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

Stability of hexagonal solidification patterns

We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary instabilities of regular hexagonal arrays and find that the stability boundaries depend significantly on the strength of crystalline anisotropy. We also find multiplet states that can be reached by applying well-defined perturbations to a pre-existing hexagonal array.Comment: Minor changes, mainly in introduction and conclusion, one reference adde

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

Computer simulation of surface and film processes

A molecular dynamics technique based upon Lennard-Jones type pair interactions is used to investigate time-dependent as well as equilibrium properties. The case study deals with systems containing Si and O atoms. In this case a more involved potential energy function (PEF) is employed and the system is simulated via a Monte-Carlo procedure. This furnishes the equilibrium properties of the system at its interfaces and surfaces as well as in the bulk

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

ESTIMATING PRICE VARIABILITY IN AGRICULTURE: IMPLICATIONS FOR DECISION MAKERS

Using a stochastic version of the POLYSYS modeling framework, an examination of projected variability in agricultural prices, supply, demand, stocks, and incomes is conducted for corn, wheat, soybeans, and cotton during the 1998-2006 period. Increased planting flexibility introduced in the 1996 farm bill results in projections of significantly higher planted acreage variability compared to recent historical levels. Variability of ending stocks and stock-to-use ratios is projected to be higher for corn and soybeans and lower for wheat and cotton compared to the 1986-96 period. Significantly higher variability is projected for corn prices, with wheat and soybean prices also being more variable. No significant change in cotton price variability is projected.POLYSYS model, Price variability, Stochastic simulation, Crop Production/Industries,

SOUTHERN AGRICULTURE UNDER THE 2002 FARM BILL: A REPRESENTATIVE FARMS APPROACH

The 2002 Farm Bill affects economic activity of farms and ranches in the southern United States. Using stochastic simulation techniques, key financial variables were projected for 39 representative farms and ranches in ten southern states. Results indicate 24 of 39 farms studied have more than a 40 percent likelihood of having annual cash flow deficits during the period 2002 through 2007. Results are largely consistent across commodities and between moderate and large size farms in the same geographic area.Agricultural and Food Policy,

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.