I. Numerical solution of exact pair equations. II. Numerical solution of first-order pair equations

Part I

Numerical solutions to the S-limit equations for the helium ground state and excited triplet state and the hydride ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial wave expansion of the exact helium atom wavefunction were solved giving accurate S-, P-, D-, F-, and G-limits. The G-limit is -2.90351 a.u. compared to the exact value of the energy of -2.90372 a.u.

Part II

The pair functions which determine the exact first-order wavefunction for the ground state of the three-electron atom are found with the matrix finite difference method. The second- and third-order energies for the (1s1s)¹S, (1s2s)³S, and (1s2s)¹S states of the two-electron atom are presented along with contour and perspective plots of the pair functions. The total energy for the three-electron atom with a nuclear charge Z is found to be E(Z) = -1.125•Z² +1.022805•Z-0.408138-0.025515•(1/Z)+O(1/Z²)a.u.

Part I: Latent heat of vaporization of n-decane. Part II: Heat and mass transfer from a cylinder placed in a turbulent air stream - Sherwood and Frössling numbers as a function of free stream turbulence level and Reynolds number

Part I

The latent heat of vaporization of n-decane is measured calorimetrically at temperatures between 160° and 340°F. The internal energy change upon vaporization, and the specific volume of the vapor at its dew point are calculated from these data and are included in this work. The measurements are in excellent agreement with available data at 77° and also at 345°F, and are presented in graphical and tabular form.

Part II

Simultaneous material and energy transport from a one-inch adiabatic porous cylinder is studied as a function of free stream Reynolds Number and turbulence level. Experimental data is presented for Reynolds Numbers between 1600 and 15,000 based on the cylinder diameter, and for apparent turbulence levels between 1.3 and 25.0 per cent. n-heptane and n-octane are the evaporating fluids used in this investigation.

Gross Sherwood Numbers are calculated from the data and are in substantial agreement with existing correlations of the results of other workers. The Sherwood Numbers, characterizing mass transfer rates, increase approximately as the 0.55 power of the Reynolds Number. At a free stream Reynolds Number of 3700 the Sherwood Number showed a 40% increase as the apparent turbulence level of the free stream was raised from 1.3 to 25 per cent.

Within the uncertainties involved in the diffusion coefficients used for n-heptane and n-octane, the Sherwood Numbers are comparable for both materials. A dimensionless Frössling Number is computed which characterizes either heat or mass transfer rates for cylinders on a comparable basis. The calculated Frössling Numbers based on mass transfer measurements are in substantial agreement with Frössling Numbers calculated from the data of other workers in heat transfer.

Applications of nuclear magnetic resonance spectroscopy to the study of medium-sized rings. I. Conformational properties of cycloheptane. II. Conformational properties of cycloöctane

Conformational equilibrium in medium-sized rings has been investigated by the temperature variation of the fluorine-19 n.m.r. spectra of 1, 1-difluorocycloalkanes and various substituted derivatives of them. Inversion has been found to be fast on the n.m.r. time scale at -180˚ for 1, 1-difluorocycloheptane, but slow for 1, 1-difluoro-4, 4-dimethylcycloheptane at -150˚. At low temperature, the latter compound affords a single AB pattern with a chemical-shift difference of 841 cps. which has been interpreted in terms of the twist-chair conformation with the methyl groups on the axis position and the fluorine atoms in the 4-position. At room temperature, the n.m.r. spectrum of 1, 1-difluoro-4-t-butylcycloheptane affords an AB pattern with a chemical-shift difference of 185 cps. The presence of distinct trans and gauche couplings from the adjacent hydrogens has been interpreted to suggest the existence of a single predominant form, the twist chair with the fluorine atoms on the axis position.

Investigation of 1, 1-difluorocycloöctane and 1, 1, 4, 4-tetrafluorocycloöctane has led to the detection of two kinetic processes both having activation energies of 8-10 kcal./mole but quite different A values. In light of these results eleven different conformations of cycloöctane along with a detailed description of the ways in which they may be interconverted are discussed. An interpretation involving the twist-boat conformation rapidly equilibrating through the saddle and the parallel-boat forms at room temperature is compatible with the results.

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. The effect of N,N,N',N' -tetramethylethylenediamine on the Schlenk Equilibrium. II. The nature of the Di-Grignard reagent

I. The influence of N,N,N’,N’-tetramethylethylenediamine on the Schlenk equilibrium

The equilibrium between ethylmagnesium bromide, diethylmagnesium, and magnesium bromide has been studied by nuclear magnetic resonance spectroscopy. The interconversion of the species is very fast on the nmr time scale, and only an averaged spectrum is observed for the ethyl species. When N,N,N’,N’-tetramethylethylenediamine is added to solutions of these reagents in tetrahydrofuran, the rate of interconversion is reduced. At temperatures near -50°, two ethylmagnesium species have been observed. These are attributed to the different ethyl groups in ethylmagnesium bromide and diethylmagnesium, two of the species involved in the Schlenk equilibrium of Grignard reagents.

II. The nature of di-Grignard reagents

Di-Grignard reagents have been examined by nuclear magnetic resonance spectroscopy in an attempt to prove that dialkylmagnesium reagents are in equilibrium with alkylmagnesium halides. The di-Grignard reagents of compounds such as 1,4-dibromobutane have been investigated. The dialkylmagnesium form of this di-Grignard reagent can exist as an intramolecular cyclic species, tetramethylene-magnesium. This cyclic form would give an nmr spectrum different from that of the classical alkylmagnesium halide di-Grignard reagent. In dimethyl ether-tetrahydrofuran solutions of di-Grignard reagents containing N N,N,N’,N’-Tetramethylethylenediamine, evidence has been found for the existence of an intramolecular dialkylmagnesium species. This species is rapidly equilibrating with other forms, but at low temperatures, the rates of interconversion are reduced. Two species can be seen in the nmr spectrum at -50°. One is the cyclic species; the other is an open form.

Inversion of the carbon at the carbon-magnesium bond in di-Grignard reagents has also been studied. This process is much faster than in corresponding monofunctional Grignard reagents.

I. The effect of droplet solidification upon two-phase flow in a rocket nozzle. II. A kinetic theory investigation of some condensation-evaporation phenomena by a moment method

Part I:

The perturbation technique developed by Rannie and Marble is used to study the effect of droplet solidification upon two-phase flow in a rocket nozzle. It is shown that under certain conditions an equilibrium flow exists, where the gas and particle phases have the same velocity and temperature at each section of the nozzle. The flow is divided into three regions: the first region, where the particles are all in the form of liquid droplets; a second region, over which the droplets solidify at constant freezing temperature; and a third region, where the particles are all solid. By a perturbation about the equilibrium flow, a solution is obtained for small particle slip velocities using the Stokes drag law and the corresponding approximation for heat transfer between the particle and gas phases. Singular perturbation procedure is required to handle the problem at points where solidification first starts and where it is complete. The effects of solidification are noticeable.

Part II:

When a liquid surface, in contact with only its pure vapor, is not in the thermodynamic equilibrium with it, a net condensation or evaporation of fluid occurs. This phenomenon is studied from a kinetic theory viewpoint by means of moment method developed by Lees. The evaporation-condensation rate is calculated for a spherical droplet and for a liquid sheet, when the temperatures and pressures are not too far removed from their equilibrium values. The solutions are valid for the whole range of Knudsen numbers from the free molecule to the continuum limit. In the continuum limit, the mass flux rate is proportional to the pressure difference alone.

Early life history studies of Yellowfin tuna, Thunnus albacares. I. Food selection of Yellowfin tuna, Thunnus albacares, larvae reared in the laboratory. II. Age validation and growth of Yellowfin tuna, Thunnus albacares, larvae reared in the laboratory

English: Food selection of first-feeding yellowfin tuna larvae was studied in the laboratory during October 1992. The larvae were hatched from eggs obtained by natural spawning of yellowfin adults held in sea pens adjacent to Ishigaki Island, Okinawa Prefecture, Japan. The larvae were fed mixed-prey assemblages consisting of size-graded wild zooplankton and cultured rotifers. Yellowfin larvae were found to be selective feeders during the first four days of feeding. Copepod nauplii dominated the diet numerically, by frequency of occurrence and by weight. The relative importance of juvenile and adult copepods (mostly cyclopoids) in the diet increased over the 4-day period. Rotifers, although they comprised 31 to 40 percent of the available forage, comprised less than 2.1 percent of the diet numerically. Prey selection indices were calculated taking into account the relative abundances of prey, the swimming speeds of yellowfin larvae and their prey, and the microscale influence of turbulence on encounter rates. Yellowfin selected for copepod nauplii and against rotifers, and consumed juvenile and adult copepods in proportion to their abundances. Yellowfin larvae may select copepod nauplii and cyclopoid juveniles and adults based on the size and discontinuous swimming motion of these prey. Rotifers may not have been selected because they were larger or because they exhibit a smooth swimming pattern. The best initial diet for the culture of yellowfin larvae may be copepod nauplii and cyclopoid juveniles and adults, due to the size, swimming motion, and nutritional content of these prey. If rotifers alone are fed to yellowfin larvae, the rotifers should be enriched with a nutritional supplement that is high in unsaturated fatty acids. Mouth size of yellowfin larvae increases rapidly within the first few days of feeding, which minimizes limitations on feeding due to prey size. Although yellowfin larvae initiate feeding on relatively small prey, they rapidly acquire the ability to add relatively large, rare prey items to the diet. This mode of feeding may be adaptive for the development of yellowfin larvae, which have high metabolic rates and live in warm mixed-layer habitats of the tropical and subtropical Pacific. Our analysis also indicates a strong potential for the influence of microscale turbulence on the feeding success of yellowfin larvae. --- Experiments designed to validate the periodicity of otolith increments and to examine growth rates of yellowfin tuna larvae were conducted at the Japan Sea-Farming Association’s (JASFA) Yaeyama Experimental Station, Ishigaki Island, Japan, in September 1992. Larvae were reared from eggs spawned by captive yellowfin enclosed in a sea pen in the bay adjacent to Yaeyama Station. Results indicate that the first increment is deposited within 12 hours of hatching in the otoliths of yellowfin larvae, and subsequent growth increments are formed dailyollowing the first 24 hours after hatching r larvae up to 16 days of age. Somatic and otolith gwth ras were examined and compared for yolksac a first-feeding larvae reared at constant water tempatures of 26�and 29°C. Despite the more rapid develo of larvae reared at 29°C, growth rates were nnificaifferent between the two treatments. Howeve to poor survival after the first four days, it was ssible to examine growth rates beyond the onset of first feeding, when growth differences may become more apparent. Somatic and otolith growth were also examined for larvae reared at ambient bay water temperatures during the first 24 days after hatching. timates of laboratory growth rates were come to previously reported values for laboratory-reared yelllarvae of a similar age range, but were lower than growth rates reported for field-collected larvae. The discrepancy between laboratory and field growth rates may be associated with suboptimal growth conditions in the laboratory. Spanish: Durante octubre de 1992 se estudió en el laboratorio la seleccalimento por larvaún aleta amarillmera alimentación. Las larvas provinieron de huevos obtenidosel desove natural de aletas amarillas adultos mantenidos en corrales marinos adyacentes a la Isla Ishigaki, Prefectura de Okinawa (Japón). Se alimentó a las larvas con presas mixtas de zooplancton silvestre clasificado por tamaño y rotíferos cultivados. Se descubrió que las larvas de aleta amarilla se alimentan de forma selectiva durante los cuatro primeros días de alimentación. Los nauplios de copépodo predominaron en la dieta en número, por frecuencia de ocurrencia y por peso. La importancia relativa de copépodos juveniles y adultos (principalmente ciclopoides) en la dieta aumentó en el transcurso del período de 4 días. Los rotíferos, pese a que formaban del 31 al 40% del alimento disponible, respondieron de menos del 2,1% de la dieta en número. Se calcularon índices de selección de presas tomando en cuenta la abundancia relativa de las presas, la velocidad de natación de las larvas de aleta amarilla y de sus presas, y la influencia a microescala de la turbulencia sobre las tasas de encuentro. Los aletas amarillas seleccionaron a favor de nauplios de copépodo y en contra de los rotíferos, y consumieron copépodos juveniles y adultos en proporción a su abundancia. Es posible que las larvas de aleta amarilla seleccionen nauplios de copépodo y ciclopoides juveniles y adultos con base en el tamaño y movimiento de natación discontinuo de estas presas. Es posible que no se hayan seleccionado los rotíferos a raíz de su mayor tamaño o su patrón continuo de natación. Es posible que la mejor dieta inicial para el cultivo de larvas de aleta amarilla sea nauplios de copépodo y ciclopoides juveniles y adultos, debido al tamaño, movimiento de natación, y contenido nutritivo de estas presas. Si se alimenta a las larvas de aleta amarilla con rotíferos solamente, se debería enriquecerlos con un suplemento nutritivo rico en ácidos grasos no saturados. El tamaño de la boca de las larvas de aleta amarilla aumenta rápidamente en los primeros pocos días de alimentación, reduciendo la limitación de la alimentación debida al tamaño de la presa. Pese a que las larvas de aleta amarilla inician su alimentación con presas relativamente pequeñas, se hacen rápidamente capaces de añadir presas relativamente grandes y poco comunes a la dieta. Este modo de alimentación podría ser adaptivo para el desarrollo de larvas de aleta amarilla, que tienen tasa metabólicas altas y viven en hábitats cálidos en la capa de mezcla en el Pacífico tropical y subtropical. Nuestro análisis indica también que la influencia de turbulencia a microescala es potencialmente importante para el éxito de la alimentación de las larvas de aleta amarilla. --- En septiembre de 1992 se realizaron en la Estación Experimental Yaeyama de la Japan Sea- Farming Association (JASFA) en la Isla Ishigaki (Japón) experimentos diseñados para validar la periodicidad de los incrementos en los otolitos y para examinar las tasas de crecimiento de las larvas de atún aleta amarilla. Se criaron las larvas de huevos puestos por aletas amarillas cautivos en un corral marino en la bahía adyacente a la Estación Yaeyama. Los resultados indican que el primer incremento es depositado menos de 12 horas después de la eclosión en los otolitos de las larvas de aleta amarilla, y que los incrementos de crecimiento subsiguientes son formados a diario a partir de las primeras 24 horas después de la eclosión en larvas de hasta 16 días de edad. Se examinaron y compararon las tasas de crecimiento somático y de los otolitos en larvas en las etapas de saco vitelino y de primera alimentación criadas en aguas de temperatura constante entre 26°C y 29°C. A pesar del desarrollo más rápido de las larvas criadas a 29°C, las tasas de crecimiento no fueron significativamente diferentes entre los dos tratamientos. Debido a la mala supervivencia a partir de los cuatro primeros días, no fue posibación, uando las diferencias en el crecimiento podrían hacerse más aparentes. Se examinó también el crecimiento somático y de los otolitos para larvas criadas en temperaturas de agua ambiental en la bahía durante los 24 días inmediatamente después de la eclosión. Nuestras estimaciones de las tasas de crecimiento en el laboratorio fueron comparables a valores reportados previamente para larvas de aleta amarilla de edades similares criadas en el laboratorio, pero más bajas que las tasas de crecimiento reportadas para larvas capturadas en el mar. La discrepancia entre las tasas de crecimiento en el laboratorio y el mar podría estar asociada con condiciones subóptimas de crecimiento en el lab