predict physical properties of soft materials, while computational approaches that also use machine learning tools are playing a progressively major role in many investigations. This Roadmap intends to give a broad overview of recent and possible future activities in the field of soft materials, with experts covering various developments and challenges in material synthesis and characterisation, instrumental, simulation and theoretical methods as well as general concepts.

36 MATERIALS SCIENCE↗

Microstructural design of fiber composites

The optimum performance design of composite microstructures is discussed. The forces driving progress in fiber composites are examined, and recent developments in the mechanics of laminated composites are surveyed, emphasizing thick laminates, hygrothermal effects, and thermal transient effects. The strength of continuous-fiber composites is discussed, presenting analyses of local load redistribution due to fiber breakages and treatments of statistical tensile strength theories. Modes of failure of laminated composites are examined. Elastic, physical, and viscoelastic properties as well as the strength and fracture behavior of short-fiber composites are studied, and it is shown how the performance of composites can be controlled by selecting material systems and their geometric distributions. 2D textile structural composites based on woven, knitted, and braided preforms are considered, and techniques for analyzing and modeling the thermomechanical behavior of 2D textile composites are presented. Recent developments in the processing of 3D textile preforms are introduced and the processing-microstructure relationship is demonstrated. Finite elastic deformation of flexible composites is addressed.

Chou, Tsu-Wei↗

First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission

The WMAP mission has mapped the full sky to determine the geometry, content, and evolution of the universe. Full sky maps are made in five microwave frequency bands to separate the temperature anisotropy of the cosmic microwave background (CMB) from foreground emission, including diffuse Galactic emission and Galactic and extragalactic point sources. We define masks that excise regions of high foreground emission, so CMB analyses can became out with minimal foreground contamination. We also present maps and spectra of the individual emission components, leading to an improved understanding of Galactic astrophysical processes. The effectiveness of template fits to remove foreground emission from the WMAP data is also examined. These efforts result in a CMB map with minimal contamination and a demonstration that the WMAP CMB power spectrum is insensitive to residual foreground emission. We use a Maximum Entropy Method to construct a model of the Galactic emission components. The observed total Galactic emission matches the model to less than 1% and the individual model components are accurate to a few percent. We find that the Milky Way resembles other normal spiral galaxies between 408 MHz and 23 GHz, with a synchrotron spectral index that is flattest (beta(sub s) approx. -2.5) near star-forming regions, especially in the plane, and steepest (beta(sub s) approx. -3) in the halo. This is consistent with a picture of relativistic cosmic ray electron generation in star-forming regions and diffusion and convection within the plane. The significant synchrotron index steepening out of the plane suggests a diffusion process in which the halo electrons are trapped in the Galactic potential long enough to suffer synchrotron and inverse Compton energy losses and hence a spectral steepening. The synchrotron index is steeper in the WMAP bands than in lower frequency radio surveys, with a spectral break near 20 GHz to beta(sub s) less than -3. The modeled thermal dust spectral index is also steep in the WMAP bands, with beta(sub d) approx. = 2.2. Our model is driven to these conclusions by the low level of total foreground contamination at approx. 60 GHz. Microwave and Ha measurements of the ionized gas agree well with one another at about the expected levels. Spinning dust emission is limited to less than 5% of the Ka-band foreground emission. A catalog of 208 point sources is presented. The reliability of the catalog is 98%, i.e., we expect five of the 208 sources to be statistically spurious. The mean spectral index of the point sources is alpha approx. 0(beta approx. -2). Derived source counts suggest a contribution to the anisotropy power from unresolved sources of (15.0 +/- 1.4) x 10(exp -3)micro sq K sr at Q-band and negligible levels at V-band and W-band. The Sunyaev-Zeldovich effect is shown to be a negligible "contamination" to the maps.

Bennett, C. L.↗

A diagnostic approach to obtaining planetary boundary layer winds using satellite-derived thermal data

The feasibility of using satellite derived thermal data to generate realistic synoptic scale winds within the planetary boundary layer (PBL) is examined. Diagnostic modified Ekman wind equations from the Air Force Global Weather Central (AFGWC) Boundary Layer Model are used to compute winds at seven levels within the PBL transition layer (50 m to 1600 m AGL). Satellite derived winds based on 62 predawn TIROS-N soundings are compared to similarly derived wind fields based on 39 AVE-SESAME II rawinsonde (RAOB) soundings taken 2 h later. Actual wind fields are also used as a basis for comparison. Qualitative and statistical comparisons show that the Ekman winds from both sources are in very close agreement, with an average vector correlation coefficient of 0.815. Best results are obtained at 300 m AGL. Satellite winds tend to be slightly weaker than their RAOB counterparts and exhibit a greater degree of cross-isobaric flow. The modified Ekman winds show a significant improvement over geostrophic values at levels nearest the surface.

Belt, Carol L.↗

Sources of noise in magneto-optical readout

The various sources of noise which are often encountered in magneto-optical readout systems are analyzed. Although the focus is on magneto-optics, most sources of noise are common among the various optical recording systems and one can easily adapt the results to other media and systems. A description of the magneto-optical readout system under consideration is given, and the standard methods and the relevant terminology of signal and noise measurement are described. The characteristics of thermal noise, which originates in the electronic circuitry of the readout system, are described. The most fundamental of all sources of noise, the shot noise, is considered, and a detailed account of its statistical properties is given. Shot noise, which is due to random fluctuations in photon arrival times, is an ever-present noise in optical detection. Since the performance of magneto-optical recording devices in use today is approaching the limit imposed by the shot noise, it is important that the reader have a good grasp of this particular source of noise. A model for the laser noise is described, and measurement results which yield numerical values for the strength of the laser power fluctuations are presented. Spatial variations of the disk reflectivity and random depolarization phenomena also contribute to the overall level of noise in readout; these and related issues are treated. Numerical simulation results describing some of the more frequently encountered sources of noise which accompany the recorded waveform itself, namely, jitter noise and signal-amplitude fluctuation noise are presented.

Mansuripur, M.↗

Development of a Computational Chemical Vapor Deposition Model: Applications to Indium Nitride and Dicyanovinylaniline

A computational chemical vapor deposition (CVD) model is presented, that couples chemical reaction mechanisms with fluid dynamic simulations for vapor deposition experiments. The chemical properties of the systems under investigation are evaluated using quantum, molecular and statistical mechanics models. The fluid dynamic computations are performed using the CFD-ACE program, which can simulate multispecies transport, heat and mass transfer, gas phase chemistry, chemistry of adsorbed species, pulsed reactant flow and variable gravity conditions. Two experimental setups are being studied, in order to fabricate films of: (a) indium nitride (InN) from the gas or surface phase reaction of trimethylindium and ammonia; and (b) 4-(1,1)dicyanovinyl-dimethylaminoaniline (DCVA) by vapor deposition. Modeling of these setups requires knowledge of three groups of properties: thermodynamic properties (heat capacity), transport properties (diffusion, viscosity, and thermal conductivity), and kinetic properties (rate constants for all possible elementary chemical reactions). These properties are evaluated using computational methods whenever experimental data is not available for the species or for the elementary reactions. The chemical vapor deposition model is applied to InN and DCVA. Several possible InN mechanisms are proposed and analyzed. The CVD model simulations of InN show that the deposition rate of InN is more efficient when pulsing chemistry is used under conditions of high pressure and microgravity. An analysis of the chemical properties of DCVA show that DCVA dimers may form under certain conditions of physical vapor transport. CVD simulations of the DCVA system suggest that deposition of the DCVA dimer may play a small role in the film and crystal growth processes.

Cardelino, Carlos↗

A phenomenological approach to multisource data integration: Analysing infrared and visible data

A new method is described for combining multisensory data for remote sensing applications. The approach uses phenomenological models which allow the specification of discriminatory features that are based on intrinsic physical properties of imaged surfaces. Thermal and visual images of scenes are analyzed to estimate surface heat fluxes. Such analysis makes available a discriminatory feature that is closely related to the thermal capacitance of the imaged objects. This feature provides a method for labelling image regions based on physical properties of imaged objects. This approach is different from existing approaches which use the signal intensities in each channel (or an arbitrary linear or nonlinear combination of signal intensities) as features - which are then classified by a statistical or evident approach.

Nandhakumar, N.↗

Dispersed ion structures at the poleward edge of the auroral oval: Low-altitude observations and numerical modeling

We have compared the AUREOL 3 (A3) observations of auroral ion precipitation, particularly ion beams, with the results from the global kinetic model of magnetotail plasma of Ashour-Abdalla et al. (1993). We have identified 101 energetic keV H(+) velocity dispersed precipitating ion structures (VDIS) with fluxes above 10(exp -3) ergs./sq cm./s in the A3 record between the end of 1981 and mid-1984. These beams display a systematic increase in energy with increasing latitude and were observed in a narrow region within less than 1 deg in latitude of the polar cap boundary. The VDIS are the most distinctive feature in the auroral zone of the plasma sheet boundary layer. We report first on a statistical analysis of the possible ralationships between magnetic activity or substorm phase and the VDIS properties. Our particle simulations of the precipitating ions have been extended by using a series of modified versions of the Tsyganenko (1989) magnetic field model and by varying the cross-magnetosphere electric field. In the simulations, plasma from a mantle source is subject to strong nonlinear acceleration, forming beams which flow along the PSBL. Only 3 to 4% of these beams precipitate into the ionosphere to form the VDIS while the majority return to the equatorial plane after mirroring and form the thermalized central plasma sheet. The final energy and the dispersion of the beams in the model depend on the amplitude of the cross-tail electric field. Two unsual observations of low-energy (less than 5 keV) O(+) VDIS, shifted by 4 deg 5 deg in invariant latitude equatorward of H(+) VDIS are analyzed in detail. The sparsity of such O(+) events and the absence of the changes in the flux and frequency of occurrence indicate a solar wind origin for the plasma. Finally, large-scale kinetic modeling, even with its simplifications and assumptions (e.g., static magnetic field, solar wind source), reproduces low-altitude auroral ion features fairly well; it may therefore be presented as an appropriate framework into which data on energization and transport of the hot plasma, obtained in the equatorial plane, could be inserted in the near future.

Bosqued, J. M.↗

Condition-Based Maintenance of a Circulating Water System of a Canadian Nuclear Power Plant using Machine Learning and Statistical Tools

Canada Deuterium Uranium pressurized-heavy-water reactors (PHWR) are a type of nuclear power plant that generate clean and reliable energy. The scope of this work is to automate data analysis methodologies to inform a condition-based maintenance strategy of a circulating water system (CWS) of a PHWR. The multiunit CWS provides a continuous supply of water to cool steam condensers, even during transient scenarios, thereby improving the thermal efficiency. This work aims to develop a machine learning (ML) based approach to detect anomalies in heterogeneous data of a CWS in a PHWR to help inform a predictive maintenance strategy. The heterogeneous data include textual and numeric time series data for a PHWR. Natural-language-processing (NLP)-based models are used to analyze textual data contained in work orders and operator logs and an event-timeseries correlation detection method is applied to assist anomalies diagnoses for CWS. An ML model Robust Linear Model (RLM) is also used to remove the seasonal variations in the system variable distributions based on distributions of environmental variables. A machine learning model, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), trained on both original data and data without any seasonal variations will then be used to detect if an anomaly exists. Thus, by moving to an automated methodology to detect, classify, and forecast anomalies, the maintenance strategy would be based on component condition instead of a time-based schedule.

97 - MATHEMATICS AND COMPUTING↗

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Abstract Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

Astronomy & Astrophysics↗

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level (bond type, non-uniform chain length, entanglement density, etc.) to macroscopic quantities that govern damage and failure must be established. Many of the most successful constitutive models for elastomers have been rooted in statistical mechanical treatments of polymer chains. Typically, such constitutive models have used variants of the freely jointed chain model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the freely jointed chain model (as derived in the u FJC framework of Buche and Silberstein (2021) and Buche et al. (2022)), which we have extended to yield a tractable, closed-form model of single chain behavior that should be amenable to continuum-level constitutive model development. Inspired by the asymptotically matched u FJC model response in both the low/intermediate chain force and high chain force regimes, a simple, quasi-polynomial bond potential energy function is derived. This bond potential exhibits harmonic behavior near the equilibrium state and anharmonic behavior for large bond stretches tending to a characteristic energy plateau (akin to the Lennard-Jones and Morse bond potentials). Using this bond potential, approximate yet highly-accurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This framework is based upon a force-modified tilted bond potential that accounts for distortional bond potential energy, allowing for the derivation and subsequent calculation of the dissipated chain scission energy. Here, the cases of rate-dependent and rate-independent scission are accounted for throughout the rupture framework. The impact of Kuhn segment number on chain rupture behavior is also investigated. The model is fit to single chain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can in the future be implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.

36 MATERIALS SCIENCE↗

Analyzing the impact of design factors on solar module thermomechanical durability using interpretable machine learning techniques

Solar modules in utility-scale systems are expected to maintain decades of lifetime to rival conventional energy sources. However, cyclic thermomechanical loading often degrades their long-term performance, highlighting the importance of effective design to mitigate thermal expansion mismatches between module materials. Given the complex composition of solar modules, isolating the impact of individual components on overall durability remains a challenging task. In this work, we analyze a comprehensive data set that comprises bill-of-materials (BOM) and thermal cycling power loss from 251 distinct module designs to identify the predominant design factors and their impacts on the thermomechanical durability of modules. The methodology of our analysis combines machine learning modeling (random forest) and Shapley additive explanation (SHAP) to correlate design factors with power loss and interpret the model’s decision-making. The interpretation reveals that silicon type (monocrystalline or polycrystalline), encapsulant thickness, busbar numbers, and wafer thickness predominantly influence the degradation. With lower power loss of around 0.6% on average in the SHAP analysis, monocrystalline cells present better durability than polycrystalline cells. This finding is further substantiated by statistical testing on our raw data set. The SHAP analysis also demonstrates that while thicker encapsulants lead to reduced power loss, further increasing their thickness over around 0.6 to 0.7 mm does not yield additional benefits, particularly for the front side one. In addition, other important BOM features such as the number of busbars are analyzed. This study provides a blueprint for utilizing explainable machine learning techniques in a complex material system and can potentially guide future research on optimizing the design of solar modules.

14 SOLAR ENERGY↗

New constraints on warm dark matter from the Lyman- α forest power spectrum

The forest of Lyman-α absorption lines detected in the spectra of distant quasars encodes information on the nature and properties of dark matter and the thermodynamics of diffuse baryonic material. Its main observable—the 1D flux power spectrum (FPS)—should exhibit a suppression on small scales and an enhancement on large scales in warm dark matter (WDM) cosmologies compared to standard Λ⁢CDM. Here, we present an unprecedented suite of 1080 high-resolution cosmological hydrodynamical simulations run with the graphics processing unit-accelerated code cholla to study the evolution of the Lyman-α forest under a wide range of physically motivated gas thermal histories along with different free-streaming lengths of WDM thermal relics in the early Universe. A statistical comparison of synthetic data with the forest FPS measured down to the smallest velocity scales ever probed at redshifts 4.0≲z≲5.2 [E. Boera et al., Revealing reionization with the thermal history of the intergalactic medium: New constraints from the Ly⁢α flux power spectrum, Astrophys. J. 872, 101 (2019)] yields a lower-limit m WDM >3.1 keV (95% C.L.) for the WDM particle mass and constrains the amplitude and spectrum of the photoheating and photoionizing background produced by star-forming galaxies and active galactic nuclei at these redshifts. Interestingly, our Bayesian inference analysis appears to weakly favor WDM models with a peak likelihood value at the thermal relic mass of m WDM =4.5 keV. In conclusion, we find that the suppression of the FPS from free-streaming saturates at k≳0.1 s km -1 because of peculiar velocity smearing, and this saturated suppression combined with a slightly lower gas temperature provides a moderately better fit to the observed small-scale FPS for WDM cosmologies.

79 ASTRONOMY AND ASTROPHYSICS↗

Deep Morphological and Spectral Study of the SNR RCW 86 with Fermi-LAT

RCW 86 is a young supernova remnant (SNR) showing a shell-type structure at several wavelengths and is thought to be an efficient cosmic-ray (CR) accelerator. Earlier Fermi Large Area Telescope results reported the detection of gamma-ray emission coincident with the position of RCW 86 but its origin (leptonic or hadronic) remained unclear due to the poor statistics. Thanks to 6.5 years of data acquired by the Fermi-LAT and the new event reconstruction Pass 8, we report the significant detection of spatially extended emission coming from RCW 86. The spectrum is described by a power-law function with a very hard photon index (Gamma = 1.42 +/- 0.1(sub stat) +/- 0.06(sub syst)) in the 0.1-500 GeV range and an energy flux above 100 MeV of (2.91 +/- 0.8(sub stat) +/- 0.12(sub syst)) x 10(exp -11) erg/(sq cms). Gathering all the available multiwavelength (MWL) data, we perform a broadband modeling of the non-thermal emission of RCW 86 to constrain parameters of the nearby medium and bring new hints about the origin of the gamma-ray emission. For the whole SNR, the modeling favors a leptonic scenario in the framework of a two-zone model with an average magnetic field of 10.2 +/- 0.7 microG and a limit on the maximum energy injected into protons of 2 x 10(exp 49) erg for a density of 1 per cu cm. In addition, parameter values are derived for the north-east and south-west (SW) regions of RCW 86, providing the first indication of a higher magnetic field in the SW region.

acceleration of particles – cosmic rays – ISM:↗