Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical modelling”

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 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Evolution of Idealized Vortices in Monsoon-Like Shears: Application to Monsoon Depressions

Abstract This study examines processes fundamental to the development of South Asian monsoon depressions using an array of integrations of an idealized convection-permitting numerical model. In each integration, a wave of initially small amplitude is subjected to a different amount of vertical and meridional wind shear, with temperature and moisture fields constructed according to realistic constraints. Based on the evolution of this disturbance into monsoon depression–like vortices, two features of the background environment emerge as important: the low-level gradient of moist static energy (MSE) and the low-level meridional shear. As the low-level MSE gradient steepens, the disturbance becomes stronger and produces more rain. This strengthening results from the interaction of the vortex with latent heat release by convection that is in turn organized by positive MSE advection in the northerly flow west of the vortex. In this region of advection, moister air from the north ascends along upward-sloping isentropes, driving moist convection. The disturbance also becomes stronger with increasing meridional shear, which makes the environment more barotropically unstable. The absence of either of these two features of the background environment prevents substantial growth of the disturbance. Our results suggest that monsoon depression growth in South Asia is fostered by the coexistence of a strong low-level MSE gradient with strong meridional wind shear associated with the monsoon trough.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

How does vertical wind shear influence entrainment in squall lines?

The influence of vertical wind shear on updraft entrainment in squall lines is not well understood. To address this knowledge gap, a suite of high-resolution idealized numerical model simulations of squall lines were run in various vertical wind shear (hereafter “shear”) environments to study the effects of shear on entrainment in deep convective updrafts. Low-level horizontal mass flux into the leading edge of the cold pool was strongest in the simulations with the strongest low-level shear. These simulations consequently displayed wider updrafts, less entrainment-driven dilution, and larger buoyancy than the simulations with comparatively weak low-level shear. An analysis of vertical accelerations along trajectories that passed through updrafts showed larger net accelerations from buoyancy in the simulations with stronger low-level shear, which demonstrates how less entrainment-driven dilution equated to stronger updrafts. Additionally, the effects of upper-level shear on entrainment and updraft vertical velocities were generally less pronounced than the effects of low-level shear. We argue that in addition to the outflow boundary-shear interactions and their effect on updraft tilt established by previous authors, decreased entrainment-driven dilution is yet another beneficial effect of strong low-level shear on squall line updraft intensity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Evaluating the Conservation of Energy Variables in Simulations of Deep Moist Convection

Abstract It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE − IB and MSE + KE, wherein IB is the path integral of buoyancy ( B ) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large-eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE − IB and MSE + KE better predict quantities along trajectories than MSE alone. MSE − IB is better conserved in isolated deep convection, whereas MSE − IB and MSE + KE perform comparably in squall-line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE − IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE − IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE − IB or MSE + KE instead of MSE with properly formulated heat capacities and latent heats.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Revisiting the Hail Radar Reflectivity–Kinetic Energy Flux Relation by Combining T-Matrix and Discrete Dipole Approximation Calculations to Size Distribution Observations

The retrieval of hail kinetic energy with weather radars or its simulation in numerical models is challenging because of the shape complexity and variable density of hailstones. We combine 3D scans of individual hailstones with measurements of the particle size distributions (PSD) and T-matrix calculations to understand how hail reflectivity Z changes when approximating hailstones as spheroids, as compared to the realistic shapes obtained by 3D scanning technology. Additionally, recent terminal velocity relations are used to compare Z to the hail kinetic energy flux E ˙ . We parameterize the hail backscattering cross sections at L, S, C, and X bands as a function of size between 0.5 and 5.0 cm, matching the range of the observed PSDs. The scattering calculations use the T-matrix method for size parameters below 1.0 and the discrete dipole approximation (DDA) method otherwise. The DDA calculations are done for 48 digital models of realistic hailstones of sizes between 1 and 5 cm. The DDA cross sections are calculated for multiple orientations and averaged assuming a fully random orientation distribution to provide a single value per hailstone. The T-matrix reflectivity assuming solid ice spheres presents negligible differences to DDA results for size parameters below 1.0. Therefore, T matrix was used to fill in the gaps left by the DDA calculations. The results are mapped to the same size bins of the observed PSDs, allowing the calculation of the radar reflectivity. This is then correlated to E ˙ , allowing a potential improvement of past retrieval methods of E ˙ from Z in multiple wavelengths.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

An Analytic Formula for Entraining CAPE in Midlatitude Storm Environments

Abstract This article introduces an analytic formula for entraining convective available potential energy (ECAPE) with an entrainment rate that is determined directly from an environmental sounding, rather than prescribed by the formula user. Entrainment is connected to the background environment using an eddy diffusivity approximation for lateral mixing, updraft geometry assumptions, and mass continuity. These approximations result in a direct correspondence between the storm-relative flow and the updraft radius and an inverse scaling between the updraft radius squared and entrainment rate. The aforementioned concepts, combined with the assumption of adiabatic conservation of moist static energy, yield an explicit analytic equation for ECAPE that depends entirely on state variables in an atmospheric profile and a few constant parameters with values that are established in past literature. Using a simplified Bernoulli-like equation, the ECAPE formula is modified to account for updraft enhancement via kinetic energy extracted from the cloud’s background environment. CAPE and ECAPE can be viewed as predictors of the maximum vertical velocity w max in an updraft. Hence, these formulas are evaluated using w max from past numerical modeling studies. Both of the new formulas improve predictions of w max substantially over commonly used diagnostic parameters, including undiluted CAPE and ECAPE with a constant prescribed entrainment rate. The formula that incorporates environmental kinetic energy contribution to the updraft correctly predicts instances of exceedance of by w max , and provides a conceptual explanation for why such exceedance is rare among past simulations. These formulas are potentially useful in nowcasting and forecasting thunderstorms and as thunderstorm proxies in climate change studies. Significance Statement Substantial mixing occurs between the upward-moving air currents in thunderstorms (updrafts) and the surrounding comparatively dry environmental air, through a process called entrainment. Entrainment controls thunderstorm intensity via its diluting effect on the buoyancy of air within updrafts. A challenge to representing entrainment in forecasting and predictions of the intensity of updrafts in future climates is to determine how much entrainment will occur in a given thunderstorm environment without a computationally expensive high-resolution simulation. To address this gap, this article derives a new formula that computes entrainment from the properties of a single environmental profile. This formula is shown to predict updraft vertical velocity more accurately than past diagnostics, and can be used in forecasting and climate prediction to improve predictions of thunderstorm behavior and impacts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Dependence of Deep Convective Cell Properties on Meteorological and Aerosol Conditions during TRACER

Deep convective cells significantly influence Earth’s energy balance and water cycle. However, their accurate representation in numerical models remains challenging due to their small spatiotemporal scales and limited observational constraints. This study examines over ∼400 deep convective cells near Houston, observed by a dual-polarization C-band radar during the Tracking Aerosol Convection Interactions Experiment (TRACER) intensive observation period (June–September 2022). Cells are categorized by lifetime into short-lived (<40 min), intermediate-lived (40–80 min), and long-lived (80+ min) groups. Long-lived cells were broader (∼13.2 km at 2–4-km height) and deeper (∼11.4 km) than short-lived cells (∼6.4-km width, ∼7.31-km height). Using random forest (RF) modeling and correlation analyses, precipitable water vapor (PWV), 2–6-km lapse rate, 0–8-km bulk shear, and fine aerosol mass concentration (Mass_f) are identified as key predictors of cell lifetime. Higher PWV is associated with significantly longer convective cell lifetimes compared to the low-PWV group, particularly within low 2–6-km temperature lapse rate (LR_26km), moderate-to-higher 0–8-km bulk shear (BS_08km), and low-to-moderate Mass_f environments. RF analysis also identifies low-level (0–2 km) equivalent potential temperature, PWV, Mass_f, and surface latent heat flux as key predictors for cell width and height. Short-lived cells have higher aerosol number concentrations (500–1000-nm size range), linked to onshore wind conditions and marine aerosols; however, their low concentration suggests the sensitivity may reflect associated meteorological regimes rather than a direct aerosol effect. Long-lived cells have higher concentrations of organic and sulfate aerosols, while short-lived cells exhibit higher black carbon concentrations. These results highlight the intricate dependence of convective cell lifetimes and structure on environmental moisture, thermodynamics, wind shear, and aerosol characteristics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Analyzing Relationships between Tropical Cyclone Intensity and Rain Rate over the Ocean Using Numerical Simulations

In this study, the relationship between tropical cyclone (TC) intensity and rain rate over the ocean is investigated using a full-physics numerical model (WRF) and a physics-based TC rainfall model (TCR). TC intensity is found to be nearly linearly correlated with the average rain rate in the inner core [~0.97 (mm h –1 m –2 )/(m s –1 )], while the correlation is weak at outer radii. This difference is induced because TC intensity is significantly correlated with both the vertical velocity and specific humidity in the inner core but is not significantly correlated with the vertical velocity in the outer radii. Further investigation shows that the intensity–rain-rate relationship at the outer radii is influenced by the TC evolution stage. The rain rate for the outer radii is positively correlated with TC intensity for nondecaying TCs, while this correlation is reduced for decaying TCs due to systematic downdrafts in the outer radii. In the context of climate change, the sensitivity of the TC rain rate to sea surface temperature (SST) is found to be +9% per 1 K increase of SST, roughly the product of the sensitivity of TC intensity to SST (+3%) and the Clausius-Clapeyron scaling (+7%). Coupled with synthetic storms, evolution of the TC rain rate over the twenty-first century under the SSP5-8.5 scenario is projected by the TCR (calibrated with the WRF simulations). The annual increase rates of averaged TC rain rate are 0.17% and 0.20% for the inner core and outer radii, respectively, larger than the annual increase rate of TC intensity (0.046%) but comparable to that of cube of intensity (0.18%).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Low-Level Liquid-Bearing Clouds Contribute to Seasonal Lower Atmosphere Stability and Surface Energy Forcing over a High-Mountain Watershed Environment

Measurements of atmospheric structure and surface energy budgets distributed along a high-altitude moun tain watershed environment near Crested Butte, Colorado, from two separate, but coordinated, field campaigns, Surface Atmosphere Integrated field Laboratory (SAIL) and Study of Precipitation, the Lower Atmosphere, and Surface for Hydrometeorology (SPLASH), are analyzed. This study identifies similarities and differences in how clouds influence the radiative budget over one snow-free summer season (2022) and two snow-covered seasons (2021/22; 2022/23) for this alpine location. A relationship between lower-tropospheric stability stratification and longwave radiative flux from the presence or absence of clouds is identified. When low clouds persisted, often with signatures of supercooled liquid in win ter, the lower troposphere experienced weaker stability, while radiatively clear skies that are less likely to be influenced by liquid droplets were associated with appreciably stronger lower-tropospheric stratification. Corresponding surface turbu lent heat fluxes partitioned differently based upon the cloud–stability stratification regime derived from early morning radiosounding profiles. Combined with the differences in the radiative budget largely resulting from dramatic seasonal dif ferences in surface albedo, the lower atmosphere stratification, surface energy budget, and near-surface thermodynamics are shown to be modified by the effective longwave radiative forcing of clouds. The diurnal evolution of thermodynamics and surface energy components varied depending on the early morning stratification state. Thus, the importance of quies cent versus synoptically active large-scale meteorology is hypothesized as a critical forcing for cloud properties and associ ated surface energy budget variations. The physical relationships between clouds, radiation, and stratification can provide a useful suite of metrics for process understanding and to evaluate numerical models in such an undersampled, highly com plex terrain environment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Polarimetric Signatures in Landfalling Tropical Cyclones

Polarimetric radar observations from the NEXRAD WSR-88D operational radar network in the contiguous United States, routinely available since 2013, are used to reveal three prominent microphysical signatures in landfalling tropical cyclones: 1) hydrometeor size sorting within the eyewall convection, 2) vertical displacement of the melting layer within the inner core, and 3) dendritic growth layers within stratiform regions of the inner core. Size sorting signatures within eyewall convection are observed with greater frequency and prominence in more intense hurricanes, and are observed predominantly within the deep-layer environmental wind shear vector-relative quadrants that harbor the greatest frequency of deep convection (i.e., downshear and left-of-shear). Melting-layer displacements are shown that exceed 1 km in altitude compared to melting-layer altitudes in outer rainbands and are complemented by analyses of archived dropsonde data. Dendritic growth and attendant snow aggregation signatures in the inner core are found to occur more often when echo-top altitudes are low (≤10 km MSL), nearer the -15°C isotherm commonly associated with dendritic growth. These signatures, uniquely observed by polarimetric radar, provide greater insight into the physical structure and thermodynamic characteristics of tropical cyclones, which are important for improving rainfall estimation and the representation of tropical cyclones in numerical models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A Doppler radar study of convective draft lengths over Darwin, Australia

Data from an upward-pointing wind profiler radar pair at Darwin in tropical Australia are used to determine the characteristics of individual convective up- and downdrafts observed at the site. Drafts are identified as vertically contiguous regions of instantaneous upward or downward motion exceeding 0.2 m s –1 . Most updrafts and downdrafts found are less than 2 km in vertical extent, and updrafts exceeding 5 km in vertical length carry no more than 33% of the total upward mass flux. Updraft length correlates positively with rain rates, and on very high rain rates (greater than 20 mm h –1 ), average updraft lengths are ~5 km. Typical peak updraft velocities increase from ~2.5 m s –1 for the smallest to ~4 m s –1 for the largest drafts, while those for downdrafts remain ~2 m s –1 regardless of size. Furthermore, these results are broadly consistent with other numerical modeling studies, but contrast with the common view of deep convection as being dominated by continuous, deep drafts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Moving-Wave Implementation in WRF to Study the Impact of Surface Water Waves on the Atmospheric Boundary Layer

Abstract While numerous modeling studies have focused on the interaction of ocean surface waves with the atmospheric boundary layer, most employ idealized waves that are either monochromatic or synthetically generated from a theoretical wave spectrum, and the atmospheric solvers are typically incompressible. To study wind–wave coupling in real-world scenarios, a model that can simulate both realistic meteorological and wave conditions is necessary. In this paper we describe the implementation of a moving bottom boundary condition into the Weather Research and Forecasting Model for large-eddy simulation applications. We first describe the moving bottom boundary conditions within WRF’s pressure-based vertical coordinate system. We then validate our code with idealized test cases that have analytical solutions, including flow over a monochromatic wave with and without viscosity. Finally, we present results from turbulent flows over a moving monochromatic wave with different wave ages, and demonstrate satisfactory agreement of the wave growth rate with results from the literature. We also compare atmospheric stress and wind parameters from two physically equivalent cases. The first specifies a wind moving in the same direction as a propagating wave, while the second involves a stationary wave with the wind adjusted such that the wind relative to the wave is the same as in the first case. Results indicate that the velocity and Reynolds stress profiles for the two cases match, further validating the moving bottom implementation.

17 WIND ENERGY↗
DOE OSTI2026

The role of equatorial waves in triggering precipitation extremes in the Maritime Continent

This review offers a comprehensive analysis of convectively coupled equatorial waves (CCEWs) and their pivotal role in driving precipitation extremes across the Maritime Continent. It examines the current understanding of CCEWs, evaluates the performance of numerical models and forecasting techniques in predicting these phenomena, and pinpoints critical areas for improvement. The discussion centers on three key types of equatorial waves: equatorial Rossby waves, Kelvin waves, and mixed Rossby–gravity waves. By connecting scientific insights with practical forecasting applications, the review sheds light on the challenges of predicting these waves while identifying opportunities to advance both fundamental knowledge and forecasting accuracy. Designed as an educational resource, it targets operational forecasting centers, meteorologists, and researchers, aiming to enhance the prediction of extreme weather events in the region.

Maritime Continent↗
DOE OSTI2023

Intensification of Hurricane Sally (2020) over the Mississippi River Plume

Abstract Tropical Cyclone (TC) Sally formed on 11 September 2020, traveled through the Gulf of Mexico (GMX), and intensified rapidly before making landfall on the Alabama coast as a devastating category-2 TC with extensive coastal and inland flooding. In this study, using a combination of observations and idealized numerical model experiments, we demonstrate that the Mississippi River plume played a key role in the intensification of Sally near the northern Gulf Coast. As the storm intensified and its translation slowed before landfall, sea surface cooling was reduced along its track, coincident with a pronounced increase in SSS. Further analysis reveals that TC Sally encountered a warm Loop Current eddy in the northern GMX close to the Mississippi River plume. Besides deepening the thermocline, the eddy advected low-salinity Mississippi River plume water into the storm’s path. This resulted in the development of strong upper-ocean salinity stratification, with a shallow layer of freshwater lying above a deep, warm “barrier layer.” Consequently, TC-induced mixing and the associated sea surface cooling were reduced, aiding Sally’s intensification. These results suggest that the Mississippi River plume and freshwater advection by the Loop Current eddies can play an important role in TC intensification near the U.S. Gulf Coast.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Machine Learning–Adjusted WRF Forecasts to Support Wind Energy Needs in Black Start Operations

Abstract The push for increased capacity of renewable sources of electricity has led to the growth of wind-power generation, with a need for accurate forecasts of winds at hub height. Forecasts for these levels were uncommon until recently, and that, combined with the nocturnal collapse of the well-mixed boundary layer and daytime growth of the boundary layer through the levels important for energy generation, has contributed to errors in numerical modeling of wind generation resources. The present study explores several machine learning algorithms to both forecast and correct standard WRF Model forecasts of winds and temperature at hub height within wind turbine plants over several different time periods that are critical for the anticipation of potential blackouts and aiding in black start operations on the power grid. It was found that mean square error for day-2 wind forecasts from the WRF Model can be improved by over 90% with the use of a multioutput neural network, and that 60-min forecasts of WRF error, which can then be used to adjust forecasts, can be made with an LSTM with great accuracy. Nowcasting of temperature and wind speed over a 10-min period using an LSTM produced very low error and especially skillful forecasts of maximum and minimum values over the turbine plant area.

17 WIND ENERGY↗
DOE OSTI2020

Effect of heating/cooling dynamics in the hysteresis loop and tunable IR emissivity of VO 2 thin films

We experimentally investigate the semiconductor-to-metal transition (SMT) in vanadium dioxide thin films using an infrared thermographic technique. During the semiconductor to metal phase change process, VO 2 optical properties dynamically change and infrared emission undergoes a hysteresis loop due to differences between heating and cooling stages. The shape of the hysteresis loop was accurately monitored under different dynamic heating/cooling rates. In order to quantify and understand the effects of different rates, we used a numerical modelling approach in which a VO 2 thin layer was modeled as metamaterial. The main experimental findings are interpreted assuming that both the rate of formation and shape of metallic inclusions are tuned with the heating/cooling rate. The structural transition from monoclinic to tetragonal phases is the main mechanism for controlling the global properties of the phase transition. However, our experimental results reveal that the dynamics of the heating/cooling process can become a useful parameter for further tuning options and lays out a macroscopic optical sensing scheme for the microscopic phase change dynamics of VO 2 . Our study sheds light on phase-transition dynamics and their effect on the infrared emission spectra of VO 2 thin films, therefore enabling the heating/cooling rate to be an additional parameter to control infrared emission characteristics of thermal emitters. The hysteresis loop represents the phase coexistence region, thus being of fundamental importance for several applications, such as the operation of radiative thermal logic elements based on phase transition materials. For such applications, the phase transition region is shifted for heating and cooling processes. We also show that, depending on the way the phase change elements are heated, the temperature operation range will be slightly modified.

42 ENGINEERING↗
DOE OSTI2021

Stabilization of the 81-channel coherent beam combination using machine learning

We develop a rapidly converging algorithm for stabilizing a large channel-count diffractive optical coherent beam combination. An 81-beam combiner is controlled by a novel, machine-learning based, iterative method to correct the optical phases, operating on an experimentally calibrated numerical model. A neural-network is trained to detect phase errors based on interference pattern recognition of uncombined beams adjacent to the combined one. Due to the non-uniqueness of solutions in the full space of possible phases, the network is trained within a limited phase perturbation/error range. This also reduces the number of samples needed for training. Simulations have proven that the network can converge in one step for small phase perturbations. When the trained neural-network is applied to a realistic case of 360 degree full range, an iterative scheme exploits random walking at the beginning, with the accuracy of prediction on phase feedback direction, to allow the neural-network to step into the training range for fast convergence. This neural-network-based iterative method of phase detection works tens of times faster than the commonly used stochastic parallel gradient descent approach (SPGD) using a single-detector and random dither when both are tested with random phase perturbations.

Wang, Dan↗
DOE OSTI2022

Nano-porous GaN cladding and scattering loss in edge emitting laser diodes

We report continuous wave operation of electrically injected InGaN laser diodes using nano-porous GaN n-side cladding with 33% porosity. At 454 nm emission wavelength, the pulsed injection slope efficiency is 0.24 W/A with a high loss of 82 cm -1 . The considerable 60 cm -1 of excess loss of the nano-porous clad lasers is attributed to scattering at pores in unintentionally 3% porosified layers, supported by numerical modeling. Simulations comparing porous GaN cladding to AlInN cladding for lasers operating at 589 nm indicate that the porous cladding provides similar internal loss and lower thermal impedance.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Third-order photon correlations extract single-nanocrystal multiexciton properties in solution

Colloidal semiconductor nanocrystals are considered promising materials for high-flux optical applications, including lasing, light-emitting diodes, biological imaging, and quantum optics. In high-flux applications, multiexcitons can significantly contribute to emission, influencing its brightness, spectral purity, and kinetics. As a result, understanding and controlling multiexciton emission in colloidal nanocrystal materials is of the utmost importance. In the past, single-nanocrystal photon correlation methods have been applied to understand biexciton and triexciton efficiencies, lifetimes, and spectra. While powerful, such methods suffer from user selection bias and require stable emission from single nanocrystals. To compensate for this shortcoming, second-order correlation methods were developed to extract sample-averaged biexciton properties from a solution of nanocrystals. Until now, however, the analogous third-order solution photon correlation methods remained unexplored. In this work, we present a pair of third-order photon correlation techniques to obtain the sample-averaged single-nanocrystal triexciton quantum yield and lifetime in a solution-phase experiment. These techniques derive from the relationship between the Poisson probability of nanocrystal photon absorption and the intrinsic probability of nanocrystal photon emission. We validate the theoretical background of these techniques by creating a numerical model to simulate the diffusion and emission of many nanocrystals in solution. Our simulations confirm that the average triexciton quantum yield and triexciton lifetime can be extracted from a solution of nanocrystals. These techniques will enable researchers to gain a better understanding of the fundamental multiexciton properties of colloidal nanocrystals.

Horowitz, Jonah R. [Massachusetts Institute of Tec↗