Calculations of Electronic Potential Energy Surfaces

It is ordinarily possible to simplify the treatment of the dynamics of a general polyatomic system by first considering only the electronic motions, for all possible configurations of artificially fixed nuclei. Any particular electronic eigenvalue, as a function of nuclear geometry, then constitutes an effective potential energy surface, which governs the nuclear motion. The calculation of potential energy surfaces for practical systems represents a major quantum mechanical undertaking which in general becomes tractable only within a framework of approximation and semi empiricism. The major part of this thesis describes calculations developed to estimate the lower lying potential surfaces for the reactive system K + NaCl = KCl + Na. A model treatment is developed and discussed in detail. Essentially the problem is reduced to the consideration of the motion of a single electron in the fields of the closed shell ions Na+, K+ and Cl-. There is good evidence that these ions can be treated as classical polarisable charged spheres in their longer range electrostatic Interactions and also that their structures are not seriously modified by the presence of the single valence electron. The electronic eigenfunction is expanded in terms of a basis set of alkali atom valence s and p-orbitals The most difficult problem is the evaluation of certain close range interactions between the electron and the ions and this matter is discussed in detail. The electronic problem is first solved in neglect of the polarisation of the ion cores and this latter effect is afterwards Introduced, resulting in a first order perturbation correction to the energy surfaces. Empirical evidence used consists of values for ionic polarisabilities and radii, together with experimental ionisation potentials. A suitably reduced version of this model is applied to the calculation of potential curves for the diatomic ions Na2+ , K2+ and NaK+ and yields encouragingly close agreement with experimentally observed properties. The results for the complete system are presented and discussed. The reaction exothermicity is slightly overestimated. There is no calculated activation barrier, the reaction appearing to conform to the "early downhill" classification. A potential well indicates that, If the excess energy were removed, a triangular complex molecule could be formed, some 13 Kcal more stable than the product. Finally there appears to be some qualitative evidence that highly energetic collisions of the reactants may lead to electronically excited product atoms, a phenomenon observed experimentally for the reaction Na+ KBr = NaBr + K. The shorter second part of the thesis presents an estimate of the Jahn-Teller effect in rhenium hexafluoride. This effect arises from the coupling between electronic and nuclear motions when two or more potential surfaces have the same energy in a non linear symmetrical configuration. In such cases the degeneracy is relieved by certain vibrational displacements, leading to a distortion in the equilibrium geometry and a complication of the vibrational spectrum. In rhenium hexafluoride it is assumed that this effect arises from a purely electrostatic Interaction between the fluorine atoms and the non-bonding 5d rhenium electron in a degenerate. r8 state arising from strong spin orbit coupling of the t2g configuration. The electrostatic potential of a fluorine atom is taken as that of a fluoride ion less some variable fraction of an electron, depending on bond ionicity, taken from a hybrid orbital directed towards the central rhenium atom. The rhenium 5d orbital is taken of Slater form with variable exponent. The results, which depend essentially on the potential surface gradients in the octahedral configuration are relatively insensitive to physically reasonable choices of these parameters. A large splitting in the V2 band of the Raman spectrum is predicted, in good order of magnitude agreement with experiment. There is a corresponding very small distortion of the molecular geometry calculated, probably in a tetragonal sense

The Effectiveness of a Sierpinski Carpet Inspired Transducer

Piezoelectric ultrasonic transducers have the ability to act both as a receiver and a transmitter of ultrasound. Standard designs have a regular structure and therefore operate effectively over narrow bandwidths due to their single length scale. Naturally occurring transducers benefit from a wide range of length scales giving rise to increased bandwidths. It is therefore of interest to investigate structures which incorporate a range of length scales, such as fractals. This paper applies an adaptation of the Green function renormalization method to analyze the propagation of an ultrasonic wave in a series of pre-fractal structures. The structure being investigated here is the Sierpinski carpet. Novel expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities as a function of the operating frequency are presented. Comparisons of metrics between three new designs alongside the standard design (Euclidean structure) and the previously investigated Sierpinski gasket device are performed. The results indicate a significant improvement in the reception sensitivity of the device, and improved bandwidth in both the receiving and transmitting responses. </jats:p

A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer

Piezoelectric ultrasonic transducers have the potential to operate as both a sensor and as an actuator of ultrasonic waves. Currently, manufactured transducers operate effectively over narrow bandwidths as a result of their regular structures which incorporate a single length scale. To increase the operational bandwidth of these devices, consideration has been given in the literature to the implementation of designs which contain a range of length scales. In this paper, a mathematical model of a novel Sierpinski tetrix fractal-inspired transducer for sensor applications is presented. To accompany the growing body of research based on fractal-inspired transducers, this paper offers the first sensor design based on a three-dimensional fractal. The three-dimensional model reduces to an effective one-dimensional model by allowing for a number of assumptions of the propagating wave in the fractal lattice. The reception sensitivity of the sensor is investigated. Comparisons of reception force response (RFR) are performed between this novel design along with a previously investigated Sierpinski gasket-inspired device and standard Euclidean design. The results indicate that the proposed device surpasses traditional design sensors

Visual crowding is unaffected by adaptation-induced spatial compression

It has recently been shown that adapting to a densely textured stimulus alters the perception of visual space, such that the distance between two points subsequently presented in the adapted region appears reduced (Hisakata, Nishida, & Johnston, 2016). We asked whether this form of adaptation-induced spatial compression alters visual crowding. To address this question, we first adapted observers to a dynamic dot texture presented within an annular region surrounding the test location. Following adaptation, observers perceived a test array comprised of multiple oriented dot dipoles as spatially compressed, resulting in an overall reduction in perceived size. We then tested to what extent this spatial compression influences crowding by measuring orientation discrimination of a single dipole flanked by randomly oriented dipoles across a range of separations. Following adaptation, we found that the magnitude of crowding was predicted by the physical-rather than perceptual-separation between centre and flanking dipoles. These findings contrast with previous studies in which crowding has been shown to increase when motion-induced position shifts act to reduce apparent separation (Dakin, Greenwood, Carlson, & Bex, 2011; Maus, Fischer, & Whitney, 2011)

A manpower utilization model for a Naval Air Rework Facility

The management personnel at the Naval Air Rework Facility, North Island Naval Air Station, San Diego, California, are currently faced with two difficult planning problems inherent in any large industrial concern. These are the inability to smooth out the workload so that it may be considered constant over a specific period of time and the determination of the optimal utilization of the direct labor force in order to produce the workload and minimum dollar wage cost. Assuming a constant workload, a mathematical model of this utilization problem, incorporating constraints and restrictions placed upon NARFSD by various agencies, is developed which can be solved as a minimal cost flow-with-gains network problem. By varying the constraint and restriction limits, several alternative manpower utilization options and their related costs are examined. Finally, various methods of smoothing variable workloads are suggested.http://archive.org/details/manpowerutilizat00clifLieutenant, United States NavyApproved for public release; distribution is unlimited

The spatial properties of adaptation-induced distance compression

Exposure to a dynamic texture reduces the perceived separation between objects, altering the mapping between physical relations in the environment and their neural representations. Here we investigated the spatial tuning and spatial frame of reference of this aftereffect to understand the stage(s) of processing where adaptation-induced changes occur. In Experiment 1, we measured apparent separation at different positions relative to the adapted area, revealing a strong but tightly tuned compression effect. We next tested the spatial frame of reference of the effect, either by introducing a gaze shift between adaptation and test phase (Experiment 2) or by decoupling the spatial selectivity of adaptation in retinotopic and world-centered coordinates (Experiment 3). Results across the two experiments indicated that both retinotopic and world-centered adaptation effects can occur independently. Spatial attention to the location of the adaptor alone could not account for the world-centered transfer we observed, and retinotopic adaptation did not transfer to world-centered coordinates after a saccade (Experiment 4). Finally, we found that aftereffects in different reference frames have a similar, narrow spatial tuning profile (Experiment 5). Together, our results suggest that the neural representation of local separation resides early in the visual cortex, but it can also be modulated by activity in higher visual areas

Vascular endothelial growth factor (VEGF) expression in locally advanced prostate cancer: secondary analysis of radiation therapy oncology group (RTOG) 8610.

BACKGROUND: Angiogenesis is a key element in solid-tumor growth, invasion, and metastasis. VEGF is among the most potent angiogenic factor thus far detected. The aim of the present study is to explore the potential of VEGF (also known as VEGF-A) as a prognostic and predictive biomarker among men with locally advanced prostate cancer. METHODS: The analysis was performed using patients enrolled on RTOG 8610, a phase III randomized control trial of radiation therapy alone (Arm 1) versus short-term neoadjuvant and concurrent androgen deprivation and radiation therapy (Arm 2) in men with locally advanced prostate carcinoma. Tissue samples were obtained from the RTOG tissue repository. Hematoxylin and eosin slides were reviewed, and paraffin blocks were immunohistochemically stained for VEGF expression and graded by Intensity score (0-3). Cox or Fine and Gray\u27s proportional hazards models were used. RESULTS: Sufficient pathologic material was available from 103 (23%) of the 456 analyzable patients enrolled in the RTOG 8610 study. There were no statistically significant differences in the pre-treatment characteristics between the patient groups with and without VEGF intensity data. Median follow-up for all surviving patients with VEGF intensity data is 12.2 years. Univariate and multivariate analyses demonstrated no statistically significant correlation between the intensity of VEGF expression and overall survival, distant metastasis, local progression, disease-free survival, or biochemical failure. VEGF expression was also not statistically significantly associated with any of the endpoints when analyzed by treatment arm. CONCLUSIONS: This study revealed no statistically significant prognostic or predictive value of VEGF expression for locally advanced prostate cancer. This analysis is among one of the largest sample bases with long-term follow-up in a well-characterized patient population. There is an urgent need to establish multidisciplinary initiatives for coordinating further research in the area of human prostate cancer biomarkers