Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “connected components”

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 991 records · Page 55

Faults in the Mojave Desert, California, as revealed on enhanced Landsat images

Landsat TM images, subjected to four-component processing through which lithologies can be discriminated by their contrasting absorption and reflection at IR wavelengths, have revealed previously unsuspected strike-slip and normal faults in the central and eastern Mojave Desert. These discriminations, which extend to ferric and ferrous iron and to hydroxyl content without compromise of landform depiction, represent a novel type of geophysical display for geologic mapping in regions of well-exposed bedrock; the faults thus discovered form part of an extensive regional network of right shear which connects Death Valley region faults with those in the San Andreas system.

Ford, J. P.↗

Dayside Proton Aurora: Comparisons between Global MHD Simulations and Image Observations

The IMAGE mission provides a unique opportunity to evaluate the accuracy of current global models of the solar wind interaction with the Earth's magnetosphere. In particular, images of proton auroras from the Far Ultraviolet Instrument (FUV) onboard the IMAGE spacecraft are well suited to support investigations of the response of the Earth's magnetosphere to interplanetary disturbances. Accordingly, we have modeled two events that occurred on June 8 and July 28, 2000, using plasma and magnetic field parameters measured upstream of the bow shock as input to three-dimensional magnetohydrodynamic (MHD) simulations. This paper begins with a discussion of images of proton auroras from the FUV SI-12 instrument in comparison with the simulation results. The comparison showed a very good agreement between intensifications in the auroral emissions measured by FUV SI-12 and the enhancement of plasma flows into the dayside ionosphere predicted by the global simulations. Subsequently, the IMAGE observations are analyzed in the context of the dayside magnetosphere's topological changes in magnetic field and plasma flows inferred from the simulation results. Finding include that the global dynamics of the auroral proton precipitation patterns observed by IMAGE are consistent with magnetic field reconnection occurring as a continuous process while the iMF changes in direction and the solar wind dynamic pressure varies. The global simulations also indicate that some of the transient patterns observed by IMAGE are consistent with sporadic reconnection processes. Global merging patterns found in the simulations agree with the antiparallel merging model. though locally component merging might broaden the merging region, especially in the region where shocked solar wind discontinuities first reach the magnetopause. Finally, the simulations predict the accretion of plasma near the bow shock in the regions threaded by newly open field lines on which plasma flows into the dayside ionosphere are enhanced. Overall the results of these initial comparisons between global MHD simulation results and IMAGE observations emphasize the interplay between reconnection and dynamic pressure processes at the dayside magnetopause. as well as the intricate connection between the bow shock and the auroral region.

Berchem, J.↗

Construction of Solar-Wind-Like Magnetic Fields

Fluctuations in the solar wind fields tend to not only have velocities and magnetic fields correlated in the sense consistent with Alfven waves traveling from the Sun, but they also have the magnitude of the magnetic field remarkably constant despite their being broadband. This paper provides, for the first time, a method for constructing fields with nearly constant magnetic field, zero divergence, and with any specified power spectrum for the fluctuations of the components of the field. Every wave vector, k, is associated with two polarizations the relative phases of these can be chosen to minimize the variance of the field magnitude while retaining the\random character of the fields. The method is applied to a case with one spatial coordinate that demonstrates good agreement with observed time series and power spectra of the magnetic field in the solar wind, as well as with the distribution of the angles of rapid changes (discontinuities), thus showing a deep connection between two seemingly unrelated issues. It is suggested that using this construction will lead to more realistic simulations of solar wind turbulence and of the propagation of energetic particles.

Roberts, Dana Aaron↗

Soil Moisture Active Passive Mission L4_C Data Product Assessment (Version 2 Validated Release)

The SMAP satellite was successfully launched January 31st 2015, and began acquiring Earth observation data following in-orbit sensor calibration. Global data products derived from the SMAP L-band microwave measurements include Level 1 calibrated and geolocated radiometric brightness temperatures, Level 23 surface soil moisture and freezethaw geophysical retrievals mapped to a fixed Earth grid, and model enhanced Level 4 data products for surface to root zone soil moisture and terrestrial carbon (CO2) fluxes. The post-launch SMAP mission CalVal Phase had two primary objectives for each science product team: 1) calibrate, verify, and improve the performance of the science algorithms, and 2) validate accuracies of the science data products as specified in the L1 science requirements. This report provides analysis and assessment of the SMAP Level 4 Carbon (L4_C) product pertaining to the validated release. The L4_C validated product release effectively replaces an earlier L4_C beta-product release (Kimball et al. 2015). The validated release described in this report incorporates a longer data record and benefits from algorithm and CalVal refinements acquired during the SMAP post-launch CalVal intensive period. The SMAP L4_C algorithms utilize a terrestrial carbon flux model informed by SMAP soil moisture inputs along with optical remote sensing (e.g. MODIS) vegetation indices and other ancillary biophysical data to estimate global daily net ecosystem CO2 exchange (NEE) and component carbon fluxes for vegetation gross primary production (GPP) and ecosystem respiration (Reco). Other L4_C product elements include surface (10 cm depth) soil organic carbon (SOC) stocks and associated environmental constraints to these processes, including soil moisture and landscape freeze/thaw (FT) controls on GPP and respiration (Kimball et al. 2012). The L4_C product encapsulates SMAP carbon cycle science objectives by: 1) providing a direct link between terrestrial carbon fluxes and underlying FT and soil moisture constraints to these processes, 2) documenting primary connections between terrestrial water, energy and carbon cycles, and 3) improving understanding of terrestrial carbon sink activity in northern ecosystems. There are no L1 science requirements for the L4_C product; however self-imposed requirements have been established focusing on NEE as the primary product field for validation, and on demonstrating L4_C accuracy and success in meeting product science requirements (Jackson et al. 2012). The other L4_C product fields also have strong utility for carbon science applications; however, analysis of these other fields is considered secondary relative to primary validation activities focusing on NEE. The L4_C targeted accuracy requirements are to meet or exceed a mean unbiased accuracy (ubRMSE) for NEE of 1.6 g C/sq m/d or 30 g C/sq m/yr, emphasizing northern (45N) boreal and arctic ecosystems; this is similar to the estimated accuracy level of in situ tower eddy covariance measurement-based observations (Baldocchi 2008).

Cal/Val↗

The Lick-Gaertner automatic measuring system

The Lick-Gaertner automatic equipment has been designed mainly for the measurement of stellar proper motions with reference to galaxies, and consists of two main components: the survey machine and the automatic measuring engine. The survey machine is used for initial inspection and selection of objects for subsequent measurement. Two plates, up to 17 x 17 inches each, are surveyed simultaneously by means of projection on a screen. The approximate positions of objects selected are measured by two optical screws: helical lines cut through an aluminum coating on glass cylinders. These approximate coordinates to a precision of the order of 0.03mm are transmitted to a card punch by encoders connected with the cylinders.

Vasilevskis, S.↗

Radiative Importance of Aerosol-Cloud Interaction

Aerosol particles are input into the troposphere by biomass burning, among other sources. These aerosol palls cover large expanses of the earth's surface. Aerosols may directly scatter solar radiation back to space, thus increasing the earth's albedo and act to cool the earth's surface and atmosphere. Aerosols also contribute to the earth's energy balance indirectly. Hygroscopic aerosol act as cloud condensation nuclei (CCN) and thus affects cloud properties. In 1977, Twomey theorized that additional available CCN would create smaller but more numerous cloud droplets in a cloud with a given amount of liquid water. This in turn would increase the cloud albedo which would scatter additional radiation back to space and create a similar cooling pattern as the direct aerosol effect. Estimates of the magnitude of the aerosol indirect effect on a global scale range from 0.0 to -4.8 W/sq m. Thus the indirect effect can be of comparable magnitude and opposite in sign to the estimates of global greenhouse gas forcing Aerosol-cloud interaction is not a one-way process. Just as aerosols have an influence on clouds through the cloud microphysics, clouds have an influence on aerosols. Cloud droplets are solutions of liquid water and CCN, now dissolved. When the cloud droplet evaporates it leaves behind an aerosol particle. This new particle does not have to have the same properties as the original CCN. In fact, studies show that aerosol particles that result from cloud processing are larger in size than the original CCN. Optical properties of aerosol particles are dependent on the size of the particles. Larger particles have a smaller backscattering fraction, and thus less incoming solar radiation will be backscattered to space if the aerosol particles are larger. Therefore, we see that aerosols and clouds modify each other to influence the radiative balance of the earth. Understanding and quantifying the spatial and seasonal patterns of the aerosol indirect forcing may have even greater consequences. Presently we know that through the use of fossil fuel and land-use changes we have increased the concentration of greenhouse gases in the atmosphere. In parallel, we have seen a modest increase of global temperature in the last century. These two observations have been linked as cause and effect by climate models, but this connection is still experimentally not verified. The spatial and seasonal distribution of aerosol forcing is different from that of greenhouse gases, thus generating a different spatial fingerprint of climate change. This fingerprint was suggested as a method to identify the response of the climate system to anthropogenic forcing of greenhouse gases and aerosol. The aerosol fingerprint may be the only way to firmly establish the presence (or absence) of human impact on climate. Aerosol-cloud interaction through the indirect effect will be an important component of establishing this fingerprint.

Tsay, Si-Chee↗

RF Device for Acquiring Images of the Human Body

A safe, non-invasive method for forming images through clothing of large groups of people, in order to search for concealed weapons either made of metal or not, has been developed. A millimeter wavelength scanner designed in a unique, ring-shaped configuration can obtain a full 360 image of the body with a resolution of less than a millimeter in only a few seconds. Millimeter waves readily penetrate normal clothing, but are highly reflected by the human body and concealed objects. Millimeter wave signals are nonionizing and are harmless to human tissues when used at low power levels. The imager (see figure) consists of a thin base that supports a small-diameter vertical post about 7 ft (=2.13 m) tall. Attached to the post is a square-shaped ring 2 in. (=5 cm) wide and 3 ft (=91 cm) on a side. The ring is oriented horizontally, and is supported halfway along one side by a connection to a linear bearing on the vertical post. A planar RF circuit board is mounted to the inside of each side of the ring. Each circuit board contains an array of 30 receivers, one transmitter, and digitization electronics. Each array element has a printed-circuit patch antenna coupled to a pair of mixers by a 90 coupler. The mixers receive a reference local oscillator signal to a subharmonic of the transmitter frequency. A single local oscillator line feeds all 30 receivers on the board. The resulting MHz IF signals are amplified and carried to the edge of the board where they are demodulated and digitized. The transmitted signal is derived from the local oscillator at a frequency offset determined by a crystal oscillator. One antenna centrally located on each side of the square ring provides the source illumination power. The total transmitted power is less than 100 mW, resulting in an exposure level that is completely safe to humans. The output signals from all four circuit boards are fed via serial connection to a data processing computer. The computer processes the approximately 1-MB data set into a three-dimensional image in a matter of seconds. The innovation is to configure the receiver array in a ring topology surrounding the scanned object. The ring is then scanned vertically to cover the necessary two-dimensional surface. This fabrication of the ring is made possible by using planar antenna and circuit technology. A planar circuit board serves as a medium for both antennas and signal processing components. Using this technique, parts counts are kept low, and the cost per element is a small fraction of a waveguide-based system.

Gaier, Todd C.↗

Solar Cycle Fine Structure and Surface Rotation from Ca II K-Line Time Series Data

Analysis of three and a half decades of data from the NSO/AFRL/Sac Peak K-line monitoring program yields evidence for four components to the variation: (a) the solar cycle, with considerable fine structure and a quasi-periodicity of 122.4 days; (b) a stochastic process, faster than (a) and largely independent of it, (c) a quasi-periodic signal due to rotational modulation, and of course (d) observational errors (shown to be quite small). Correlation and power spectrum analyses elucidate periodic and aperiodic variation of these chromospheric parameters. Time-frequency analysis is especially useful for extracting information about differential rotation, and in particular elucidates the connection between its behavior and fine structure of the solar cycle on approximately one-year time scales. These results further suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as those being produced at NASA's Kepler observatory.

Scargle, Jeff↗

Analysis of the dynamics and frequency spectrum synthesis of an optical-mechanical scanning device

A two-coordinate optical-mechanical scanning device (OMSD), the operating unit of which is a scanning disk, with directional and focusing optics and a board, on which the data carrier is placed, is examined. The disk and board are kinematically connected by a transmission mechanism, consisting of a worm and complex gear drive and a tightening screw-nut with correcting device, and it is run by a synchronous type motor. The dynamic errors in the system depend, first, on irregularities in rotation of the disk, fluctuations in its axis and vibrations of the table in the plane parallel to the plane of the disk. The basic sources of the fluctuations referred to above are residual disbalance of the rotor and other rotating masses, the periodic component of the driving torque of the synchronous motor, variability in the resistance, kinematic errors in the drive and other things. The fluctuations can be transmitted to the operating units through the kinematic link as a flexural-torsional system, as well as through vibrations of the housing of the device.

Andryushkevichyus, A. I.↗

Comparison of Structural Concepts for Transport Aircraft with a Tail Cone Turbine

An evaluation of three structural concepts for an advanced aircraft design with a tail cone turbine is presented. Structural models were developed using an innovative rapid finite element modeling tool called Conceptual Design Shop (CDS). CDS is an attempt to fill a gap in current finite element modeling software to automatically connect wings and tails to the fuselage with sufficient support structure in airframe models. For comparison with actual aircraft structures, a model of a transport aircraft design developed using CDS is compared with published structural weight data for a Boeing 737-200. A method for computing aerodynamic stability parameters from an MSC/NASTRAN finite element analysis output deck is also discussed. Finally, the weight effects for using a tail cone turbine in an advanced transport aircraft design are evaluated by comparing three composite structural models, for which component thicknesses and cross-sections are sized by the Hypersizer software.

Mason, Brian H.↗

Coupling of Dust Mineralogy to Radiation in NASA GISS ModelE: Impact Upon Dust Optical Properties and Direct Radiative Effect

Estimates of dust direct radiative effect (DRE) are still largely uncertain mainly due to the poor constraining of regional variations of dust absorption, whose known connection with mineral composition is still largely neglected by most Earth System Models. The inaccurate knowledge of soil mineralogy and insufficient measurements of dust physical and optical properties still present the main challenges for a proper representation of the dust-radiation interaction in climate models. We recently upgraded the coupling of dust minerals to shortwave radiation in the NASA GISS ModelE. In particular, we extended the interaction to online-calculated minerals and implemented two different mixing configurations: i) external mixing of three main mineral components and ii) internal mixing of all minerals, allowing a dynamic fraction of iron oxides. We used a semi-empirical approach for the optical calculations, mostly based on aerosol chamber measurements from natural soils, aiming to reduce the influence of uncertain assumptions on the optical properties and mixing state of individual minerals. In this contribution, we present the results of our first calculations of dust optical properties and DREs based on different mixing configurations of interactive minerals. We show the changes to dust optical depth and single scattering albedo, with respect to the control case using homogeneous dust composition, and the consequent global and regional variations in dust DREs at the top of atmosphere and at surface. We also compare the model optical properties with AERONET data, filtered to identify dust scenes. We find that accounting for the diverse properties of dust minerals modifies the pattern of regional dust absorption and therefore its impact upon climate. We also show that the mineralogy effect is sensitive to the assumed mixing state of minerals.

dust direct radiative effect↗

On the connection between multigrid and cyclic reduction

A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.

Merriam, M. L.↗

Establishing the connection between peanut-shaped bulges and galactic bars

It has been suggested that the peanut-shaped bulges seen in some edge-on disk galaxies are due to the presence of a central bar. Although bars cannot be detected photometrically in edge-on galaxies, we show that barred potentials produce a strong kinematic signature in the form of double-peaked line-of-sight velocity distributions with a characteristic 'figure-of-eight' variation with radius. We have obtained spectroscopic observations of two edge-on galaxies with peanut-shaped bulges (NGC 5746 and NGC 5965), and they reveal exactly such line-of-sight velocity distributions in both their gaseous (emission line) and their stellar (absorption line) components. These observations provide strong observational evidence that peanut-shaped bulges are a by-product of bar formation.

Kuijken, Konrad↗

Towards Flange-to-Flange Turbopump Simulations for Liquid Rocket Engines

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbopump geometry through numerical simulation will be of significant value toward design. This will help to improve safety of future space missions. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the MPI and MLP versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology. INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbopump simulations, moving boundary capability and an efficient time-accurate integration methods are build in the flow solver. To handle the geometric complexity and moving boundary problems, overset grid scheme is incorporated with the solver that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. The performance of the two time integration schemes for time-accurate computations is investigated. For an unsteady flow which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive. The current geometry for the LOX boost turbopump has various rotating and stationary components, such as inducer, stators, kicker, hydrolic turbine, where the flow is extremely unsteady. Figure 1 shows the geometry and computed surface pressure of the inducer. The inducer and the hydrolic turbine rotate in different rotational speed.

Kiris, Cetin↗

Relativistic enhancement of the Compton-reflected component in active galactic nuclei

Compton reflection may be an important process in AGNs, since it provides an improvement over power-law fits to AGN spectra observed by Ginga and can also explain the spectrum of the cosmic X-ray background. The fraction of the total X-ray luminosity which is incident upon a thin steady alpha-disk if the X-rays are produced by inverse-Compton scattering of soft, disk photons off relativistic electrons located above the disk is calculated. This fraction is called the Compton reflection covering factor, f, and it is found that it can range between 0.5 and 0.88. This large range in f, due to a relativistic kinematic effect first calculated in this connection by Ghisellini et al (1991) is sufficient to explain the typical covering (about 0.5) observed in bright AGNs by Ginga as well as the large covering factor (about 0.9) required to explain the cosmic X-ray background in the Compton reflection model.

Rogers, R. D.↗

Petrogenesis of the western highlands of the moon - Evidence from a diverse group of whitlockite-rich rocks from the Fra Mauro formation

A group of KREEPy basalts has been discovered in Apollo 14 soils. These samples exhibit similarities to both HA and VHK basalts, albeit with much higher REE abundances, and contain up to 2 vol pct whitlockite and can be explained by assimilation of a K-, REE- and P-rich fluids by an original HA or VHK basalt. This KREEP component could have been produced late in the evolution of the lunar magma ocean and is similar in composition to QMD at Apollo 14. Two rocks have trace element compositions that are representative of actual KREEP. One of the samples appears to be petrographically pristine and could represent an actual KREEP basalt rock. Five subophitic high-Al basalts represent sampling of either a slowly cooled impact melt sheet or, more likely, the same basalt flow. Two 'quasi-pristine' highland rocks confirm the postulate of a connection between KREEP and the alkali suite. A newly discovered alkali anorthosite is a plagioclase cumulate with about 15 percent trapped KREEPy liquid.

Snyder, Gregory A.↗

Building a standardized Observing System Simulation Experiment (OSSE) framework for Mars

We advocate that the Decadal Survey recommends the NASA Science Mission Directorate to develop a rigorous Observing System Simulation Experiment (OSSE) framework for Mars, to optimize future atmospheric observations. Atmospheric conditions on Mars are a potential hazard source for landing missions. Errors in the estimates of atmospheric density profiles, inadequate knowledge of wind vertical structure and dust concentration as a function of height are likely causes of uncertainty at the landing site on the order of kilometers. An operational real-time weather forecasting capability for Mars would reduce such uncertainties, carrying enormous benefits to future robotic missions, and would be an invaluable prerequisite for human missions.A real-time forecasting capability relies upon three fundamental components: a critical mass of observing systems, a data assimilation system (DAS), and a global forecast model. The DAS allows the model to ingest the data effectively, optimizing the observational information content,and transforming them into a gridded representation of the atmosphere at a given time, called an ‘analysis’. The analysis is the best estimate of the atmospheric state for that time, and also represents a set of ‘initial conditions’ from which a global model can be initialized, to predict a future state of the atmosphere. The connection between analysis and forecast represents the foundation of modern weather forecasting. However, from the point of view of a forecast system,not all observations are equally impactful, partially because of the problem of “observational error correlation”, one important research topic in data assimilation development. For the Earth, partly due to the spontaneous and deregulated development of observations and forecast capabilities worldwide for more than half a century,the use of observations in contemporary operational forecast systems is suboptimal, with many potentially useful data being underutilized. On the contrary, Mars atmospheric scientists are in the unique situation of designing the next-generation observing systems by learning from the experience gathered on the Earth, so as to assure that the future instruments are specifically optimized to give the maximum benefit to a future weather forecast capability.An immensely powerful tool that has been firmly established by atmospheric scientists on the Earth is represented by a properly designed OSSE framework. A realistic OSSE framework cannot only quantify the benefit of future data types, be them surface based or space borne, but can also help design and optimize an entire observational network. Furthermore, OSSEs can provide deep insights into an atmosphere’s behavior, by addressing conceptual problems of its intrinsic predictability and delineating the regions or features of the atmosphere which are more sensitive to additional data and would benefit from a denser sampling. The difficulties posed by OSSEs are fundamentally different for Earth and Mars. For Earth, the enormous data volume imposes a tremendous constraint on any innovation in the observing systems: it is very hard for a single sensor to impact the skill. For Mars, the problem is the opposite: almost any additional instrument will exert some impact. However, OSSEs can help to evaluate the cost/benefit for every sensor and suggest optimal data configuration and density.The purpose of this white paper is to provide an introduction to a rigorously designed OSSE framework, explain the underlying problems and challenges, and engage the Mars community to collaborate with Earth Atmospheric scientists in order to develop a joint-OSSE framework for Mars with the largest consensual basis possible. An OSSE infrastructure would increase the understanding of the Martian atmosphere, would help NASA to optimize instrument specifications and orbit choice, providing the maximium benefit for a given expenditure of resources, and could even help establishing a roadmap for a future real-time weather forecasting capability.

Oreste Reale↗

Solar heating and hot water system installed at Saint Louis, Missouri

The solar heating and hot water system installed at the William Tao & Associates, Inc., office building in St. Louis, Missouri is described, including maintenance and construction problems, final drawings, system requirements, and manufacturer's component data. The solar system was designed to provide 50 percent of the hot water requirements and 45 percent of the space heating needs for a 900 sq ft office space and drafting room. The solar facility has 252 sq ft of glass tube concentrator collectors and a 1000 gallon steel storage tank buried below a concrete slab floor. Freeze protection is provided by a propylene glycol/water mixture in the collector loop. The collectors are roof mounted on a variable tilt array which is adjusted seasonally and is connected to the solar thermal storage tank by a tube-in-shell heat exchanger. Incoming city water is preheated through the solar energy thermal storage tank.

Source record↗