Statistical analysis of time series. With compelling arguments we show that the Diffusion Entropy Analysis (DEA) is the only method of the literature of the Science of Complexity that correctly determines the scaling hidden within a time series reflecting a Complex Process. The time series is thought of as a source of fluctuations, and the DEA is based on the Shannon entropy of the diffusion process generated by these fluctuations. All traditional methods of scaling analysis, instead, are based on the variance of this diffusion process. The variance methods detect the real scaling only if the Gaussian assumption holds true. We call H the scaling exponent detected by the variance methods and d the real scaling exponent. If the time series is characterized by Fractional Brownian Motion, we have H¹d and the scaling can be safely determined, in this case, by using the variance methods. If, on the contrary, the time series is characterized, for example, by Lévy statistics, H ¹ d and the variance methods cannot be used to detect the true scaling. Lévy walk yields the relation d=1/(3-2H). In the case of Lévy flights, the variance diverges and the exponent H cannot be determined, whereas the scaling d …

The first part of this paper describes the Meissner effect in superconductors which serves as the most definitive evidence for superconductivity. It is shown that the microwave perturbation technique may be used to demonstrate this effect. By measuring the changes of resonant frequency and inverse quality factor Q of a microwave cavity with a small volume of sample loading, the Meissner effect can be shown by using the Slater perturbation equation. The experimental system is described with details and the basic principle of each component discussed. The second part of this work describes the technique employed to do the actual measurements. The experiments were conducted on samples of Gallium Arsenide (GaAs) and lead zirconate titanate (PZT) to look for the possible high temperature superconductivity properties. Results of these experiments are presented and discussed. Conclusion and suggestions to future exploration are made.

The results of a statistical study of hard x-ray solar flares are presented in this dissertation. Two methods of analysis were used, the Diffusion Entropy (DE) method coupled with an analysis of the data distributions and the Rescaled Range (R/S) Method, sometimes referred to as "Hurst's method". Chapter one provides an introduction to hard x-ray flares within the context of the solar environment and a summary of the statistical paradigms solar astronomers currently work under. Chapter two presents the theory behind the DE and R/S methods. Chapter three presents the results of the two analysis methodologies: most notably important evidence of the conflicting results of the R/S and DE methods, evidence of a Levy statistical signature for the underlying dynamics of the hard x-ray flaring process and a possible separate memory signature for the waiting times. In addition, the stationary and nonstationary characteristics of the waiting times and peak intensities, are revealed. Chapter four provides a concise summary and discussion of the results.

Accurate knowledge of stopping powers is essential for these for quantitative analysis and surface characterization of thin films using ion beam analysis (IBA). These values are also of interest in radiobiology and radiotherapy, and in ion- implantation technology where shrinking feature sizes puts high demands on the accuracy of range calculations. A theory that predicts stopping powers and ranges for all projectile-target combinations is needed. The most important database used to report the stopping powers is the SRIM/TRIM program developed by Ziegler and coworkers. However, other researchers report that at times, these values differ significantly from experimental values. In this study the stopping powers of Si, P and S ions have been measured in Ni, Cu, Ge and GaAs absorbers in the energy range ~ 2-10 MeV. For elemental films of Ni, Cu and Ge, the stopping of heavy ions was measured using a novel ERD (Elastic Recoil Detection) based technique. In which an elastically recoiled lighter atom is used to indirectly measure the energy of the incoming heavy ion using a surface barrier detector. In this way it was possible to reduce the damage and to improve the FWHM of the detector. The results were compared to SRIM-2000 predictions …