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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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

FleCSPH notes

FleCSI is a compile-time con gurable framework designed to support multi-physics application development. As such, FleCSI provides a very general set of infrastructure design patterns that can be specialized and extended to suit the needs of a broad variety of solver and data requirements. FleCSI currently supports multi-dimensional mesh topology, geometry, and adjacency information, as well as n-dimensional hashed-tree data structures, graph partitioning interfaces, and dependency closures. FleCSI introduces a functional programming model with control, execution, and data abstractions that are consistent both with MPI and with state-of-the-art, task-based runtimes such as Legion and Charm++. The abstraction layer insulates developers from the underlying runtime, while allowing support for multiple runtime systems including conventional models like asynchronous MPI. The intent is to provide developers with a concrete set of user-friendly programming tools that can be used now, while allowing exibility in choosing runtime implementations and optimization that can be applied to future architectures and runtimes. FleCSI's control and execution models provide formal nomenclature for describing poorly understood concepts such as kernels and tasks. FleCSI's data model provides a low-buy-in approach that makes it an attractive option for many application projects, as developers are not locked into particular layouts or data structure representations. FleCSI currently provides a parallel but not distributed implementation of Binary, Quad and Oct-tree topology. This implementation is base on space lling curves domain decomposition, the Morton order. The current FleCSI version requires the implementation of a driver and a specialization driver. The role of the specialization driver is to provide the data distribution. This feature is not complete in FleCSI code and we provide it. The next step will be to incorporate it directly from FleCSPH to FleCSI as we reach a good level of performance. Then the driver represent the general execution of the resolution without worrying of the data locality and communications. As FleCSI is an On-Development code the structure may change in the future and we keep track of these changes in FleCSPH.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Radioisotope identification method for poorly resolved gamma-ray spectrum of nuclear security concern

Gamma-ray signal can be used as a fingerprint for radioisotope identification. In the context of radioactive and nuclear materials security at the border control point, the detection task can present a significant challenge due to various constraints such as the limited measurement time, the shielding conditions, and the noise interference. This study proposes a novel method to identify the signal of one or several radioisotopes from a poorly resolved gamma-ray spectrum. In this method, the noise component in the raw spectrum is reduced by the wavelet decomposition approach, and the removal of the continuum background is performed using the baseline determination algorithm. Finally, the identification of radioisotope is completed using the matrix linear regression method. The proposed method has been verified by experiments using the poorly resolved gamma-ray signals from various scenarios including single source, mixing of natural uranium with five of the most common industrial radioactive sources (57Co, 60Co, 133Ba, 137Cs, and 241Am). The preliminary results show that the proposed algorithm is comparable with the commercial method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Simplified Predictive Models for CO 2 Sequestration Performance Assessment: Research Topical Report on Task #4 - Reduced-Order Method (ROM) Based Models

Reduced-order models provide a means for greatly accelerating the detailed simulations that will be required to manage CO 2 storage operations. In this work, we investigate the use of one such method, POD-TPWL, which has previously been shown to be effective in oil reservoir simulation problems. This method combines trajectory piecewise linearization (TPWL), in which the solution to a new (test) problem is represented through a linearization around the solution to a previously-simulated (training) problem, with proper orthogonal decomposition (POD), which enables solution states to be expressed in terms of a relatively small number of parameters. We describe the application of POD-TPWL for CO 2 -water systems simulated using a compositional procedure. Stanford’s Automatic Differentiation-based General Purpose Research Simulator (AD-GPRS) performs the full-order training simulations and provides the output (derivative matrices and system states) required by the POD-TPWL method. A new POD-TPWL capability introduced in this work is the use of horizontal injection wells that operate under rate (rather than bottom-hole pressure) control. Simulation results are presented for CO 2 injection into a synthetic aquifer and into a simplified model of the Mount Simon formation. Test cases involve the use of time-varying well controls that differ from those used in training runs. Results of reasonable accuracy are consistently achieved for relevant well quantities. Runtime speedups of around a factor of 370 relative to full- order AD-GPRS simulations are achieved, though the preprocessing needed for POD-TPWL model construction corresponds to the computational requirements for about 2.3 full-order simulation runs. A preliminary treatment for POD-TPWL modeling in which test cases differ from training runs in terms of geological parameters (rather than well controls) is also presented. Results in this case involve only small differences between training and test runs, though they do demonstrate that the approach is able to capture basic solution trends. The impact of some of the detailed numerical treatments within the POD-TPWL formulation is considered in an Appendix.

Mishra, Srikanta↗
DOE OSTI2023

Build Optimization Software Tools (BOOST) v2.0.0

Build Optimization Software Tools (BOOST) accelerate the design of DNA, RNA and protein sequences for their synthesis and assembly in an automated and scalable fashion. The BOOST Juggler automates the following two design tasks: - Reverse-Translation of protein sequences into DNA sequences - Codon Juggling of DNA sequences The BOOST Polisher provides the following design tasks: - The Verification of DNA sequences against DNA synthesis constraints - The Modification of DNA sequences in case they violate any DNA synthesis constraint In addition, the BOOST Polisher can be instructed to verify and modify DNA sequences against sequence patterns, such as restriction sites. The BOOST Partitioner supports both Gibson/chewback and Yeast assembly (also known as Transformation-Associated Recombination, or TAR) methods when performing the decomposition of large sequences that exceed the maximum length of DNA synthesis into synthesizable building blocks. The Partitioner can be instructed to find building blocks with appropriate overlap sequences, making their assembly into the complete construct more efficient. BOOST Workflows enable, in a customized fashion, the execution of the Juggler, Polisher, and Partitioner tools on a batch of sequences.

Sharkey, Michael↗
DOE OSTI2023

Identifying human failure events (HFEs) for external hazard probabilistic risk assessment

In recent years, several advancements in nuclear power plant (NPP) probabilistic risk assessment (PRA) have been driven by increased understanding of external hazards, plant response, and uncertainties. However, major sources of uncertainty associated with external hazard PRA remain. One important source is how risk-significant human actions that are carried out to enable plant response and recovery from natural hazards cause the close coupling of physical impacts on plants and overall plant risk during these hazard events. This makes human reliability and human-plant interactions important elements to consider in resolving PRA gaps in external hazards. One of the challenges in considering human response in external hazard probabilistic risk assessment (XHPRA) is that most existing human reliability analysis (HRA) models were not developed for assessing actions outside the control room (termed ex-control room actions) and hazard response. To support this new scope, HRA models will need to be developed or modified to support identification of human activities, causal factors, and uncertainties inherent in external hazard response, thereby providing insights regarding event timing and physical event conditions as they relate to human performance. In this study, there are two main objectives: (1) evaluate the applicability of an existing cognitive-based HRA method, Phoenix, to ex-control room actions, and (2) identify sources of uncertainty to be characterized or reduced in order to make this method suitable for XHPRA. The first step of such work is performed by assessing the suitability of existing HRA methods to support identifying human failure events (HFEs) for human response to flooding hazards. These HFEs are human actions or inactions that are involved in human responses to flooding hazards and could contribute to the loss of a critical function for the plant in the scenario being examined. Here, in this work, decomposition analyses using the cognitive-based Phoenix HRA model are used to identify HFEs. The Phoenix method was found to be suitable for analyzing ex-control room actions as well as identifying specific HFEs and underlying crew failure modes (CFMs). However, the method's suitability for use in ex-control room actions would benefit from expanding the available CFMs to accommodate a larger variety of physical and communication tasks.

42 ENGINEERING↗
DOE OSTI2024

Nanoscopic Imaging of Self-Propelled Ultrasmall Catalytic Nanomotors

Ultrasmall nanomotors (<100 nm) are highly desirable nanomachines for their size-specific advantages over their larger counterparts in applications spanning nanomedicine, directed assembly, active sensing, and environmental remediation. While there are extensive studies on motors larger than 100 nm, the design and understanding of ultrasmall nanomotors have been scant due to the lack of high-resolution imaging of their propelled motions with orientation and shape details resolved. Here, we report the imaging of the propelled motions of catalytically powered ultrasmall nanomotors─hundreds of them─at the nanometer resolution using liquid-phase transmission electron microscopy. These nanomotors are Pt nanoparticles of asymmetric shapes (“tadpoles” and “boomerangs”), which are colloidally synthesized and observed to be fueled by the catalyzed decomposition of NaBH4 in solution. Statistical analysis of the orientation and position trajectories of fueled and unfueled motors, coupled with finite element simulation, reveals that the shape asymmetry alone is sufficient to induce local chemical concentration gradient and self-diffusiophoresis to act against random Brownian motion. Our work elucidates the colloidal design and fundamental forces involved in the motions of ultrasmall nanomotors, which hold promise as active nanomachines to perform tasks in confined environments such as drug delivery and chemical sensing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

IR spectral assignments for the hydrated excess proton in liquid water

The local environmental sensitivity of infrared (IR) spectroscopy to a hydrogen-bonding structure makes it a powerful tool for investigating the structure and dynamics of excess protons in water. Although of significant interest, the line broadening that results from the ultrafast evolution of different solvated proton-water structures makes the assignment of liquid-phase IR spectra a challenging task. In this paper, we apply a normal mode analysis using density functional theory of thousands of proton-water clusters taken from reactive molecular dynamics trajectories of the latest generation multistate empirical valence bond proton model (MS-EVB 3.2). These calculations are used to obtain a vibrational density of states and IR spectral density, which are decomposed on the basis of solvated proton structure and the frequency dependent mode character. Decompositions are presented on the basis of the proton sharing parameter δ, often used to distinguish Eigen and Zundel species, the stretch and bend character of the modes, the mode delocalization, and the vibrational mode symmetry. We find there is a wide distribution of vibrational frequencies spanning 1200-3000 cm -1 for every local proton configuration, with the region 2000-2600 cm -1 being mostly governed by the distorted Eigen-like configuration. Finally, we find a continuous red shift of the special-pair O∙∙∙H + ∙∙∙O stretching frequency, and an increase in the flanking water bending intensity with decreasing δ. Also, we find that the flanking water stretch mode of the Zundel-like species is strongly mixed with the flanking water bend, and the special pair proton oscillation band is strongly coupled with the bend modes of the central H 5 O 2 + moiety.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Nonnegative tensor decomposition with custom clustering for microphase separation of block copolymers

High–dimensional datasets are becoming ubiquitous in many applications and therefore unsupervised tensor methods to interrogate them are needed. Here, we report a new unsupervised machine learning (ML) approach (NTFk) based on nonnegative tensor factorization integrated with a custom k–means clustering. We demonstrate the ability of NTFk to extracting temporal and spatial features of phase separation of copolymers as they are modeled by self–consistent field theory. Microphase separation of block copolymers has been extensively studied both experimentally and theoretically. However, the interpretation of computer simulations and/or experimental data, representing temporal and spatial changes of molecular species concentration is still a challenging task. Thus, extracting the phase diagram from simulations or experimental data as well as the interpretation of data requires discernment of the model/experimental parameters (such as, temperature, concentrations, the number of molecular species and the interaction between species) impact on the microphase separation process. An attractive and unique aspect of the introduced ML method is that it ensures the nonnegativity of the extracted latent features. Nonnegativity is an essential constraint needed to obtain interpretable and sparse latent features that are parts–based representation of the data. The custom clustering in NTFk serves to estimate the number of latent features in the data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Spinning metasurface stack for spectro-polarimetric thermal imaging

Spectro-polarimetric imaging in the long-wave infrared (LWIR) region plays a crucial role in applications from night vision and machine perception to trace gas sensing and thermography. However, the current generation of spectro-polarimetric LWIR imagers suffers from limitations in size, spectral resolution, and field of view (FOV). While meta-optics-based strategies for spectro-polarimetric imaging have been explored in the visible spectrum, their potential for thermal imaging remains largely unexplored. In this work, we introduce an approach for spectro-polarimetric decomposition by combining large-area stacked meta-optical devices with advanced computational imaging algorithms. The co-design of a stack of spinning dispersive metasurfaces along with compressive sensing and dictionary learning algorithms allows simultaneous spectral and polarimetric resolution without the need for bulky filter wheels or interferometers. Our spinning-metasurface-based spectro-polarimetric stack is compact (<10×10×10cm) and robust, and it offers a wide field of view (20.5°). We show that the spectral resolving power of our system substantially enhances performance in machine learning tasks such as material classification, a challenge for conventional panchromatic thermal cameras. Our approach represents a significant advance in the field of thermal imaging for a wide range of applications including heat-assisted detection and ranging (HADAR).

Optics↗
DOE OSTI2025

Tropical Cyclone Super Resolution using conditional diffusion denoising probabilistic model from mesoscale simulation to LES

Accurate modeling of tropical cyclone wind fields is essential for the design, risk assessment, and operational planning of offshore energy infrastructure. While mesoscale simulations are widely used thanks to their computational efficiency, they lack the necessary resolution to capture key features such as wind shear and veer profiles as well as the distribution turbulent kinetic energy (TKE). High-fidelity large-eddy simulation (LES) models on the other hand, can resolve turbulent structures and provide a more accurate representation of the complex wind field, albeit at a higher computational cost. To address this modeling gap, we introduce a two-part generative framework to enhance the resolution and physics-capturing ability of mesoscale simulations. First, a reduced-order model based on Karhunen–Loève (KL) decomposition is used to extract dominant spatial modes from one-dimensional mean wind profiles. A multilayer perceptron (MLP) is trained to map mesoscale mode weights to their LES counterparts, enabling accurate reconstruction of vertical velocity profiles. Second, a conditional Diffusion Denoising Probabilistic Model (DDPM) is developed to super-resolve coarse and low-fidelity mesoscale velocity fields, recovering fine-scale turbulence structures and stress distributions. The framework is evaluated across different tropical cyclone intensity categories defined by the Saffir–Simpson scale and demonstrates strong performance in both interpolation and extrapolation tasks. The generated fields accurately reproduce spatial coherence, stress distributions, and spectral energy characteristics observed in LES data. By bridging the fidelity gap between mesoscale and LES outputs, this approach offers a scalable, data-driven solution for enhancing the representation of tropical cyclone wind fields, enabling more robust offshore energy infrastructure systems design in tropical-cyclone-prone areas.

17 WIND ENERGY↗
DOE OSTI2011

High Efficiency Generation of Hydrogen Fuels Using Solar Thermochemical Splitting of Water

The objective of this work is to identify economically feasible concepts for the production of hydrogen from water using solar energy. The ultimate project objective was to select one or more competitive concepts for pilot-scale demonstration using concentrated solar energy. Results of pilot scale plant performance would be used as foundation for seeking public and private resources for full-scale plant development and testing. Economical success in this venture would afford the public with a renewable and limitless source of energy carrier for use in electric power load-leveling and as a carbon-free transportation fuel. The Solar Hydrogen Generation Research (SHGR) project embraces technologies relevant to hydrogen research under the Office of Hydrogen Fuel Cells and Infrastructure Technology (HFCIT) as well as concentrated solar power under the Office of Solar Energy Technologies (SET). Although the photoelectrochemical work is aligned with HFCIT, some of the technologies in this effort are also consistent with the skills and technologies found in concentrated solar power and photovoltaic technology under the Office of Solar Energy Technologies (SET). Hydrogen production by thermo-chemical water-splitting is a chemical process that accomplishes the decomposition of water into hydrogen and oxygen using only heat or a combination of heat and electrolysis instead of pure electrolysis and meets the goals for hydrogen production using only water and renewable solar energy as feed-stocks. Photoelectrochemical hydrogen production also meets these goals by implementing photo-electrolysis at the surface of a semiconductor in contact with an electrolyte with bias provided by a photovoltaic source. Here, water splitting is a photo-electrolytic process in which hydrogen is produced using only solar photons and water as feed-stocks. The thermochemical hydrogen task engendered formal collaborations among two universities, three national laboratories and two private sector entities. The photoelectrochemical hydrogen task included formal collaborations with three universities and one national laboratory. The formal participants in these two tasks are listed above. Informal collaborations in both projects included one additional university (the University of Nevada, Reno) and two additional national laboratories (Lawrence Livermore National Laboratory and Lawrence Berkeley National Laboratory).

08 HYDROGEN↗
DOE OSTI2022

HiPACE++: A portable, 3D quasi-static particle-in-cell code

Modeling plasma accelerators is a computationally challenging task and the quasi-static particle-in-cell algorithm is a method of choice in a wide range of situations. In this work, we present the first performance-portable, quasi-static, three-dimensional particle-in-cell code HiPACE++. By decomposing all the computation of a 3D domain in successive 2D transverse operations and choosing appropriate memory management, HiPACE++ demonstrates orders-of-magnitude speedups on modern scientific GPUs over CPU-only implementations. The 2D transverse operations are performed on a single GPU, avoiding time-consuming communications. The longitudinal parallelization is done through temporal domain decomposition, enabling near-optimal strong scaling from 1 to 512 GPUs. HiPACE++ is a modular, open-source code enabling efficient modeling of plasma accelerators from laptops to state-of-the-art supercomputers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. Here, to ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

42 ENGINEERING↗
DOE OSTI2017

Contaminant source identification using semi-supervised machine learning

Identification of the original groundwater types present in geochemical mixtures observed in an aquifer is a challenging but very important task. Frequently, some of the groundwater types are related to different infiltration and/or contamination sources associated with various geochemical signatures and origins. The characterization of groundwater mixing processes typically requires solving complex inverse models representing groundwater flow and geochemical transport in the aquifer, where the inverse analysis accounts for available site data. Usually, the model is calibrated against the available data characterizing the spatial and temporal distribution of the observed geochemical types. Numerous different geochemical constituents and processes may need to be simulated in these models which further complicates the analyses. In this paper, we propose a new contaminant source identification approach that performs decomposition of the observation mixtures based on Non-negative Matrix Factorization (NMF) method for Blind Source Separation (BSS), coupled with a custom semi-supervised clustering algorithm. Our methodology, called NMFk, is capable of identifying (a) the unknown number of groundwater types and (b) the original geochemical concentration of the contaminant sources from measured geochemical mixtures with unknown mixing ratios without any additional site information. NMFk is tested on synthetic and real-world site data. Finally, the NMFk algorithm works with geochemical data represented in the form of concentrations, ratios (of two constituents; for example, isotope ratios), and delta notations (standard normalized stable isotope ratios).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Security-Constrained Unit Commitment for Electricity Market: Modeling, Solution Methods, and Future Challenges

This paper summarizes the technical activities of the IEEE Task Force on Solving Large Scale Optimization Problems in Electricity Market and Power System Applications. This Task Force was established by the IEEE Technology and Innovation Subcommittee to first review the state-of-the-art of the security-constrained unit commitment (SCUC) business model, its mathematical formulation, and solution techniques in solving electricity market clearing problems. The Task Force then investigated the emerging challenges of future market clearing problems and presented efforts in building benchmark mathematical and business models.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2012

Fate of phosphorus in Everglades agricultural soils after fertilizer application

Land use changes, agricultural drainage and conventional cultivation of winter vegetables and sugarcane cropping in the Everglades Agricultural Area (EAA) may alter soil conditions and organic matter decomposition and ultimately influence the fate of phosphorus (P). Theses agricultural practices promote soil subsidence, reduce the soil depth to bedrock limestone and increase the potential for incorporation of limestone into the root zone of crops. The incorporation of limestone into surface soil has significantly increased soil pH which in turns causes greater fixation of P fertilizer into unavailable forms for plant growth. Additional P fertilization is thus required to satisfy crop nutrient requirements in plant-available P form. It is important to determine how the mixing of bedrock limestone into soils influences the behavior of P fertilizers after their application. To accomplish this task, P fertilizers were applied to (1) typical cultivated soils and to (2) soils that have never been fertilized or extensively tilled. The changes in P concentrations over time were then compared between the two land uses, with differences being attributable to the impacts of cultivation practices. The P distribution in soil varied between land uses, with sugarcane having more P in inorganic pools while the uncultivated soil had more in organic pools. Water-soluble P concentrations in soil increased with increasing fertilizer application rates for all sampling times and both land uses. However, concentrations in uncultivated soil increased proportionally to P-fertilized soil due to organic P mineralization. At all sampling times, plant-available P concentrations remained higher for uncultivated than sugarcane soil. Lower P concentrations for sugarcane were related to adsorption by mineral components (e.g. limestone). Cultivated soils have higher calcium concentrations resulting from incorporation of bedrock limestone into soil by tillage, which increased pH and fostered sequestration of plant-available P into stable calcium-bound P pools. This greater P retention for sugarcane was reflected in the greater proportion of P in inorganic pools compared to uncultivated soils. Some lands within the EAA, including wetlands and seasonally-flooded prairies, are being reclaimed for water quality purposes. However, long-term effects of fertilization and cropping practices described in this document indicate that direct conversion from active farming, such as from sugarcane production directly to wetlands, may be problematic due to the changes in nutrient dynamics that may occur. The shift directly to wetlands may, in fact, release considerable amounts of P into the Everglades, thwarting the intent of the land use change. The inorganic P component in sugarcane soils may lead to the regeneration of soluble P in frequently flooded land uses such as wetlands. While most of the inorganic P pools are unavailable to sugarcane, the direct conversion of sugarcane soils to wetlands may facilitate P release. Here, reclamation of sugarcane fields for environment uses would benefit by an intermediate step to allow for a short duration of seasonal flooding allowing for P conversion from inorganic to organic forms. Prolonged flooding of organic soils previously used for intensive agriculture is not recommended.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence.

97 MATHEMATICS AND COMPUTING↗