One-dimensional potential for image-potential states on graphene

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrodinger equation. The imagepotential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the nonlocal dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.

Mathematical models for the prediction of temperature distributions resulting from the discharge of heated water into large bodies of water

Mathematical models for heated water outfalls were developed for three flow regions. Near the source, the subsurface discharge into a stratified ambient water issuing from a row of buoyant jets was solved with the jet interference included in the analysis. The analysis of the flow zone close to and at intermediate distances from a surface buoyant jet was developed for the two-dimensional and axisymmetric cases. Far away from the source, a passive dispersion model was solved for a two dimensional situation taking into consideration the effects of shear current and vertical changes in diffusivity. A significant result from the surface buoyant jet analysis is the ability to predict the onset and location of an internal hydraulic jump. Prediction can be made simply from the knowledge of the source Froude number and a dimensionless surface exchange coefficient. Parametric computer programs of the above models are also developed as a part of this study. This report was submitted in fulfillment of Contract No. 14-12-570 under the sponsorship of the Federal Water Quality Administration.

Prediction and confirmation of seasonal migration of Pacific sardine (Sardinops sagax) in the California Current Ecosystem

During the last century, the population of Pacific sardine (Sardinops sagax) in the California Current Ecosystem has exhibited large fluctuations in abundance and migration behavior. From approximately 1900 to 1940, the abundance of sardine reached 3.6 million metric tons and the “northern stock” migrated from offshore of California in the spring to the coastal areas near Oregon, Washington, and Vancouver Island in the summer. In the 1940s, the sardine stock collapsed and the few remaining sardine schools concentrated in the coastal region off southern California, year-round, for the next 50 years. The stock gradually recovered in the late 1980s and resumed its seasonal migration between regions off southern California and Canada. Recently, a model was developed which predicts the potential habitat for the northern stock of Pacific sardine and its seasonal dynamics. The habitat predictions were successfully validated using data from sardine surveys using the daily egg production method; scientific trawl surveys off the Columbia River mouth; and commercial sardine landings off Oregon, Washington, and Vancouver Island. Here, the predictions of the potential habitat and seasonal migration of the northern stock of sardine are validated using data from “acoustic–trawl” surveys of the entire west coast of the United States during the spring and summer of 2008. The estimates of sardine biomass and lengths from the two surveys are not significantly different between spring and summer, indicating that they are representative of the entire stock. The results also confirm that the model of potential sardine habitat can be used to optimally apply survey effort and thus minimize random and systematic sampling error in the biomass estimates. Furthermore, the acoustic–trawl survey data are useful to estimate concurrently the distributions and abundances of other pelagic fishes.

Prediction of discard mortality for Alaskan crabs after exposure to freezing temperatures, based on a reflex impairment index

Millions of crabs are sorted and discarded in freezing conditions each year in Alaskan fisheries for Tanner crab (Chionoecetes bairdi) and snow crab (C. opilio). However, cold exposures vary widely over the fishing season and among different vessels, and mortalities are difficult to estimate. A shipboard experiment was conducted to determine whether simple behavioral observations can be used to evaluate crab condition after low-temperature exposures. Crabs were systematically subjected to cold in seven different exposure treatments. They were then tested for righting behavior and six different ref lex actions and held to monitor mortality. Crabs lost limbs, showed ref lex impairment, and died in direct proportion to increases in cold exposure. Righting behavior was a poor predictor of mortality, whereas reflex impairment (scored as the sum of reflex actions that were lost) was an excellent predictor. This composite index could be measured quickly and easily in hand, and logistic regression revealed that the relationship between reflex impairment and mortality correctly predicted 80.0% of the mortality and survival for C. bairdi, and 79.4% for C. opilio. These relationships provide substantial improvements over earlier approaches to mortality estimation and were independent of crab size and exposure temperature.

Avaliação dos algoritmos de Picard-Krylov e Newton-Krylov na solução da equação de Richards

A engenharia geotécnica é uma das grandes áreas da engenharia civil que estuda a interação entre as construções realizadas pelo homem ou de fenômenos naturais com o ambiente geológico, que na grande maioria das vezes trata-se de solos parcialmente saturados. Neste sentido, o desempenho de obras como estabilização, contenção de barragens, muros de contenção, fundações e estradas estão condicionados a uma correta predição do fluxo de água no interior dos solos. Porém, como a área das regiões a serem estudas com relação à predição do fluxo de água são comumente da ordem de quilômetros quadrados, as soluções dos modelos matemáticos exigem malhas computacionais de grandes proporções, ocasionando sérias limitações associadas aos requisitos de memória computacional e tempo de processamento. A fim de contornar estas limitações, métodos numéricos eficientes devem ser empregados na solução do problema em análise. Portanto, métodos iterativos para solução de sistemas não lineares e lineares esparsos de grande porte devem ser utilizados neste tipo de aplicação. Em suma, visto a relevância do tema, esta pesquisa aproximou uma solução para a equação diferencial parcial de Richards pelo método dos volumes finitos em duas dimensões, empregando o método de Picard e Newton com maior eficiência computacional. Para tanto, foram utilizadas técnicas iterativas de resolução de sistemas lineares baseados no espaço de Krylov com matrizes pré-condicionadoras com a biblioteca numérica Portable, Extensible Toolkit for Scientific Computation (PETSc). Os resultados indicam que quando se resolve a equação de Richards considerando-se o método de PICARD-KRYLOV, não importando o modelo de avaliação do solo, a melhor combinação para resolução dos sistemas lineares é o método dos gradientes biconjugados estabilizado mais o pré-condicionador SOR. Por outro lado, quando se utiliza as equações de van Genuchten deve ser optar pela combinação do método dos gradientes conjugados em conjunto com pré-condicionador SOR. Quando se adota o método de NEWTON-KRYLOV, o método gradientes biconjugados estabilizado é o mais eficiente na resolução do sistema linear do passo de Newton, com relação ao pré-condicionador deve-se dar preferência ao bloco Jacobi. Por fim, há evidências que apontam que o método PICARD-KRYLOV pode ser mais vantajoso que o método de NEWTON-KRYLOV, quando empregados na resolução da equação diferencial parcial de Richards.