Inaug.-diss.--Berlin. / Vita.

Inaug.-diss.--Berlin. / Vita.

Thesis--Friedrich-Wilhelms-Universität Berlin, 1865. / Vita.

Thesis--Copenhagen.

Ab initio prediction of the electronic properties of solids is traditionally performed using groundstate Density Functional Theory. These methods are unreliable however, for a class of important problems involving weak attractive forces. These problems include (i) the energetics of hydrogen storage and metal interactions in graphene, (ii) cohesion properties of some polymer systems and (iii) possibly, the weak hydrophobic forces in biomolecules. For these cases a more powerful method than groundstate DFT are timedependent DFT (tdDFT) methods related to the Random-Phase Approximation (RPA). All of these methods proceed by looking at the dynamic density-density response function, whose long-ranged properties naturally lead to the weak forces referred to above. In this thesis we have tested these ideas by investigating electronic response and correlation on the predicted properties of spherical atoms. We have developed and tested a variety of approximations to the timedependent response function through approximations of the tdDFT class and a new method involving greater self-consistency in the screening equation, the inhomogenous STLS approach. Through the development of new methods and computer code, we have solved the response equation allowing us to test our approximations on atoms. Calculation of certain dynamic and static properties of a variety of atoms within our approximations generally agree well with known results. In this thesis we have calculated excitation energies of Helium, dipole polarisabilities and C6 van der Waals (vdW) coefficients of a variety of atoms, and groundstate correlation energies Ec of some atoms. The excitation spectra of Helium generated in our new PGG+c approximation are in good agreement with experiment. The dipole polarisabilities are generally in good agreement with known results, with the exception of Magnesium, Beryllium and Sodium. The C6 coefficients are a little poorer with the exception of Helium where they are nearly exact. Correlation energies are generally reasonable in the PGG+c approximation although they are considerably less accurate than the other properties we have calculated for all atoms other than He. The ISTLS correlation energy of Helium is within 5% suggesting that this method may perform well for larger atoms where our present numerical techniques require improvement. These generally positive results suggest that the approximations we have developed may be applied to more complicated systems such as those described above with good results.

The structure of Euclidean, spherical, and hyperbolic geometries are compared, considering specifically postulates, curvature of the plane, and visual models. Implications for distance, the sum of the angles of triangles, and circumference to diameter ratios are investigated. / text

No description available.

A spherical indentation test is considered to be invalid if there is presence of a visible mark on the side of the sheet metal facing the anvil and exactly below the indentation. With the available standard loads of the conventional testers such as Brinell and Rockwell hardness testers, it is difficult to avoid this anvil effect while dealing with the sheet metals. The penetration depth increases when the thickness of the sheet is reduced at constant indentation pressures. The reason behind this is the change in mode of deformation. When the thickness of the sheet metal is reduced, and the indentation test is carried out on it, then the sheet metal experiences first indentation, then bending, followed by lifting of the sheet from the anvil which leads to a forging mode of deformation. The modes of deformation were identified using a finite element simulation of the indentation process. Plots of normalized depth against normalized thickness were created for the same indentation pressure, and a second order polynomial curve was fitted to the data points. The equation of this curve quantifies the anvil effect. The anvil effect was identified as a function of sheet thickness, indenter radius, indentation load and two material constants. A method to correct this anvil effect was also developed using the equation representing the anvil effect. It is possible to obtain the equivalent geometry of indentation without anvil effect. A MATLAB program is developed to obtain the parameters defining the curve for the anvil effect. Indentation test on a sheet using three different indenters and corresponding loads is required for this method. For accurate prediction of the equivalent depth of indentation, a lower limit of 10 % and upper limit of 80 % for penetration depth (ratio of depth of indentation and thickness of sheet metal) was identified for the spherical indentation testing on the sheet metals. Verification of the curve fitting model was carried out with the indentation experiments on commercially available Niobium, Al2024-T3, Al7075-T6 and 1020 low carbon steel sheets. These tests show good agreement between fit, prediction, and experiments for the anvil effect.

Spherical aberration limits the ability of a human eye to form a clear image. The amount of Spherical Aberration found in a given eye is different across a population and is actively changing as a function of accommodation, light level, and age. Any attempt made to correct spherical aberration will need to have an accurate understanding of what the appropriate correction should be. Objective measurement of the Spherical Aberration inherent to the eye's optical systems helps to answer part of the question, but there are other factors in the human visual system, such as processing in the brain that affect what is "seen". Hence, a vision correction approach based purely on objective measurement of the eye's aberrations may not necessarily correspond to better vision. The Spherical Aberration Gauge has been developed to allow subjects to deter- mine for themselves the appropriate amount of correction required. The Gauge is designed to allow users to view an eye chart or scene while adjusting the amount of spherical aberration being introduced. It produces a wide range of spherical aberration levels from which a user can determine a single level that provides best vision. The amount selected by the user is considered a subjective spherical aberration correction and can then be applied to standard vision correction devices or procedures. This project attempts to bridge the gap between what is known about ocular spherical aberration and how the brain interprets the correction. The outcome of this project is to provide a tool that identifies the preferred amounts of spherical aberration correction and that gives insight from subjective feedback on the visual benefit thereof.

Characteristic features of the long atmospheric waves are discussed on the basis of spherical harmonic analysis of global weather charts for September 1957. At first, there is a discussion of the Trapezoidal and Simpson's numerical integration rules as applied to the computation of the Spherical harmonic coefficients. [...]