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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Sensitivity Study of LIFE Chamber Dynamics (Final Report)

The objective of this research is to investigate the turbulent flow state in a prototype of the LIFE fusion chamber, over many fusion cycles, using high-fidelity three-dimensional computational modeling. A fusion cycle duration is defined here as the time between laser shots (that induce fusion of the fuel stored in the capsule). The main problem of interest discussed in this report is the study of the sensitivity of the flow conditions in the fusion chamber to the radiation parameters used in the BUCKY code (Univ. Wisconsin Madison) that give the initial conditions for the present simulations. Of particular interest is the asymptotic “nth-state” cycle in the model fusion chamber and vacuum vessel assembly. The asymptotic (but unsteady) state was reached by advancing in time an initial value problem with estimated initial data that are thought to be representative of the fusion chamber state (in the mean). These conditions were provided to the Illinois team by LLNL. Many details of the flow solver, strategy and other auxiliary information can be found in a previous report entitled “CFD Simulation in Support of the Dynamic Chamber Systems Strategic Initiative.” Here, several quantities were investigated in detail. First, the global balance of mass in the fusion chamber and vacuum vessel. Second, the state of the density field inside the chamber: turbulence and density spectra, mean and fluctuation of the density. Third, to develop an understanding of the effect of forced recirculation imposed on the chamber-vacuum vessel ensemble, to understand the behavior and distribution of the capsule debris throughout the domain and instantaneous fluxes through the numerous ports and openings of the chamber. Fourth, and finally, to elucidate transport properties near the relatively cold walls of the chamber that might affect the chemistry of the complex fluid mixture from calculated temperature condition on the walls. These four questions have been investigated with different degrees of fidelity (as detailed below) assuming as few simplifications as possible while maintaining many elements of the complex geometry of the fusion chamber. Finally, the simulations do not include the effects of radiation explicitly, which is expected to be critical during the instants immediately after a laser pulse and fusion ignition, and instead a rational “handshake” procedure was developed to derive initial conditions consistent with those produced by BUCKY under different assumptions.

42 ENGINEERING↗
DOE OSTI2013

Phase shift method to estimate solids circulation rate in circulating fluidized beds

While solids circulation rate is a critical design and control parameter in circulating fluidized bed (CFB) reactor systems, there are no available techniques to measure it directly at conditions of industrial interest. Cold flow tests have been conducted at NETL in an industrial scale CFB unit where the solids flow has been the topic of research in order to develop an independent method which could be applied to CFBs operating under the erosive and corrosive high temperatures and pressures of a coal fired boiler or gasifier. The dynamic responses of the CFB loop to modest modulated aeration flows in the return leg or standpipe were imposed to establish a periodic response in the unit without causing upset in the process performance. The resulting periodic behavior could then be analyzed with a dynamic model and the average solids circulation rate could be established. This method was applied to the CFB unit operated under a wide range of operating conditions including fast fluidization, core annular flow, dilute and dense transport, and dense suspension upflow. In addition, the system was operated in both low and high total solids inventories to explore the influence of inventory limiting cases on the estimated results. The technique was able to estimate the solids circulation rate for all transport circulating fluidized beds when operating above upper transport velocity, U{sub tr2}. For CFB operating in the fast fluidized bed regime (i.e., U{sub g}< U{sub tr2}), the phase shift technique was not successful. The riser pressure drop becomes independent of the solids circulation rate and the mass flow rate out of the riser does not show modulated behavior even when the riser pressure drop does.

42 ENGINEERING↗
DOE OSTI2016

The MOSDEF Survey: Dynamical and baryonic masses and kinematic structures of star-forming galaxies AT 1.4 ≤ z ≤ 2.6

We present Hα gas kinematics for 178 star-forming galaxies at z∼2 from the MOSFIRE Deep Evolution Field survey. We have developed models to interpret the kinematic measurements from fixed-angle multi-object spectroscopy, using structural parameters derived from Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey Hubble Space Telescope/F160W imaging. For 35 galaxies, we measure resolved rotation with a median of (V/σ{sub V,0}){sub R{sub E}} = 2.1. We derive dynamical masses from the kinematics and sizes and compare them to baryonic masses, with gas masses estimated from dust-corrected Hα star formation rates (SFRs) and the Kennicutt–Schmidt relation. When assuming that galaxies with and without observed rotation have the same median (V/σ{sub V,0}){sub R{sub E}}, we find good agreement between the dynamical and baryonic masses, with a scatter of σ{sub rms} = 0.34 dex and a median offset of Δlog{sub 10} M = 0.04 dex. This comparison implies a low dark matter fraction (8% within an effective radius) for a Chabrier initial mass function (IMF), and disfavors a Salpeter IMF. Moreover, the requirement that M{sub dyn}/M{sub baryon} should be independent of inclination yields a median value of (V/σ{sub V,0}){sub R{sub E}} = 2.1 for galaxies without observed rotation. If, instead, we treat the galaxies without detected rotation as early-type galaxies, the masses are also in reasonable agreement (Δlog{sub 10} M = −0.07 dex, σ{sub rms} = 0.37 dex). The inclusion of gas masses is critical in this comparison; if gas masses are excluded, there is an increasing trend of M{sub dyn}/M{sub ∗} with higher specific SFR (SSFR). Furthermore, we find indications that V/σ decreases with increasing Hα SSFR for our full sample, which may reflect disk settling. We also study the Tully–Fisher relation and find that at fixed stellar mass S{sub 0.5} = (0.5V{sub 2.2}{sup 2}+σ{sub V,0}{sup 2}){sup 1/2} was higher at earlier times. At fixed baryonic mass, we observe the opposite trend. Finally, the baryonic and dynamical masses of the active galactic nuclei in our sample are also in excellent agreement, suggesting that the kinematics trace the host galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

MULTI-DIMENSIONAL MODELING OF THE CFR ENGINE FOR THE INVESTIGATION OF SI NATURAL GAS COMBUSTION AND CONTROLLED END-GAS AUTOIGNITION

Engine knock and misfire are barriers to pathways leading to high-efficiency Spark-Ignited (SI) Natural Gas engines. The general tendency to knock is highly dependent on engine operating conditions and the fuel reactivity. The problem is further complicated by low emission limits and the wide range of chemical reactivity in pipeline quality natural gas. Depending on the region and the source of the natural gas, its reactivity, described by its methane number (analogous to the octane number for liquid SI fuels) can span from 65 - 95. In order to realize diesel-like efficiencies, SI natural gas engines must be designed to operate at high BMEP near knock limits over a wide range of fuel reactivity. This requires a deep understanding regarding the combustion-engine interactions pertaining to flame propagation and end-gas autoignition (EGAI). However, EGAI, if controlled, provides an opportunity to increase SI natural gas engine efficiency by increasing combustion rate and the total burned fuel, mitigating the effects of the slow flame speeds of natural gas fuels which generally reduce BMEP and increase unburned hydrocarbon emissions. For this reason, in order to study EGAI phenomenon, the present work highlights multi-dimensional computational fluid dynamics (CFD) models of the Cooperative Fuel Research (CFR) engine. The CFR engine models are used to investigate fuel-engine interactions that lead to EGAI with natural gas, including effects of fuel reactivity, engine operating parameters, and exhaust gas recirculation (EGR). A Three-Pressure Analysis, performed with GT-Power, was used to estimate initial and boundary conditions for the three-dimensional CFD model. CONVERGE CFD v2.4 was used for the three-dimensional CFD modeling where the level set G-Equation model and SAGE detailed chemical kinetics solver were used. An assessment of the different modeling approaches is also provided to evaluate their limitations, advantages and disadvantages, and for which situations they are most applicable. Model validation was performed with experimental data taken with a CFR engine over varying compression ratio, CA50, EGR fraction, and IMEP and shows good agreement in Peak Cylinder Pressure (PCP), PCP crank angle, and the location of the 10%, 50%, and 90% mass fraction burned (CA10, CA50, and CA90, respectively). The models can predict the onset crank angle and pressure rise rate for light, medium, and heavy EGAI under a variety of fuel reactivities and engine operating conditions.

Bestel, Diego↗
DOE OSTI2014

SU-E-QI-03: Compartment Modeling of Dynamic Brain PET - The Effect of Scatter and Random Corrections On Parameter Errors

Purpose: To investigate the effects of corrections for random and scattered coincidences on kinetic parameters in brain tumors, by using ten Monte Carlo (MC) simulated dynamic FLT-PET brain scans. Methods: The GATE MC software was used to simulate ten repetitions of a 1 hour dynamic FLT-PET scan of a voxelized head phantom. The phantom comprised six normal head tissues, plus inserted regions for blood and tumor tissue. Different time-activity-curves (TACs) for all eight tissue types were used in the simulation and were generated in Matlab using a 2-tissue model with preset parameter values (K1,k2,k3,k4,Va,Ki). The PET data was reconstructed into 28 frames by both ordered-subset expectation maximization (OSEM) and 3D filtered back-projection (3DFBP). Five image sets were reconstructed, all with normalization and different additional corrections C (A=attenuation, R=random, S=scatter): Trues (AC), trues+randoms (ARC), trues+scatters (ASC), total counts (ARSC) and total counts (AC). Corrections for randoms and scatters were based on real random and scatter sinograms that were back-projected, blurred and then forward projected and scaled to match the real counts. Weighted non-linearleast- squares fitting of TACs from the blood and tumor regions was used to obtain parameter estimates. Results: The bias was not significantly different for trues (AC), trues+randoms (ARC), trues+scatters (ASC) and total counts (ARSC) for either 3DFBP or OSEM (p<0.05). Total counts with only AC stood out however, with an up to 160% larger bias. In general, there was no difference in bias found between 3DFBP and OSEM, except in parameter Va and Ki. Conclusion: According to our results, the methodology of correcting the PET data for randoms and scatters performed well for the dynamic images where frames have much lower counts compared to static images. Generally, no bias was introduced by the corrections and their importance was emphasized since omitting them increased bias extensively.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Modelling dislocation-graphene interactions in a BCC Fe matrix by molecular dynamics simulations and gradient plasticity theory

We report graphene nanosheets (GNS) can enhance the strength and ductility of metal-based composites as they can obstruct the propagation of dislocations. The present article employs Molecular Dynamics (MD) simulations to investigate dislocation-GNS interaction mechanisms and possible influencing factors, including the number of GNS layers, the thickness of the metallic amorphous layer and the C - C bond strength. The results indicated that the shear strength of the metal/GNS interface and the bending stiffness of GNS determined the ability of GNS to block dislocation transmission. A physically based phenomenological parameter that can capture such dislocation-GNS interactions is the mechanical interface energy that has been put forth within gradient plasticity. By fitting the theoretical expressions to the simulation data, it was possible to obtain estimates for the mechanical interface energy for the GNS. It was found that increasing the GNS layers and adding an amorphous layer resulted in a strengthening in the stress–strain response and increased the value of this interfacial parameter. This indicates that the mechanical interfacial energy can be a unified measure for capturing and tuning the strength of various interfaces such as grain boundaries, GNS, amorphous-crystalline interface and bimetal interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. Here, a sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Impact of crowding on the diversity of expanding populations

Crowding effects critically impact the self-organization of densely packed cellular assemblies, such as biofilms, solid tumors, and developing tissues. When cells grow and divide, they push each other apart, remodeling the structure and extent of the population’s range. Recent work has shown that crowding has a strong impact on the strength of natural selection. However, the impact of crowding on neutral processes, which controls the fate of new variants as long as they are rare, remains unclear. Here, we quantify the genetic diversity of expanding microbial colonies and uncover signatures of crowding in the site frequency spectrum. By combining Luria–Delbrück fluctuation tests, lineage tracing in a novel microfluidic incubator, cell-based simulations, and theoretical modeling, we find that the majority of mutations arise behind the expanding frontier, giving rise to clones that are mechanically “pushed out” of the growing region by the proliferating cells in front. These excluded-volume interactions result in a clone-size distribution that solely depends on where the mutation first arose relative to the front and is characterized by a simple power law for low-frequency clones. Our model predicts that the distribution depends on a single parameter—the characteristic growth layer thickness—and hence allows estimation of the mutation rate in a variety of crowded cellular populations. Combined with previous studies on high-frequency mutations, our finding provides a unified picture of the genetic diversity in expanding populations over the whole frequency range and suggests a practical method to assess growth dynamics by sequencing populations across spatial scales.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

DFT + DMFT calculations of the complex band and tunneling behavior for the transition metal monoxides MnO, FeO, CoO, and NiO

Here, we report complex band structure (CBS) calculations for the four late transition metal monoxides MnO, FeO, CoO, and NiO in their paramagnetic phase. The CBS is obtained from density functional theory plus dynamical mean field theory (DMFT) calculations to take into account correlation effects. The so-called β parameters, governing the exponential decay of the transmission probability in the nonresonant tunneling regime of these oxides, are extracted from the CBS. Different model constructions are examined in the DMFT part of the calculation. The calculated β parameters provide theoretical estimation for the decay length in the evanescent channel, which would be useful for tunnel junction applications of these materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Time-Resolved X-ray Operando Observations of Lithiation Gradients across the Cathode Matrix and Individual Oxide Particles during Fast Cycling of a Li-Ion Cell

Lithiated transition metal oxides serve as active materials in the positive electrode (cathode) of lithium-ion cells. During electrochemical cycling, lithium ions intercalate and deintercalate into these oxide particles. This behavior causes two types of lithiation gradients to emerge: (i) a bulk gradient across the depth of the cathode matrix (averaged over individual oxide particles) and (ii) a microscopic gradient across the particles themselves, which also depends on their location in the electrode. Here we show how both gradients can be studied using operando X-ray diffraction during 4C charge and 4C discharge. The oxide (de)lithiation is estimated from the unit cell parameters by indexing the X-ray diffraction spectra. By fitting the lithiation profiles with orthogonal polynomials, the bulk gradients across the electrode thickness are quantified. These gradients develop as the current flows through the cell and dissipate during open-circuit and potentiostatic-hold periods. Further details of lithiation dynamics can be obtained through shape analysis of the Bragg peaks. In particular, from electrochemical model simulations, we show that the width and skewness of the (003) peak track (de)lithiation fronts moving across the individual oxide particles.

(003) peak↗
DOE OSTI2024

PRIME - A Software Toolkit for the Characterization of Partially Observed Epidemics in a Bayesian Framework

PRIME is a modeling framework designed for the “real-time’” characterization and forecasting of partially observed epidemics. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. The estimation problem is posed as one of Bayesian inference and solved using a Markov Chain Monte Carlo technique. The framework can accommodate multiple epidemic waves and can help identify different disease dynamics at the regional, state, and country levels. We include examples using publicly available COVID-19 data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

3-D Modeling off the CFR Engine for the Investigation of Knock on Natural Gas

Engine knock and misfire are barriers to pathways leading to high-efficiency Natural Gas (NG) engines. The general tendency to knock is highly dependent on engine operating conditions and the fuel reactivity. The problem is further complicated by low emissions limits and the wide range of chemical reactivity in pipeline quality NG (65< MN<95). In order to realize diesel-like efficiencies, spark-ignited NG engines must be designed to operate at high BMEP near knock limits over a wide range of fuel reactivity. This requires a deep understanding regarding combustion-engine interactions important in flame propagation and end-gas autoignition. The present work highlights a three-dimensional computational fluid dynamics (CFD) model of the Cooperative Fuel Research (CFR) engine to investigate knock behavior with NG. The CFR engine model is used to investigate fuel-engine interactions that lead to knock with NG, including effects of fuel reactivity, engine operating parameters, and exhaust gas recirculation (EGR). Cylinder wall, piston, valves, and port surface temperatures are estimated with a 1-D Three-Pressure Analysis (TPA) model. Model validation was performed by comparing model predictions with experimental data taken with a CFR engine over varying compression ratio, CA50, EGR fraction and BMEP.

Bestel, Diego↗
DOE OSTI2018

Smoothing of Gaussian quantum dynamics for force detection

Building on recent work by Gammelmark et al. we develop a formalism for prediction and retrodiction of Gaussian quantum systems undergoing continuous measurements. We apply the resulting formalism to study the advantage of incorporating a full measurement record and retrodiction for impulselike force detection and accelerometry. Here, we find that using retrodiction can only increase accuracy in a limited parameter regime, but that the reduction in estimation noise that it yields results in better detection of impulselike forces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Variation of Radiative Properties During Black Carbon Aging. Theoretical and Experimental Intercomparison

A theoretical model is developed to account for black carbon (BC) aging during three major evolution stages, i.e., freshly emitted aggregates, coated particles by soluble materials, and those after further hygroscopic growth. The geometric-optics surface-wave approach is employed to compute BC single-scattering properties at each stage, which are compared with laboratory measurements. Theoretical predictions using input parameters determined from experiments are consistent with measurements in extinction and scattering cross sections for coated BC (within 30 20%) and absorption enhancement from coating (within 15%). The calculated scattering cross sections of fresh BC aggregates are larger than those experimentally measured, because of uncertainties in measurements and calculations. We apply the aging model to compute BC direct radiative forcing (DRF) over the LA Basin using the CalNex 2010 field measurements. Our results demonstrate that accounting for the interactive radiative properties during BC aging is essential in obtaining reliable DRF estimates within a regional context.

He, Cenlin↗
DOE OSTI2025

The decay of HIV under anti-retroviral therapy is biphasic even in humanized mice with just T cells

HIV-1 plasma viral load decays in a biphasic manner during antiretroviral therapy (ART). It was hypothesized that this is due to infection of different cell types, namely CD4+ T cells and macrophages. We studied this possibility directly by modeling the decay of HIV-1 in humanized mice. We utilized previously published data from humanized T-cell only mice (TOM) and myeloid-only mice (MOM) infected with HIV-1 and treated with a potent ART regimen. Viral load decay dynamics were modeled using either a single or a biexponential decay fitted using nonlinear mixed effects techniques. Fits were compared using the corrected Bayesian information criterion (BICc). In TOM, the biphasic model was significantly better than a single-phase decay model (ΔBICc ≈ 16) despite additional parameters. In MOM, the biphasic decay was statistically better, but there was substantial uncertainty because the virus goes below detection very fast. The first-phase half-life was consistent between groups (1.2 days in MOM and 1.3 days in TOM) and similar to the half-life estimated in human infection. The second-phase decay in these mice was minimal likely due to low initial viral loads. Additional analyses with mice containing both CD4+ T cells and macrophages or X4-tropic virus-infected MOM mice confirmed the biphasic pattern, demonstrating the robustness of this result. The biphasic decline in HIV-1 occurs, even with only CD4+ T cells, refuting the hypothesis that distinct cell populations (CD4+ T cells and macrophages) drive each decay phase. These findings support an alternative model in which the observed dynamics arise from intrinsic properties of the viral infection lifecycle rather than from cellular compartmentalization.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2012

Optimization of in-line phase contrast particle image velocimetry using a laboratory x-ray source

Phase contrast particle image velocimetry (PIV) using a laboratory x-ray microfocus source is investigated using a numerical model. Phase contrast images of 75 {mu}m air bubbles, embedded within water exhibiting steady-state vortical flow, are generated under the paraxial approximation using a tungsten x-ray spectrum at 30 kVp. Propagation-based x-ray phase-contrast speckle images at a range of source-object and object-detector distances are generated, and used as input into a simulated PIV measurement. The effects of source-size-induced penumbral blurring, together with the finite dynamic range of the detector, are accounted for in the simulation. The PIV measurement procedure involves using the cross-correlation between temporally sequential speckle images to estimate the transverse displacement field for the fluid. The global error in the PIV reconstruction, for the set of simulations that was performed, suggests that geometric magnification is the key parameter for designing a laboratory-based x-ray phase-contrast PIV system. For the modeled system, x-ray phase-contrast PIV data measurement can be optimized to obtain low error (<0.2 effective pixel of the detector) in the system with magnification lying in the range between 1.5 and 3. For large effective pixel size (>15 {mu}m) of the detector, high geometric magnification (>2.5) is desired, while for large source size system (FWHM > 30 {mu}m), low magnification (<1.5) would be suggested instead. The methods developed in this paper can be applied to optimizing phase-contrast velocimetry using a variety of laboratory x-ray sources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Detectability of standing accretion shock instabilities activity in supernova neutrino signals

We introduce a novel methodology for establishing the presence of standing accretion shock instabilities (SASI) in the dynamics of a core collapse supernova from the observed neutrino event rate at water- or ice- based neutrino detectors. The methodology uses a likelihood ratio in the frequency domain as a test- statistics; it is also employed to assess the potential to estimate the frequency and the amplitude of the SASI modulations of the neutrino signal. The parameter estimation errors are consistent with the minimum possible errors as evaluated from the inverse of the Fisher information matrix, and close to the theoretical minimum for the SASI amplitude. Using results from a core-collapse simulation of a 15 solar-mass star by Kuroda et al. [Astrophys. J. 851, 62 (2017).] as a test bed for the method, we find that SASI can be identified with high confidence for a distance to the supernova of up to ~6 kpc for IceCube and up to ~3 kpc for a 0.4 Mt mass water Cherenkov detector. This methodology will aid the investigation of a future galactic supernova.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Modelling individual variability in growth of bull trout in the Walla Walla River Basin using a hierarchical von Bertalanffy growth model

Abstract We examined growth in length of fluvial bull trout ( Salvelinus confluentus ) in the Walla Walla River Basin, Washington and Oregon. Our objectives were to quantify individual variability in growth; examine growth within and among years, life history forms, life stages and sexes; and estimate von Bertalanffy growth parameters. Individual variability was evaluated by modelling asymptotic length ( L ∞ ) and the growth coefficient ( k ) as random variables. All models were fit with Bayesian methods and were evaluated for fit by the deviance information criterion. By incorporating individual variability, population‐level estimates of L ∞ and k appeared appropriate and estimated growth trajectories for specific bull trout fit individual observed patterns in growth. Growth trajectories and positive correlation between individual estimates of L ∞ and k suggest that some individuals grow at a faster rate and reach a larger maximum size than other individuals and those differences are maintained throughout life. Selected models suggest that fluvial migrants have higher estimates of L ∞ and k than residents, but there were only slight differences in parameter estimates among migrants from two adjacent spawning populations in the Walla Walla River Basin, as well as between males and females. Growth rates increased for fluvial migrants after subadult emigration. Individual variability in growth is consistent with the life history diversity assumed essential for bull trout population persistence. Quantifying this variability is important for modelling population dynamics and viability to conserve this threatened species.

Harris, Julianne E.↗