Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “sub scale”

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 1,441 records · Page 80
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Scalable Detector Design for a High-Resolution Fast-Neutron Radiography Panel

Development of a scalable flat-panel neutron radiography device is needed to meet the nondestructive testing needs of a growing industrial market. Flood field images from a Cs-137 gamma source and a Cf-252 fission neutron source were generated using a detector composed of a 3-mm-thick sheet of EJ-200, and 3-mm-thick sheet of acrylic light spreader, an 8 $\times$ 8 array of SensL MICROFJ-60035-TSV SiPMs, and an IDEAS ROSSPAD readout module. The readout module can be tiled together with similar systems to create a panel of any size, and is only limited by the number of available Ethernet ports in a switching system. A collimated gamma line image demonstrated a 90% spatial resolution of approximately 0.47 line pairs per centimeter and a 10% spatial resolution of approximately 2.32 line pairs per centimeter. A neutron edge image demonstrated a 90% spatial resolution of approximately 0.70 line pairs per centimeter and a 10% spatial resolution of approximately 3.35 line pairs per centimeter. Both of these images show the ability to generate radiographs with sub-SiPM spatial resolution. Using these readout modules, a large-scale radiographic panel can be developed by tiling ROSSPAD modules together.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Field-scale dynamics of planting dates in the US Corn Belt from 2000 to 2020

Crop planting dates are a dynamic feature of agricultural systems that respond to short- and long-term climate signals, crop and cultivar selection, and technology changes. Planting date records are essential for yield gap analyses, accurate crop modeling, and tracking farmer adaptations to weather and climate change. Although planting dates have high variation at local scales due to heterogeneity in farm resources and decision-making, available long-term data on planting dates is largely restricted to aggregated regional statistics or, at best, satellite-derived datasets with limited spatiotemporal extent and at resolutions unable to distinguish individual fields (> 250 m). Here, we generated retrospective annual field-scale (30 m) planting date maps for both maize and soybeans spanning 2000-2020 across a 12 state region in the United States Corn Belt based on Landsat satellite data and a large ground sample of over 28,000 maize and soybean fields. Using training data from 2015-2020 for model selection, we found that planting date predictions improved with harmonic regression of Landsat data and additional annual weather covariates. The preferred random forests model approximately doubled performance compared to a null model based on state median planting dates, capturing 47% of field-level variation for maize (mean absolute error, MAE = 7.4 days) and 44% for soybeans (MAE = 7.5 days) against held-out ground truth test data for 2008-2014. We also evaluated the full 2000-2020 dataset with state agricultural statistics, finding strong agreement with median planting dates for maize (R 2 = 0.76, MAE = 4.4 days) and slightly lower agreement for soybeans (R 2 = 0.65, MAE = 5.4 days) when aggregated to the state level. We then used this new dataset to analyze environmental determinants of planting dates at a finer-scale than previously possible, controlling for unobserved variation at the sub-state district level. We found that during 2000-2020, each standard deviation increase in rainfall delayed planting by ~ 2.5 days, and fields with higher soil productivity ratings tended to be planted earlier. We did not find meaningful trends over the last two decades in planting dates for maize or soybeans, in contrast to trends towards earlier planting dates late last century and predicted for this period in climate adaptation studies. We hypothesize increases in early season rainfall may have inhibited these shifts towards earlier planting. Remotely sensed planting dates will be a useful tool for yield gap analyses, crop simulation modeling, and ongoing assessment of climate adaptation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A symmetry algebra in double-scaled SYK

The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the “chord Hilbert space”. We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the \mathfrak{sl}_2 𝔰 𝔩 2 near-horizon symmetries. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to \mathfrak{sl}_2 𝔰 𝔩 2 , but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2 𝔰 𝔩 2 algebra more standard at the cost of extending the boundary circle to include some “fake” portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Scalability of Real-time Distribution Models

This work will focus on developing the capabilities and validating the models for a sub transmission network with multiple feeders and microgrids. To achieve this scale of Hardware-in-the-loop (HitL) simulation, it is necessary to federate and collaborate. The work aims to design the large-scale feeder models to allow federation with complementary testbeds in the future. The feeder would be designed to be reconfigurable to put the system into a variety of modes. Aggregators models will be included in each distribution network’s federate to take control actions and interact with the management systems. Lastly, the feeder model will support large scale resilience studies involving complex Distributed Energy Resources (DER) controls, microgrid studies and emulation of complex data flows in future grid architectures.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Testing and Validation of Wireless Communication Architecture for Heliostat Fields: SIPS Final Report

This work focuses on the development and testing of a low-cost wireless communication system for heliostat fields, enabling significant capital costs reductions for concentrating solar thermal systems. Outputs of this work include a working demonstration of a multi-node communication system, clear reporting of system performance, and technical documentation of system development and architecture for reproducibility. Through this process, an open-source repository was created for manufacturing hardware at ~$30/heliostat. The system includes software for cybersecurity, achieving sub-second communication latencies and derisking of hardware for eventual scale-up to tens of thousands of heliostats. While the system is not currently off-the-shelf ready, there is now a clearly defined pathway for scaling up and completing the commercial development process.

14 SOLAR ENERGY↗
NASA NTRS1987

Micro and macro approaches to tough polymers for composites

The progress to date on the development of techniques to toughen continuous thermoplastic composites is summarized. The work, using the approach of toughening the polycarbonate composite matrix with rubber particles, has focused on determining the differences between Double Cantilever Beam (DCB) samples molded inhouse and those molded by NASA. Specifically, an effort was made to account for the differences in fracture toughness observed between the various specimens. In addition, preliminary results of tensile dilatometry tests are described; these tests suggest that processes leading to increased volume and enhanced shear banding are occurring within the rubber toughened system. The results of the effort using another approach, the preparation of random block copolycarbonates, are presented. The synthetic route to these species was modified so that higher molecular weights of these materials can be obtained. In addition, an attempt is being made to determine the exact block length or the number of functional groups in the oligomers since this procedure also should lead to high molecular weight materials. Dynamic mechanical analysis of the copolymer prepared so far indicates that the scale of cooperative molecular motion of the PBA polycarbonate at sub-Tg temperatures is larger than five monomer units. Efforts to find a suitable rubber-toughener for a thermoset system (bismaleimides) is also discussed. Included is a description of the various tougheners intended for use or currently being used.

Yee, Albert F.↗
NASA NTRS1989

Studies of superconducting materials with muon spin rotation

The muon spin rotation/relaxation technique was found to be an exceptionally effective means of measuring the magnetic properties of superconductors, including the new high temperature superconductor materials, at the microscopic level. The technique directly measures the magnetic penetration depth (type II superconductors (SC's)) and detects the presence of magnetic ordering (antiferromagnetism or spin-glass ordering were observed in some high temperature superconductor (HTSC's) and in many closely related compounds). Extensive studies of HTSC materials were conducted by the Virginia State University - College of William and Mary - Columbia University collaboration at Brookhaven National Laboratory and TRIUMF (Vancouver). A survey of LaSrCuO and YBaCaCuO systems shows an essentially linear relationship between the transition temperature T(sub c) and the relaxation rate. This appears to be a manifestation of the proportionality between T(sub c) and the Fermi energy, which suggests a high energy scale for the SC coupling, and which is not consistent with the weak coupling of phonon-mediated SC. Studies of LaCuO and YBaCuO parent compounds show clear evidence of antiferromagnetism. YBa2Cu(3-x)CO(x)O7 shows the simultaneous presence of spin-glass magnetic ordering and superconductivity. Three-dimensional SC, (Ba, K) BiO3, unlike the layered CuO-based compounds, shows no suggestion of magnetic ordering. Experimental techniques and theoretical implications are discussed.

Davis, Michael R.↗
NASA NTRS1990

Development of Renormalization Group Analysis of Turbulence

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

L M Smith↗
NASA NTRS1992

Regenerable biocide delivery unit, volume 1

The Microbial Check Valve (MCV), which is currently used aboard the Shuttle Orbiter for disinfection of the potable water supply, is an expendable flow-through canister containing iodinated ion exchange resin. Means for extension of MCV life are desirable to avoid resupply penalties. The Phase 1 Regenerable Biocide Delivery Unit program demonstrated the feasibility of regenerating an MCV in situ, using a strong aqueous elemental iodine solution resulting from diversion of the MCV influent to a packed bed containing iodine crystals. In small column tests, eight manual regenerations of an MCV resin were accomplished. The term Regenerative Microbial Check Valve (RMCV) was adopted describing this new technology. The Phase 2 program resulted in the development of a full scale and fully autonomous prototype RMCV, capable of maintaining residual I(sub 2) levels between 2.0 - 4.0 mg/L for prolonged periods. During six months of testing at the Space Station baseline flow rate of 120 cm(sup 3)/min, the prototype RMCV underwent nine regenerations. RMCV life cycle tests, using a variety of influent streams, were conducted over an eighteen month period to determine the useful lives of MCV's incorporating this new technology and to determine ultimate failure mechanisms. MCV life extensions of 130 fold were demonstrated, limited only by the Phase 2 performance period. Based upon this work, it is certain that RMCV units can be developed to provide unattended biocide addition for the thirty year life of Space Station Freedom, or for other longer duration applications such as a Lunar Base or Mars mission. RMCV technology was also demonstrated capable of delivering, on demand, a concentrated aqueous I(sub 2) solution for potential use as a disinfectant during transient episodes of microbial surface contamination, for the control of biofilm formation, or as a preventative measure in systems which are particularly susceptible to the growth of microorganisms.

Atwater, James E.↗
NASA NTRS1993

The starburst-AGN connection - A sensitive VLBI survey of luminous IRAS galaxies

Results of an 18 cm VLBI survey of 31 luminous, radio-compact IR galaxies are presented. Over half the sample galaxies show high-brightness temperature emission, with T sub b greater than 10 exp 5 K and structure on scales of 5-150 mas. The limits for nondetected sources are similar, consistent with a picture in which most of these galaxies have compact cores at a level of a few percent of the total radio flux density. Characteristics of the extended radio structure, infrared properties, and optical excitation are not good indicators of the detectability of VLBI-scale emission. Structural information and energetic considerations rule out a single supernova interpretation of the compact emission in these galaxies, although we cannot exclude the possibility of several simultaneous extraordinarily luminous radio supernovae within the central few hundred cubic parsec. Our results instead favor the presence of an AGN obscured by starburst-related dust.

Lonsdale, Colin J.↗
NASA NTRS1946

An Experimental Investigation of Flow Conditions in the Vicinity of an NACA D(sub S)-type Cowling

Data are presented of the flow conditions in the vicinity of an NACA D sub S -type cowling. Tests were made of a 1/2 scale-nacelle model at inlet-velocity ratios ranging from 0.23 to 1.02 and angles of attack from 6 deg to 10 deg. The velocity and direction of flow in the vertical plane of symmetry of the cowling were determined from orifices and tufts installed on a board aligned with the flow. Diagrams showing velocity ratio contours and lines of constant flow angles are given.

FLAPPED↗
NASA NTRS1995

Premixed turbulent flame propagation in microgravity

To reduce pollutant formation there is, at present, an increased interest in employing premixed fuel/air mixture in combustion devices. It is well known that greater control over local temperature can be achieved with premixed flames and with lean premixed mixtures, significant reduction of pollutants such as NO(x) can be achieved. However, an issue that is still unresolved is the predictability of the flame propagation speed in turbulent premixed mixtures, especially in lean mixtures. Although substantial progress has been made in recent years, there is still no direct verification that flame speeds in turbulent premixed flows are highly predictable in complex flow fields found in realistic combustors. One of the problems associated with experimental verification is the difficulty in obtaining access to all scales of motion in typical high Reynolds number flows, since, such flows contain scales of motion that range from the size of the device to the smallest Kolmogorov scale. The overall objective of this study is to characterize the behavior of turbulent premixed flames at reasonable high Reynolds number, Re(sub L). Of particular interest here is the thin flame limit where the laminar flame thickness is much smaller than the Kolmogorov scale. Thin flames occur in many practical combustion devices and will be numerically studied using a recently developed new formulation that is briefly described.

Menon, S.↗
NASA NTRS2000

On-Orbit Calibration of ADEOS OCTS with an AVIRIS Underflight

The Ocean Color Temperature Scanner (OCTS) onboard the Advanced Earth Observation Satellite (ADEOS) was launched on August 17, 1996. Calibration of OCTS is required for use of the on-orbit measured data for retrieval of physical properties of the ocean. In the solar reflected portion of the electromagnetic spectrum, OCTS measures images with nominally 700-m spatial resolution through eight multispectral bands. The objective of this research was to establish the absolute radiometric calibration of OCTS on orbit through an underflight by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). AVIRIS is a NASA earth-observing imaging spectrometer designed, built and operated by the Jet Propulsion Laboratory (JPL). AVIRIS acquires data from 20-km altitude on a NASA ER-2 aircraft, above most of the Earth's atmosphere. AVIRIS measures the solar reflected spectrum from 370 nm to 2500 nm through 224 contiguous spectral channels. The full width at half maximum (FWHM) of the spectral channels is nominally 10-nm. AVIRIS spectra are acquired as images of 11 km by up to 800 km extent with 20-m spatial resolution. The high spectral resolution of AVIRIS data allows direct convolution to the spectral response functions of the eight multispectral bands of OCTS. The high spatial resolution of AVIRIS data allows for spatial re-sampling of the data to match the ADEOS sensors spatial resolution. In addition, the AVIRIS high spatial resolution allows assessment of the scaling effects due to environmental factors of thin cirrus clouds, sub-pixel cloud cover, white caps, ocean foam, sun-glint, and bright-target adjacency. The platform navigation information recorded by AVIRIS allows calculation of the position and observation geometry of each spectrum for matching to the OCTS measurement. AVIRIS is rigorously characterized and calibrated in the laboratory prior to and following the flight season. The stability and repeatability of AVIRIS calibration have been validated through an extensive series of inflight calibration experiments. In the OCTS portion of the spectrum, using pre-and post-flight runway calibrations of AVIRIS coupled with the on-board calibrator an absolute calibration accuracy of better than 3% spectral, 2% radiometric and 5% spatial has been achieved. An analogous satellite underflight calibration experiment was performed with AVIRIS and the Optical Sensor (OPS) onboard the Japanese Earth Resources Satellite (JERS).

Green, Robert O.↗
NASA NTRS1998

On-Orbit Calibration of ADEOS OCTS with an AVIRIS Underflight

The Ocean Color Temperature Scanner (OCTS) onboard the Advanced Earth Observation Satellite (ADEOS) was launched on August 17, 1996. Calibration of OCTS is required for use of the on-orbit measured data for retrieval of physical properties of the ocean. In the solar reflected portion of the electromagnetic spectrum, OCTS measures images with nominally 700-m spatial resolution through eight multispectral bands. The objective of this research was to establish the absolute radiometric calibration of OCTS on orbit through an underflight by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). AVIRIS is a NASA Earth-observing imaging spectrometer designed, built and operated by the Jet Propulsion Laboratory (JPL). AVIRIS acquires data from 20-km altitude on a NASA ER-2 aircraft, above most of the Earth's atmosphere. AVIRIS measures the solar reflected spectrum from 370 nm to 2500 nm through 224 contiguous spectral channels. The full width at half maximum (FWHM) of the spectral channels is nominally 10-nm. AVIRIS spectra are acquired as images of 11 km by up to 800 km extent with 20-m spatial resolution. The high spectral resolution of AVIRIS data allows direct convolution to the spectral response functions of the eight multispectral bands of OCTS. The high spatial resolution of AVIRIS data allows for spatial re-sampling of the data to match the ADEOS sensors spatial resolution. In addition, the AVIRIS high spatial resolution allows assessment of the scaling effects due to environmental factors of thin cirrus clouds, sub-pixel cloud cover, white caps, ocean foam, sun-glint, and bright-target adjacency. The platform navigation information recorded by AVIRIS allows calculation of the position and observation geometry of each spectrum for matching to the OCTS measurement. AVIRIS is rigorously characterized and calibrated in the laboratory prior to and following the flight season. The stability and repeatability of AVIRIS calibration have been validated through an extensive series of inflight calibration experiments. In the OCTS portion of the spectrum, using pre- and post-flight runway calibrations of AVIRIS coupled with the on-board calibrator an absolute calibration accuracy of better than 3% spectral, 2% radiometric, and 5% spatial, has been achieved. An analogous satellite underflight calibration experiment was performed with AVIRIS and the Optical Sensor (OPS) onboard the Japanese Earth Resources Satellite (JERS).

Green, Robert O.↗
NASA NTRS2004

Discovery of Presolar Corundum (and SiC?) in an Interplanetary Dust Particle

This work is part of an ongoing investigation [1-3] of isotopically anomalous phases in interplanetary dust particles (IDPs) on a scale of 100 nm. Previously, such NanoSIMS studies have found sub-micrometer sized, isotopically distinct presolar grains in IDPs at higher abundances than in primitive meteorites [1-5], which demonstrates the unique and primitive nature of IDPs. Although not all presolar grains found so far in IDPs have been chemically or petrographically characterized, the majority appear to be silicate stardust. Conspicuously absent from the presolar grain inventory in IDPs have been other grain types, which are commonly found in primitive meteorites, such as SiC and corundum (Al2O3).

Stadermann, F. J.↗
NASA NTRS2005

Warm Molecular Gas Traced with CO J = 7 --> 6 in the Galaxy's Central 2 Parsecs: Dynamical Heating of the Circumnuclear Disks

We present an 11" resolution map of the central 2 pc of the Galaxy in the CO J = 7 --> 6 rotational transition. The CO emission shows rotation about Sgr A* but also evidence for noncircular turbulent motion and a clumpy morphology. We combine our data set with available CO measurements to model the physical conditions in the disk. We find that the molecular gas in the region is both warm and dense, with T approx. 200-300 K and n(sub H2) approx. (5-7) x 10(exp 4) cm(exp -3). The mass of warm molecular gas we measure in the central 2 pc is at least 2000 M(solar), about 20 times the UV-excited atomic gas mass, ruling out a UV heating scenario for the molecular material. We compare the available spectral tracers with theoretical models and conclude that molecular gas is heated with magnetohydrodynamic shocks with v approx. 10-20 km s(exp -1) and B approx. 0.3- 0.5 mG. Using the conditions derived with the CO analysis, we include the other important coolants, neutral oxygen and molecular hydrogen, to estimate the total cooling budget of the molecular material. We derive a mass-to-luminosity ratio of approx. 2-3 M(solar)(L(solar)exp -1), which is consistent with the total power dissipated via turbulent decay in 0.1 pc cells with v(sub rms) approx. 15 kilometers per second. These size and velocity scales are comparable to the observed clumping scale and the velocity dispersion. At this rate, the material near Sgr A* is dissipating its orbital energy on an orbital timescale and cannot last for more than a few orbits. Our conclusions support a scenario in which the features near Sgr A* such as the circumnuclear disk and northern arm are generated by infalling clouds with low specific angular momentum.

galatic nuclei↗
NASA NTRS2013

Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results

We present cosmological parameter constraints based on the final nine-year Wilkinson Microwave Anisotropy Probe (WMAP) data, in conjunction with a number of additional cosmological data sets. The WMAP data alone, and in combination, continue to be remarkably well fit by a six-parameter Lambda-CDM model. When WMAP data are combined with measurements of the high-l cosmic microwave background anisotropy, the baryon acoustic oscillation scale, and the Hubble constant, the matter and energy densities Omega(sub b)h(exp 2), Omega(sub c)h(exp 2)and Omega(sub Lambda), are each determined to a precision of approx. 1.5%. The amplitude of the primordial spectrum is measured to within 3%, and there is now evidence for a tilt in the primordial spectrum at the 5 sigma level, confirming the first detection of tilt based on the five-year WMAP data. At the end of the WMAP mission, the nine-year data decrease the allowable volume of the six-dimensional Lambda-CDM parameter space by a factor of 68,000 relative to pre-WMAP measurements. We investigate a number of data combinations and show that their Lambda-CDM parameter fits are consistent. New limits on deviations from the six-parameter model are presented, for example: the fractional contribution of tensor modes is limited to r < 0.13 (95% CL); the spatial curvature parameter is limited to Omega(sub kappa) = (0.0027 (sub +0.0039) (sup −0.0038;) the summed mass of neutrinos is limited to Sigma M(sub nu) < 0.44 eV (95% CL); and the number of relativistic species is found to lie within N(sub eff) = 3.84 +/- 0+/-40, when the full data are analyzed. The joint constraint on N(sub eff) and the primordial helium abundance, Y(sub He), agrees with the prediction of standard big bang nucleosynthesis. We compare recent Planck measurements of the Sunyaev-Zel'dovich effect with our seven-year measurements, and show their mutual agreement. Our analysis of the polarization pattern around temperature extrema is updated. This confirms a fundamental prediction of the standard cosmological model and provides a striking illustration of acoustic oscillations and adiabatic initial conditions in the early universe.

cosmology↗
NASA NTRS2015

Turbulent Concentration of mm-Size Particles in the Protoplanetary Nebula: Scale-Dependent Cascades

The initial accretion of primitive bodies (here, asteroids in particular) from freely-floating nebula particles remains problematic. Traditional growth-by-sticking models encounter a formidable "meter-size barrier" (or even a mm-to-cm-size barrier) in turbulent nebulae, making the preconditions for so-called "streaming instabilities" difficult to achieve even for so-called "lucky" particles. Even if growth by sticking could somehow breach the meter size barrier, turbulent nebulae present further obstacles through the 1-10km size range. On the other hand, nonturbulent nebulae form large asteroids too quickly to explain long spreads in formation times, or the dearth of melted asteroids. Theoretical understanding of nebula turbulence is itself in flux; recent models of MRI (magnetically-driven) turbulence favor low-or- no-turbulence environments, but purely hydrodynamic turbulence is making a comeback, with two recently discovered mechanisms generating robust turbulence which do not rely on magnetic fields at all. An important clue regarding planetesimal formation is an apparent 100km diameter peak in the pre-depletion, pre-erosion mass distribution of asteroids; scenarios leading directly from independent nebula particulates to large objects of this size, which avoid the problematic m-km size range, could be called "leapfrog" scenarios. The leapfrog scenario we have studied in detail involves formation of dense clumps of aerodynamically selected, typically mm-size particles in turbulence, which can under certain conditions shrink inexorably on 100-1000 orbit timescales and form 10-100km diameter sandpile planetesimals. There is evidence that at least the ordinary chondrite parent bodies were initially composed entirely of a homogeneous mix of such particles. Thus, while they are arcane, turbulent concentration models acting directly on chondrule size particles are worthy of deeper study. The typical sizes of planetesimals and the rate of their formation can be estimated using a statistical model with properties inferred from large numerical simulations of turbulence. Nebula turbulence is described by its Reynolds number Re = (L/eta)(exp 4/3), where L = H alpha(exp 1/2) is the largest eddy scale, H is the nebula gas vertical scale height, alpha the turbulent viscosity parameter, and eta is the Kolmogorov or smallest scale in turbulence (typically about 1km), with eddy turnover time t(sub eta). In the nebula, Re is far larger than any numerical simulation can handle, so some physical arguments are needed to extend the results of numerical simulations to nebula conditions. In this paper, we report new physics to be incorporated into our statistical models.

mm-size particles↗