Search NASA⌕ Search

SEARCH · Search NASA

Results for “radiation testing”

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 145 records · Page 8

Offline Maximizing Minimally Invasive Proper Orthogonal Decomposition for Reduced-Order Modeling of S n Radiation Transport

Deterministic solutions to the Sn radiation transport equation can be computationally expensive to calculate. Reduced-order modeling enables efficient approximation of the full-order model (FOM) solution. We propose a novel method for constructing reduced-order models (ROMs) of the S n radiation transport equation, offline maximizing minimally invasive (OMMI) proper orthogonal decomposition (POD). POD uses the method of snapshots to create a reduced-order basis for constructing an ROM. Minimally invasive POD leverages the sweep infrastructure existing in deterministic transport codes to create a POD-based ROM, even when infeasible by traditional methods. Offline maximizing minimally invasive proper orthogonal decomposition (OMMI-POD) extends minimally invasive POD by performing sweeps offline, therefore maximizing the potential speedup. OMMI-POD does so by creating a library of reduced systems from a training set. This library of reduced systems is then interpolated to provide a rapid approximate solution of the S n radiation transport equation. The model is evaluated on a set of test problems, achieving a low error with a 466 times speedup over the FOM. Also presented is a study of the effect of sampling method on the performance of OMMI-POD, specifically comparing naive uniform sampling to the more accurate and computationally expensive greedy sampling.

97 MATHEMATICS AND COMPUTING↗

Discriminator Threshold Study for Scint 1

During electronics testing at NSRL, the fluence/spill is recorded from the QC1 chamber. This chamber, which is a permanent fixture on the NSRL beamline, requires calibration from an external radiation detector that can measure ion flux directly. A 1.0 × 1.0 × 0.5 cm 3 scintillator is used at the testing location to calibrate all NSRL beams for electronic experiments. A calibration factor is derived by comparing the ions observed by the scintillator and QC1 during an exposure of at least 10 5 scintillator counts or total ions.

43 PARTICLE ACCELERATORS↗

Simulating Magnetic Reconnection in ‘Two Ribbon’ Type Solar Flares

Magnetic reconnection is an astrophysical process where neighboring magnetic field lines, facing anti-parallel, are reconfigured. This reconfiguration results in built up magnetic energy being explosively released as it is being converted to plasma kinetic and thermal energies. There are various kinds of simulations used to simulation reconnection; our work begins with Athena++, a magnetohydrodynamic (MHD) simulation code typically used for astrophysical problems, and a reconnection specific code file. The resistive MHD equations are solved with Riemann solvers. There was an initial test run without modifying the code to understand the dynamics of the simulation. We expand on the original reconnection problem file by implementing a radiative cooling term specific to the corona. The radiative cooling is theorized to have an effect on solar coronal plasma and magnetic reconnection dynamics. The cooling term will be tested with various parameters and compared to the case without cooling to study these dynamics. The condensation found in only the with cooling case emphasizes the importance of implementing this feature and will be later tested with a thermal conduction term. We want to determine the parameter regime where non-equilibrium cooling will be important for the reconnection dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗

The impact of cloud microphysics and ice nucleation on Southern Ocean clouds assessed with single-column modeling and instrument simulators

Abstract. Supercooled liquid clouds are common at higher latitudes (especially over the Southern Ocean) and are critical for constraining climate projections. We take advantage of the Macquarie Island Cloud and Radiation Experiment (MICRE) to perform an analysis of observed and simulated cloud processes over the Southern Ocean in a region and season dominated by supercooled liquid clouds. Using a single-column version of the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS), we compare two different cloud microphysical schemes to ground-based observations of cloud, precipitation, and radiation over a 2.5-month period (1 January–17 March 2017). Both schemes are able to reproduce aspects of the cloud and radiation observations during MICRE to within the uncertainty of the data when the thermodynamic profile is prescribed with relaxation. There are differences in water mass and representation of reflectivity between the schemes. A sensitivity study of the cloud microphysics schemes, one a bulk one-moment scheme and the other a two-moment scheme with prediction of mass and number, indicates that several key processes create differences between the schemes. Surface radiative fluxes and total water path are highly sensitive to the formation and fall speed of precipitation. The prediction of hydrometeor number with the two-moment scheme yields a better comparison with observed reflectivity and radiative fluxes, despite predicting higher liquid water contents than observed. With the two-moment scheme, we are also able to test the sensitivity of the results to the input of liquid cloud condensation nuclei (CCN) and ice nuclei (IN). The cloud properties and resulting radiative effects are found to be sensitive to the CCN and IN concentrations. More CCN and IN increase liquid and ice water paths, respectively. Thus, both the dynamic environment and aerosols, integrated through the cloud microphysics, are important for properly representing Southern Ocean cloud radiative effects.

58 GEOSCIENCES↗

Promoting regulatory acceptance of combined ion and neutron irradiation testing of nuclear reactor materials: Modeling and software considerations

As the needs for the nuclear energy industry continue to evolve in the 21st century, timely adoption of new technological solutions acceptable to regulatory agencies is critical. Quantitative prediction of radiation damage in materials and its impact on mechanical properties is a key component of licensing and regulatory decisions regarding nuclear power plants. Accelerated testing methodologies such as combined ion and neutron irradiation data sets are crucial for the development and deployment of new materials and new manufacturing methods (e.g., additive manufacturing). However, regulatory acceptance of accelerated testing methodologies is necessary for their adoption. Further, the present work discusses the fundamental basis for comparing ion- and neutron-induced material microstructures, the theory behind interpreting radiation damage across length and time scales and radiation types, and the codes, standards, and quality assurance concerns surrounding different modeling methods and software. In particular, recommendations are given as to the path forward that will enable national laboratories, academia, and industry to develop the modeling and software basis for regulatory acceptance of the combined use of ion and neutron irradiation for material performance evaluation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Do We Know How to Model Reionization?

I compare the power spectra of the radiation fields from two recent sets of fully-coupled simulations that model cosmic reionization: “Cosmic Reionization On Computers” (CROC) and “Thesan”. While both simulations have similar power spectra of the radiation sources, the power spectra of the photoionization rate are significantly different at the same values of cosmic time or the same values of the mean neutral hydrogen fraction. However, the power spectra of the photoionization rate can be matched at large scales for the two simulations when the matching snapshots are allowed to vary independently. I.e., on large scales, the clustering of the radiation field in two simulations evolves similarly, but the exact timing of this evolution is different in different simulations and is not parameterized by an easily interpretable physical quantity like the mean neutral fraction or the mean free path. On small scales, large differences are present and remain partially unexplained. Both CROC and Thesan use the Variable Eddington Tensor approximation for modeling radiative transfer, but adopt different closure relations (optically thin OTVET versus M1). The role of this key difference is tested by using smaller simulations with a new cosmological simulation code that implements both closure relations in a controlled environment (the same hydro, cooling, and gravity solvers and the star formation recipe). In these controlled tests, both the M1 closure and the OTVET ansatz follow the expected behavior from a simple analytical approximation, demonstrating that the differences in the 2-point function of the radiation field induced by the choice of the Eddington tensor are not dominant.

79 ASTRONOMY AND ASTROPHYSICS↗

Tensorized Interior Radiative Heat Transfer for a Scalable and Calibrated Building Energy Simulator

Building energy simulation is a critical tool for developing and testing advanced control strategies, such as Reinforcement Learning (RL), to provide demand flexibility and affordable energy costs. The recently introduced Smart Buildings Control Suite (sbsim) provides a lightweight, scalable, and data-calibrated simulation environment based on a 2D finite-difference model. However, the initial model primarily focused on conductive and convective heat transfer, neglecting the significant impact of long-wave radiative heat exchange between interior surfaces. This paper presents a significant extension to the sbsim framework by incorporating a physically-grounded model for interior radiative heat transfer. Our primary contribution is the development and integration of a fully tensorized radiative heat transfer module, which preserves the computational efficiency and scalability of the original simulator. This was achieved by developing a pipeline for view factor calculation, including an algorithm to identify directly seeing surfaces within complex floor plans, and formulating the net radiation equations for efficient execution on modern hardware accelerators. We validate the numerical accuracy of our tensorized implementation by comparing its results against a traditional iterative approach, demonstrating identical outcomes. This enhancement increases the physical fidelity of sbsim, enabling more accurate training of RL agents for building energy optimization.

Ham, Sang woo↗

Comparative Mechanical Properties Analysis of Triple Ion-Beam Irradiated and Neutron Irradiated Potential Plasma Facing Components

Abstract Several classes of materials are being proposed for use in fusion reactors including oxide dispersion strengthened (ODS) and reduced activation ferritic-martensitic (RAF/M) steels to withstand the severe and harsh conditions. In this work, the mechanical properties of a Fe-16Cr-4Al-2W-0.3Ti-0.3Y 2 O 3 (K3) (ODS) ferritic steel and a Fe-8.9Cr-1.1W-0.47Mn-0.2V-0.14Ta-0.11C (Eurofer 97) (RAF/M) steel) after triple ion beam irradiation were locally evaluated utilizing in-situ micro-pillar compression tests, and continuous stiffness/quasi-static nanoindentation. No change in mechanical properties was observed in the K3 ODS steel. However, the Eurofer 97 RAF/M steel exhibited radiation-induced effects via increases in yield strength. Micro-pillar techniques were expanded to neutron-irradiated materials via an in-situ testing technique employing lift-out methods on Fe-14Cr-0.9Ti-0.3Mo-0.25Y 2 O 3 (MA957) ODS ferritic steel. Both the non-irradiated and irradiated compressive yield stresses of the MA 957 micro-pillars were in good agreement with bulk yield stress values reported in the literature, suggesting that the lift-out micro-pillar compression testing technique is a promising method. The demonstration of these techniques on ion beam and neutron irradiated ODS steels and ion beam RAF/M steels gives information to inform models of the material degradation during use in a fusion device.

alloys↗

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. Here, we present a spectral decomposition method that allows for corrections to line positions and bound–bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

47 OTHER INSTRUMENTATION↗

Design, fabrication, and testing of diamond axicons for X-ray microscopy applications

This work presents the design, fabrication, and experimental validation of a refractive diamond axicon for X-ray beam shaping. The diamond axicon was developed to overcome the limitations of polymer-based axicons particularly for application in Transmission X-ray Microscopy (TXM) systems, offering superior mechanical strength, thermal stability, and radiation resistance, making it ideal for synchrotron applications. The axicon was fabricated using femtosecond laser ablation and tested at 11 keV under various coherence conditions. Results demonstrated that the axicon efficiently transformed the X-ray beam into a ring-shaped profile with over 80% transmission. Simulations confirmed the experimental findings and highlighted the potential for further improvements. This work paves the way for the use of diamond axicons in next-generation synchrotron facilities, with future efforts focusing on optimizing fabrication and testing the axicon in full TXM systems.

Samadi, Nazanin↗

The effect of ICRH and NBI on tungsten transport in neon edge radiation cooled discharges in TEXTOR

Tungsten is planned to be the plasma-facing material for the main chamber and divertor in future devices like ITER, SPARC, and DTT. To address risks associated with tungsten, R&D is being carried out on various toroidal confinement devices. One particular research question is related to the optimum heating mix for ITER. To investigate the influence of the heating scheme on the release and transport of tungsten, a comparison of neutral beam injection (NBI) and ion cyclotron resonance frequency (ICRF) heating was carried out in TEXTOR tungsten test limiter experiments. The experiments were performed under standard L-mode conditions and in radiative improved-mode operation with neon seeding and boronized walls covering the graphite plasma-facing components. The plasma was heated with hydrogen or deuterium NBI alone or with deuterium NBI in combination with H-minority, ion cyclotron resonance heating. A movable solid tungsten limiter was inserted through a limiter lock system into the edge plasma. The impurity release from this limiter was evaluated from visible spectroscopy. The tungsten concentrations in the plasma core were determined by extreme ultraviolet spectroscopy and bolometry. With deuterium NBI alone, strong central radiation and accumulation of W was observed. This can, however, be avoided by adding ICRF heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Radiation‐Resistant Aluminum Alloy for Space Missions in the Extreme Environment of the Solar System

Future human exploration of the solar system demands advanced materials capable of withstanding extreme environments, particularly exposure to solar energetic particle radiation. Current material selection criteria for space applications prioritize a high strength-to-weight ratio, high corrosion resistance and manufacturability, favoring age-hardenable Al-based alloys. However, conventional precipitation-hardened Al alloys suffer from irradiation-assisted dissolution of strengthening phases at doses as low as 0.2 displacements-per-atom (dpa), undermining their performance. Furthermore, these alloys develop radiation-induced defects, such as dislocation loops and voids, even at low doses. This study presents a novel ultrafine-grained (UFG) Al-based alloy, designed using the crossover alloying concept and strengthened by T-phase precipitates, featuring a chemically-complex structure with 162 atoms in its unit cell composed of Mg 32 (Zn,Al) 49 . It is showed that T-phase precipitates have exceptional radiation tolerance up to 24 dpa. Owing to the nanoscale UFG structure, dislocation loops are suppressed, and voids are only observed beyond 75 dpa. Microtensile tests up to 20 dpa confirm the preservation of mechanical performance under irradiation. The results underline the potential of this alloy as a radiation-resistant, lightweight material for future space applications. Three key strategies enable this performance: (i) stabilization of a UFG microstructure, (ii) T-phase precipitation featuring a highly negative Gibbs free energy and chemically-complex giant unit cell, and (iii) precise process control to prevent grain growth during heat treatment and irradiation.

36 MATERIALS SCIENCE↗

Testing and Characterization to Develop a Mechanistic Explanation for Unsaturated Drift of Fiber Optic Sensors during High-Dose Irradiation

The primary limitation for any optical fiber-based sensor for nuclear reactor applications is radiation-induced attenuation (RIA) of the transmitted and/or reflected signals. Based on several recent studies, RIA is tolerable for some fused silica optical fibers with the proper choice of sensing wavelength and fiber dopants. For extreme temperature applications (> 1000°C), sapphire optical fibers have been proposed; however, recent optical transmission measurements performed on bulk sapphire samples showed prohibitively large RIA. For some sensors, radiation-induced dimensional changes in the fiber materials can also cause significant drift. Moreover, the drift that was observed in numerous experiments performed in the High Flux Isotope Reactor (HFIR), the Advanced Test Reactor, the Massachusetts Institute of Technology Reactor, and other international facilities far exceeded what would be expected based on compaction of fused silica glass. Clearly, additional work is needed to better understand the origins of both RIA and radiation-induced drift in both silica and sapphire optical fiber-based sensors before these sensors can be reliably deployed for nuclear applications. This work evaluated the underlying mechanisms that may be responsible for RIA and drift in silica and sapphire materials. First, detailed characterization was performed on bulk fused silica glass samples that were previously irradiated to different neutron fluences at different temperatures to better understand the structural changes that drive radiation-induced drift in the absence of coating effects that are discussed later. Results show that the non-monotonic compaction that occurs with increasing neutron fluence continues up to fast neutron fluences approaching 10 22 n/cm 2 , which has important implications for physics-based models that may be used to compensate for the sensor drift. Initial Raman spectroscopy and synchrotron x-ray diffraction provide insights into the nature of the structural changes. Next, detailed characterizations were performed on silica fibers with various coatings that were subjected to several different thermal treatments. The hypothesis is that the coatings convert to carbon-rich materials that compact under irradiation, putting a large compressive strain on the fiber. Out-of-pile testing confirms that both polyimide and acrylate fiber coatings convert to glassy carbon (GC) materials when heated under inert conditions, and the degree of order (i.e., graphitization) increases with increasing temperature. The results provide increasingly strong evidence that the combination of polymeric coatings and inert (or vacuum) conditions render fiber optic sensors susceptible to significant radiation-induced drift that would not otherwise exist in uncoated fibers. Finally, transmission electron microscopy was performed on bulk sapphire samples that were irradiated to two neutron fluences at different temperatures to gain insights into the potential mechanisms driving the prohibitive RIA at higher neutron fluences and temperatures. Contrary to previous hypotheses, results show that scattering from radiation-induced voids cannot explain the observed RIA. Similarly, models for scattering losses from dislocation loops also do not agree with the experimental results. Instead, fitting to the experimental data shows that increased absorption from aluminum vacancy centers is the most likely explanation for the the prohibitively large RIA that was observed at high irradiation temperature and dose. In addition, the voids that formed in these single-crystal samples were found to align along the basal plane (a-axis) as opposed to that seen in previous observations of c-axis alignment in polycrystalline samples, which could have important implications for anisotropic swelling and other phenomena that could affect sensor performance at high neutron fluence.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Testing and Characterization to Develop a Mechanistic Explanation for Unsaturated Drift of Fiber Optic Sensors during High-Dose Irradiation

The primary limitation for any optical fiber-based sensor for nuclear reactor applications is radiation-induced attenuation (RIA) of the transmitted and/or reflected signals. Based on several recent studies, RIA is tolerable for some fused silica optical fibers with the proper choice of sensing wavelength and fiber dopants. For extreme temperature applications (> 1000°C), sapphire optical fibers have been proposed; however, recent optical transmission measurements performed on bulk sapphire samples showed prohibitively large RIA. For some sensors, radiation-induced dimensional changes in the fiber materials can also cause significant drift. Moreover, the drift that was observed in numerous experiments performed in the High Flux Isotope Reactor (HFIR), the Advanced Test Reactor, the Massachusetts Institute of Technology Reactor, and other international facilities far exceeded what would be expected based on compaction of fused silica glass. Clearly, additional work is needed to better understand the origins of both RIA and radiation-induced drift in both silica and sapphire optical fiber-based sensors before these sensors can be reliably deployed for nuclear applications. This work evaluated the underlying mechanisms that may be responsible for RIA and drift in silica and sapphire materials. First, detailed characterization was performed on bulk fused silica glass samples that were previously irradiated to different neutron fluences at different temperatures to better understand the structural changes that drive radiation-induced drift in the absence of coating effects that are discussed later. Results show that the non-monotonic compaction that occurs with increasing neutron fluence continues up to fast neutron fluences approaching 10 22 n/cm 2 , which has important implications for physics-based models that may be used to compensate for the sensor drift. Initial Raman spectroscopy and synchrotron x-ray diffraction provide insights into the nature of the structural changes. Next, detailed characterizations were performed on silica fibers with various coatings that were subjected to several different thermal treatments. The hypothesis is that the coatings convert to carbon-rich materials that compact under irradiation, putting a large compressive strain on the fiber. Out-of-pile testing confirms that both polyimide and acrylate fiber coatings convert to glassy carbon (GC) materials when heated under inert conditions, and the degree of order (i.e., graphitization) increases with increasing temperature. The results provide increasingly strong evidence that the combination of polymeric coatings and inert (or vacuum) conditions render fiber optic sensors susceptible to significant radiation-induced drift that would not otherwise exist in uncoated fibers. Finally, transmission electron microscopy was performed on bulk sapphire samples that were irradiated to two neutron fluences at different temperatures to gain insights into the potential mechanisms driving the prohibitive RIA at higher neutron fluences and temperatures. Contrary to previous hypotheses, results show that scattering from radiation-induced voids cannot explain the observed RIA. Similarly, models for scattering losses from dislocation loops also do not agree with the experimental results. Instead, fitting to the experimental data shows that increased absorption from aluminum vacancy centers is the most likely explanation for the the prohibitively large RIA that was observed at high irradiation temperature and dose. In addition, the voids that formed in these single-crystal samples were found to align along the basal plane (a-axis) as opposed to that seen in previous observations of c-axis alignment in polycrystalline samples, which could have important implications for anisotropic swelling and other phenomena that could affect sensor performance at high neutron fluence.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Development and Experimental Optimization of High-Temperature Modeling Tools and Methods for Concentrated Solar Power Particle - Systems

A novel, open-source radiative modeling toolset was developed to extend the functionality of particle-based modeling software (e.g. discrete element method (DEM)) to environmental conditions relevant to concentrated solar power applications. This toolset was optimized for deployment on desktop workstations instead of high-performance computing systems, to render such tools more accessible to the research community. Both particle-based modeling and radiative exchange modeling are computationally expensive and often require specialized programming expertise, making these methods cumbersome to use. Recent developments in DEM software by DCS Computing have greatly reduced these challenges, providing a graphical-user-interface based platform and modeling optimization for desktop workstations, HPCs, and cloud computing. The University of Dayton leveraged the experience of DCS Computing in developing a user-friendly, open-source radiative heat transfer expansion for DEM modeling. The University of Dayton DEM+ radiative modeling toolset was developed using a combination of fundamental experimental measurements, modeling, and simplified flow experiments over a range of temperatures and flow conditions. The toolset provides researchers with access to multiple radiative models including an accelerated Monte-Carlo Ray Tracing (application agnostic, highly computationally expensive), an expanded database of distance-based approximations (application limited, computationally light), and a weighted blending of the two methods capable of achieving over 90% reduction in computation time with equivalent accuracy compared to Monte-Carlo Ray Tracing. Through a graphical user interface, users can customize the radiative models to match their desired accuracy and available computational resources, improving access to particle based modeling for the research community. Ceramic sintered bauxite proppants were used in modeling and experimentally as a baseline. Both the radiative heat transfer and flow properties for particulate systems were investigated at elevated temperatures up to 800 °C. The major accomplishments for this work include a verified, open-source radiative modeling toolset to be distributed amongst the research community and the fabrication of three small-scale test facilities to investigate particle behavior and tune DEM flow properties for operation up to 800 °C. The findings have been shared with the research community via conference modeling workshops, deployment of the tools in DCS Computing Aspherix®, and open-source access to the developed radiative modeling tool. The development of next-generation CSP facilities and thermal energy storage systems based on ceramic particles requires providing access to computationally efficient and accurate modeling tools. Particles will experience a wide range of environments (20-800 °C) and handling conditions (dilute curtains or dense packing), requiring specially designed and optimized equipment. Optimizing solid particle physics models and establishing best-practices for particle modeling in CSP environments will assist researchers with designing optimized equipment, accelerating the deployment of more economically-competitive CSP facilities.

14 SOLAR ENERGY↗

Statistical inference of anomalous thermal transport with uncertainty quantification for interpretive 2D SOL models

The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity $\chi_\perp$ from an interpretive 2D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2D profiles that match 1D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.

Bayesian optimization↗