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At least 1,261 records · Page 70

Linking topographic variation in belowground C processes with hydrological processes to improve Earth system models

The effects of topography on belowground processes were investigated at the Susquehanna-Shale Hills Critical Zone Observatory in central Pennsylvania. Hill slope had stronger effects on aboveground biomass allocation than belowground allocation. Hills slope position affected the respiratory response to temperature with a 10-degree increase having more influence in slope positions characterized by higher moisture. A spatial distributed forest model that includes nitrogen transport was developed from a 1-dimensional biogeochemical model and a spatially distributed land surface hydrological model. This model can simulate the impact of topography-driven spatially-distributed soil moisture, soil temperature, solar radiation, and soil mineral N on watershed carbon processes. This project helped in the training of four PhD students.

54 ENVIRONMENTAL SCIENCES↗

Boxy/Peanut/X-Shaped Bulges: Steep Inner Rotation Curve Leads to Barlens Face-on Morphology

We use stellar dynamical bulge/disk/halo simulations to study whether barlenses (lens-like structures embedded in the narrow bar component) are only the face-on counterparts of Boxy/Peanut/X-shapes (B/P/X) seen in edge-on bars, or if some additional physical parameter affects that morphology. A range of bulge-to-disk mass and size ratios are explored: our nominal parameters (B/D=0.08, r{sub eff}/h{sub r}=0.07, disk comprising two-thirds of total force at 2.2h{sub r}) correspond to typical Milky Way mass galaxies. In all models, a bar with pronounced B/P/X forms in a few Gyr, visible in the edge-on view. However, the pure barlens morphology forms only in models with sufficiently steep inner rotation curves, dV{sub cir}/dr≳5V{sub max}/h{sub r}, achieved when including a small classical bulge with B/D≳0.02 and r{sub eff}/h{sub r}≲0.1. For shallower slopes, the central structure still resembles a barlens, but shows a clear X signature even in low inclinations. A similar result holds for bulge-less simulations, where the central slope is modified by changing the halo concentration. The predicted sensitivity on the inner rotation curve is consistent with the slopes that are estimated from gravitational potentials calculated from the 3.6 μm images, for the observed barlens and X-shaped galaxies in the Spitzer Survey of Stellar Structure in Galaxies (S{sup 4}G). For inclinations <60° the galaxies with barlenses have on average twice steeper inner rotation curves than galaxies with X shapes: the limiting slope is ∼250 km s{sup −1} kpc{sup −1}. Among barred galaxies, those with barlenses have both the strongest bars and the largest relative excess of inner surface density, both in barlens regions (≲0.5h{sub r}) and near the center (≲0.1h{sub r}); this provides evidence for bar-driven secular evolution in galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Mapping of Benthic Habitats at Marine Renewable Energy Sites Using Multibeam Echosounder and Sediment Profile Imaging Technologies

Objectives/Scope: The goal of this work was to develop a consistent and semi-automated seafloor survey method for generating high-resolution, benthic habitat maps for environmental assessments and monitoring of marine renewable energy sites. Sediment profile and plan view imaging (SPI/PV) technology was combined with multibeam bathymetry and acoustic backscatter methods to demonstrate a rapid, cost-effective benthic mapping protocol. A key technical innovation of this project was the development of an image processing platform that automatically measures key features from the images. Methods: Multibeam echosounder (MBES) acoustic and SPI/PV surveys were conducted at three coastal areas off the U.S. west coast, including the PacWave South energy test site off of Newport, Oregon. Point data on physical and biological sediment conditions obtained from the SPI/PV imagery were used to efficiently ground-truth the high-resolution MBES bathymetry and backscatter mosaics. The SPI camera is an optical corer that obtains an undisturbed 21 by 15 cm, high-resolution, cross-sectional image of the sediment–water interface and upper sediment column. The plan view camera attached to the SPI camera frame captures a downward looking view of the seabed immediately before the SPI image is obtained. As part of this project, we developed a computer vision image processing platform (iSPI) that uses deep convolutional neural networks and other approaches to automatically identify and measure key features in the images, such as grain size and surface relief. Results: Detailed benthic habitat maps were generated using this mapping approach for three different marine settings. The sites mapped included a silt-dominated embayment; a sloping, nearshore, transitional very fine to coarse sand bottom; and a medium, sand-dominated continental shelf marine energy test site. In each case, acoustic and imaging surveys were completed in less than week, and detailed benthic habitat maps were generated within 60 days. The results were placed within the Coastal and Marine Ecological Classification Standard (CMECS) habitat mapping framework, and various combinations of the bathymetry, backscatter, and SPI and PV data were used to generate CMECS component maps. Novel Information: This project developed and demonstrated a repeatable and cost-effective approach for efficiently mapping benthic habitat conditions over broad areas of the seafloor by combining state-of-the-art acoustic and imaging techniques. The primary survey tools used in this project have been used previously in both the offshore renewable (wind) and oil and gas sectors to map and monitor benthic environments. This project’s innovations include 1) the focused use of high-resolution SPI/PV imagery to ground-truth acoustic mosaics, and 2) the development of a computer automated image analysis processing tool that both streamlines and standardizes the generation of data from the imagery and makes the data extraction process more cost-effective and repeatable.

13 HYDRO ENERGY↗

Distribution and flux of micrometeoroids

The mass distribution, flux, and distribution in space of the micrometeoroid complex at 1 AU are estimated on the basis of data from Apollo 17 rocks and recent calibrations of solar-flare track-production rates. It is found that the size frequency distribution of microcraters on lunar rocks suggests a bimodal mass distribution of micrometeoroids, but the precise form of the curve requires further definition, particularly insofar as the degree of depletion of particles producing craters 10 to 100 microns in diameter is concerned. Variations in slope with crater-diameter or particle-mass increments are shown to indicate that different processes affect one or more particle populations. Fluxes corresponding to varied lunar surface orientation and residence time are calculated, but no striking difference is observed between the flux of submicron-diameter particles with orbits in the plane of the ecliptic and fluxes of particles with orbits normal to the plane in the solar apex direction.

Morrison, D. A.↗

Proceedings of the 39th Lunar and Planetary Science Conference

Sessions with oral presentations include: A SPECIAL SESSION: MESSENGER at Mercury, Mars: Pingos, Polygons, and Other Puzzles, Solar Wind and Genesis: Measurements and Interpretation, Asteroids, Comets, and Small Bodies, Mars: Ice On the Ground and In the Ground, SPECIAL SESSION: Results from Kaguya (SELENE) Mission to the Moon, Outer Planet Satellites: Not Titan, Not Enceladus, SPECIAL SESSION: Lunar Science: Past, Present, and Future, Mars: North Pole, South Pole - Structure and Evolution, Refractory Inclusions, Impact Events: Modeling, Experiments, and Observations, Mars Sedimentary Processes from Victoria Crater to the Columbia Hills, Formation and Alteration of Carbonaceous Chondrites, New Achondrite GRA 06128/GRA 06129 - Origins Unknown, The Science Behind Lunar Missions, Mars Volcanics and Tectonics, From Dust to Planets (Planetary Formation and Planetesimals):When, Where, and Kaboom! Astrobiology: Biosignatures, Impacts, Habitability, Excavating a Comet, Mars Interior Dynamics to Exterior Impacts, Achondrites, Lunar Remote Sensing, Mars Aeolian Processes and Gully Formation Mechanisms, Solar Nebula Shake and Bake: Mixing and Isotopes, Lunar Geophysics, Meteorites from Mars: Shergottite and Nakhlite Invasion, Mars Fluvial Geomorphology, Chondrules and Chondrule Formation, Lunar Samples: Chronology, Geochemistry, and Petrology, Enceladus, Venus: Resurfacing and Topography (with Pancakes!), Overview of the Lunar Reconnaissance Orbiter Mission, Mars Sulfates, Phyllosilicates, and Their Aqueous Sources, Ordinary and Enstatite Chondrites, Impact Calibration and Effects, Comparative Planetology, Analogs: Environments and Materials, Mars: The Orbital View of Sediments and Aqueous Mineralogy, Planetary Differentiation, Titan, Presolar Grains: Still More Isotopes Out of This World, Poster sessions include: Education and Public Outreach Programs, Early Solar System and Planet Formation, Solar Wind and Genesis, Asteroids, Comets, and Small Bodies, Carbonaceous Chondrites, Chondrules and Chondrule Formation, Chondrites, Refractory Inclusions, Organics in Chondrites, Meteorites: Techniques, Experiments, and Physical Properties, MESSENGER and Mercury, Lunar Science Present: Kaguya (SELENE) Results, Lunar Remote Sensing: Basins and Mapping of Geology and Geochemistry, Lunar Science: Dust and Ice, Lunar Science: Missions and Planning, Mars: Layered, Icy, and Polygonal, Mars Stratigraphy and Sedimentology, Mars (Peri)Glacial, Mars Polar (and Vast), Mars, You are Here: Landing Sites and Imagery, Mars Volcanics and Magmas, Mars Atmosphere, Impact Events: Modeling, Experiments, and Observation, Ice is Nice: Mostly Outer Planet Satellites, Galilean Satellites, The Big Giant Planets, Astrobiology, In Situ Instrumentation, Rocket Scientist's Toolbox: Mission Science and Operations, Spacecraft Missions, Presolar Grains, Micrometeorites, Condensation-Evaporation: Stardust Ties, Comet Dust, Comparative Planetology, Planetary Differentiation, Lunar Meteorites, Nonchondritic Meteorites, Martian Meteorites, Apollo Samples and Lunar Interior, Lunar Geophysics, Lunar Science: Geophysics, Surface Science, and Extralunar Components, Mars, Remotely, Mars Orbital Data - Methods and Interpretation, Mars Tectonics and Dynamics, Mars Craters: Tiny to Humongous, Mars Sedimentary Mineralogy, Martian Gullies and Slope Streaks, Mars Fluvial Geomorphology, Mars Aeolian Processes, Mars Data and Mission,s Venus Mapping, Modeling, and Data Analysis, Titan, Icy Dwarf Satellites, Rocket Scientist's Toolbox: In Situ Analysis, Remote Sensing Approaches, Advances, and Applications, Analogs: Sulfates - Earth and Lab to Mars, Analogs: Remote Sensing and Spectroscopy, Analogs: Methods and Instruments, Analogs: Weird Places!. Print Only Early Solar System, Solar Wind, IDPs, Presolar/Solar Grains, Stardust, Comets, Asteroids, and Phobos, Venus, Mercury, Moon, Meteorites, Mars, Astrobiology, Impacts, Outer Planets, Satellites, and Rings, Support for Mission Operations, Analog Education and Public Outreach.

Source record↗

A Parametric Study of the Aerodynamic Characteristics of Nose-Cylinder-Flare Bodies at a Mach Number of 6.0

Force tests were conducted at a Mach number of 6.0 on nose-cylinder-flare bodies to determine the effect of nose shape, cylinder length, flare angle, and flare length on the longitudinal aerodynamic characteristics. A particular investigation was conducted to determine the effect of flare angle for constant flare length, surface area, and diameter. Results indicated that at a Reynolds number of approximately 0.92 x l0 (exp 6) (based on body diameter), the boundary-layer separation effects were significant only with respect to the slope of the normal-force and pitching-moment curve at low angles of attack. The variations of the aerodynamic characteristics with the various parameters were, in general, similar to those predicted by Newtonian theory below a flare angle of 30 degrees and a ratio of flare base diameter to cylinder diameter of less than approximately 2.2. The limiting diameter ratio is consistent with the extent of the low-constant dynamic-pressure region near the body caused by the bow-shock influences as predicted by axisymmetric characteristic theory. The effects of the various parameters for the flares that exceeded the limiting diameter ratio follow the trends predicted by the computed flow-field properties. The axial force for these flare configurations at zero angle of attack was, in general, computed within 10 percent by using these properties. For a constant flare length and surface area the flare effectiveness increased with increasing flare angle; however, for constant flare diameter only the axial-force coefficient was affected by flare angle.

Ashby, George C., Jr.↗

Martian Terrain Ages

The cratering record in the inner Solar System shows two crater populations based on their size/frequency distributions. The heavily cratered surfaces of the Moon, Mercury and Mars all show a similar multisloped crater size distribution which represents the period of heavy bombardment. On the younger plains units of the Moon and Mars the crater size/frequency distribution has about a -3 slope over the same diameter range. The different crater population represents the accumulation of craters since the end of heavy bombardment. The high flux of the early impacting objects dominated the cratering record prior to 3.8 BY. If heavy bombardment was primarily the result of comets (1) or a disrupted planetesimal (2), then heavy bombardment ended simultaneously on all of the inner planets. If, on the other, heavy bombardment was caused by accretional remnants, then it may have extended as much as 1 BY later on Mars than on the Moon and other terrestrial planets (3). Martian surfaces can be dated relative to the end of heavy bombardment by the type of crater population superposed on them. The relative ages of surfaces within these two time divisions can be determined by crater densities.

Strom, R. G.↗

The impact cratering record on Triton

Impact craters on Triton are scarce owing to the relatively recent resurfacing by icy melts. The most heavily cratered surface has a crater density about the same as the lunar maria. The transition diameter from simple to complex craters occurs at a diameter of about 11 kilometers, and the depth-diameter relationship is similar to that of other icy satellites when gravity is taken into account. The crater size-frequency distribution has a differential -3 slope (cumulative -2 slope) and is the same as that for the fresh crater population on Miranda. The most heavily cratered region is on the leading hemisphere in Triton's orbit. Triton may have a leading-trailing asymmetry in its crater population. Based primarily on the similarity of size distributions on Triton and Miranda and the relatively young surface on Triton, the source of Triton's craters is probably comets. The very peculiar size distribution of sharp craters on the 'cantaloupe' terrain and other evidence suggests thay are volcanic explosion craters.

Strom, Robert G.↗

Anisotropic multiband superconductivity in 2 M − WS 2 probed by controlled disorder

The intrinsically superconducting Dirac semimetal 2 M − WS 2 is a promising candidate for realizing proximity-induced topological superconductivity in its protected surface states. A precise characterization of the bulk superconducting state is essential to understand the nature of surface superconductivity in the system. Here, we report a detailed experimental study of the temperature-dependent London penetration depth, λ ( T ) , the upper critical field, H c 2 ( T ) , and the effects of nonmagnetic disorder on these quantities, as well as on the superconducting transition temperature T c in single crystals of 2 M − WS 2 . We observe a power-law variation of λ ( T ) ∝ T 3 at temperatures below 0.35 T c . Nonmagnetic pointlike disorder induced by 2.5 MeV electron irradiation at various doses results in a significant suppression of T c . These observations are markedly different from expectations for a fully gapped isotropic s − wave superconductor. Together with the substantial increase of slope, d H c 2 / d T | T = T c , with increasing disorder, our results suggest a strongly anisotropic s + + multiband superconducting state. These results have direct consequences for the expected proximity-induced superconductivity of the topological surface states. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Advances in Measuring Antarctic Sea-Ice Thickness and Ice-Sheet Elevations with ICESat Laser Altimetry

NASA's Ice, Cloud and Land Elevation Satellite (ICESat) has been measuring elevations of the Antarctic ice sheet and sea-ice freeboard elevations with unprecedented accuracy. Since February 20,2003, data has been acquired during three periods of laser operation varying from 36 to 54 days, which is less than the continuous operation of 3 to 5 years planned for the mission. The primary purpose of ICESat is to measure time-series of ice-sheet elevation changes for determination of the present-day mass balance of the ice sheets, study of associations between observed ice changes and polar climate, and estimation of the present and future contributions of the ice sheets to global sea level rise. ICESat data will continue to be acquired for approximately 33 days periods at 3 to 6 month intervals with the second of ICESat's three lasers, and eventually with the third laser. The laser footprints are about 70 m on the surface and are spaced at 172 m along-track. The on-board GPS receiver enables radial orbit determinations to an accuracy better than 5 cm. The orbital altitude is around 600 km at an inclination of 94 degrees with a 8-day repeat pattern for the calibration and validation period, followed by a 91 -day repeat period for the rest of the mission. The expected range precision of single footprint measurements was 10 cm, but the actual range precision of the data has been shown to be much better at 2 to 3 cm. The star-tracking attitude-determination system should enable footprints to be located to 6 m horizontally when attitude calibrations are completed. With the present attitude calibration, the elevation accuracy over the ice sheets ranges from about 30 cm over the low-slope areas to about 80 cm over areas with slopes of 1 to 2 degrees, which is much better than radar altimetry. After the first period of data collection, the spacecraft attitude was controlled to point the laser beam to within 50 m of reference surface tracks over the ice sheets. Detection of ice elevation changes over select areas of the ice sheet is demonstrated with using both crossover analysis and precise-repeat track analysis. Sea ice freeboard-height distributions over the Antarctic sea pack are derived over distances of 50 km and converted into maps of average freeboard thickness and sea-ice thickness.

Zwally, H. Jay↗

Aging effect in magnetotransport property of oxygen adsorbed BaFe{sub 2}As{sub 2}

Presence of oxygen (O{sub 2}) has been found by Energy Dispersive X-ray Analysis (EDAX) on the surfaces of flux grown BaFe{sub 2}As{sub 2} single crystals which were kept in air ambience for several months. Transport studies show that the O{sub 2} adsorbed crystals are more resistive and do not display any sharp slope change near 140 K which is the well known Spin Density Wave (SDW) transition temperature (T{sub SDW}) accompanying structural transition for as grown BaFe{sub 2}As{sub 2}. An anomalous slope change in resistivity is observed around 18 K at 0 and 5T. Magnetoresistance (MR) is noticed to increase as a function of applied field (H) quite differently than that for as grown crystals below T{sub SDW} which may be attributed to aging effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Regional Groundwater and Storms Are Hydrologic Controls on the Quality and Export of Dissolved Organic Matter in Two Tropical Rainforest Streams, Costa Rica

A paired-watershed approach was used to compare the quality and fluxes of dissolved organic matter (DOM) during stormflow and baseflow in two lowland tropical rainforest streams located in northeastern Costa Rica. The Arboleda stream received regional groundwater (RGW) flow, whereas the Taconazo stream did not. DOM quality was assessed with absorbance and fluorescence and stable carbon isotope (δ 13 C-DOC) values. RGW DOM lacked detectable fluorescence and had specific ultraviolet absorption (SUVA 254 ) and absorbance slope ratio (S R ) values consistent with low aromaticity and low molecular weight material, respectively. We attributed these properties to microbial degradation and sorption of humic DOM to mineral surfaces during transport through bedrock. SUVA 254 values were lower and SR values were higher in the Arboleda stream during baseflow compared to the Taconazo stream, presumably due to dilution by RGW. However, no significant difference in SUVA 254 or SR occurred between the streams during stormflow. SUVA254 was negatively correlated to δ13C-DOC (r 2 = 0.61, P < 0.001), demonstrating a strong linkage between stream DOM characteristics and the relative amounts of RGW flow and local watershed runoff containing soil and throughfall C sources. Mean DOC export from the Taconazo stream during the study period was 2.62 ± 0.39 g C m -2 year -1 -2 year -1 , one of the highest exports reported and demonstrating a substantial impact of old RGW from outside the watershed boundary can have on surface water carbon cycling.

54 ENVIRONMENTAL SCIENCES↗

Investigating the Relative Roles of INPs and CCN in a Simulated Thunderstorm Using a New Immersion Freezing Algorithm

Microphysical processes in deep convective clouds are sensitive to the number concentrations of cloud condensation nuclei (CCN) and ice nucleating particles (INPs), but the effects of INPs are less studied. Modeling studies investigating the effects of INPs and/or CCN on deep convection typically retain a volume‐dependent raindrop freezing relation. The resulting neglect of aerosol accumulation in raindrops via drop collisions has likely produced unrealistic storm responses to INPs in past studies. To address this deficiency, a new immersion freezing algorithm was developed and embedded in a bulk microphysics scheme that freezes both cloud drops and raindrops using the same immersion freezing INP (IF‐INP) activity spectrum based on measurements. Multiple idealized simulations of a single case of deep convection observed during the Clouds, Aerosols, and Complex Terrain Interactions (CACTI) field campaign were conducted, with microphysical differences produced by independently altering IF‐INP temperature dependencies and CCN number concentrations from their observed values. Surface precipitation in all simulations resulted almost exclusively from riming graupel that melted upon descending to the surface. Rainfall and cold pools were substantially and systematically weakened with increased CCN due to decreased graupel riming rates but were relatively insensitive to variations in the magnitude and slope of IF‐INP spectra due to compensating depletion of supercooled liquid water. These compensating processes were a consequence of the accumulation of IF‐INPs in raindrops, encouraging caution in studying IF‐INP effects upon thunderstorms using traditional volume‐dependent drop freezing relationships.

CCN↗

Genome-Resolved Metagenomic Analysis Reveals Roles for Candidate Phyla and Other Microbial Community Members in Biogeochemical Transformations in Oil Reservoirs

Oil reservoirs are major sites of methane production and carbon turnover, processes with significant impacts on energy resources and global biogeochemical cycles. We applied a cultivation-independent genomic approach to define microbial community membership and predict roles for specific organisms in biogeochemical transformations in Alaska North Slope oil fields. Produced water samples were collected from six locations between 1,128 m (24 to 27°C) and 2,743 m (80 to 83°C) below the surface. Microbial community complexity decreased with increasing temperature, and the potential to degrade hydrocarbon compounds was most prevalent in the lower-temperature reservoirs. Sulfate availability, rather than sulfate reduction potential, seems to be the limiting factor for sulfide production in some of the reservoirs under investigation. Most microorganisms in the intermediate- and higher-temperature samples were related to previously studied methanogenic and nonmethanogenic archaea and thermophilic bacteria, but one candidate phylum bacterium, a member of the Acetothermia (OP1), was present in Kuparuk sample K3. The greatest numbers of candidate phyla were recovered from the mesothermic reservoir samples SB1 and SB2. We reconstructed a nearly complete genome for an organism from the candidate phylum Parcubacteria (OD1) that was abundant in sample SB1. Consistent with prior findings for members of this lineage, the OD1 genome is small, and metabolic predictions support an obligately anaerobic, fermentation-based lifestyle. At moderate abundance in samples SB1 and SB2 were members of bacteria from other candidate phyla, including Microgenomates (OP11), Atribacteria (OP9), candidate phyla TA06 and WS6, and Marinimicrobia (SAR406). The results presented here elucidate potential roles of organisms in oil reservoir biological processes. The activities of microorganisms in oil reservoirs impact petroleum resource quality and the global carbon cycle. In conclusion, we show that bacteria belonging to candidate phyla are present in some oil reservoirs and provide the first insights into their potential roles in biogeochemical processes based on several nearly complete genomes.

59 BASIC BIOLOGICAL SCIENCES↗

A high frequency correction to the Kirchhoff approximation, with application to rough surface EM wave scattering

A high frequency correction to the Kirchhoff approximation is developed for application to rough surface scattering. An approximate solution to the magnetic field integral equation for perfect conductivity and plane wave excitation yields a perturbed surface current expressed as a linear function of the second derivatives of surface height. The corrected surface current vector is substituted into the far field Stratton-Chu integral and average backscattered powers for the four polarization combinations are computed on the assumption that the surface is describable as a stationary Gaussian random process. The strength of this scattering solution is that it can account for height curvature correlation without requiring small height and slope.

Jackson, F. C.↗

Study of polyphenyl ether fluid /5P4E/ in operating elastohydrodynamic contacts by infrared emission spectroscopy

Infrared emission spectra of 5P4E polyphenyl ether were obtained from an operating elastohydrodynamic sliding contact at different speeds and loads by Fourier emission microspectrophotometry. The spectra were found to be polarized with respect to the direction of the conjunction line, especially at high shear rates. Film and metal surface temperatures were calculated from the spectra, and film thicknesses were determined under various operating conditions. Changes of polarized band structure above a critical shear rate, at which the slope of the film temperature versus shear curve changes abruptly and at which the film thickness assumes a minimum value, are consistent with a transition of the lubricant from a viscous liquid to a viscoelastic liquid or to an elastic solid.

Lauer, J. L.↗

Mobility of water ice on Callisto - Evidence and implications

Voyager images of Callisto reveal evidence for the accumulation of a bright volatile, presumably water ice, on north-facing slopes in the north polar region. The geometry of these accumulations suggests that ice migration in Callistoan high latitudes is dominated by thermal sublimation, controlled by insolation-dependent surface temperature contrasts. Such sublimation-dominated migration may result in the cold-trapping of most of the surface ice in discrete high-albedo regions.

Spencer, J. R.↗

Curvature continuity in arbitrary bicubic Bezier patches

Two methods are outlined for imposing interpatch curvature continuity in existing Bezier bicubic patch surfaces. Each method assumes that coordinates of the corners of the patches can not be altered but the interior Bezier control point can. Each method also preserves outer edge slope and outer corner twist derivatives. Neither method requires intersection or C0 continuity nor slope or C1 continuity at the start. A computer program for each method is given in the appendices.

Roach, Robert L.↗