Fractal Strings and Multifractal Zeta Functions

For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to certain multifractal measures. However, we primarily show that they associate a new zeta function, the topological zeta function, to a fractal string in order to take into account the topology of its fractal boundary. This expands upon the geometric information garnered by the traditional geometric zeta function of a fractal string in the theory of complex dimensions. In particular, one can distinguish between a fractal string whose boundary is the classical Cantor set, and one whose boundary has a single limit point but has the same sequence of lengths as the complement of the Cantor set. Later work will address related, but somewhat different, approaches to multifractals themselves, via zeta functions, partly motivated by the present paper.Comment: 32 pages, 9 figures. This revised version contains new sections and figures illustrating the main results of this paper and recent results from others. Sections 0, 2, and 6 have been significantly rewritte

Rapid evaluation of ion thruster lifetime using optical emission spectroscopy

A major life-limiting phenomenon of electric thrusters is the sputter erosion of discharge chamber components. Thrusters for space propulsion are required to operate for extended periods of time, usually in excess of 10,000 hr. Lengthy and very costly life-tests in high-vacuum facilities have been required in the past to determine the erosion rates of thruster components. Alternative methods for determining erosion rates which can be performed in relatively short periods of time at considerably lower costs are studied. An attempt to relate optical emission intensity from an ion bombarded surface (screen grid) to the sputtering rate of that surface is made. The model used a kinetic steady-state (KSS) approach, balancing the rates of population and depopulation of ten low-lying excited states of the sputtered molybdenum atom (MoI) with those of the ground state to relate the spectral intensities of the various transitions of the MoI to the population densities. Once this is accomplished, the population density can be related to the sputtering rate of the target. Radiative and collisional modes of excitation and decay are considered. Since actual data has not been published for MoI excitation rate and decay constants, semiempirical equations are used. The calculated sputtering rate and intensity is compared to the measured intensity and sputtering rates of the 8 and 30 cm ion thrusters

Characterization of physio-chemical properties of polymeric and electrochemical materials for aerospace flight

Sealed nickel cadmium cells having undergone a large number of cycles were discharged using the Hg/HgO reference electrode. The negative electrode exhibited the second plateau. SEM of negative plates of such cells show clusters of large crystals of cadmium hydroxide. These large crystals on the negative plates disappear after continuous overcharging in flooded cells. Atomic Absorption Spectroscopy and standard wet chemical methods are being used to determine the cell materials viz: nickel, cadmium, cobalt, potassum and carbonate. The anodes and cathodes are analyzed after careful examination and the condition of the separator material is evaluated

Possible Signatures Of Dissipation From Time-Series Analysis Techniques Using A Turbulent Laboratory Magnetohydrodynamic Plasma

The frequency spectrum of magnetic fluctuations as measured on the Swarthmore Spheromak Experiment is broadband and exhibits a nearly Kolmogorov 5/3 scaling. It features a steepening region which is indicative of dissipation of magnetic fluctuation energy similar to that observed in fluid and magnetohydrodynamic turbulence systems. Two non-spectrum based time-series analysis techniques are implemented on this data set in order to seek other possible signatures of turbulent dissipation beyond just the steepening of fluctuation spectra. Presented here are results for the flatness, permutation entropy, and statistical complexity, each of which exhibits a particular character at spectral steepening scales which can then be compared to the behavior of the frequency spectrum

Robust detection, isolation and accommodation for sensor failures

The objective is to extend the recent advances in robust control system design of multivariable systems to sensor failure detection, isolation, and accommodation (DIA), and estimator design. This effort provides analysis tools to quantify the trade-off between performance robustness and DIA sensitivity, which are to be used to achieve higher levels of performance robustness for given levels of DIA sensitivity. An innovations-based DIA scheme is used. Estimators, which depend upon a model of the process and process inputs and outputs, are used to generate these innovations. Thresholds used to determine failure detection are computed based on bounds on modeling errors, noise properties, and the class of failures. The applicability of the newly developed tools are demonstrated on a multivariable aircraft turbojet engine example. A new concept call the threshold selector was developed. It represents a significant and innovative tool for the analysis and synthesis of DiA algorithms. The estimators were made robust by introduction of an internal model and by frequency shaping. The internal mode provides asymptotically unbiased filter estimates.The incorporation of frequency shaping of the Linear Quadratic Gaussian cost functional modifies the estimator design to make it suitable for sensor failure DIA. The results are compared with previous studies which used thresholds that were selcted empirically. Comparison of these two techniques on a nonlinear dynamic engine simulation shows improved performance of the new method compared to previous technique

Insurance Contracts - Waiver by Estoppel

Surrender by an insured of the right to change the beneficiary of his life insurance policy creates a vested interest in the then designated beneficiary and an acceptance by the company of the insured\u27s subsequent request to change the beneficiary constitutes a waiver of the prohibition against such change and an estoppel to deny liability to the new beneficiary. Phillips v. Continental Assurance Co., 210 Pa. Super. 178, 231 A.2d 422 (1967), allocatur denied, 231 A.2d 422 (1967)

Thermal Zoning For HVAC Design

The thermal zoning for heating, ventilation, and air conditioning (HVAC) system design, and the factors affecting zoning decisions are discussed. Spaces within buildings have varying thermal loads. To maintain the desired indoor temperature and humidity under transient sensible and latent heat gains and losses, these spaces need HVAC equipment with different capacities and separate control loops. The need for HVAC designers to select the thermal zones before the detailed loads are known is also cited