Calculation of the magnetic field penetration depth for high-Tc cuprate superconductors based on the Interlayer Pair Tunneling model /

In this work, the magnetic field penetration depth for high-Tc cuprate superconductors is calculated using a recent Interlayer Pair Tunneling (ILPT) model proposed by Chakravarty, Sudb0, Anderson, and Strong [1] to explain high temperature superconductivity. This model involves a "hopping" of Cooper pairs between layers of the unit cell which acts to amplify the pairing mechanism within the planes themselves. Recent work has shown that this model can account reasonably well for the isotope effect and the dependence of Tc on nonmagnetic in-plane impurities [2] , as well as the Knight shift curves [3] and the presence of a magnetic peak in the neutron scattering intensity [4]. In the latter case, Yin et al. emphasize that the pair tunneling must be the dominant pairing mechanism in the high-Tc cuprates in order to capture the features found in experiments. The goal of this work is to determine whether or not the ILPT model can account for the experimental observations of the magnetic field penetration depth in YBa2Cu307_a7. Calculations are performed in the weak and strong coupling limits, and the efi"ects of both small and large strengths of interlayer pair tunneling are investigated. Furthermore, as a follow up to the penetration depth calculations, both the neutron scattering intensity and the Knight shift are calculated within the ILPT formalism. The aim is to determine if the ILPT model can yield results consistent with experiments performed for these properties. The results for all three thermodynamic properties considered are not consistent with the notion that the interlayer pair tunneling must be the dominate pairing mechanism in these high-Tc cuprate superconductors. Instead, it is found that reasonable agreement with experiments is obtained for small strengths of pair tunneling, and that large pair tunneling yields results which do not resemble those of the experiments.

Calculation of nondifferential properties for atomic ground states /

A new method for sampling the exact (within the nodal error) ground state distribution and nondiflPerential properties of multielectron systems is developed and applied to firstrow atoms. Calculated properties are the distribution moments and the electronic density at the nucleus (the 6 operator). For this purpose, new simple trial functions are developed and optimized. First, using Hydrogen as a test case, we demonstrate the accuracy of our algorithm and its sensitivity to error in the trial function. Applications to first row atoms are then described. We obtain results which are more satisfactory than the ones obtained previously using Monte Carlo methods, despite the relative crudeness of our trial functions. Also, a comparison is made with results of highly accurate post-Hartree Fock calculations, thereby illuminating the nodal error in our estimates. Taking into account the CPU time spent, our results, particularly for the 8 operator, have a relatively large variance. Several ways of improving the eflSciency together with some extensions of the algorithm are suggested.

Fluorescence spectra and ab initio theoretical studies of HCOOH /

A fluorescence excitation spectrum of formic acid monomer (HCOOH) , has been recorded in the 278-246 nm region and has been attributed to an n >7r* electron promotion in the anti conformer. The S^< S^ electronic origins of the HCOOH/HCOOD/DCOOH/DCOOD isotopomers were assigned to weak bands observed at 37431.5/37461.5/37445.5/37479.3 cm'''. From a band contour analysis of the 0°^ band of HCOOH, the rotational constants for the excited state were estimated: A'=1.8619, B'=0.4073, and C'=0.3730 cm'\ Four vibrational modes, 1/3(0=0), j/^(0-C=0) , J/g(C-H^^^) and i/,(0-H^yJ were observed in the spectrum. The activity of the antisymmetric aldehyde wagging and hydroxyl torsional modes in forming progressions is central to the analysis, leading to the conclusion that the two hydrogens are distorted from the molecular plane, 0-C=0, in the upper S. state. Ab initio calculations were performed at the 6-3 IG* SCF level using the Gaussian 86 system of programs to aid in the vibrational assignments. The computations show that the potential surface which describes the low frequency OH torsion (twisting motion) and the CH wagging (molecular inversion) motions is complex in the S^ excited electronic state. The OH and CH bonds were calculated to be twisted with respect to the 0-C=0 molecular frame by 63.66 and 4 5.76 degrees, respectively. The calculations predicted the existence of the second (syn) rotamer which is 338 cm'^ above the equilibrium configuration with OH and CH angles displaced from the plane by 47.91 and 41.32 degrees.

A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Calculation of the optical conductivity for the Anderson impurity model using the slave boson technique

The optical conductivity of the Anderson impurity mode l has been calculated by emp l oying the slave boson technique and an expansion in powers of l i N, where N is the d egeneracy o f the f electron level . This method has been used to find the effective mass of the conduction electrons for temperatures above and below the Kondo tempera ture. For low temperatures, the mass enhancement is f ound to be large while a t high t emperatures, the mass enhancement is sma ll. The conductivity i s f ound to be Drude like with frequency dependent effective mass and scattering time for low independent effective mass and temperatures and scattering time f requency for high t emperatures. The behavior of both the effective mass and the conductivity is in qualitative agreement with experimental r esul t s .

Exchange energy calculation of He-He with supermolecular one-matrix

Exch~nge energy of the He-He system is calculated using the one-density matrix which has been modified according to the supermolecular density formula quoted by Kolos. The exchange energy integrals are computed analytically and by the Monte Carlo method. The results obtained from both ways compared favourably,with the results obtained from the SCF program HONDO

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

On the formulation and the calculation of the harmonic contributions to the Debye-Waller factor in metals (sodium)

The algebraic expressions for the anharmonic contributions to the Debye-Waller factor up to 0(A ) and 0 L% ) £ where ^ is the scattering wave-vector] have been derived in a form suitable for cubic metals with small ion cores where the interatomic potential extends to many neighbours. This has been achieved in terms of various wave-vector dependent tensors, following the work of Shukla and Taylor (1974) on the cubic anharmonic Helmholtz free energy. The contribution to the various wave-vector dependent tensors from the coulomb and the electron-ion terms in the interatomic metallic potential has been obtained by the Ewald procedure. All the restricted multiple whole B r i l l o u i n zone (B.Z.) sums are reduced to single whole B.Z. sums by using the plane wave representation of the delta function. These single whole B.Z. sums are further reduced to the •%?? portion of the B.Z. following Shukla and Wilk (1974) and Shukla and Taylor (1974). Numerical calculations have been performed for sodium where the Born-Mayer term in the interatomic potential has been neglected because i t is small £ Vosko (1964)3 • *n o^er to compare our calculated results with the experimental results of Dawton (1937), we have also calculated the r a t io of the intensities at different temperatures for the lowest five reflections (110), (200), (220), (310) and (400) . Our calculated quasi-harmonic results agree reasonably well with the experimental results at temperatures (T) of the order of the Debye temperature ( 0 ). For T » © ^ 9 our calculated anharmonic results are found to be in good agreement with the experimental results.The anomalous terms in the Debye-Waller factor are found not to be negligible for certain reflections even for T ^ ©^ . At temperature T yy Op 9 where the temperature is of the order of the melting temperature (Xm) » "the anomalous terms are found to be important almost for all the f i ve reflections.

A microanalysis of EMG and EEG changes during the sleep onset period (SOP) : a theoretical investigation with practical applications /

The present study has both theoretical and practical aspects. The theoretical intent of the study was to closely examine the relationship between muscle activity (EMG) and EEG state during the process of falling asleep. Sleep stages during sleep onset (SO) have been generally defined with regards to brain wave activity (Recht schaff en & Kales (1968); and more precisely by Hori, Hayashi, & Morikawa (1994)). However, no previous study has attempted to quantify the changes in muscle activity during this same process. The practical aspect of the study examined the reliability ofa commercially developed wrist-worn alerting device (NovAlert™) that utilizes changes in muscle activity/tension in order to alert its user in the event that he/she experiences reduced wakefulness that may result in dangerous consequences. Twelve female participants (aged 18-42) sp-ent three consecutive nights in the sleep lab ("Adaptation", "EMG", and "NOVA" nights). Each night participants were given 5, twenty-minute nap opportunities. On the EMG night, participants were allowed to fall asleep freely. On the NOV A night, participants wore the Nov Alert™ wrist device that administered a Psychomotor Vigilance Test (PVT) when it detected that muscle activity levels had dropped below baseline. Nap sessions were scored using Hori's 9-stage scoring system (Hori et aI, 1994). Power spectral analyses (FFT) were also performed. Effects ofthe PVT administration on EMG and EEG frequencies were also examined. Both chin and wrist EMG activity showed reliable and significant decline during the early stages ofHori staging (stages HO to H3 characterized by decreases in alpha activity). All frequency bands studied went through significant changes as the participants progressed through each ofHori's 9 SO stages. Delta, theta, and sigma activity increased later in the SO continuum while a clear alpha dominance shift was noted as alpha activity shifted from the posterior regions of the brain (during Hori stages HO to H3) to the anterior portions (during Hori stages H7 to H9). Administration of the PVT produced significant increases in EMG activity and was effective in reversing subjective drowsiness experienced during the later stages of sleep onset. Limitations of the alerting effects of the PVTs were evident following 60 to 75 minutes of use in that PVTs delivered afterwards were no longer able to significantly increase EMG levels. The present study provides a clearer picture of the changes in EMG and EEG during the sleep onset period while testing the efficacy of a commercially developed alerting device. EMG decreases were found to begin during Hori stage 0 when EEG was - dominated by alpha wave activity and were maximal as Hori stages 2 to 5 were traversed (coincident with alpha and beta activity). This signifies that EMG decrements and the loss of resting alpha activity are closely related. Since decreased alpha has long been associated with drowsiness and impending sleep, this investigation links drops in muscle tone with sleepiness more directly than in previous investigations. The EMG changes were reliably demonstrated across participants and the NovAlert™ detected the EMG decrements when Hori stage 3 was entered. The alerting vibrations produced by the NovAlert™ occurred early enough in the SO process to be of practical importance as a sleepiness monitoring and alerting device.

Flow regime prediction via froude number calculation in a rock-bedded stream

Mathematical predictions of flow conditions along a steep gradient rock bedded stream are examined. Stream gage discharge data and Manning's Equation are used to calculate alternative velocities, and subsequently Froude Numbers, assuming varying values of velocity coefficient, full depth or depth adjusted for vertical flow separation. Comparison of the results with photos show that Froude Numbers calculated from velocities derived from Manning's Equation, assuming a velocity coefficient of 1.30 and full depth, most accurately predict flow conditions, when supercritical flow is defined as Froude Number values above 0.84. Calculated Froude Number values between 0.8 and 1.1 correlate well with observed transitional flow, defined as the first appearance of small diagonal waves. Transitions from subcritical through transitional to clearly supercritical flow are predictable. Froude Number contour maps reveal a sinuous rise and fall of values reminiscent of pool riffle energy distribution.

Understanding the Origin of Selectivity in the Asymmetric Lithiation Reaction of N-Heterocycles: A Theoretical Study

The natural abundance of the N-heterocycle containing compounds has pushed the synthetic community toward the invention of new synthetic methods that result in the structural diversity of N-heterocycles. Among this, is the efficient and highly selective diamine mediated asymmetric lithiation process. Amongst the diamine chiral ligands, (-)-sparterine, which is a naturally occurring alkaloid proved to be an efficient one. Many successful, good yielding and highly selective lithiation reactions have been accomplished with the mediation by this chiral diamine base. Although, there are some examples of experimental and theoretical mechanistic studies in the literature, there is a lack of detailed understanding as to how it exactly induces the chirality. In this thesis is described a systematic investigation of how (-)-sparteine influences the stereoselectivity in the course of asymmetric lithiation reaction. This led us to the establishment of the function of A-ring’s β-CH2 effect and D-ring effect. Consequently, the importance of the A-ring and D-ring portions of (-)-sparteine in the stereoselectivity is unraveled. Another part of this thesis deals with the asymmetric lithiation of BF3-activated N,N- dimethylaminoferrocene in the presence of (1R, 2R)-N1,N2-bis(3,3-dimethylbutyl)-N1,N2-dimethylcyclohexane-1,2-diamine ( a (R,R)-TMCDA surrogate) with i-PrLi. Computational findings were in full accord with the experimental observations. Subsequently, the theoretically provided insights into the mechanism of the reaction were exploited in computational design of a new ligand. Unfortunately, the outcome of this design was not experimentally robust and an updated approach towards a successful design was explained.

Spectroscopic and theoretical considerations of cyclopropenone

Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999 P65 D53 2007

The Effects of Body Posture on Emotion Perception: A Developmental and Theoretical Analysis

Previously, studies investigating emotional face perception - regardless of whether they involved adults or children - presented participants with static photos of faces in isolation. In the natural world, faces are rarely encountered in isolation. In the few studies that have presented faces in context, the perception of emotional facial expressions is altered when paired with an incongruent context. For both adults and 8- year-old children, reaction times increase and accuracy decreases when facial expressions are presented in an incongruent context depicting a similar emotion (e.g., sad face on a fear body) compared to when presented in a congruent context (e.g., sad face on a sad body; Meeren, van Heijnsbergen, & de Gelder, 2005; Mondloch, 2012). This effect is called a congruency effect and does not exist for dissimilar emotions (e.g., happy and sad; Mondloch, 2012). Two models characterize similarity between emotional expressions differently; the emotional seed model bases similarity on physical features, whereas the dimensional model bases similarity on underlying dimensions of valence an . arousal. Study 1 investigated the emergence of an adult-like pattern of congruency effects in pre-school aged children. Using a child-friendly sorting task, we identified the youngest age at which children could accurately sort isolated facial expressions and body postures and then measured whether an incongruent context disrupted the perception of emotional facial expressions. Six-year-old children showed congruency effects for sad/fear but 4-year-old children did not for sad/happy. This pattern of congruency effects is consistent with both models and indicates that an adult-like pattern exists at the youngest age children can reliably sort emotional expressions in isolation. In Study 2, we compared the two models to determine their predictive abilities. The two models make different predictions about the size of congruency effects for three emotions: sad, anger, and fear. The emotional seed model predicts larger congruency effects when sad is paired with either anger or fear compared to when anger and fear are paired with each other. The dimensional model predicts larger congruency effects when anger and fear are paired together compared to when either is paired with sad. In both a speeded and unspeeded task the results failed to support either model, but the pattern of results indicated fearful bodies have a special effect. Fearful bodies reduced accuracy, increased reaction times more than any other posture, and shifted the pattern of errors. To determine whether the results were specific to bodies, we ran the reverse task to determine if faces could disrupt the perception of body postures. This experiment did not produce congruency effects, meaning faces do not influence the perception of body postures. In the final experiment, participants performed a flanker task to determine whether the effect of fearful bodies was specific to faces or whether fearful bodies would also produce a larger effect in an unrelated task in which faces were absent. Reaction times did not differ across trials, meaning fearful bodies' large effect is specific to situations with faces. Collectively, these studies provide novel insights, both developmentally and theoretically, into how emotional faces are perceived in context.

Calculation of ditching in the south side of the feeder from Brown’s ditch culvert to lot no.5

Calculation of ditching in the south side of the feeder from Brown’s ditch culvert to lot no.5, n.d.