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At least 469 records · Page 26

Sulfuric Acid Monohydrate: Formation and Heterogeneous Chemistry in the Stratosphere

We have investigated some thermodynamic properties (i.e., freezing/melting points) and heterogeneous chemistry of sulfuric acid monohydrate (SAM, H2SO4.H2O), using a fast flow reactor coupled to a quadrupole mass spectrometer. The freezing point observations of thin liquid sulfuric acid films show that for acid contents between 75 and 85 wt % the monohydrate crystallizes readily at temperatures between 220 and 240 K on a glass substrate. Once formed, SAM can be thermodynamically stable in the H2O partial pressure range of (1-4) x 10(exp -4) torr and in the temperature range of 220-240 K. For a constant H2O partial pressure, lowering the temperature causes SAM to melt when the temperature and water partial pressure conditions are out of its stability regime. The reaction probability measurements indicate that the hydrolysis of N2O5 is significantly suppressed owing to the formation of crystalline SAM: The reaction probability on water-rich SAM (with higher relative humidity, or RH) is of the order of 10(exp -3) at 210 K and decreases by more than an order of magnitude for the acid-rich form (with lower RH). The hydrolysis rate of ClONO2 on water-rich SAM is even smaller, of the order of 10(exp -4) at 195 K. These reported values on crystalline SAM are much smaller than those on liquid solutions. No enhancement of these reactions is observed in the presence of HCl vapor at the stratospheric concentrations. In addition, Brunauer, Emmett, and Teller analysis of gas adsorption isotherms and photomicrography have been performed to characterize the surface roughness and porosities of the SAM substrate. The results suggest the possible formation of SAM in some regions of the middle- or low-latitude stratosphere and, consequently, much slower heterogeneous reactions on the frozen aerosols.

Zhang, Renyi↗

Behavior of Windblown Sand on Mars: Results from Single-Particle Experiments

Experiments are investigating the behavior of individual sand grains in the high-energy martian aeolian regime. Energy partitioning during impact of a saltating grain determines grain longevity, but it also influences the way in which the bed becomes mobilized by reptation. When single grains of sand are fired into loose beds, the bed can absorb up to 90% of the impact energy by momentum transfer to other grains; it has been discovered that the impacting grains cause circular craters even at low impact angles. Hundreds of grains can be splashed by a single high-velocity (100 m/s) impact causing more bed disturbance through reptation than previously thought. The research is supported by NASA's PG&G Program. Because the martian aeolian environment in both high energy and of long duration, the most mobile fractions of windblown sand should have eradicated themselves by attrition, unless sand supply has kept pace with destruction. It is therefore important to understand the rate of grain attrition in order to make sense of the existence of vast dune fields on Mars. Attrition, has been addressed in other studies, but precise data for a single saltating grain striking a loose bed of sand have not been acquired -- the quintessential case to be understood for dunes on Mars. To acquire these data, we are employing a compound crossbow which has the bolt-firing mechanism replaced with a pneumatically-automated sabot system. The sabot can launch individual grains of sand of any size between several millimeters and about 50 microns, at velocities up to 100m/s. This is around the maximum velocity expected for saltating grains on Mars. The sabot sled is equipped with photoelectric sensors for measuring shot velocity. Baffling of the grain's exit orifice has enabled projection of single grains without significant aerodynamic effects from the sabot. Grains are fired into loose beds of sand at about 15 degrees from the horizontal (typical saltation trajectory at impact) while being filmed on high-speed video. High-intensity pulse illumination for the grains is triggered by the solenoid-operated bow trigger. A 45 degree mirror over the impact site provides simultaneous horizontal and vertical images of the impact on each video frame. UV fluorescence is enabling grain and grain-fragment recovery. At 100 m/s, grains of all sizes shatter into many fragments when the sand is replaced with a solid target. Kinetic energy of the grains at this velocity exceeds the critical energy for catastrophic failure of minerals. Although probably exceptional as a grain speed, it suggests that conditions on Mars might elevate materials into an attrition regime not encountered on other planets; individual grains blown across rock pavements on Mars will have short lifespans. When experimental grains impact loose (dune) sand, much, if not most of the kinetic energy is converted into momentum of other grains. Using high-speed filming, the energy involved in splashing grains at the impact site can be derived from the size of the crater, the speed of the splashed grains, and the rebound speed of the impactor. The amount of energy partitioned into material failure (as opposed to momentum) is too small a fraction of the total to be calculated under these circumstances. This does not necessarily mean that little damage occurs to the grains (the full extent of the damage has yet to be determined) because only a small fraction of the impact energy is required for inducing brittle fracture. Damage is orders of magnitude less than during impact against solid surfaces.

Marshall, J. R.↗

Service Life Extension of the Propulsion System of Long-Term Manned Orbital Stations

One of the critical non-replaceable systems of a long-term manned orbital station is the propulsion system. Since the propulsion system operates beginning with the launch of station elements into orbit, its service life determines the service life of the station overall. Weighing almost a million pounds, the International Space Station (ISS) is about four times as large as the Russian space station Mir and about five times as large as the U.S. Skylab. Constructed over a span of more than a decade with the help of over 100 space flights, elements and modules of the ISS provide more research space than any spacecraft ever built. Originally envisaged for a service life of fifteen years, this Earth orbiting laboratory has been in orbit since 1998. Some elements that have been launched later in the assembly sequence were not yet built when the first elements were placed in orbit. Hence, some of the early modules that were launched at the inception of the program were already nearing the end of their design life when the ISS was finally ready and operational. To maximize the return on global investments on ISS, it is essential for the valuable research on ISS to continue as long as the station can be sustained safely in orbit. This paper describes the work performed to extend the service life of the ISS propulsion system. A system comprises of many components with varying failure rates. Reliability of a system is the probability that it will perform its intended function under encountered operating conditions, for a specified period of time. As we are interested in finding out how reliable a system would be in the future, reliability expressed as a function of time provides valuable insight. In a hypothetical bathtub shaped failure rate curve, the failure rate, defined as the number of failures per unit time that a currently healthy component will suffer in a given future time interval, decreases during infant-mortality period, stays nearly constant during the service life and increases at the end when the design service life ends and wear-out phase begins. However, the component failure rates do not remain constant over the entire cycle life. The failure rate depends on various factors such as design complexity, current age of the component, operating conditions, severity of environmental stress factors, etc. Development, qualification and acceptance test processes provide rigorous screening of components to weed out imperfections that might otherwise cause infant mortality failures. If sufficient samples are tested to failure, the failure time versus failure quantity can be analyzed statistically to develop a failure probability distribution function (PDF), a statistical model of the probability of failure versus time. Driven by cost and schedule constraints however, spacecraft components are generally not tested in large numbers. Uncertainties in failure rate and remaining life estimates increase when fewer units are tested. To account for this, spacecraft operators prefer to limit useful operations to a period shorter than the maximum demonstrated service life of the weakest component. Running each component to its failure to determine the maximum possible service life of a system can become overly expensive and impractical. Spacecraft operators therefore, specify the required service life and an acceptable factor of safety (FOS). The designers use these requirements to limit the life test duration. Midway through the design life, when benefits justify additional investments, supplementary life test may be performed to demonstrate the capability to safely extend the service life of the system. An innovative approach is required to evaluate the entire system, without having to go through an elaborate test program of propulsion system elements. Evaluating every component through a brute force test program would be a cost prohibitive and time consuming endeavor. ISS propulsion system components were designed and built decades ago. There are no representative ground test articles for some of the components. A 'test everything' approach would require manufacturing new test articles. The paper outlines some of the techniques used for selective testing, by way of cherry picking candidate components based on failure mode effects analysis, system level impacts, hazard analysis, etc. The type of testing required for extending the service life depends on the design and criticality of the component, failure modes and failure mechanisms, life cycle margin provided by the original certification, operational and environmental stresses encountered, etc. When specific failure mechanism being considered and the underlying relationship of that mode to the stresses provided in the test can be correlated by supporting analysis, time and effort required for conducting life extension testing can be significantly reduced. Exposure to corrosive propellants over long periods of time, for instance, lead to specific failure mechanisms in several components used in the propulsion system. Using Arrhenius model, which is tied to chemically dependent failure mechanisms such as corrosion or chemical reactions, it is possible to subject carefully selected test articles to accelerated life test. Arrhenius model reflects the proportional relationship between time to failure of a component and the exponential of the inverse of absolute temperature acting on the component. The acceleration factor is used to perform tests at higher stresses that allow direct correlation between the times to failure at a high test temperature to the temperatures to be expected in actual use. As long as the temperatures are such that new failure mechanisms are not introduced, this becomes a very useful method for testing to failure a relatively small sample of items for a much shorter amount of time. In this article, based on the example of the propulsion system of the first ISS module Zarya, theoretical approaches and practical activities of extending the service life of the propulsion system are reviewed with the goal of determining the maximum duration of its safe operation.

Kamath, Ulhas↗

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ* scales weakly with system size, i.e., the dependence of ℓ* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim L→∞ (ℓ*/L) = 0. In particular, for (2+1)-dimensional interfaces ℓ* is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. Overall, this weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Towards a Global Water Scarcity Risk Assessment Framework: Incorporation of Probability Distributions and Hydro-Climatic Variability

Changing hydro-climatic and socioeconomic conditions increasingly put pressure on fresh water resources and are expected to aggravate water scarcity conditions towards the future. Despite numerous calls for risk-based water scarcity assessments, a global-scale framework that includes UNISDR's definition of risk does not yet exist. This study provides a first step towards such a risk based assessment, applying a Gamma distribution to estimate water scarcity conditions at the global scale under historic and future conditions, using multiple climate change and population growth scenarios. Our study highlights that water scarcity risk, expressed in terms of expected annual exposed population, increases given all future scenarios, up to greater than 56.2% of the global population in 2080. Looking at the drivers of risk, we find that population growth outweigh the impacts of climate change at global and regional scales. Using a risk-based method to assess water scarcity, we show the results to be less sensitive than traditional water scarcity assessments to the use of fixed threshold to represent different levels of water scarcity. This becomes especially important when moving from global to local scales, whereby deviations increase up to 50% of estimated risk levels.

Populations↗

Design and development of a ceramic radial turbine for the AGT101

An acceptable and feasible ceramic turbine wheel design has been achieved, and the relevant temperature, stress, and success probability analyses are discussed. The design is described, the materials selection presented, and the engine cycle conditions analysis parameters shown. Measured MOR four-point strengths are indicated for room and elevated temperatures, and engine conditions are analyzed for various cycle states, materials, power states, turbine inlet temperatures, and speeds. An advanced gas turbine ceramic turbine rotor thermal and stress model is developed, and cumulative probability of survival is shown for first and third-year properties of SiC and Si3N4 rotors under different operating conditions, computed for both blade and hub regions. Temperature and stress distributions for steady-state and worst-case shutdown transients are depicted.

Finger, D. G.↗

Going through a quantum phase

Phase measurements on a single-mode radiation field are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator; its phase eigenkets generate the probability operator measure (POM) for maximum likelihood phase estimation. A commuting observables description for the SG-POM on a signal x apparatus state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyning realizes the annihilation operator POM, this analogy may help realize the SG-POM. The wave function representation associated with the SG POM is then used to prove the duality between the phase measurement and the number operator measurement, from which a number-phase uncertainty principle is obtained, via Fourier theory, without recourse to linearization. Fourier theory is also employed to establish the principle of number-ket causality, leading to a Paley-Wiener condition that must be satisfied by the phase-measurement probability density function (PDF) for a single-mode field in an arbitrary quantum state. Finally, a two-mode phase measurement is shown to afford phase-conjugate quantum communication at zero error probability with finite average photon number. Application of this construct to interferometric precision measurements is briefly discussed.

Shapiro, Jeffrey H.↗

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗

Intrinsic oxygen fugacities of diogenites and mesosiderite clasts

Oxygen fugacities of diogenite and mesosiderite clast material were measured with the double ZrO2 cell technique between 800 and 1150 C. The samples were taken from large clasts in the diogenites Johnstown (En73) and Tatahouine (En75), and the mesosiderites Estherville (En81), West Point (Fo88) and Emery (En68). Fugacity values for all except Emery plot near the wuestite-iron buffer curve and are interpreted as indicating similar source regions and environments of crystallization for the two suites. Emery orthopyroxene records a lower fugacity, close to the fayalite-quartz-iron buffer curve, probably as a result of equilibration with the mesosiderite matrix assemblage. The similarity of redox conditions experienced by mesosiderite orthopyroxenite and diogenites is not sufficient to require a single parent body and, if the common achondrites were derived from Vesta, mesosiderites probably came from a different body.

Hewins, R. H.↗

Integration of Nuclear Material Accounting Data and Process Monitoring Data for Improvement on Detection Probability in Safeguarding Electrochemical Processing Facilities (Final Technical Report)

The KAERI advanced spent fuel conditioning process (ACP) process is a critical component of the US- South Korean nuclear cooperation and the following “123 Agreement.” Its development has received considerable attention in both countries. The ACP is an electrochemical processing (pyroprocessing) that recycles over 96% of the used nuclear fuel (UNF). It is also intrinsically proliferation-resistant in theory. In normal operation, the U/TRU product is very hot radiologically. In addition, the Cm provides a high level of spontaneous neutrons, making the product unsuitable for weapon use. However, as pointed in some study, “the need for safeguards to protect against the diversion and misuse of separated plutonium applies essentially equally to all grades of plutonium.” As pointed by many studies, the well-established traditional Nuclear Material Accounting (NMA) approach cannot be directly applied to electrochemical processing because of the lack of an input accountability tank, the non-continuous material flow, and the unsatisfactory level of confidence in sampling methods. Therefore, nuclear safeguards remain a grand challenge in the developing of commercial electrochemical separations facilities, especially around the heart of such facilities, the electrorefiner (ER) systems. In contrast to NMA data, process monitoring (PM) data is normally an indirect measurement of the SNM and is acquired much more frequently. In a broad sense, PM includes monitoring by various types of equipment, e.g. radiation detectors, cameras, voltage, current sensors. Because it is already being collected by the operator, the additional cost to safeguards is low. It has long been believed that PM data can supplement NMA data and help improve safeguards, although the benefits are hard to quantify. The U.S. DOE’s Material Protection, Accounting, and Control Technology (MPACT) campaign has made substantial investments into innovative PM sensor technology and predictive model development for real- or near real-time measurement and prediction of molten salt density and level, salt composition and actinide concentration especially Pu, the cell voltage, and the cell current to supplement traditional NMA. For aqueous-based reprocessing facilities, it is reported that PM, integrated with traditional NMA, have a high detection probability for specific diversions. For electrochemical reprocessing, preliminary studies have shown that PM data can support traditional NMA in various ways by providing a basis to estimate some of the in-processing nuclear material inventories. Despite early success, further studies on fusion of PM data and NMA data are still needed, which is the goal of this proposed work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

PRIME: A bottom-up approach to probabilistic rule development

PRIME is a system to be used by an intelligent machine to allow it to operate in an abstract but uncertain (or stochastic) environment. It maintains a model of the effects of the machine's actions in the form of a rule base, which is induced from experience. This bottom-up approach to rule development allows the model to adapt to changes in the environment. Each rule consists of a condition under which the rule is active, an action, the effect of the action on the environment, and an estimate of the probability of this effect occurring. The effect probabilities are used to model the uncertainty in the environment, permitting multiple possible effects for a single action under a particular set of conditions. The objective of the intelligent machine is to satisfy user-specified goals with maximum probability of success. PRIME fulfills this requirement in two ways: it continuously updates the rule base with the most recent information, to ensure the validity of the model; and it generates plans which have the maximum probability of achieving the goals, based on the probability estimates in the rule base. PRIME is composed of three main processes: exploration, generalization, and planning. In exploration, the machine executes various randomly chosen actions, observes the effects on the environment, and updates the rule base accordingly. This process is used to develop the rule base in simulation, as well as to supplement the current knowledge during normal operation. Generalization is the procedure used to induce general rules from experience, which is encoded in the form of specific rules. These general rules extend the machine's knowledge to situations which have not been encountered yet, thereby increasing the capability of the machine to plan effectively. Planning is the process of constructing an optimal sequence of actions to satisfy a goal, using the rule base to predict the effects of these actions and to determine the probability of success of the plan. The rule representation and many other data structures were specifically chosen to maximize the efficiency of these processes. A simulated environment was designed to test the performance of PRIME. The results of experimentation were largely negative. The main problem was that the domain coverage of the rules was inadequate for the number of rules stored in the rule base, due to redundancies in general rules and numerous rules covering ineffective actions. It was determined that a more efficient generalization, and some form of goal-directed exploration, are necessary in order to solve most of the current deficiencies in PRIME.

Miller, Scott A.↗

Plasmaspheric Drainage Plumes: Inner-Magnetospheric Coupling from the IMAGE/EUV Perspective

Plasmaspheric drainage plumes appear in the aftermath of periods of enhanced convection/erosion and are interpreted as a near-equatorial signature of the redistribution of thermal plasma along streamlines. Analysis of IMAGE/EUV observations from "FirstLight" through the end of calendar year 2002 reveals that for Kp greater than or equal to 3, there is an 84% probability of observing a plasmaspheric plume in EUV data. We present a statistical analysis of the geomagnetic conditions [Kp, Dst, and solar wind-induced electric field] associated with EUV plume observations. This analysis yields a peak in observational probability when Kp = 4 and Dst = -50 nT. Additionally, EUV pllume observations are associated with a solar wind-induced convection electric field at Earth [Ev, SM] characterized by bi-modal behavior with a positive mode peaked at approximately 4 m V(raised dot) m(sup -1) and a negative model that peaks at -2 mV (raised dot) m(sup -1). Analysis of the time rate of change of the plume-associated Ev, SM indicated that once the mechanism for plume formation is initiated, a slowly changing convection environment is required to allow for sufficient plume development prior to EUV detection.

Adrian, Mark L.↗

Quantifying Human Behavior and Decision Errors in Security Screening Operations

The potential for human errors in conducting security related screening operations can lead to inadvertent and adverse decision outcomes. This paper overviews an initial mathematical framework designed to model and quantify the various human factors and decision outcomes that may occur in conducting security screening operations, such as U.S. port of entry radiological and nuclear (rad/nuc) security screening. This framework is based on the Human Error Assessment and Reduction (HEART) technique. As applied here, the framework incorporates a set of rules for human engagement, including a prescribed concept of operations (CONOPS) and deviations that may occur from this established CONOPS due to inadvertent personnel decision errors. We also review some of the various factors that may adversely influence such decisions by security screening personnel. Some of these factors include current workload, environmental conditions, training, and various other intangible factors. Using the HEART methodology, we translate each of these factors into error producing conditions, their effects on error, an assessed proportion of effects, and finally the overall probability of human error at each stage of the screening process. We then include a small scale example to demonstrate the methodology and results based on an assumed set of input conditions at a notional port of entry.

Brigantic, Robert T.↗

Analysis and prediction of intersection traffic violations using automated enforcement system data

We report that the automated enforcement system (AES) is an effective way of supplementing traditional traffic enforcement, and the traffic violation data from AES can also be effectively used for safety research. In this study, traffic violation data were used to analyze the influencing factors associated with traffic violations and to predict the probability of violations at intersections. The potential factors influencing violations include 24 independent factors related to time, space, traffic and weather. Results from a logistic model showed that the midday period, weekends, residential districts, collector roads, congested traffic conditions, high traffic flow, lower wind speed and low temperature would increase the probability of traffic violations. The probability of violations was predicted by the random forest algorithm, which was proven to be the best traffic violation prediction model among logistic regression, Gaussian naive Bayes, and support vector machine. Moreover, the proximity weighted synthetic oversampling technique (ProWSyn) method was applied to reduce the impact of the imbalance ratio (IR) and improve the model’s prediction performance. The receiver operating characteristics (ROC) curves and Precision-Recall (PR) curves illustrated that the random forest algorithm using oversampling data had the best classifier prediction performance than undersampling data. The area under curve (AUC) and out-of-bag (OOB) error with IR = 1 reached 0.914 and 0.0787, which showed the better performance of the random forest algorithm using ProWSyn in dealing with imbalanced traffic violation data.

42 ENGINEERING↗

On signal design by the R sub 0 criterion for non-white Gaussian noise channels

The use of the R sub 0 criterion for modulation system design is investigated for channels with non-white Gaussian noise. A signal space representation of the waveform channel is developed, and the cut-off rate R sub 0 for vector channels with additive nonwhite Gaussian noise and unquantized demodulation is derived. When the signal unput to the channel is a continuous random vector, maximization of R sub 0 with constrained average signal energy leads to a water-filling interpretation of optimal energy distribution in signal space. The necessary condition for a finite signal set to maximize R sub 0 with constrained energy and an equally likely probability assignment of signal vectors is presented, and an algorithm is outlined for numerically computing the optimum signal set. A necessary condition on a constrained energy, finite signal set is found which maximizes a Taylor series approximation of R sub 0. This signal set is compared with the finite signal set which has the water-filling average energy distribution.

Bordelon, D. L.↗

Enhancement of Far Field Sound Levels by Refractive Focusing

The enhancement of sound pressure levels resulting from refractive focusing was calculated for meteorological conditions representative of those observed at the MOD-1 site near Boone, N.C. The results show that 10 to 20dB enhancements can occur over ranges of several hundred meters. Localized enhancements in excess of 20dB can occur but will probably be of limited duration as a consequence of normal temporally varying meteorological conditions.

Thomson, D. W.↗

Fast and efficient identification of anomalous galaxy spectra with neural density estimation

ABSTRACT Current large-scale astrophysical experiments produce unprecedented amounts of rich and diverse data. This creates a growing need for fast and flexible automated data inspection methods. Deep learning algorithms can capture and pick up subtle variations in rich data sets and are fast to apply once trained. Here, we study the applicability of an unsupervised and probabilistic deep learning framework, the probabilistic auto-encoder, to the detection of peculiar objects in galaxy spectra from the SDSS survey. Different to supervised algorithms, this algorithm is not trained to detect a specific feature or type of anomaly, instead it learns the complex and diverse distribution of galaxy spectra from training data and identifies outliers with respect to the learned distribution. We find that the algorithm assigns consistently lower probabilities (higher anomaly score) to spectra that exhibit unusual features. For example, the majority of outliers among quiescent galaxies are E+A galaxies, whose spectra combine features from old and young stellar population. Other identified outliers include LINERs, supernovae, and overlapping objects. Conditional modelling further allows us to incorporate additional information. Namely, we evaluate the probability of an object being anomalous given a certain spectral class, but other information such as metrics of data quality or estimated redshift could be incorporated as well. We make our code publicly available.

Böhm, Vanessa↗