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At least 829 records · Page 46

Turbulent mixing and removal of ozone within an Amazon rainforest canopy

Simultaneous profiles of turbulence statistics and mean ozone mixing ratio are used to establish a relation between eddy diffusivity and ozone mixing within the Amazon forest. A one–dimensional diffusion model is proposed and used to infer mixing time scales from the eddy diffusivity profiles. Data and model results indicate that during daytime conditions, the upper (lower) half of the canopy is well (partially) mixed most of the time and that most of the vertical extent of the forest can be mixed in less than an hour. During nighttime, most of the canopy is predominantly poorly mixed, except for periods with bursts of intermittent turbulence. Even though turbulence is faster than chemistry during daytime, both processes have comparable time scales in the lower canopy layers during nighttime conditions. Nonchemical loss time scales (associated with stomatal uptake and dry deposition) for the entire forest are comparable to turbulent mixing time scale in the lower canopy during the day and in the entire canopy during the night, indicating a tight coupling between turbulent transport and dry deposition and stomatal uptake processes. Because of the significant time of day and height variability of the turbulent mixing time scale inside the canopy, it is important to take it into account when studying chemical and biophysical processes happening in the forest environment. In conclusion, the method proposed here to estimate turbulent mixing time scales is a reliable alternative to currently used models, especially for situations in which the vertical distribution of the time scale is relevant.

54 ENVIRONMENTAL SCIENCES↗

Investigation of Homogeneous Relaxation Model Parameters and their Implications for Gasoline Injectors

Flash boiling is known to be a common phenomenon for gasoline direct injection (GDI) engine sprays. The Homogeneous Relaxation Model has been adopted in many recent numerical studies for predicting cavitation and flash boiling. The Homogeneous Relaxation Model is assessed in this study. Sensitivity analysis of the model parameters has been documented to infer the driving factors for the flash-boiling predictions. The model parameters have been varied over a range and the differences in predictions of the extent of flashing have been studied. Apart from flashing in the near nozzle regions, mild cavitation is also predicted inside the gasoline injectors. The variation in the predicted time scales through the model parameters for predicting these two different thermodynamic phenomena (cavitation, flash) have been elaborated in this study. Turbulence model effects have also been investigated by comparing predictions from the standard and Re-Normalization Group (RNG) k-ε turbulence models.

33 ADVANCED PROPULSION SYSTEMS↗

Spectroscopy outperforms leaf trait relationships for predicting photosynthetic capacity across different forest types

Leaf trait relationships are widely used to predict ecosystem function in Terrestrial Biosphere Models (TBMs), in which leaf maximum carboxylation capacity (V c,max ), an important trait for modelling photosynthesis, can be inferred from other easier- to-measure traits. However, whether trait-V c,max relationships are robust across different forest types remains unclear. Here we used measurements of leaf traits, including one morphological trait (leaf mass per area), three biochemical traits (leaf water content, area-based leaf nitrogen content, and leaf chlorophyll content), one physiological trait (V c,max ), as well as leaf reflectance spectra, and explored their relationships within and across three contrasting forest types in China. We found weak and forest type-specific relationships between V c,max and the four morphological and biochemical traits (R 2 ≤ 0.15), indicated by significantly changing slopes and intercepts across forest types. In contrast, reflectance spectroscopy effectively collapsed the differences in the trait-V c,max relationships across three forest biomes into a single robust model for V c,max (R 2 = 0.77), and also accurately estimated the four traits (R 2 = 0.75-0.94). Furthermore, these findings challenge the traditional use of empirical trait-V c,max relationships in TBMs for estimating terrestrial plant photosynthesis, but also highlight spectroscopy as an efficient alternative for characterizing V c,max and multi-trait variability, with critical insights into ecosystem modeling and functional trait ecology.

54 ENVIRONMENTAL SCIENCES↗

A comparison of histopathology imaging comprehension algorithms based on multiple instance learning

Whole slide imaging (WSI), also called digital virtual microscopy, is a new imaging modality. It allows for the application of AI and machine learning methods to cancer pathology to help establish a means for the automatic diagnosis of cancer cases. However, designing machine-learning models for WSI is computationally challenging due to its required ultra-high resolution. The current state-of-the-art models use multiple instance learning (MIL). MIL is a weakly-supervised learning method in which the model uses an array of inferences from many smaller instances to make a final classification about the entire set. In the context of WSI, researchers divide the ultra-high-resolution image into many patches. The model then classifies the slide based on an array of inferences from the patches. Among several ways of making the final classification, attention-based mechanisms have resulted in superb accuracy scores. The Transformer, one attention-based algorithm, has reported substantial improvements for WSI comprehension tasks. In this project, we studied and compared several WSI comprehension algorithms. We used the following three datasets: CAMELYON16+17, TCGALung, and TCGA-Kidney. We found that attention-based MIL algorithms performed better than standard MIL algorithms for classifying WSI images, achieving a higher mean accuracy and AUC. However, none of the attention-based algorithms performed significantly better than the others, reporting accuracy scores that varied widely. Presumably, it is due to the limited availability of training samples in the data corpus. Since it is not easy to increase the samples from human subjects, some machine learning techniques like transfer learning could help mitigate this issue.

Saunders, Adam↗

Automated Bayesian high-throughput estimation of plasma temperature and density from emission spectroscopy

Here, this paper introduces a novel approach for automated high-throughput estimation of plasma temperature and density using atomic emission spectroscopy, integrating Bayesian inference with sophisticated physical models. We provide an in-depth examination of Bayesian methods applied to the complexities of plasma diagnostics, supported by a robust framework of physical and measurement models. Our methodology is demonstrated using experimental observations in the field of magneto-inertial fusion, focusing on individual and sequential shot analyses of the Plasma Liner Experiment at LANL. The results demonstrate the effectiveness of our approach in enhancing the accuracy and reliability of plasma parameter estimation and in using the analysis to reveal the deep hidden structure in the data. This study not only offers a new perspective of plasma analysis but also paves the way for further research and applications in nuclear instrumentation and related domains.

Bayesian inference↗

Understanding the fusion yield dependencies in OMEGA DT-layered implosion experiments using a physics-based statistical mapping model

Improving the performance of inertial confinement fusion implosions requires physics models that can accurately predict the response to changes in the experimental inputs. Good predictive capability has been demonstrated for the fusion yield using a statistical mapping of simulated outcomes to experimental data [Gopalaswamy et al., Nature 565(771), 581–586 (2019)]. In this paper, a physics-based statistical mapping approach is used to extract and quantify all the major sources of degradation of fusion yield for direct-drive implosions on the OMEGA laser. Here, the yield is found to be dependent on the age of the deuterium tritium fill, the ℓ = 1 asymmetry in the implosion core, the laser beam-to-target size ratio, and parameters related to the hydrodynamic stability. A controlled set of experiments were carried out where only the target fill age was varied while keeping all other parameters constant. The measurements were found to be in excellent agreement with the fill age dependency inferred using the mapping model. In addition, a new implosion design was created, guided by the statistical mapping model by optimizing the trade-offs between increased laser energy coupling at larger target size and the degradations caused by the laser beam-to-target size ratio and hydrodynamic instabilities. When experimentally performed, an increased fusion yield was demonstrated in targets with larger diameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Landmark-embedded Gaussian process with applications for functional data modeling

In practice, we often need to infer the value of a target variable from functional observation data. A challenge in this task is that the relationship between the functional data and the target variable is very complex: the target variable not only influences the shape but also the location of the functional data. In addition, due to the uncertainties in the environment, the relationship is probabilistic, that is, for a given fixed target variable value, we still see variations in the shape and location of the functional data. To address this challenge, we present a landmark-embedded Gaussian process model that describes the relationship between the functional data and the target variable. A unique feature of the model is that landmark information is embedded in the Gaussian process model so that both the shape and location information of the functional data are considered simultaneously in a unified manner. Gibbs-Metropolis-Hasting algorithm is used for model parameters estimation and target variable inference. The performance of the proposed framework is evaluated by extensive numerical studies and a case study of nano-sensor calibration.

42 ENGINEERING↗

Wassersplines for Neural Vector Field-Controlled Animation

Much of computer-generated animation is created by manipulating meshes with rigs. While this approach works well for animating articulated objects like animals, it has limited flexibility for animating less structured free-form objects. Here we introduce Wassersplines, a novel trajectory inference method for animating unstructured densities based on recent advances in continuous normalizing flows and optimal transport. The key idea is to train a neurally-parameterized velocity field that represents the motion between keyframes. Trajectories are then computed by advecting keyframes through the velocity field. We solve an additional Wasserstein barycenter interpolation problem to guarantee strict adherence to keyframes. Our tool can stylize trajectories through a variety of PDE-based regularizers to create different visual effects. We demonstrate our tool on various keyframe interpolation problems to produce temporally-coherent animations without meshing or rigging.

97 MATHEMATICS AND COMPUTING↗

Conditional H I Mass Functions and the H I -to-halo Mass Relation in the Local Universe

We present a new H I mass estimator that relates log 10 (M HI /M * ) to a linear combination of four galaxy properties: stellar surface mass density, color index u - r, stellar mass, and concentration index, with the scatter of individual galaxies around the mean H I mass modeled with a Gaussian distribution function. We calibrate the estimator using the xGASS sample, including both H I detection and nondetection, and constrain the model parameters through Bayesian inferences. Tests with mock catalogs demonstrate that our estimator provides unbiased H I masses for optical samples like SDSS. We apply our estimator to the SDSS spectroscopic sample to estimate the H I mass function (HIMF) of local galaxies, as well as the conditional H I mass function in galaxy groups and the H I –halo mass relation. Our HIMF agrees with the ALFALFA measurements at M HI ≳ 5 × 10 9 M ⊙ , but with higher amplitude and a steeper slope at lower masses. We show that this discrepancy is caused primarily by the cosmic variance, which is corrected for the SDSS sample but not for ALFALFA. The total CHIMFs for all halo masses can be described by a single Schechter function, while those of central galaxies show a double-Gaussian profile. The total H I mass in a group increases monotonically with halo mass, but for central galaxies, the H I mass shows weak dependence on halo mass when M h ≳ 10 12 M ⊙ . The observed H I –halo mass relation is not reproduced by current hydrodynamic simulations and semianalytic models of galaxy formation.

79 ASTRONOMY AND ASTROPHYSICS↗

The solar cycle variation of ozone in the stratosphere inferred from Nimbus 7 and NOAA 11 satellites

The combined Nimbus 7 solar backscattered ultraviolet (SBUV) and NOAA 11 SBUV/2 ozone data, covering a period of more than a solar cycle (about 15 years), are used to study the UV response of ozone in the stratosphere. The study shows that about 2% change in total column ozone and about 5-7% change in ozone mixing ratio in the upper stratosphere (0.7 to 2 hPa) may be attributed to the change in the solar UV flux over a solar cycle. In the upper stratosphere, where photochemical processes are expected to play a major role, the measured solar cycle variation of ozone is significantly larger than inferred either from the photochemical models or from the ozone response to the 27-day solar UV modulation. For example, the observed solar cycle related change in ozone mixing ratio at 2 hPa is about 1% for 1% change in the solar UV flux near 200 nm. The inferred change in ozone from either the photochemical models or from the 27-day ozone-UV response is about a factor of 2-3 lower than this value.

Chandra, S.↗

Constraints on hydrothermal heat flux through the oceanic lithosphere from global heat flow

A significant discrepancy exists between the heat flow measured at the seafloor and the higher values predicted by thermal models of the cooling lithosphere. This discrepancy is generally interpreted as indicating that the upper oceanic crust is cooled significantly by hydrothermal circulation. The magnitude of this heat flow discrepancy is the primary datum used to estimate the volume of hydrothermal flow, and the variation in the discrepancy with lithospheric age is the primary constraint on how the hydrothermal flux is divided between near-ridge and off-ridge environments. The resulting estimates are important for investigation of both the thermal structure of the lithosphere and the chemistry of the oceans. We reevaluate the magnitude and age variation of the discrepancy using a global heat flow data set substantially larger than in earlier studies, and the GDHI (Global Depth and Heat Flow) model that better predicts the heat flow. We estimate that of the predicted global oceanic heat flux of 32 x 10(exp 12) W, 34% (11 x 10(exp 12) W) occurs by hydrothermal flow. Approximately 30% of the hydrothermal heat flux occurs in crust younger than 1 Ma, so the majority of this flux is off-ridge. These hydrothermal heat flux estimates are upper bounds, because heat flow measurements require sediment at the site and so are made preferentially at topographic lows, where heat flow may be depressed. Because the water temperature for the near-ridge flow exceeds that for the off-ridge flow, the near-ridge water flow will be even a smaller fraction of the total water flow. As a result, in estimating fluxes from geochemical data, use of the high water temperatures appropriate for the ridge axis may significantly overestimate the heat flux for an assumed water flux or underestimate the water flux for an assumed heat flux. Our data also permit improved estimates of the 'sealing' age, defined as the age where the observed heat flow approximately equals that predicted, suggesting that hydrothermal heat transfer has largely ceased. Although earlier studies suggested major differences in sealing ages for different ocean basins, we find that the sealing ages for the Atlantic, Pacific, and Indian oceans are similar and consistent with the sealing age for the entire data set, 65 +/- 10 Ma. The previous inference of a young (approximately 20 Ma) sealing age for the Pacific appears to have biased downward several previous estimates of the global hydrothermal flux. The heat flow data also provide indirect evidence for the mechanism by which the hydrothermal heat flux becomes small, which has often been ascribed to isolation of the igneous crust from seawater due to the hydraulic conductivity of the intervening sediment. We find, however, that even the least sedimented sites show the systematic increase of the ratio of observed to predicted heat flow with age, although the more sedimented sites have a younger sealing age. Moreover, the heat flow discrepancy persists at heavily sedimented sites until approximately 50 Ma. It thus appears that approximately 100-200 m of sediment is neither necessary nor sufficient to stop hydrothermal heat transfer. We therefore conclude that the age of the crust is the primary control on the fraction of heat transported by hydrothermal flow and that sediment thickness has a lesser effect. This inference is consistent with models in which hydrothermal flow decreases with age due to reduced crustal porosity and hence permeability.

Stein, Carol A.↗

AI-Based Analytics and Energy Modeling Framework for Characterizing Urban Energy Systems

Developing location-specific district energy models is essential for understanding energy patterns and supporting efficient management and planning decisions. However, accurately characterizing these models remains challenging due to gaps in building characteristics and labor-intensive traditional modeling workflows. To address these challenges, we develop an AI-based framework that integrates top-down and bottom-up building energy data to automate urban energy model characterization. The framework trains multimodal deep learning models using heterogeneous ResStockTM datasets to infer missing building characteristics from varying levels of known information and generate simulation-ready inputs for district-scale energy modeling. It also employs a conditioning-based injection approach to generate ”what-if” scenarios, enabling users to explore retrofit, efficiency, and technology-upgrade pathways. Integrated within URBANoptTM, a bottom-up district energy modeling platform for simulating co-located buildings, the framework infers detailed building-level inputs required for bottom-up simulations. Both localized and generalized AI models are developed to learn relationships across categorical, numerical, and time-series data, enabling reconstruction of missing attributes and generation of targeted upgrade scenarios. We demonstrate this methodology on a residential neighborhood in Baltimore, MD, assessing internal consistency against ResStock reference data and URBANopt simulation, and comparing selected attributes against real-world building characteristics. Results show strong overall predictive accuracy in data completion and scenario generation, with localized and generalized models offering complementary trade-offs between precision and scalability. Overall, our automated framework streamlines energy modeling and provides a reliable framework for urban building energy characterization.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

The mass distribution of quasars in optical time-domain surveys

The determination of supermassive black hole (SMBH) masses is the key to understanding the host galaxy build-up and the SMBH mass assembly histories. The SMBH masses of non-local quasars are frequently estimated via the single-epoch virial black-hole mass estimators, which may suffer from significant biases. Here we demonstrate a new approach to infer the mass distribution of SMBHs in quasars by modelling quasar ultraviolet /optical variability. Here, our inferred black hole masses are systematically smaller than the virial ones by 0.3–0.6 dex; the ∼0.3 dex offsets are roughly consistent with the expected biases of the virial black-hole mass estimators. In the upcoming time-domain astronomy era, our methodology can be used to constrain the cosmic evolution of quasar mass distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

Instantiation of HCML Demonstrating Bayesian Predictive Modeling for Attentional Control

The research team developed models of Attentional Control (AC) that are unique to existing modeling approaches in the literature. The goal was to enable the research team to (1) make predictions about AC and human performance in real-world scenarios and (2) to make predictions about individual characteristics based on human data. First, the team developed a proof-of-concept approach for representing an experimental design and human subjects data in a Bayesian model, then demonstrated an ability to draw inferences about conditions of interest relevant to real-world scenarios. Ultimately, this effort was successful, and we were able to make reasonable (meaning supported by behavioral data) inferences about conditions of interest to develop a risk model for AC (where risk is defined as a mismatch between AC and attentional demand). The team additionally defined a path forward for a human-constrained machine learning (HCML) approach to make predictions about an individual's state based on performance data. The effort represents a successful first step in both modeling efforts and serves as a basis for future work activities. Numerous opportunities for future work have been defined.

97 MATHEMATICS AND COMPUTING↗

More rain compensation results

To reduce the impact of rain-induced attenuation in the 20/30 GHz band, the attenuation at a specified signal frequency must be estimated and extrapolated forward in time on the basis of a noisy beacon measurement. Several studies have used model based procedures for solving this problem in statistical inference. Perhaps the most widely used model-based paradigm leads to the Kalman filter and its lineal variants. In this formulation, the dynamic features of the attenuation are represented by a state process (x(sub t)). The observation process (y(sub t)) is derived from beacon measurements. Some ideas relating to the signal processing problems related to uplink power control are presented. It is shown that some easily implemented algorithms hold promise for use in estimating rain induced fades. The algorithms were applied to actual data generated at the Virginia Polytechnic Institute and State University (VPI) test facility. Because only one such event was studied, it is not clear that the algorithms will have the same effectiveness when a wide range of events are studied.

Sworder, D. D.↗

Advanced Analytics Studies Applied to US Department of Veterans Affairs' Corporate Data Warehouse (Initial Draft)

In this report, we describe our experience of applying several advanced analytics algorithms to the US Department of Veterans Affairs’ (VA’s) Corporate Data Warehouse (CDW) electronic health records datasets during FY2017-18. While various algorithms were applied to the CDW data, the main goal of this effort was to provide useful insights into the operational aspects (as opposed to the purely clinical aspect) of this specific implementation. Since there are not many reports in the public literature on advanced analytics applied to this data, this report provides unique insight in this regard. We focused on two machine learning (ML) applications: (1) clinical pathway inference (patterns dominating clinical pathways applied to a male dataset of Stable Ischemic Heart Disease patients as use case) and (2) medical-concept representation learning’s capability to inform and refine cohort membership based on probable patient outcomes. During our study on clinical pathway inference, we used two main modeling techniques: (a) topic probabilistic modeling (latent Dirichlet allocation [LDA]) and (b) feature imbedding. We observed that the applicability of LDA to the pathway inference remains in question. LDA provides results that are intuitive and easy for humans to comprehend; however, when applied to the pathway inference, it also generates pathway patterns that consist of a few dominant pathway components. In addition, LDA provides no information regarding the relationships among components in the same pathway. The outputs of LDA are also found to categorize patients based on their trace data of clinical procedures. However, the results suggest that LDA is biased toward statistically dominant components. This makes it particularly hard to discriminate pathway subbranches. To address the issue, we designed a new pathway inference methodology that integrates temporal ordering of pathway components into LDA results, as existing feature embedding tools such as word2vec are not readily applicable to our task. In addition, we developed our own feature embedding tool customized for patient traces. We conclude this study by suggesting two approaches to use embedding representation of a component into LDA and briefly list our lessons learned and recommendations for future work. For our study on medical-concept representation learning ability to inform and refine cohort membership based on probable patient outcomes, during our empirical evaluation we compared methods from medical-concept learning to standard one of a kind (one-of-K) encoding to evaluate the change in effectiveness as done in Choi, Schuetz, Stewart, and Sun (2016). We performed two primary empirical evaluations. The first evaluation was on a curated collection of 60,000 patients with no more than 1 year of medical history included. The second was a collection of patients with no restriction to the amount of medical history included. The hypothesis across both evaluations is that representation learning is broadly useful independent of downstream processing models; thus, for each experiment, we trained three models—a logistic regression model, a two-layer neural network model, and a nearest-neighbor model—and then averaged the results. Each model was trained using fivefold cross validation. We provided evidence that medical-representation learning improves predictions of the primary diagnosis category of a short patient history through 12 experiments. In addition, we provided evidence that medical-representation learning fails to improve prediction of the primary diagnosis category of an arbitrarily long patient history through 12 experiments. We conclude this study with a brief list of our lessons learned and recommendations for future work. We conclude the report with a discussion of recent technology trends as they relate to our artificial intelligence and, more specifically, to our ML research and approaches as described previously.

97 MATHEMATICS AND COMPUTING↗

Comparison of ANN (MLP), ANFIS, SVM, and RF models for the online classification of heating value of burning municipal solid waste in circulating fluidized bed incinerators

Highlights: • A rapid, cost-effective, and comparative methodology was proposed to evaluate the HVs of burning MSW online. • Models ranked in descending order of performance are ANFIS, RF, SVM, MLP. • A well trained model is capable of characterizing the variation trend of HVs accurately. - Abstract: The heating values, particularly lower heating values of burning municipal solid waste are critically important parameters in operating circulating fluidized bed incineration systems. However, the heating values change widely and frequently, while there is no reliable real-time instrument to measure heating values in the process of incinerating municipal solid waste. A rapid, cost-effective, and comparative methodology was proposed to evaluate the heating values of burning MSW online based on prior knowledge, expert experience, and data-mining techniques. First, selecting the input variables of the model by analyzing the operational mechanism of circulating fluidized bed incinerators, and the corresponding heating value was classified into one of nine fuzzy expressions according to expert advice. Development of prediction models by employing four different nonlinear models was undertaken, including a multilayer perceptron neural network, a support vector machine, an adaptive neuro-fuzzy inference system, and a random forest; a series of optimization schemes were implemented simultaneously in order to improve the performance of each model. Finally, a comprehensive comparison study was carried out to evaluate the performance of the models. Results indicate that the adaptive neuro-fuzzy inference system model outperforms the other three models, with the random forest model performing second-best, and the multilayer perceptron model performing at the worst level. A model with sufficient accuracy would contribute adequately to the control of circulating fluidized bed incinerator operation and provide reliable heating value signals for an automatic combustion control system.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Radiative Losses in the Chromosphere During A C-Class Flare

Context. Solar flares release an enormous amount of energy (~10(exp 32) erg) into the corona. A substantial fraction of this energy is transported to the lower atmosphere, which results in chromospheric heating. The mechanisms that transport energy to the lower solar atmosphere during a flare are still not fully understood. Aims. We aim to estimate the temporal evolution of the radiative losses in the chromosphere at the footpoints of a C-class flare, in order to set observational constraints on the electron beam parameters of a RADYN flare simulation. Methods. We estimated the radiative losses from hydrogen, and singly ionized Ca and Mg using semiempirical model atmospheres, which were inferred from a multiline inversion of observed Stokes profiles obtained with the CRISP and CHROMIS instruments on the Swedish 1-m Solar Telescope. The radiative losses were computed taking into account the effect of partial redistribution and non-local thermodynamic equilibrium. To estimate the integrated radiative losses in the chromosphere, the net cooling rates were integrated between the temperature minimum and the height where the temperature reaches 10 kK. We also compared our time series of radiative losses with those from the RADYN flare simulations. Results. We obtained a high spatial-resolution map of integrated radiative losses around the flare peak time. The stratification of the net cooling rate suggests that the Ca IR triplet lines are responsible for most of the radiative losses in the flaring atmosphere. During the flare peak time, the contribution from Ca II H and K and Mgii h and k lines are strong and comparable to the Ca IR triplet (~32kW m(exp -2)). Since our flare is a relatively weak event, the chromosphere is not heated above 11 kK, which in turn yields a subdued Lyα contribution (~7kW m(exp -2)) in the selected limits of the chromosphere. The temporal evolution of total integrated radiative losses exhibits sharply rising losses (0.4kW m(exp -2) (s(exp -1)) and a relatively slow decay (0.23kW m(exp -2) s(exp -1)). The maximum value of total radiative losses is reached around the flare peak time and can go up to 175kWm􀀀2 for a single pixel located at footpoint. After a small parameter study, we find the best model-data consistency in terms of the amplitude of radiative losses and the overall atmospheric structure with a RADYN flare simulation in the injected energy flux of 5 × 10(exp 10) erg s(exp -1) cm(exp -2).

Chromosphere↗