Comparison of Two Algebraic Methods for Curve/curve Intersection

Most geometric modeling systems use either polynomial or rational functions to represent geometry. In such systems most computational problems can be formulated as systems of polynomials in one or more variables. Classical elimination theory can be used to solve such systems. Here Cayley's method of elimination is summarized and it is shown how it can best be used to solve the curve/curve intersection problem. Cayley's method was found to be a more straightforward approach. Furthermore, it is computationally simpler, since the elements of the Cayley matrix are one variable instead of two variable polynomials. Researchers implemented and tested both methods and found Cayley's to be more efficient. Six pairs of curves, representing mixtures of lines, circles, and cubic arcs were used. Several examples had multiple intersection points. For all six cases Cayley's required less CPU time than the other method. The average time ratio of method 1 to method 2 was 3.13:1, the least difference was 2.33:1, and the most dramatic was 6.25:1. Both of the above methods can be extended to solve the surface/surface intersection problem

Liquid metal embrittlement

Crack propagation is discussed for metals with liquid metal in the crack space. The change in electrochemical potential of an electron in a metal due to changes in stress level along the crack surface was investigated along with the change in local chemistry, and interfacial energy due to atomic redistribution in the liquid. Coupled elastic-elastrostatic equations, stress effects on electron energy states, and crack propagation via surface roughening are discussed

Computer simulation of surface and film processes

Adequate computer methods, based on interactions between discrete particles, provide information leading to an atomic level understanding of various physical processes. The success of these simulation methods, however, is related to the accuracy of the potential energy function representing the interactions among the particles. The development of a potential energy function for crystalline SiO2 forms that can be employed in lengthy computer modelling procedures was investigated. In many of the simulation methods which deal with discrete particles, semiempirical two body potentials were employed to analyze energy and structure related properties of the system. Many body interactions are required for a proper representation of the total energy for many systems. Many body interactions for simulations based on discrete particles are discussed

Direct observation of interface instability during crystal growth

The general aim of this investigation was to study interface stability and solute segregation phenomena during crystallization of a model system. Emphasis was to be placed on direct observational studies partly because this offered the possibility at a later stage of performing related experiments under substantially convection-free conditions in the space shuttle. The major achievements described in this report are: (1) the development of a new model system for fundamental studies of crystal growth from the melt and the measurement of a range of material parameters necessary for comparison of experiment with theory. (2) The introduction of a new method of measuring segregation coefficient using absorption of a laser beam by the liquid phase. (3) The comparison of segregation in crystals grown by gradient freezing and by pulling from the melt. (4) The introduction into the theory of solute segregation of an interface field term and comparison with experiment. (5) The introduction of the interface field term into the theories of constitutional supercooling and morphological stability and assessment of its importance

Effects of low level military training flights on wading bird colonies in Florida

During 1983 and 1984 the effect of low level military training flights on the establishment. size and reproductive success of wading bird colonies was studied in Florida. Based on the indirect evidence of colony distributions and turnover rates in relation to military areas (training routes designated to 500 feet or less above ground level and military operations areas). there was no demonstrated effect of military activity on wading bird colony establishment or size on a statewide basis. Colony distributions were random with respect to military areas and turnover rates were within 2% when military and non-military areas were compared. Colony distributions and turnover rates, however. were related to the amount and type.Les tuer-tne or freshwater) of wetland. respectively. During two breeding seasons the behavioral responses and reproductive success of selected species were monitored in a non-habituated treatment colony (military overflights) and a control colony (no overflights). Breeding wading birds responded to F-16 overflights at 420 knots indicated airspeed. 82-84% maximum rpm. 500 feet above ground level and sound levels ranging from 55-100 dBA by exhibiting no response. looking up or changing position (usually to an alert posture): no productivity limiting responses were observed. High-nesting Great Egrets responded more than other species, nestling Great Egrets and Cattle Egrets responded significantly (r <.05) more intensely than adults of their respective species, and adults responded less during incubation and late chick-rearing than at other times. In addition, no differences in adult attendance, aggressive interactions or chick feeding rates were observed to result from F-16 overflights. No evidence of habituation to overflights was noted. Humans entering the colony or airboats approaching the colony vicinity elicited the most severe responses (flushing and panic flights) observed at both sites. Since relatively little coastal military activity occurs at low levels ( ~500 ft) and only one Brown Pelican colony (5-6% of the breeding population) was located in such an area, the reproductive success of five, more lIexposedll study species (Great Egrets, Snowy Egrets, Tricolored Herons, Little Blue Herons, Cattle Egrets) nesting in interior freshwater colonies was studied. Reproductive activity including such factors as nest success, nestling survival, nestling mortality, and nesting chronology was independent of F-16 overflights but related to ecological factors including colony location, colony characteristics and climatology. The responses to and effects of F-16 overflights, as reported here, should not be considered representative of military aircraft at lower altitudes or greater noise levels. (194 pages

PMM2-CDG caused by uniparental disomy: Case reportand literature review

Background Phosphomannomutase 2 deficiency (PMM2-CDG) affects glycosylation pathways such as the N-glycosylation pathway, resulting in loss of function of multiple proteins. This disorder causes multisystem involvement with a high variability among patients. PMM2-CDG is an autosomal recessive disorder, which can be caused by inheriting two pathogenic variants, de novo mutations or uniparental disomy. Case Presentation Our patient presented with multisystem symptoms at an early age including developmental delay, ataxia, and seizures. No diagnosis was obtained till the age of 31 years, when genetic testing was reinitiated. The patient was diagnosed with a complete maternal mixed hetero/isodisomy of chromosome 16, with a homozygous pathogenic PMM2 variant (p.Phe119Leu) causing PMM2-CDG. A literature review revealed eight cases of uniparental disomy as an underlying cause of CDG, four of which are PMM2-CDG. Conclusion Since the incidence of homozygosity for PMM2 variants is rare, we suggest further investigations for every homozygous PMM2-CDG patient where the segregation does not fit. These investigations include testing for UPD or a deletion in one of the two alleles, as this will have an impact on recurrence risk in genetic counselingWe thank the patient described in this case report for all-owing us to share her details, and we thank C. Pérez-Cerdá of the Center of Molecular Biology-Severo Ochoa,Madrid, for her contribution. This work is funded by thegrant titled Frontiers in Congenital Disorders of Glycosylation (1U54NS115198-01) from the National Institute ofNeurological Diseases and Stroke (NINDS) and theNational Center for Advancing Translational Sciences(NCATS), and the Rare Disorders Consortium DiseaseNetwork (E.M. and S.K.

Eutectic Colony Formation: A Stability Analysis

Experiments have widely shown that a steady-state lamellar eutectic solidification front is destabilized on a scale much larger than the lamellar spacing by the rejection of a dilute ternary impurity and forms two-phase cells commonly referred to as `eutectic colonies'. We extend the stability analysis of Datye and Langer for a binary eutectic to include the effect of a ternary impurity. We find that the expressions for the critical onset velocity and morphological instability wavelength are analogous to those for the classic Mullins-Sekerka instability of a monophase planar interface, albeit with an effective surface tension that depends on the geometry of the lamellar interface and, non-trivially, on interlamellar diffusion. A qualitatively new aspect of this instability is the occurence of oscillatory modes due to the interplay between the destabilizing effect of the ternary impurity and the dynamical feedback of the local change in lamellar spacing on the front motion. In a transient regime, these modes lead to the formation of large scale oscillatory microstructures for which there is recent experimental evidence in a transparent organic system. Moreover, it is shown that the eutectic front dynamics on a scale larger than the lamellar spacing can be formulated as an effective monophase interface free boundary problem with a modified Gibbs-Thomson condition that is coupled to a slow evolution equation for the lamellar spacing. This formulation provides additional physical insights into the nature of the instability and a simple means to calculate an approximate stability spectrum. Finally, we investigate the influence of the ternary impurity on a short wavelength oscillatory instability that is already present at off-eutectic compositions in binary eutectics.Comment: 26 pages RevTex, 14 figures (28 EPS files); some minor changes; references adde

Probing the dynamics of quasicrystal growth using synchrotron live imaging

The dynamics of quasicrystal growth remains an unsolved problem in condensed matter. By means of synchrotron live imaging, facetted growth proceeding by the tangential motion of ledges at the solid-melt interface is clearly evidenced all along the solidification of icosahedral AlPdMn quasicrystals. The effect of interface kinetics is significant so that nucleation and free growth of new facetted grains occur in the melt when the solidification rate is increased. The evolution of these grains is explained in details, which reveals the crucial role of aluminum rejection, both in the poisoning of grain growth and driving fluid flow