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At least 19 records

Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation

We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz-Christoffel transformation. The new algorithm, CRDT, is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT can never fail to converge to the correct Riemann mapping, but the correctness and convergence proof depend on conjectures that we have so far not been able to prove. We demonstrate convergence with computational experiments. The Riemann mapping has applications to problems in two-dimensional potential theory and to finite-difference mesh generation. We use CRDT to produce a mapping and solve a boundary value problem on long, thin regions for which no other algorithm can solve these problems.

Driscoll, Tobin A.↗

Ice Cloud Formation and Dehydration in the Tropical Tropopause Layer

Stratospheric water vapor is important not only for its greenhouse forcing, but also because it plays a significant role in stratospheric chemistry. Several recent studies have focused on the potential for dehydration due to ice cloud formation in air rising slowly through the tropical tropopause layer (TTL). Holton and Gettelman showed that temperature variations associated with horizontal transport of air in the TTL can drive ice cloud formation and dehydration, and Gettelman et al. recently examined the cloud formation and dehydration along kinematic trajectories using simple assumptions about the cloud properties. In this study, a Lagrangian, one-dimensional cloud model has been used to further investigate cloud formation and dehydration as air is transported horizontally and vertically through the TTL. Time-height curtains of temperature are extracted from meteorological analyses. The model tracks the growth, advection, and sedimentation of individual cloud particles. The regional distribution of clouds simulated in the model is comparable to the subvisible cirrus distribution indicated by SAGE II. The simulated cloud properties and cloud frequencies depend strongly on the assumed supersaturation threshold for ice nucleation. The clouds typically do not dehydrate the air along trajectories down to the temperature minimum saturation mixing ratio. Rather the water vapor mixing ratio crossing the tropopause along trajectories is 10-50% larger than the saturation mixing ratio. I will also discuss the impacts of Kelvin waves and gravity waves on cloud properties and dehydration efficiency. These simulations can be used to determine whether observed lower stratospheric water vapor mixing ratios can be explained by dehydration associated with in situ TTL cloud formation alone.

Jensen, Eric↗

Ice Cloud Formation and Dehydration in the Tropical Tropopause Layer

Stratospheric water vapor is important not only for its greenhouse forcing, but also because it plays a significant role in stratospheric chemistry. several recent studies have focused on the potential for dehydration due to ice cloud formation in air rising slowly through the tropical tropopause layer. Holton and Gettelman showed that temperature variations associated with horizontal transport of air in the tropopause layer can drive ice cloud formation and dehydration, and Gettelman et al. recently examined the cloud formation and dehydration along kinematic trajectories using simple assumptions about the cloud properties. In this study, we use a Lagrangian, one-dimensional cloud model to further investigate cloud formation and dehydration as air is transported horizontally and vertically through the tropical tropopause layer. Time-height curtains of temperature are extracted from meteorological analyses. The model tracks the growth and sedimentation of individual cloud particles. The regional distribution of clouds simulated in the model is comparable to the subvisible cirrus distribution indicated by SAGE II. The simulated cloud properties depend strongly on the assumed ice supersaturation threshold for ice nucleation. with effective nuclei present (low supersaturation threshold), ice number densities are high (0.1--10 cm(circumflex)-3), and ice crystals do not grow large enough to fall very far, resulting in limited dehydration. With higher supersaturation thresholds, ice number densities are much lower (less than 0.01 cm(circumflex)-3), and ice crystals grow large enough to fall substantially; however, supersaturated air often crosses the tropopause without cloud formation. The clouds typically do not dehydrate the air along trajectories down to the temperature minimum saturation mixing ratio. Rather the water vapor mixing ratio crossing the tropopause along trajectories is typically 10-50% larger than the saturation mixing ratio.

Jensen, Eric↗

Determination of photoionization branching ratios and total photoionization cross sections at 304 A from experimental ionospheric photoelectron fluxes

High-resolution measurements of the ionospheric photoelectron spectrum are used to derive photoionization cross sections and branching ratios for N2 and O at 304 A, the wavelength of the intense He II solar radiation. Based on a theory in which the measured fluxes at energies 22.5, 24.5, 25.5 and 27.5 eV are determined by the ratio of the production rate and the loss rate coefficient, values are obtained for the ratio of molecular nitrogen density to atomic oxygen density as a function of altitude, the sum of the total photoionization cross sections, the 2P/4S and 2D/4S branching ratios for O and the B/X and A/X branching ratios for N2 photoionization and the ratios and the interspecies cross section ratios 2D/A, 4S/X and 2P/B. The values obtained are in accord with the photoionization cross sections of Kirby et al. (1979).

Richards, P. G.↗

Behavior of atmospheric ozone determined from Nimbus satellite backscatter ultraviolet data

A substantial global data base on the spatial and temporal variations of high level atmospheric ozone distribution and total ozone amount for the time period 1970 through 1973 was obtained by the Backscatter Ultraviolet (BUV) instrument onboard the Nimbus 4 satellite. BUV total ozone data from all available orbits on each day of the period were processed to obtain zonal mean ozone amounts. Northern Hemisphere ozone and Southern Hemisphere ozone values are given, and the interhemispheric relationships identified. Vertical ozone profile information is interpreted to furnish data on seasonal total ozone changes. Selected ozone mixing ratio cross sections were analyzed, and the resulting zonally-symmetric patterns are presented.

Krueger, A. J.↗

Calculation of three-dimensional unsteady transonic flows past helicopter blades

A finite difference code for predicting the high speed flow over the advancing helicopter rotor is presented. The code solves the low frequency, transonic small disturbance equation and is suitable for modeling the effects of advancing blade unsteadiness on blades of nearly arbitrary planform. The method employs a quasi-conservative mixed differencing scheme and solves the resulting difference equations by an alternating direction scheme. Computed results showed good agreement with experimental blade pressure data and illustrate some of the effects of varying the rotor planform. The flow unsteadiness is shown to be an indispensible part of a transonic solution. Close to the tip at high advance ratio, cross flow effects can significantly affect the solution.

Chattot, J. J.↗

The design and preliminary calibration of a boundary-layer flow channel

Design procedures for a new low-speed boundary-layer research channel are described. The channel is an open-circuit wind tunnel for the study of two-dimensional boundary layers under controlled pressure gradients, and follows design guidelines from published literature on blower tunnels with wide-angle diffusers. The contraction was arranged in a modular fashion permitting two different test sections of square and high-aspect-ratio cross section. A radical type of wide-angle diffuser was employed, and a stream-tube computer code (GE Streamtube Curvature Code) was used to check the contraction designs. The alternate test sections have the following specifications: 2- by 2-foot cross section with a fixed velocity of 23 ft/sec, and a boundary-layer section with a 0.5- by 2-foot cross section at a fixed velocity of approximately 89 ft/sec. Experimental techniques and data are described for the evaluation of diffuser effectiveness, boundary-layer channel characteristics, and overall performance of the facility.

Rao, Dhanvada M.↗

Deriving Laws from Ordering Relations

It took much effort in the early days of non-Euclidean geometry to break away from the mindset that all spaces are flat and that two distinct parallel lines do not cross. Up to that point, all that was known was Euclidean geometry, and it was difficult to imagine anything else. We have suffered a similar handicap brought on by the enormous relevance of Boolean algebra to the problems of our age-logic and set theory. Previously, I demonstrated that the algebra of questions is not Boolean, but rather is described by the free distributive algebra. To get to this stage took much effort, as many obstacles-most self-placed-had to be overcome. As Boolean algebras were all I had ever known, it was almost impossible for me to imagine working with an algebra where elements do not have complements. With this realization, it became very clear that the sum and product rules of probability theory at the most basic level had absolutely nothing to do with the Boolean algebra of logical statements. Instead, a measure of degree of inclusion can be invented for many different partially ordered sets, and the sum and product rules fall out of the associativity and distributivity of the algebra. To reinforce this very important idea, this paper will go over how these constructions are made, while focusing on the underlying assumptions. I will derive the sum and product rules for a distributive lattice in general and demonstrate how this leads to probability theory on the Boolean lattice and is related to the calculus of quantum mechanical amplitudes on the partially ordered set of experimental setups. I will also discuss the rules that can be derived from modular lattices and their relevance to the cross-ratio of projective geometry.

Knuth, Kevin H.↗

Predictions of Poisson's ratio in cross-ply laminates containing matrix cracks and delaminations

A damage-dependent constitutive model for laminated composites has been developed for the combined damage modes of matrix cracks and delaminations. The model is based on the concept of continuum damage mechanics and uses second-order tensor valued internal state variables to represent each mode of damage. The internal state variables are defined as the local volume average of the relative crack face displacements. Since the local volume for delaminations is specified at the laminate level, the constitutive model takes the form of laminate analysis equations modified by the internal state variables. Model implementation is demonstrated for the laminate engineering modulus E(x) and Poisson's ratio nu(xy) of quasi-isotropic and cross-ply laminates. The model predictions are in close agreement to experimental results obtained for graphite/epoxy laminates.

Harris, Charles E.↗

Synthesis of phthalocyanine doped sol-gel materials

The synthesis of sol-gel silica materials doped with three different types of metallophthalocyanines has been studied. Homogeneous materials of good optical quality were prepared and the first optical limiting measurements of dyes in sol-gel hosts were carried out. The properties of these solid state limiters are similar to limiters based on phthalocyanine (Pc) in solution. Sol-gel silica materials containing copper, tin and germanium phthalocyanines were investigated. The initial step in all cases was to prepare silica sols by the sonogel method using tetramethoxy silane (TMOS), HCl and distilled water. Thereafter, the synthesis depended upon the specific Pc and its solubility characteristics. Copper phthalocyanine tetrasulfonic acid tetra sodium salt (CuPc4S) is soluble in water and various doping levels (1 x 10 (exp -4) M to 1 x 10 (exp -5) M) were added to the sol. The group IV Pc's, SnPc(OSi(n-hexyl)3)2 and GePc(OSi(n-hexyl)3)2, are insoluble in water and the process was changed accordingly. In these cases, the compounds were dissolved in THF and then added to the sol. The Pc concentration in the sol was 2 x 10(exp -5)M. The samples were then aged and dried in the standard method of making xerogel monoliths. Comparative nanosecond optical limiting experiments were performed on silica xerogels that were doped with the different metallophthalocyanines. The ratio of the net excited state absorption cross section (sigma(sub e)) to the ground state cross section (sigma(sub g)) is an important figure of merit that is used to characterize these materials. By this standard the SnPc sample exhibits the best limiting for the Pc doped sol-gel materials. Its cross section ratio of 19 compares favorably with the value of 22 that was measured in toluene. The GePc materials appear to not be as useful as those containing SnPc. The GePc doped solids exhibit a higher onset energy (2.5 mj and lower cross section ratio, 7. The CuPc4S sol-gel material has a still lower cross section ratio, 4, however, the tetrasulfonate groups make the dye soluble in water which greatly facilitates its incorporation into the sol-gel matrix. The nonlinear transmission of CuPc4S in a pH 2 buffer solution and in a silica xerogel were compared. It is evident that the CuPc4S preserves its optical limiting behavior in the sol-gel matrix, indicating that the fundamental excited state absorption process is essentially the same for a molecule in solution or in the solid state. Although the spectroscopic details of energy level lifetimes are unknown, the significance is that passive optical limiting has been achieved in the solid state via incorporation of a dye into an inorganic host. The only compromise occurs at the extremely high energy regime where photobleaching is observed. This is a result of the limited mobility of the dye molecules in the solid silica host relative to a liquid host. The effects of photodegradation in the xerogel are additive, whereas the solution provides a supply of fresh molecules that are free to enter the active volume between pulses.

Dunn, Bruce↗

Efficiencies for production of atomic nitrogen and oxygen by relativistic proton impact in air

Relativistic electron and proton impact cross sections are obtained and represented by analytic forms which span the energy range from threshold to 1 GeV. For ionization processes, the Massey-Mohr continuum generalized oscillator strength surface is parameterized. Parameters are determined by simultaneous fitting to (1) empirical data, (2) the Bethe sum rule, and (3) doubly differential cross sections for ionization. Branching ratios for dissociation and predissociation from important states of N2 and O2 are determined. The efficiency for the production of atomic nitrogen and oxygen by protons with kinetic energy less than 1 GeV is determined using these branching ratio and cross section assignments.

Porter, H. S.↗

Laboratory tank studies of a single species of phytoplankton using a remote sensing fluorosensor

Phytoplankton were grown in the laboratory for the purpose of testing a remote fluorosensor. The fluorosensor uses a unique four-wavelength dye laser system to excite phytoplankton bearing chlorophyll and to measure the chlorophyll fluorescence generated by this excitation. Six different species were tested, one at a time, and each was grown two to four times. Fluorescence measured by the fluorosensor provides good quantitative measurement of chlorophyll concentrations for all species tested while the cultures were in log phase growth. Fluorescene cross section ratios obtained in the single species tank tests support the hypothesis that the shape of the fluorescence cross section curve remains constant with the species (differences in fluorescence cross section ratios are a basis for determining composition of phytoplankton according to color group when a multiwavelength source of excitation is used. Linear relationships exist between extracted chlorophyll concentration and fluorescence measured by the remote fluorosensor during the log phase growth of phytoplankton cultures tested.

Brown, C. A., Jr.↗

Dilution jet mixing

Schematics are given for test section configurations, orifice configurations, and the dilution jet mixing test rig used to collect a data base on mixing a single sided and a two sided row of jets with a confined cross flow. Parameters investigated include momentum ratio; nonuniform cross stream temperature and velocity profiles; cold/hot injection, and cross stream flow area convergence. Graphs show measured theta momentum distributions for: (1) in line and staggered orifice configurations; and (2) the profiled mainstream; and (3) flow area convergence.

Srinivasan, S.↗

The 200 MeV Pi+ induced single-nucleon removal from 24Mg

Nuclear gamma-rays in coincidence with outgoing pions or protons following single nucleon removal from Mg-24 by 200 MeV pions (+) were detected with Ge(Li) detectors. Differential cross sections are reported for gamma-rays from the first excited mirror states of Na-23 and Mg-23 in coincidence with positive pions or protons detected in particle telescopes at 30, 60, 90, 120, and 150 deg; angle-integrated absolute cross sections and cross section ratios are calculated. These results are compared with the predictions of a Pauli-blocked plane-wave impulse approximation (PWIA) and the intranuclear cascade (INC) and nucleon charge exchange (NCX) reaction models. The PWIA and the INC calculations generally agree with the angular dependence of the experimental results but not the absolute magnitude. The NCX calculation does not reproduce the observed cross section charge ratios.

Joyce, Donald↗

Measurement of C-12, O-16, and Fe-56 charge changing cross sections in helium at high energy, comparison with cross sections in hydrogen, and application to cosmic-ray propagation

We present measurements of the spallation cross sections of carbon, oxygen, and iron in helium and hydrogen, at beam energies from 540 to 1600 MeV/nucleon, performed by exposing liquid helium, CH2, and C targets. Charge changing cross sections are reported for fragments down to Ne for Fe + alpha and Fe + p reactions, and down to B for O + alpha, O + p, C + alpha, and C + p reactions. Alpha- to p-induced cross section ratios (sigma(sub alpha)/sigma(sub p)) are determined at the same energy per nucleon. From these measurements an empirical formula for the (sigma(sub alpha)/sigma(sub p)) ratios is derived and is found in good agreement with available isotopic cross sections data from radioactivity and radiochemical techniques. These results are applied to the propagation of heavy charged cosmic rays in an interstellar medium with a helium to hydrogen abundance ratio of 0.10. It is shown that the Sc-Mn/Fe ratio prediction is decreased relative to the B/C ratio when compared to propagation calculations in a pure hydrogen interstellar medium.

Ferrando, P.↗