I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.

The structure of liquid argon as determined by x-ray diffraction

X-ray diffraction measurements and subsequent data analyses have been carried out on liquid argon at five states in the density range of 0.91 to 1.135 gm/cc and temperature range of 127 to 143°K. Duplicate measurements were made on all states. These data yielded radial distribution and direct correlation functions which were then used to compute the pair potential using the Percus-Yevick equation. The potential minima are in the range of -105 to -120°K and appear to substantiate current theoretical estimates of the effective pair potential in the presence of a weak three-body force.

The data analysis procedure used was new and does not distinguish between the coherent and incoherent absorption factors for the cell scattering which were essentially equal. With this simplification, the argon scattering estimate was compared to the gas scattering estimate on the laboratory frame of reference and the two estimates coincided, indicating the data normalized. The argon scattering on the laboratory frame of reference was examined for the existence of the peaks in the structure factor and the existence of an observable third peak was considered doubtful.

Numerical studies of the effect of truncation, normalization, the subsidiary peak phenomenon in the radial distribution function, uncertainties in the low angle data relative to errors in the direct correlation function and the distortion phenomenon are presented.

The distortion phenomenon for this experiment explains why the Mikolaj-Pings argon data yielded pair potential well depths from the Percus-Yevick equation that were too shallow and an apparent slope with respect to density that was too steep compared to theoretical estimates.

The data presented for each measurement are: empty cell and cell plus argon intensity, absorption factors, argon intensity, smoothed argon intensity, smoothed argon intensity corrected for distortion, structure factor, radial distribution function, direct correlation function and the pair potential from the Percus-Yevick equation.

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

立方反射镜失调特性的研究

结合理想坐标系下立方镜镜面微小倾斜后其三个平面法线坐标，利用刚体微量转动的反射法线向量公式，获得非理想立方镜反射矩阵；为了研究在光斜入射时镜面倾斜对出射光方向的影响，利用立方镜绕顶点旋转等效于光斜入射的方法，计算出光束夹角δ与单一镜面偏差角ε和立方镜旋转角θ之间的关系式；对于理想情况下的立方镜，利用几何光学可以证明出射光与入射光不但平行，而且过顶点作任意截面交于两光线所得的两个交点关于顶点对称，从而计算出立方镜绕顶点以外任意轴旋转造成出射光束相对原出射光的偏移量与旋转角关系式，理论计算值与实验数据吻合得很

Determinação de uma fonte de contaminantes no estuário do Rio Macaé através da técnica de problemas inversos

Um grande desafio da atualidade é a preservação dos recursos hídricos, bem como o correto manejo dos mesmos, frente à expansão das cidades e às atividades humanas. A qualidade de um corpo hídrico é usualmente avaliada através da análise de parâmetros biológicos, físicos e químicos. O comportamento de tais parâmetros pode convenientemente ser simulado através de modelos matemáticos e computacionais, que surgem assim como uma ferramenta bastante útil, por sua capacidade de geração de cenários que possam embasar, por exemplo, tomadas de decisão. Nesta tese são discutidas técnicas de estimação da localização e intensidade de uma fonte de contaminante conservativo, hipoteticamente lançado na região predominantemente fluvial de um estuário. O lançamento aqui considerado se dá de forma pontual e contínua e a região enfocada compreendeu o estuário do Rio Macaé, localizado na costa norte do Rio de Janeiro. O trabalho compreende a solução de um problema direto, que consiste no transporte bidimensional (integrado na vertical) desse contaminante hipotético, bem como a aplicação de técnicas de problemas inversos. Para a solução do transporte do contaminante, aqui modelada pela versão 2D horizontal da equação de advecção-difusão, foram utilizados como métodos de discretização o Método de Elementos Finitos e o Método de Diferenças Finitas. Para o problema hidrodinâmico foram utilizados dados de uma solução já desenvolvida para estuário do Rio Macaé. Analisada a malha de acordo com o método de discretização, foram definidas a geometria do estuário e os parâmetros hidrodinâmicos e de transporte. Para a estimação dos parâmetros propostos foi utilizada a técnica de problemas inversos, com o uso dos métodos Luus-Jaakola, Algoritmo de Colisão de Partículas e Otimização por Colônia de Formigas para a estimação da localização e do método Seção Áurea para a estimação do parâmetro de intensidade da fonte. Para a definição de uma fonte, com o objetivo de propor um cenário experimental idealizado e de coleta de dados de amostragem, foi realizada a análise de sensibilidade quanto aos parâmetros a serem estimados. Como os dados de amostragem de concentração foram sintéticos, o problema inverso foi resolvido utilizando-os com e sem ruído, esse introduzido de forma artificial e aleatória. Sem o uso de ruído, os três métodos mostraram-se igualmente eficientes, com uma estimação precisa em 95% das execuções. Já com o uso de dados de amostragem com ruídos de 5%, o método Luus-Jaakola mostrou-se mais eficiente em esforço e custo computacional, embora todos tenham estimado precisamente a fonte em 80% das execuções. Considerando os resultados alcançados neste trabalho tem-se que é possível estimar uma fonte de constituintes, quanto à sua localização e intensidade, através da técnica de problemas inversos. Além disso, os métodos aplicados mostraram-se eficientes na estimação de tais parâmetros, com estimações precisas para a maioria de suas execuções. Sendo assim, o estudo do comportamento de contaminantes, e principalmente da identificação de fontes externas, torna-se uma importante ferramenta para a gestão dos recursos hídricos, possibilitando, inclusive, a identificação de possíveis responsáveis por passivos ambientais.

The center of mass and center of charge of the electron

9th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields (IARD)

Length-weight relationship of Gulf of Thailand fishes

The length-weight relationship of 26 fish species belonging to 17 families obtained from the Gulf of Thailand was examined. As seven species were obtained from different survey periods and three were from two different locations, seasonal and geographic variations of the equation between body weight W and total length L, W = aL super(b), were examined. The b values of the 27 species were tested for their significant differences from the value of 3; this confirmed that a few species showed significant differences of b value from 3. It is suggested that the 'cube law (b = 3)' can be applied to the length-weight relationship of most fishes in the Gulf of Thailand, with a few exceptions. This was confirmed by the analysis of b values from 72 additional species from the South China Sea area.

Offshore Migratory Corridors and Aerial Photogrammetric Body Length Comparisons of Southbound Gray Whales, Eschrichtius robustus, in the Southern California Bight, 1988–1990

Through most of their annual migration, gray whales, Eschrichtius robustus, remain within 10 km of shore, but in the Southern California Bight many individuals migrate much farther from shore. This paper summarizes aerial survey and photogrammetric efforts to determine body lengths and temporal and spatial distributions of migratory gray whales in the southern portion of the Southern California Bight. Aerial surveys were flown along 13 east–west transects between lat. 32°35′N and 33°30′N during the southbound gray whale migratory seasons of 1988–90 in the Southern California Bight. Photogrammetry was used to obtain body length estimates of animals during some of the surveys. A total of 1,878 whales in 675 groups were sighted along 25,440 km of transect distance flown and 217 body lengths were measured. Using position and heading data, three major migratory pathways or corridors in the southern portion of the bight are defined. Those migrating offshore were split almost evenly between two corridors along the west sides of Santa Catalina and San Clemente Islands. These corridors converge on the mainland coast between San Diego and the United States–Mexico border. No whales larger than 11.5 m were photographed within 30 km of the mainland coast, suggesting that smaller, and presumably younger, whales use the coastal migratory corridor through the California Bight.

Reactions of fishes to two underwater survey tools, a manned submersible and a remotely operated vehicle

We examined the reactions of fishes to a manned submersible and a remotely operated vehicle (ROV) during surveys conducted in habitats of rock and mud at depths of 30–408 m off central California in 2007. We observed 26 taxa for 10,550 fishes observed from the submersible and for 16,158 fishes observed from the ROV. A reaction was defined as a distinct movement of a fish that, for a benthic or hovering individual, was greater than one body length away from its initial position or, for a swimming individual, was a change of course or speed. Of the observed fishes, 57% reacted to the ROV and 11% reacted to the submersible. Aggregating species and those species initially observed off the seafloor reacted most often to both vehicles. Fishes reacted more often to each vehicle when they were >1 m above the seafloor (22% of all fishes >1 m above the seafloor reacted to the submersible and 73% to the ROV) than when they were in contact with the seafloor (2% of all reactions to the submersible and 18% to the ROV). Fishes reacted by swimming away from both vehicles rather than toward them. Consideration of these reactions can inform survey designs and selection of survey tools and can, thereby, increase the reliability of fish assemblage metrics (e.g., abundance, density, and biomass) and assessments of fish and habitat associations.

Brevetoxin in two planktivorous fishes after exposure to Karenia brevis: implications for food-web transfer to bottlenose dolphins

Brevetoxin uptake was analyzed in 2 common planktivorous fish that are likely foodweb vectors for dolphin mortality events associated with brevetoxin-producing red tides. Fish were exposed to brevetoxin-producing Karenia brevis for 10 h under conditions previously reported to produce optimal uptake of toxin in blood after oral exposure. Striped mullet Mugil cephalus were exposed to a low dose of brevetoxin, and uptake and depuration by specific organs were evaluated over a 2 mo period. Atlantic menhaden Brevoortia tyrannus specimens were used to characterize a higher brevetoxin dose uptake into whole body components and evaluate depuration over 1 mo. We found a high uptake of toxin by menhaden, with a body to water ratio of 57 after a 10 h exposure and a slow elimination with a half life (t1/2) of 24 d. Elimination occurred rapidly from the intestine (t1/2 < 1 wk) and muscle (t1/2 ≈ 1 wk) compartments and redistributed to liver which continued to accumulate body stores of toxin for 4 wk. The accumulation and elimination characteristics of the vectoring capacity of these 2 fish species are interpreted in relation to data from the Florida Panhandle dolphin mortality event of 2004. We show that due to slow elimination rate of brevetoxin in planktivorous fish, brevetoxin-related dolphin mortality events may occur without evidence of a concurrent harmful algal bloom event.

Some aspects of reproductive biology of two sciaenids, Otolithes cuvieri Trewavas and Johnius elongatus Mohan: maturation, spawning, sex ratio and fecundity

The gonads of Otolithes cuvieri and Johnius elongatus are described in seven maturity stages. O. Cuvieri spawns once a year from April to September as evidence by ova diameter frequency distribution and GSI values. 50% maturity is attained at 210mm TL in males and 200mm TL in females. Fecundity ranged from 2387 to 104379 with a mean value of 33502. Log-Log relationship between fecundity and total lenght, body weight and ovary weight were determined. An overall sex ratio of 1.54:1.00 was unequal in favour of males. Johnius elongatus spawns twice a year from January-February to Aprile-May and from August to October as evidence by ova diameter frequency distribution and GSI values. 50% maturity is attained at 140-143mm TL in both sexes. Fecundity ranged from 4238 to 167669 with a mean value of 42818. Log-Log relationship between fecundity and total lenght, body weign and ovary weight were determined. An overall sex ratio of 1.00:1.20 was unequal in favour of females.

A study on the lipid distribution pattern in muscles of two teleosts, Arius dussumieri and Ophiocephalus striatus

The muscles of the various regions and zones of the body of the two teleosts, A. dussumieri and O. striatus have been analyzed for lipid contents. There is a significant dorsum-ventral gradient in lipid concentration exhibited by both the fishes with higher lipid values in the ventral aspect of the body, especially the belly flaps. As regards the vertical series, both the fishes exhibit comparatively higher lipid contents at the dorsal aspects of the caudal region and at anterior portion of the dorsal fin area with lower lipid values at cephalic and middle portions of the body. The red muscle of Arius exhibits higher lipid content than the white muscle.

A comparative study of the morphometrics and the proximate composition of two edible molluscs Crassostrea cuculata (Born) and Perna perna (L.)

The morphometrics and the bio-chemical characteristics of Crassostrea cuculata and Perna perna were studied. In the oyster, the length was found to be positively correlated with breadth and total body weight. There was also a positive relationship between the total body weight and the total muscle weight. In the mytilid the total body weight was positively correlated with length and total muscle weight. The muscle weight was also found to be highly correlated with the length. In both animals the relationship between the length and the total body weight was curvilinear. In the oyster, the protein content was found to increase with the total body weight and the total muscle weight. In the mytilid the protein content increased not only with the total body weight but also with the length. In both animals, the relative content of protein is higher than that of carbohydrates, lipids and ash.

Early developmental stages of two Secutor species (Family: Leiognathidae) collected from the Bak-khali river estuary of the Bay of Bengal, Bangladesh

Early developmental stages of two Secutor species, Secutor insidiator (Bloch) (11.9-36.0 mm standard length, SL) and Secutor ruconius (Hamilton-Buchanan) (14.0-33.0 mm SL) collected by ichthyoplankton net from the Bak-khali river estuary of the Bay of Bengal, Cox's Bazar, Bangladesh are described and illustrated. All of the fins with supporting spines and rays were present in the smallest collected sizes of both species. With growth of the specimens, significant changes in melanophore patterns were found. S. insidiator is similar to S. ruconius in having upward protracting mouth parts and body colouration, but can be distinguished easily by its more elongate body shape (body depth 38-47% of SL compared with 46-52% of SL in Secutor ruconius). Both the species occurred round the year from August 1998 to July 1999. The surface water temperature and salinity during the study period varied from 22.0-32) C and 10-37 ppt respectively.