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Research concerning the net flux of radiation in the atmosphere of Jupiter

The plan of the NFR (Net Flux of Radiation) team is for the data from the two solar channels (B and E) of NFR to be reduced with the goal of determining the solar heating rate. In order to determine the solar heating rate from the NFR measurements, effects due to the instrument's spatial and spectral response functions, to the temperature variation of the instrument (and associated drift of calibration), to the setting sun, and to the rotation of the probe (initially at a rate comparable to the NFR sampling frequency), all must be well modelled. In the past year, a forward modeling routine was created to simulate NFR data return in the B and E channels. The effects of varying parameters describing the atmospheric model (such as cloud location and thickness) and the descent profile (such as rotation rate) were investigated and an inversion routine was developed. For the forward modeling, existing radiative transfer codes were used to determine intensity fields within the Jovian atmosphere. A routine was developed to determine instantaneous instrument response by integrating the intensity field over the instrument response functions. A second routine was developed to determine the actual output of the NFR by integrating along an arbitrary descent trajectory. Near the top of the atmosphere, the upflux data alone are used to constrain the cloud structure of he atmosphere. To accomplish this, models are used to describe the variation in up flux between consecutive measurements in terms of variations of cloud opacity and variations in known parameters such as the solar zenith angle. This allows us to develop a zero-order model of cloud structure. Lower in the atmosphere, at levels where there is little or no azimuthal structure to the net flux measurements, both the up flux and net flux are used to derive layer transmission and reflection functions, which then determine layer opacity and single scattering albedo. A preliminary analysis of the data began in December 1995. In these data we could see the rapid oscillations expected at the beginning of the data due to probe rotation and the sun passing through the edge of the field of view. In addition, the time when this oscillation stopped was clearly visible. This sets the rough optical depth above the probe at this time.

Tomasko, M. G.↗

Effects of Nonuniform Beam Filling on Rainfall Retrieval for the TRMM Precipitation Radar

The Tropical Rainfall Measuring Mission (TRMM) will carry the first spaceborne radar for rainfall observation. Because the TRMM Precipitation Radar (PR) footprint size of 4.3 km is greater than the scale of some convective rainfall events, there is concern that nonuniform filling of the PR antenna beam may bias the retrieved rain-rate profile. The authors investigate this effect theoretically and then observationally using data from the NASA Jet Propulsion Laboratory Airborne Rain Mapping Radar (ARMAR), acquired during Tropical Oceans Global Atmosphere Coupled Ocean Atmosphere Response Experiment in early 1993. The authors' observational approach is to simulate TRMM PR data using the ARMAR data and compare the radar observables and retrieved rain rate from the simulated PR data with those corresponding to the high-resolution radar measurements. The authors find that the path-integrated attenuation and the resulting path-averaged rain rate are underestimated. The reflectivity and rain rate near the top of the rainfall column are overestimated. The near-surface reflectivity can be overestimated or underestimated, with a mean error very close to zero. The near-surface rain rate, however, is usually underestimated, sometimes severely.

Durden, Stephen L.↗

Computational Modeling of Space Physiology for Informing Spaceflight Countermeasure Design and Predictions of Efficacy

MOTIVATION: Spaceflight countermeasures mitigate the harmful effects of the space environment on astronaut health and performance. Exercise has historically been used as a countermeasure to physical deconditioning, and additional countermeasures including lower body negative pressure, blood flow occlusion and artificial gravity are being researched as countermeasures to spaceflight-induced fluid shifts. The NASA Digital Astronaut Project uses computational models of physiological systems to inform countermeasure design and to predict countermeasure efficacy.OVERVIEW: Computational modeling supports the development of the exercise devices that will be flown on NASAs new exploration crew vehicles. Biomechanical modeling is used to inform design requirements to ensure that exercises can be properly performed within the volume allocated for exercise and to determine whether the limited mass, volume and power requirements of the devices will affect biomechanical outcomes. Models of muscle atrophy and bone remodeling can predict device efficacy for protecting musculoskeletal health during long-duration missions. A lumped-parameter whole-body model of the fluids within the body, which includes the blood within the cardiovascular system, the cerebral spinal fluid, interstitial fluid and lymphatic system fluid, estimates compartmental changes in pressure and volume due to gravitational changes. These models simulate fluid shift countermeasure effects and predict the associated changes in tissue strain in areas of physiological interest to aid in predicting countermeasure effectiveness. SIGNIFICANCE: Development and testing of spaceflight countermeasure prototypes are resource-intensive efforts. Computational modeling can supplement this process by performing simulations that reduce the amount of necessary experimental testing. Outcomes of the simulations are often important for the definition of design requirements and the identification of factors essential in ensuring countermeasure efficacy.

biomedical data↗

CVS Filtering of 3D Turbulent Mixing Layers Using Orthogonal Wavelets

Coherent Vortex Simulation (CVS) filtering has been applied to Direct Numerical Simulation (DNS) data of forced and unforced time-developing turbulent mixing layers. CVS filtering splits the turbulent flow into two orthogonal parts, one corresponding to coherent vortices and the other to incoherent background flow. We have shown that the coherent vortices can be represented by few wavelet modes and that these modes are sufficient to reproduce the vorticity probability distribution function (PDF) and the energy spectrum over the entire inertial range. The remaining incoherent background flow is homogeneous, has small amplitude, and is uncorrelated. These results are compared with those obtained for the same compression rate using large eddy simulation (LES) filtering. In contrast to the incoherent background flow of CVS filtering, the LES subgrid scales have a much larger amplitude and are correlated, which makes their statistical modeling more difficult.

Schneider, Kai↗

Comprehensive Understanding for Vegetated Scene Radiance Relationships

Directional reflectance distributions spanning the entire existent hemisphere were measured in two field studies; one using a Mark III 3-band radiometer and one using the rapid scanning bidirectional field instrument called PARABOLA. Surfaces measured included corn, soybeans, bare soils, grass lawn, orchard grass, alfalfa, cotton row crops, plowed field, annual grassland, stipa grass, hard wheat, salt plain shrubland, and irrigated wheat. Analysis of field data showed unique reflectance distributions ranging from bare soil to complete vegetation canopies. Physical mechanisms causing these trends were proposed. A 3-D model was developed and is unique in that it predicts: (1) the directional spectral reflectance factors as a function of the sensor's azimuth and zenith angles and the sensor's position above the canopy; (2) the spectral absorption as a function of location within the scene; and (3) the directional spectral radiance as a function of the sensor's location within the scene. Initial verification of the model as applied to a soybean row crop showed that the simulated directional data corresponded relatively well in gross trends to the measured data. The model was expanded to include the anisotropic scattering properties of leaves as a function of the leaf orientation distribution in both the zenith and azimuth angle modes.

Kimes, D. S.↗

Assimilation of GPM-retrieved Ocean Surface Meteorology Data for Two Snowstorm Events during ICE-POP 2018

As a component of the National Aeronautics and Space Administration (NASA) Weather Focus Area and Global Precipitation Measurement (GPM) Ground Validation participation in the International Collaborative Experiments for PyeongChang 2018 Olympic and Paralympic Winter Games (ICE-POP 2018) field research and forecast demonstration programs, hourly ocean surface meteorology properties were retrieved from the GPM microwave observations for January – March 2018. In this study, the retrieved ocean surface meteorological products – 2-m temperature, 2-m specific humidity, and 10-m wind speed were assimilated into a regional numerical weather prediction (NWP) framework to explore the application of these observations for two heavy snowfall events during the ICE-POP 2018: 27-28 February, and 7-8 March 2018. The Weather Research and Forecasting (WRF) model and the community Gridpoint Statistical Interpolation (GSI) were used to conduct high resolution simulations and data assimilation experiments. The results indicate that the data assimilation has a large influence on surface thermodynamic and wind fields in the model initial condition for both events. With cycled data assimilation, significantly positive influence of the retrieved surface observation was found for the March case with improved quantitative precipitation forecast and reduced error in temperature forecast. A slightly smaller yet positive impact was also found in the forecast of the February case.

assimilation↗

Cloud Thermodynamic Phase Detection with Polarimetrically Sensitive Passive Sky Radiometers

The primary goal of this project has been to investigate if ground-based visible and near-infrared passive radiometers that have polarization sensitivity can determine the thermodynamic phase of overlying clouds, i.e. if they are comprised of liquid droplets or ice particles. While this knowledge is important by itself for our understanding of the global climate, it can also help improve cloud property retrieval algorithms that use total (unpolarized) radiance to determine Cloud Optical Depth (COD). This is a potentially unexploited capability of some instruments in the NASA Aerosol Robotic Network (AERONET), which, if practical, could expand the products of that global instrument network at minimal additional cost. We performed simulations that found, for zenith observations, cloud thermodynamic phase is often expressed in the sign of the Q component of the Stokes polarization vector. We chose our reference frame as the plane containing solar and observation vectors, so the sign of Q indicates the polarization direction, parallel (negative) or perpendicular (positive) to that plane. Since the quantity of polarization is inversely proportional to COD, optically thin clouds are most likely to create a signal greater than instrument noise. Besides COD and instrument accuracy, other important factors for the determination of cloud thermodynamic phase are the solar and observation geometry (scattering angles between 40 and 60 degrees are best), and the properties of ice particles (pristine particles may have halos or other features that make them difficult to distinguish from water droplets at specific scattering angles, while extreme ice crystal aspect ratios polarize more than compact particles). We tested the conclusions of our simulations using data from polarimetrically sensitive versions of the Cimel 318 sun photometerradiometer that comprise AERONET. Most algorithms that exploit Cimel polarized observations use the Degree of Linear Polarization (DoLP), not the individual Stokes vector elements (such as Q). For this reason, we had no information about the accuracy of Cimel observed Q and the potential for cloud phase determination. Indeed, comparisons to ceilometer observations with a single polarized spectral channel version of the Cimel at a site in the Netherlands showed little correlation. Comparisons to Lidar observations with a more recently developed, multi-wavelength polarized Cimel in Maryland, USA, show more promise. This divergence between simulations and observations has prompted us to begin the development of a small test instrument called the Sky Polarization Radiometric Instrument for Test and Evaluation (SPRITE). This instrument is specifically devoted to the accurate observation of Q, and the testing of calibration and uncertainty assessment techniques, with the ultimate goal of understanding the practical feasibility of these measurements.

Knobelspiesse, Kirk D.↗

Materials selection for long life in LEO: A critical evaluation of atomic oxygen testing with thermal atom systems

The use of thermal atom test methods as a materials selection and screening technique for low-Earth orbit (LEO) spacecraft is critically evaluated. The chemistry and physics of thermal atom environments are compared with the LEO environment. The relative reactivities of a number of materials determined to be in thermal atom environments are compared to those observed in LEO and in high quality LEO simulations. Reaction efficiencies measured in a new type of thermal atom apparatus are one-hundredth to one-thousandth those observed in LEO, and many materials showing nearly identical reactivities in LEO show relative reactivities differing by as much as a factor of 8 in thermal atom systems. A simple phenomenological kinetic model for the reaction of oxygen atoms with organic materials can be used to explain the differences in reactivity in different environments. Certain specific thermal test environments can be used as reliable materials screening tools. Using thermal atom methods to predict material lifetime in LEO requires direct calibration of the method against LEO data or high quality simulation data for each material.

Koontz, S. L.↗

The Spacelab Experiment Interface Device (SEID)

The Spacelab experiment interface device (SEID) is described which simulates the electrical, and logical connections of the Spacelab remote acquisition unit (RAU), the interface functions of the Spacelab experiment computer software, and the electrical aspects of the high rate multiplexer. Simulated RAU interfaces include PCM serial channels (up to four), user time clock (UTC), flexible inputs (up to 128) and discrete outputs (up to 64). Connectors are logically compatible with the rau. be instructed to execute sequences of input/output commands to the RAU, similar to those performed during flight. This approximation of the experiment computer software is adequate to detect interface problems and prevent these from occurring during Spacelab payload integration. The SEID hardware is a microprocessor based system, utilizing an 8085 microprocessor with 6K of PROM and 4K of static RAM. The basic unit is augmented with an LSI-11 microcomputer to provide disk storage and a more dynamic environment for generation of control data. A simulation of the general monitoring loop is provided to emulate Spacelab system timing.

Kallus, R.↗

Stalled Pulsing Inertial Oscillation Model for a Tornadic Cyclone

A supercell storm is a tall, rotating thunderstorm that can generate hail and tornadoes. Two models exist for the development of the storm's rotation or mesocyclone - the conventional splitting-storm model, and the more recent pulsing inertial oscillation (PIO) model, in which a nonlinear pulse represents the supercell. Although data support both models and both could operate in the same supercell, neither model has satisfactorily explained the tornadic cyclone. A tornadic cyclone is an elevated vorticity concentration of Rossby number approximately 1000 that develops within the contracting mesocyclone shortly before a major tornado appears at the surface. We now show that if the internal temperature excess due to latent energy release is limited to the realistic range of -12 K to +12 K, the PIO model can stall part way through the pulse in a state of contraction and spin-up. Should this happen, the stalled-PIO model can evolve into a tornadic cyclone with a central pressure deficit that exceeds 40 mb, which is greater than the largest measured value. This simulation uses data from a major tornadic supercell that occurred over Oklahoma City, Oklahoma, USA, on May 3, 1999. The stalled-PIO mechanism also provides a strategy for human intervention to retard or reverse the development of a tornadic cyclone and its pendant tornado.

Costen, Robert C.↗

NASA's Integrated Instrument Simulator Suite for Atmospheric Remote Sensing from Spaceborne Platforms (ISSARS) and Its Role for the ACE and GPM Missions

Forward simulation is an indispensable tool for evaluation of precipitation retrieval algorithms as well as for studying snow/ice microphysics and their radiative properties. The main challenge of the implementation arises due to the size of the problem domain. To overcome this hurdle, assumptions need to be made to simplify compiles cloud microphysics. It is important that these assumptions are applied consistently throughout the simulation process. ISSARS addresses this issue by providing a computationally efficient and modular framework that can integrate currently existing models and is also capable of expanding for future development. ISSARS is designed to accommodate the simulation needs of the Aerosol/Clouds/Ecosystems (ACE) mission and the Global Precipitation Measurement (GPM) mission: radars, microwave radiometers, and optical instruments such as lidars and polarimeter. ISSARS's computation is performed in three stages: input reconditioning (IRM), electromagnetic properties (scattering/emission/absorption) calculation (SEAM), and instrument simulation (ISM). The computation is implemented as a web service while its configuration can be accessed through a web-based interface.

real-aperture instruments↗

Clipping polygon faces through a polyhedron of vision

A flight simulator combines flight data and polygon face terrain data to provide a CRT display at each window of the simulated aircraft. The data base specifies the relative position of each vertex of each polygon face therein. Only those terrain faces currently appearing within the pyramid of vision defined by the pilots eye and the edges of the pilots window need be displayed at any given time. As the orientation of the pyramid of vision changes in response to flight data, the displayed faces are correspondingly displaced, eventually moving out of the pyramid of vision. Faces which are currently not visible (outside the pyramid of vision) are clipped from the data flow. In addition, faces which are only partially outside of pyramid of vision are reconstructed to eliminate the outside portion. Window coordinates are generated defining the distance between each vertex and each of the boundary planes forming the pyramid of vision. The sign bit of each window coordinate indicates whether the vertex is on the pyramid of vision side of the associated boundary panel (positive), or on the other side thereof (negative). The set of sign bits accompanying each vertex constitute the outcode of that vertex. The outcodes (O.C.) are systematically processed and examined to determine which faces are completely inside the pyramid of vision (Case A--all signs positive), which faces are completely outside (Case C--All signs negative) and which faces must be reconstructed (Case B--both positive and negative signs).

Rohner, Michel A.↗

Optimal Estimation-Based Algorithm to Retrieve Aerosol Optical Properties for GEMS Measurements Over Asia

The Geostationary Environment Monitoring Spectrometer (GEMS) is scheduled to be in orbit in 2019 onboard the GEO-KOMPSAT 2B satellite and will continuously monitor air quality over Asia. The GEMS will make measurements in the UV spectrum (300-500 nm) with 0.6 nm resolution. In this study, an algorithm is developed to retrieve aerosol optical properties from UV-visible measurements for the future satellite instrument and is tested using 3 years of existing OMI L1B data. This algorithm provides aerosol optical depth (AOD), single scattering albedo (SSA) and aerosol layer height (ALH) using an optimized estimation method. The retrieved AOD shows good correlation with Aerosol Robotic Network (AERONET) AOD with correlation coefficients of 0.83, 0.73 and 0.80 for heavy-absorbing fine (HAF) particles, dust and non-absorbing (NA) particles, respectively. However, regression tests indicate underestimation and overestimation of HAF and NA AOD, respectively. In comparison with AOD from the OMI/Aura Near-UV Aerosol Optical Depth and Single Scattering Albedo 1-orbit L2 Swath 13 km x 24 km V003 (OMAERUV) algorithm, the retrieved AOD has a correlation coefficient of 0.86 and linear regression equation, AOD(sub GEMS) = 1.18AOD(sub OMAERUV) + 0.09. An uncertainty test based on a reference method, which estimates retrieval error by applying the algorithm to simulated radiance data, revealed that assumptions in the spectral dependency of aerosol absorptivity in the UV cause significant errors in aerosol property retrieval, particularly the SSA retrieval. Consequently, retrieved SSAs did not show good correlation with AERONET values. The ALH results were qualitatively compared with the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) products and were found to be well correlated for highly absorbing aerosols. The difference between the attenuated-backscatter-weighted height from CALIOP and retrieved ALH were mostly closed to zero when the retrieved AOD is higher than 0.8 and SSA is lower than 0.93. Although retrieval accuracy was not significantly improved, the simultaneous consistent retrieval of AOD, SSA and ALH alone demonstrates the value of this stand-alone algorithm, given their nature for error using other methods. The use of these properties as input parameters for the air mass factor calculation is expected to improve the retrieval of other trace gases over Asia.

Geostationary Environment Monitoring Spectrometer ↗

Measurement and Simulation of Spontaneous Raman Scattering Spectra in High-Pressure, Fuel-Rich H2-Air Flames

Rotational vibrational spontaneous Raman spectra (SRS) of H2, N2, and H2O have been measured in H2-air flames at pressures up to 30 atm as a first stem towards establishing a comprehensive Raman spectral database for temperatures and species in high-pressure combustion. A newly developed high-pressure burner facility provides steady, reproducible flames with a high degree of flow precision. We have obtained an initial set of measurements that indicate the spectra are of sufficient quality in terms of spectral resolution, wavelength coverage, and signal-to-noise ratio for use in future reference standards. The fully resolved Stokes and anti-Stokes shifted SRS spectra were collected in the visible wavelength range (400-700 nm) using pulse-stretched 532 nm excitation and a non-intensified CCD spectrograph with a high-speed shutter. Reasonable temperatures were determined via the intensity distribution of rotational H2 lines at stoichiometry and fuel-rich conditions. Theoretical Raman spectra of H2 were computed using a semi-classical harmonic-oscillator model with recent pressure broadening data and were compared with experimental results. The data and simulation indicated that high-J rotational lines of H2 might interfere with the N2 vibrational Q-branch lines, and this could lead to errors in N2-Raman thermometry based on the line-fitting method. From a comparison of N2 Q-branch spectra in lean H2 low-pressure (1.2 atm) and high-pressure (30 atm) flames, we found no significant line-narrowing or -broadening effects at the current spectrometer resolution of 0.04 nm.

Kojima, Jun↗

Earth System Digital Twins (ESDT) Technology for NASA Earth Science

For NASA's Advanced Information Systems Technology (AIST) Program, an Earth System Digital Twin (ESDT) is defined as an interactive and integrated multidomain, multiscale, digital replica of the state and temporal evolution of Earth systems. It dynamically integrates: relevant Earth system models and simulations; other relevant models (e.g., related to the world's infrastructure); continuous and timely (including near real time and direct readout) observations (e.g., space, air, ground, over/underwater, Internet of Things (IoT), socioeconomic); long-time records; as well as analytics and artificial intelligence tools. Effective ESDTs enable users to run hypothetical scenarios to improve the understanding, prediction of and mitigation/response to Earth system processes, natural phenomena and human activities as well as their many interactions. An ESDT is a type of integrated information system that, for example, enables continuous assessment of impact from naturally occurring and/or human activities on physical and natural environments. AIST ESDT strategic goals are to: 1. Develop information system frameworks to provide continuous and accurate representations of systems as they change over time; 2. Mirror various Earth Science systems and utilize the combination of Data Analytics, Artificial Intelligence, Digital Thread, and state-of-the-art models to help predict the Earth’s response to various phenomena; 3. Provide the tools to conduct "what if" investigations that can result in actionable predictions. The AIST ESDT thrust is developing capabilities toward the development of future digital twins of the Earth or of subcomponents of the Earth. This will enable the development of an overarching framework that will integrate New Observing Strategies (NOS) to enable new observation measurements, i.e., multi-source, coordinated, dynamic and responsive to needs and requests defined by Analytic Collaborative Frameworks (ACF) that enable agile science investigations fusing and analyzing very large amounts of diverse data. NOS and ACF capabilities along with open access to various science, infrastructure and human data, interconnected modeling, data assimilation, simulations, surrogate modeling, high-performance computing and advanced visualization, will define a powerful framework that could be utilized for local, regional or global and/or thematic digital twins. This presentation will describe a general overview of the AIST ESDT vision including prior work done in the areas of NOS and ACF as well as current and upcoming ESDT projects.

Jacqueline Le Moigne↗

Equiaxed Dendritic Solidification Experiment (EDSE)

The objective of the research is to quantitatively determine and understand the fundamental mechanisms that control the microstructural evolution during equiaxed dendritic solidification. A microgravity experiment will be conducted to obtain benchmark data on the transient growth and interaction of up to four equiaxed crystals of a pure and transparent metal analog (succinonitrile, SCN) under strictly diffusion-dominated conditions. Of interest in the experiment are the transient evolution of the primary and secondary dendrite tip speeds, the dendrite morphology and solid fraction, the tip selection criterion, and the temperature field in the melt for a range of interaction "strengths" between the crystals. The experiment extends the microgravity measurements of Glicksman and co-workers isothermal dendritic growth experiment (IDGE) for steady growth of a single dendrite to a case where growth transients are introduced due to thermal interactions between neighboring dendrites - a situation closer to actual casting conditions. Corresponding Earth-based experiments will be conducted to ascertain the influence of melt convection. The experiments are supported by a variety of analytical models and numerical simulations. The data will be used to develop and test theories of transient dendritic growth and the solidification of multiple interacting equiaxed crystals in a supercooled melt.

Beckermann, C.↗

Fault Diagnosis of Power Components with Reliability Assessment in Extraterrestrial Microgrids

This research investigates the possible failures caused by aging and other environmental and external factors that could significantly impact the performance of extraterrestrial power systems. Additionally, it presents a reliability assessment model for the space microgrid based on fault tree analysis (FTA). The reliability assessment model developed in this paper represents a tool that can be used by engineers to harden the system design for operational and economic benefits. To improve the reliability of the system, this work provides a broad review of the different fault detection and diagnosis (FDD) algorithms used for power microgrids and space applications. Using data sets from the Habitat Simulator developed through the NASA-funded Resilient Extraterrestrial Habitat Institute, this paper compares the applicability and accuracy of the different FDD methods. The primary FDD approach proposed and assessed in this work is based on the Markov reliability model. It predicts and detects future faults in the space microgrids by using past data samples and categorizing them into different classes. Data-driven-based models such as artificial neural networks are also investigated, tested, and evaluated using simulation data sets. According to the simulation results and the broad FDD algorithm comparison, this study provides the crew or maintenance engineers with a clear methodology to detect and localize power system failures.

Leila Chebbo↗

Equiaxed Dendritic Solidification Experiment (EDSE)

The objective of the research is to quantitatively determine and understand the fundamental mechanisms that control the microstructural evolution during solidification of an assemblage of equiaxed dendritic crystals. A microgravity experiment will be conducted to obtain benchmark data on the transient growth and interaction of up to four equiaxed crystals of a pure and transparent metal analog (succinonitrile, SCN) under strictly diffusion dominated conditions. Of interest in the experiment are the transient evolution of the primary and secondary dendrite tip speeds, the dendrite morphology (i.e., tip radii, branch spacings, etc.) and solid fraction, the tip selection criterion, and the temperature field in the melt for a range of initial supercoolings and, thus, interaction "strengths" between the crystals. The experiment thus extends the microgravity measurements of Glicksman and coworkers for steady growth of a single dendrite [Isothermal Dendritic Growth Experiment (IDGE), first flown on USMP-2] to a case where growth transients are introduced due to thermal interactions between neighboring dendrites - a situation more close to actual casting conditions. Corresponding earth-based experiments will be conducted to ascertain the influence of melt convection. The experiments are supported by a variety of analytical models and numerical simulations. The data will primarily be used to develop and test theories of transient dendritic growth and the solidification of multiple interacting equiaxed crystals in a supercooled melt.

Beckermann, C.↗