Search NASA⌕ Search

SEARCH · Search NASA

Results for “generalized gradient approximations”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A benchmark of Gutzwiller conjugate gradient minimization method in ground state energy calculations of dimers

Herein we present numerical results of ground-state energies of 9 molecules in the well-established G2 molecule set given by the Gutzwiller conjugate gradient minimization (GCGM) method. The method, beyond the commonly used Gutzwiller approximation, was recently developed based on Gutzwiller variational wave functions. We find that compared to benchmark data given by full configuration interaction, GCGM total energies are reasonably well reproduced with the minimum basis set. To include the dynamical correlation beyond the minimal basis calculations, we adopt the local density approximation for the dynamical correlation energy $E_c$. By comparing the results with benchmark data given by experiments and large-basis configuration interaction, the GCGM total energies with $E_c$ are in general better reproduced, but discrepancies are still observed for some dimers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

Osher, Stanley↗
NASA NTRS1957

Experimental Investigation of Effects of Moderate Sideslip on the Flow Fields near a 45 Degree Swept-wing-fuselage Combination at Low Speed

The flow fields near a 45 degree swept-wing-fuselage combination at moderate angles of sideslip (plus-or-minus 8 degrees), as determined experimentally at low speed, are presented as variations with chordwise distance for various spanwise and vertical locations and angles of attack. The results indicated that for positions close to the fuselage (on and near the plane of symmetry) changes in the angle of sideslip caused large changes in the flow-field characteristics and particularly in the local angles of sideslip, which in some cases were nearly double the static angle of sideslip. In general, the effects of changing the angle of sideslip on the flow-field characteristics for all of the outboard underwing locations were qualitatively similar, although conditions at the more inboard and outboard locations were somewhat more severe for lifting conditions than at the one-half semispan location. The chordwise gradients in the flow parameters for the underwing locations were more severe than for the fuselage locations although the effect of changing the angle of sideslip was less severe, in that the incremental changes in the local angles of sideslip were approximately equal to the static angle of sideslip. Flow conditions near the wing tip were found to be critically dependent on vertical location, with the largest sideslip-induced variations occurring at the nearest vertical locations. The results also indicated that for the outboard underwing locations the wing was the predominant factor in disturbing the field of flow for the conditions investigated.

Alford, William J , Jr↗
NASA NTRS1993

The role of large-scale eddies in the climate equilibrium. Part 2: Variable static stability

Lorenz's two-level model on a sphere is used to investigate how the results of Part 1 are modified when the interaction of the vertical eddy heat flux and static stability is included. In general, the climate state does not depend very much on whether or not this interaction is included, because the poleward eddy heat transport dominates the eddy forcing of mean temperature and wind fields. However, the climatic sensitivity is significantly affected. Compared to two-level model results with fixed static stability, the poleward eddy heat flux is less sensitive to the meridional temperature gradient and the gradient is more sensitive to the forcing. For example, the logarithmic derivative of the eddy flux with respect to the gradient has a slope that is reduced from approximately 15 on a beta-plane with fixed static stability and approximately 6 on a sphere with fixed static stability, to approximately 3 to 4 in the present model. This last result is more in line with analyses from observations. The present model also has a stronger baroclinic adjustment than that in Part 1, more like that in two-level beta-plane models with fixed static stability, that is, the midlatitude isentropic slope is very insensitive to the forcing, the diabatic heating, and the friction, unless the forcing is very weak.

Zhou, Shuntai↗
NASA NTRS1986

Simulation of the thermospheric tides by use of the NCAR thermospheric general circulation model

Numerical calculations of the thermospheric tidal winds and temperatures at equinox are presented. The calculations were made using the National Center for Atmospheric Research Thermospheric General Circulation Model (TGCM), which includes the effects of viscosity, conductivity, diffusion, ion drag, winds, and temperature gradients. The thermospheric diurnal and semidiurnal tides are excited in situ by solar heating and by ion-neutral momentum coupling. The semidiurnal tidal calculations also include the effects of upward propagating waves generated by heating in the lower atmosphere. This semidiurnal propagating component is modeled by use of the classical tidal perturbations as lower boundary conditions. The model is tuned by adjusting the propagating tidal forcing term until calculated semidiurnal wind and temperature fields best approximate incoherent scatter observations. The tidal TGCM results are consistent with previous theoretical work and successfully reproduce high altitude temperature and meridional velocity data, but they give significantly lower magnitudes for velocities and temperatures near 160 km than are seen by observations.

Fensen, C. G.↗
NASA NTRS1992

Learning and tuning fuzzy logic controllers through reinforcements

A new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. In particular, our Generalized Approximate Reasoning-based Intelligent Control (GARIC) architecture: (1) learns and tunes a fuzzy logic controller even when only weak reinforcements, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto, Sutton, and Anderson to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and has demonstrated significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Berenji, Hamid R.↗
NASA NTRS1997

Chemical and physical gradients along the OMC-1 ridge

We present a survey of the distribution of 20 chemical and isotopic molecular species along the central ridge of the Orion molecular cloud from 6' north to 6' south of BN-KL observed with the QUARRY focal plane array on the FCRAO 14 m telescope, which provides an angular resolution of approximately 50" in the 3 mm wavelength region. We use standard tools of multivariate analysis for a systematic investigation of the similarities and differences among the maps of integrated intensities of the 32 lines observed. The maps fall in three broad classes: first, those strongly peaked toward BN-KL; second, those having rather flat distributions along the ridge; and third, those with a clear north-south gradient or contrast. We identify six positions or regions where we calculate relative abundances. Line velocities and line widths indicate that the optically thin lines generally trace the same volume of dense gas, except in the molecular bar, where C18O, C34S, H13CO+, CN, C2H, SO, and C3H2 have velocities characteristic of the bar itself, whereas the emission from other detected species is dominated by the background cloud. The strongest abundance variations in our data are the well-known enhancements seen in HCN, CH3OH, HC3N, and SO toward BN-KL and, less strongly, toward the Orion-South outflow 1'.3S. The principal result of this study is that along the extended quiescent ridge the chemical abundances, within factors of 3-4, exhibit an impressive degree of uniformity. The northern part of the ridge has a chemistry closest to that found in quiescent dense clouds. While temperature and density are similar around the northern radical-ion peak near 3'.5N and in the southern core near 4'.2S, some abundances, in particular, those of the ions HCO+ and N2H+, are significantly lower toward 4'.2S. The areas near 4.'2S and the molecular bar itself around (1'.7E, 2'.4S) stand out with peculiar and similar properties probably caused by stronger UV fields penetrating deeper into the clumpy molecular gas. This leads to higher electron abundances and thereby reduced abundances of the ions, as well as a lack of complex molecules.

NASA Discipline Exobiology↗
NASA NTRS1992

Learning and tuning fuzzy logic controllers through reinforcements

This paper presents a new method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system. In particular, our generalized approximate reasoning-based intelligent control (GARIC) architecture (1) learns and tunes a fuzzy logic controller even when only weak reinforcement, such as a binary failure signal, is available; (2) introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; (3) introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and (4) learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward neural network, which can then adaptively improve performance by using gradient descent methods. We extend the AHC algorithm of Barto et al. (1983) to include the prior control knowledge of human operators. The GARIC architecture is applied to a cart-pole balancing system and demonstrates significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing.

Berenji, Hamid R.↗
NASA NTRS2000

Analysis of the Radar Reflectivity of Aircraft Vortex Wakes

Radar has been proposed as a way to track wake vortices to reduce aircraft spacing and tests have revealed radar echoes from aircraft wakes in clear air. The results are always interpreted qualitatively using Tatarski's theory of weak scattering by isotropic atmospheric turbulence. The goal of the present work was to predict the value of the radar cross-section (RCS) using simpler models. This is accomplished in two steps. First, the refractive index is obtained. Since the structure of the aircraft wakes is different from atmospheric turbulence, three simple mechanisms specific to vortex wakes are considered: (1) Radial density gradient in a two-dimensional vortex, (2) three-dimensional fluctuations in the vortex cores, and (3) Adiabatic transport of the atmospheric fluid in a two-dimensional oval surrounding the pair of vortices. The index of refraction is obtained more precisely for the two-dimensional mechanisms than for the three-dimensional ones. In the second step, knowing the index of refraction, a scattering analysis is performed. Tatarski's weak scattering approximation is kept but the usual assumptions of a far-field and a uniform incident wave are dropped. Neither assumption is generally valid for a wake that is coherent across the radar beam. For analytical insight, a simpler approximation that invokes, in addition to weak scattering, the far-field and wide cylindrical beam assumptions, is also developed and compared with the more general analysis. The predicted RCS values for the oval surround the vortices (mechanism C) agree with the experiments of Bilson conducted over a wide range of frequencies. However, the predictions have a cut-off away from normal incidence which is not present in the measurements. Estimates suggest that this is due to turbulence in the baroclinic vorticity generated at the boundary of the oval. The reflectivity of a vortex itself (mechanism A) is comparable to that of the oval (mechanism C) but cuts-off at frequencies lower than those considered in all the experiments to date. The RCS of a vortex happens to peak at the frequency (about 49 MHz) where atmospheric radars (known as ST radars) operate and so the present prediction could be verified in the future. Finally , we suggest that hot engine exhaust could increase RCE by 40 db and reveal vortex circulation, provided its mixing with the surroundings is prevented in the laminarising flow of the vortices.

Shariff, Karim↗
NASA NTRS1999

Swept-Wing Receptivity Studies Using Distributed Roughness

Transition to turbulence in swept-wing flows has resisted correlation with linear theory because of its sensitivity to freestream conditions and 3-D roughness and because one of the principal instability modes quickly 'becomes nonlinear. In the face of such a formidable problem, two rather long-term fundamental efforts have been underway at DLR Gottinberg and Arizona State University that address swept-wing transition. These efforts have been recently reviewed by Bippes (1997) and Reibert and Saric (1997). Thus, the present work is a continuation of a series of studies on swept-wing boundary layers which have led to a better understanding of the transition process. In particular, we have taken advantage of the sensitivity to 3-D roughness and the modal nature of the instability in order to propose a particular control strategy. Complementing the two aforementioned reviews, general reviews of the swept-wing transition problem are found in Arnal (1997) and Kachanov (1996). Other recent reviews include Reshotko (t997), Crouch (1997), and Herbert (1997a,b). The failure of linear theory is discussed in Reed et al. (1996). The historical work is found in Reed and Sar-ic (1989). The basic idea is that the combination of sweep and chordwise pressure gradient within the boundary layer creates a velocity component perpendicular to the inviscid streamline. This crossflow profile is inflectional and exhibits both traveling and stationary unstable waves called crossflow vortices that are (approximately) aligned along the inviscid streamlines. Under conditions of low freestream turbulence levels, the dominant crossflow wave is stationary (Reibert and Saric t997) while moderate to high turbulence levels initiate dominant traveling waves (Dehle and Bippes 1996; Bippes 1997). 'Me mechanism is relatively insensitive to sound and 2-D surface roughness (Radeztsky et al. 1993) but very sensitive to 3-D roughness near the attachment line. We concentrate our work on low-turbulence freestream flows and stationary crossflow waves. Although the v' and w' components of the disturbances are very small, by convecting streamwise momentum in the wall-normal direction, they produce 0(l) changes inu'.Thus the mean flow is highly distorted with localized inflection points. Transition is then triggered by a high-frequency secondary instability of the distorted mean profile.

Saric, William S.↗
NASA NTRS1987

Measurement of heat and moisture fluxes at the top of the rain forest during ABLE

Observations are presented of turbulent heat, moisture, and momentum transport made at two levels, approximately 5 and 10 m above the Amazon rain forest canopy. Data acquired at 10 Hz included variances and some mixed third moments of vertical velocity, temperature, and humidity. Two features of the data appear to question the displacement height hypothesis: (1) The characteristic dissipation length scale in the near-canopy layer varied between 20 m in stable conditions to approximately 150 m during afternoon convective conditions, generally larger scales than would be expected; and (2) No appreciable difference in dissipation scales was seen at the two observed levels. Observed peaks in vertical velocity-temperature cospectra lead to similar length scale estimates for dominant eddies. Heat budgets on selected days show that frequent periods with negative heat flux concurrent with continuing positive moisture flux occur in early afternoon, and this is believed to indicate the patchy nature of canopy-atmosphere coupling. Vertical velocity skewness was observed to be negative on three successive days and exhibited a sharp positive gradient.

Fitzjarrald, David R.↗
NASA NTRS1989

The stability of a compressible stratified shear layer

The stability of a shear layer under the effect of gravity is investigated using the compressible magnetohydrodynamic (MHD) equations, including an effective gravity term to represent the curvature effects of the flow and magnetic field line geometry. A general eigenmode equation is derived for a two-dimensional MHD fluid, and an energy-principle analysis to explain the effect of compressibility on the critical Richardson number is presented. For the case of a hyperbolic tangent shear flow and exponential density profile, it was found that, in the Boussinesq approximation, the compressibility raises the critical Richardson number from 1/4 to as much as 1/2, with the exact value depending on the value of the magnetic field at infinity. Under approximation of a strong asymptotic magnetic field, without invoking the Boussinesq approximation, it is shown both analytically and numerically that the density gradient terms cause the shear instability to be dispersive. The long-wavelength stability boundary for the Richardson number J = 0 is characterized by a normalized phase velocity c =

Wang, Z.↗
DOE OSTI2022

Exploring the S-process History in the Galactic Disk: Cerium Abundances and Gradients in Open Clusters from the OCCAM/APOGEE Sample

The APOGEE Open Cluster Chemical Abundances and Mapping survey is used to probe the chemical evolution of the s-process element cerium in the Galactic disk. Cerium abundances were derived from measurements of Ce ii lines in the APOGEE spectra using the Brussels Automatic Code for Characterizing High Accuracy Spectra in 218 stars belonging to 42 open clusters. Our results indicate that, in general, for ages < 4 Gyr, younger open clusters have higher [Ce/Fe] and [Ce/α-element] ratios than older clusters. In addition, metallicity segregates open clusters in the [Ce/X]–age plane (where X can be H, Fe, or the α-elements O, Mg, Si, or Ca). These metallicity-dependent relations result in [Ce/Fe] and [Ce/α] ratios with ages that are not universal clocks. Radial gradients of [Ce/H] and [Ce/Fe] ratios in open clusters, binned by age, were derived for the first time, with d[Ce/H]/dR GC being negative, while d[Ce/Fe]/dR GC is positive. [Ce/H] and [Ce/Fe] gradients are approximately constant over time, with the [Ce/Fe] gradient becoming slightly steeper, changing by ~+0.009 dex kpc -1 Gyr -1 . Both the [Ce/H] and [Ce/Fe] gradients are shifted to lower values of [Ce/H] and [Ce/Fe] for older open clusters. The chemical pattern of Ce in open clusters across the Galactic disk is discussed within the context of s-process yields from asymptotic giant branch (AGB) stars, gigayear time delays in Ce enrichment of the interstellar medium, and the strong dependence of Ce nucleosynthesis on the metallicity of its AGB stellar sources.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1999

Ocean Turbulence I: One-Point Closure Model Momentum and Heat Vertical Diffusivities

Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable underestimate of the extent of turbulent mixing and thus to an incorrect mixed layer depth. The predicted temperature and salinity profiles (vs. depth) are presented and compared with those of the Kolmogorov-Petruvsky-Piskunuv (KPP) model and Levitus data.

Canuto, V. M.↗
NASA NTRS1980

A rapid method for the approximate determination of nonlinear solutions Application to aerodynamic flows

A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.

Stahara, S. S.↗
NASA NTRS2003

Pore Formation and Mobility Investigation (PFMI): Description and Initial Analysis of Experiments Conducted Aboard the International Space Station

Flow Visualization experiments on the controlled melting and solidification of succinonitrile were conducted in the glovebox facility of the International Space Station (ISS). The experimental samples were prepared on ground by filling glass tubes, 1 cm 1D and approximately 30 cm in length, with pure succinonitrile (SCN) under 450 millibar of nitrogen. Porosity in the samples arose from natural shrinkage, and in some cases by direct insertion of nitrogen bubbles, during solidification of the liquid SCN. The samples were processed in the Pore Formation and Mobility Investigation (PFMI) apparatus that is placed in the glovebox facility (GBX) aboard the ISS. Experimental processing parameters of temperature gradient and translation speed, as well as camera settings, were remotely monitored and manipulated from the ground Telescience Center (TSC) at the Marshall Space Flight Center. During the experiments, the sample is first subjected to a unidirectional melt back, generally at 10 microns per second, with a constant temperature gradient ahead of the melting interface. The temperatures in the sample are monitored by six in situ thermocouples. Real time visualization of the controlled directional melt back shows bubbles of different sizes initiating at the melt interface and, upon dislodging from the melting solid, migrating at different speeds into the temperature field ahead of them, before coming to rest. The thermocapillary flow field set up in the melt, ahead of the interface, is dramatic in the context of the large bubbles, and plays a major role in dislodging the bubble. A preliminary analysis of the observed bubble formation and mobility during melt back and its implication to future microgravity experiments is presented and discussed.

Grugel, R. N.↗
NASA NTRS2003

Bubble Formation and Transport during Microgravity Materials Processing: Model Experiments on the International Space Station

Flow Visualization experiments on the controlled melting and solidification of succinonitrile were conducted in the glovebox facility of the International Space Station (ISS). The experimental samples were prepared on ground by filling glass tubes, 1 cm ID and approximately 30 cm in length, with pure succinonitrile (SCN) under 450 millibar of nitrogen. Porosity in the samples arose from natural shrinkage, and in some cases by direct insertion of nitrogen bubbles, during solidification of the liquid SCN. The samples were processed in the Pore Formation and Mobility Investigation (PFMI) apparatus that is placed in the glovebox facility (GBX) aboard the ISS. Experimental processing parameters of temperature gradient and translation speed, as well as camera settings, were remotely monitored and manipulated from the ground Telescience Center (TSC) at the Marshall Space Flight Center. During the experiments, the sample is first subjected to a unidirectional melt back, generally at 10 microns per second, with a constant temperature gradient ahead of the melting interface. The temperatures in the sample are monitored by six in situ thermocouples. Real time visualization of the controlled directional melt back shows bubbles of different sizes initiating at the melt interface and, upon dislodging from the melting solid, migrating at different speeds into the temperature field ahead of them, before coming to rest. The thermocapillary flow field set up in the melt, ahead of the interface, is dramatic in the context of the large bubbles, and plays a major role in dislodging the bubble. A preliminary analysis of the observed bubble formation and mobility during melt back and its implication to future microgravity experiments is presented and discussed.

Grugel, R. N.↗
NASA NTRS2003

Bubble Formation and Transport during Microgravity Materials Processing: Model Experiments on the International Space Station

Flow Visualization experiments on the controlled melting and solidification of succinonitrile were conducted in the glovebox facility of the International Space Station (ISS). The experimental samples were prepared on ground by filling glass tubes, 1 cm ID and approximately 30 cm in length, with pure succinonitrile (SCN) under 450 millibar of nitrogen. Porosity in the samples arose from natural shrinkage, and in some cases by direct insertion of nitrogen bubbles, during solidification of the liquid SCN. The samples were processed in the Pore Formation and Mobility Investigation (PFMI) apparatus that is placed in the glovebox facility (GBX) aboard the ISS. Experimental processing parameters of temperature gradient and translation speed, as well as camera settings, were remotely monitored and manipulated from the ground Telescience Center (TSC) at the Marshall Space Flight Center. During the experiments, the sample is first subjected to a unidirectional melt back, generally at 10 microns per second, with a constant temperature gradient ahead of the melting interface. The temperatures in the sample are monitored by six in situ thermocouples. Real time visualization of the controlled directional melt back shows bubbles of different sizes initiating at the melt interface and, upon dislodging from the melting solid, migrating at different speeds into the temperature field ahead of them, before coming to rest. The thermocapillary flow field set up in the melt, ahead of the interface, is dramatic in the context of the large bubbles, and plays a major role in dislodging the bubble. A preliminary analysis of the observed bubble formation and mobility during melt back and its implication to future microgravity experiments is presented and discussed.

Grugel, R. N.↗