Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Dr. Dimitri Mavris; Committee Member: Dean Ward; Committee Member: Dr. Daniel Schrage; Committee Member: Dr. Danielle Soban; Committee Member: Dr. Sriram Rallabhandi; Committee Member: Mathias Emeneth.

We investigate dynamical processes on random and regular fractals. The (static) problem of percolation in the semi-infinite plane introduces many pertinent ideas including real space renormalisation group (RSRG) fugacity transformations and scaling forms. We study the percolation probability to determine the surface critical behaviour and to establish exponent relations. The fugacity approach is generalised to study random walks on diffusion-limited aggregates (DLA). Using regular and random models, we calculate the walk dimensionality and demonstrate that it is consistent with a conjecture by Aharony and Stauffer. It is shown that the kinetically grown DLA is in a distinct dynamic universality class to lattice animals. Similarly, the speculation of Helman-Coniglio-Tsallis regarding diffusion on self-avoiding walks (SAWs) is shown to be incorrect. The results are corroborated by an exact enumeration analysis of the internal structure of SAWs. A 'spin' and field theoretic Hamiltonian formulation for the conformational and resistance properties of random walks is presented. We consider Gaussian random walks, SAWs, spiral SAWs and valence walks. We express resistive susceptibilities as correlation functions and hence e-expansions are calculated for the resistance exponents. For SAWs, the local crosslinks are shown to be irrelevant and we calculate corrections to scaling. A scaling description is introduced into an equation-of-motion method in order to study spin wave damping in d-dimensional isotropic Heisenberg ferro-, antiferro- and ferri- magnets near pc . Dynamic scaling is shown to be obeyed by the Lorentzian spin wave response function and lifetime. The ensemble of finite clusters and multicritical behaviour is also treated. In contrast, the relaxational dynamics of the dilute Anisotropic Heisenberg model is shown to violate conventional dynamic scaling near the percolation bicritical point but satisfies instead a singular scaling behaviour arising from activation of Bloch walls over percolation cluster energy barriers.

Thesis (M.Sc.)--York University, 2005. Graduate Programme in Earth and Space Science. / Typescript. Includes bibliographical references (leaves 130-140). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss &rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR11761

Weigh scaling is a method of estimating the total volume of timber harvested from a given region. The implementation of statistical sampling techniques in weigh scaling is described, along with related issues. A review of ratio estimators, along with variance estimators of the classical ratio estimator is conducted. The estimation of the variance of the estimated total volume is considered using jackknife- and bootstrap-based variance estimators. Weighted versions of the jackknife and bootstrap variance estimators are derived using influence functions and Fisher Information matrices. Empirical studies of analytic and resampling-based variance estimators are conducted, with particular emphasis on small sample properties and on robustness with respect to both the homoscedastic variance and zero-intercept population characteristics. With a squared error loss function, the resampling-based variance estimators are shown to perform very well at all sample sizes in finite populations with normally distributed errors. These estimators are found to have small negative biases for small sample sizes and to be robust with respect to heteroscedasticity. / Science, Faculty of / Statistics, Department of / Graduate

Call number: LD2668 .T4 1979 N48 / Master of Science

The statistics describing variations of turbulent motions within the so called inertial range of length scales depend on the scale over which the motions are varying and the "average" rate at which the turbulent kinetic energy is being dissipated on the molecular scale. This hypothesis stemmed from the similarity arguments published by A. N. Kolmogorov in 1941 and implies specific scaling relations between the average amplitude and length scale of turbulent motions. Turbulent motions agree to a good approximation with Kolmogorov scaling provided the fluid flow admits to the underlying assumptions. More recently it has been recognized that the large spatial variations in the rate of turbulent kinetic energy dissipation may be a partial explanation for deviations from Kolmogorov scaling. This recognition is due in part to the observation that the total volume occupied by turbulent motions of a given scale decreases as the scale decreases. These observations imply that active small scale turbulence is intermittent. This study aims to better understand how scaling relations describing more active regions are different from the relations describing turbulence where the small scales are less active. The thesis is that the relations are different. An 18 hour segment of wind data measured in near-neutral stratification 45 meters above a relatively flat ground is analyzed. There is virtually no trend in the mean wind speed, so the describing statistics are essentially stationary. Small scale activity is measured in terms of the difference in wind speed (structure function) at a separation distance of 1/16 of a second, which translates to about a meter. The differences in wind speed are raised to the sixth power and then averaged over 4 second (50 meter) windows. Non-overlapping windows containing a local maximum in the averaged sixth order structure function form one (MASC) ensemble of more active small scale samples and the local minima form another (LASC) ensemble of less active small scale samples. The variations in wind speed as a function of length scale within each ensemble are decomposed five different ways. Each of the five decompositions obey scaling relationships that are approximately linear in log-log coordinates. The MASC and LASC ensembles include 32% and 46% of the record, respectively. The turbulent kinetic energy as a function of scale falls off at a slower rate in the MASC ensemble versus the LASC ensemble and in magnitude the energy is greater at all scales in the MASC ensemble. This implies the transfer rate of turbulent kinetic energy toward small scales is more rapid on average in the MASC samples. Samples in the MASC ensemble occupied 30% less of the record, implying the flattening effect on the spectral slope exhibited by the samples contained in the MASC ensemble is less influential than the steepening influence of samples of the type in the LASC ensemble. The results are robust with respect to the choice of a basis set in representing the variance as a function of scale. / Graduation date: 1994

Consider a cognitive overlaid network (CON) that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio (CR) technologies. The primary tier consists of randomly distributed primary radios (PRs) of density n, which have an absolute priority to access the spectrum. The secondary tier consists of randomly distributed CRs of density m = n^y with y greater than or equal to 1, which can only access the spectrum opportunistically to limit the interference to PRs. In this dissertation, the fundamental limits of such a network are investigated in terms of the asymptotic throughput and packet delay performance when m and n approaches infinity. The following two types of CONs are considered: 1) selfish CONs, in which neither the primary tier nor the secondary tier is willing to route the packets for the other, and 2) supportive CONs, in which the secondary tier is willing to route the packets for the primary tier while the primary tier does not. It is shown that in selfish CONs, both tiers can achieve the same throughput and delay scaling laws as a stand-alone network. In supportive CONs, the throughput and delay scaling laws of the primary tier could be significantly improved with the aid of the secondary tier, while the secondary tier can still achieve the same throughput and delay scaling laws as a stand-alone network. Finally, the throughput and packet delay of a CON with a small number of nodes are investigated. Specifically, we investigate the power and rate control schemes for multiple CR links in the same neighborhood, which operate over multiple channels (frequency bands) in the presence of PRs with a delay constraint imposed on data transmission. By further considering practical limitations in spectrum sensing, an efficient algorithm is proposed to maximize the average sum-rate of the CR links over a finite time horizon under the constraints on the CR-to-PR interference and the average transmit power for each CR link. In the proposed algorithm, the PR occupancy of each channel is modeled as a discrete-time Markov chain (DTMC). Based on such a model, a novel power and rate control strategy based on dynamic programming (DP) is derived, which is a function of the spectrum sensing output, the instantaneous channel gains for the CR links, and the remaining power budget for the CR transmitter. Simulation results show that the proposed algorithm leads to a significant performance improvement over heuristic algorithms.

Secondary (recycled) aluminum constitutes around 48% of the total aluminum used in the United States. Secondary aluminum melting is accomplished in large reverberatory furnaces, and improving its energy efficiency has been one of the major interests to aluminum industries. To assist the industries in improving energy efficiency in aluminum melting, an experimental research furnace (ERF), with 907 kg (2000 lbs) capacity, has been built at the Albany Research Center of the U.S. Department of Energy as part of this multi-partner research program. To verify that the experimental results obtained in the ERF furnace are valid for the operation of industrial furnaces, we used scale modeling technology to assist the validation. In this thesis, scaling laws, which are applied to the thermal conduction loss through the model furnace, were developed and the partial modeling relaxation technique was applied to the development of modeling to derive achievable scaling laws. The model experiments were conducted in the model furnace, which was a one-fourth scaled-down version from the ERF furnace (as a prototype), and then compared to the tests in the ERF furnace. The temperature distributions across both the model and prototype were shown to be in good agreement. Confirmation of the scaling laws demonstrated the usefulness of the scale modeling concept and its applicability to analyze complex melting processes in aluminum melting.

A recently-proposed modification of the Thurstone-Mosteller method of paired comparisons makes possible the analysis of data involving tied observations. The modification includes the postulating of an angular response law such that the response proportions are scaled with arc sine transforms instead of with normal deviates. In this paper a comparison is made of the arc sine and normal curve scaling procedures in paired comparisons involving ties. This is done by applying both methods to data from to important fields of application. Comparisons are also made on several series of hypothetical data. The criterion of comparison is the goodness of fit between the observations and the expected numbers computed from the solution, as measured by means of a chi-square statistic. Computations of parameter estimates and chi-square statistics are made with the aid of an IBM-650, for which the necessary programs have been written. It is concluded that for data conforming well to the model as proposed, both scaling procedures tend to give results in satisfactory agreement with the observations. There is some evidence that, for the cases considered, the preference, if any, is for the normal curve procedure. / Master of Science

Drastic changes in aircraft operational requirements and the emergence of new enabling technologies often occur symbiotically with advances in technology inducing new requirements and vice versa. These changes sometimes lead to the design of vehicle concepts for which no prior art exists. They lead to revolutionary concepts. In such cases the basic form of the vehicle geometry can no longer be determined through an ex ante survey of prior art as depicted by aircraft concepts in the historical domain. Ideally, baseline geometries for revolutionary concepts would be the result of exhaustive configuration space exploration and optimization. Numerous component layouts and their implications for the minimum external dimensions of the resultant vehicle would be evaluated. The dimensions of the minimum enclosing envelope for the best component layout(s) (as per the design need) would then be used as a basis for the selection of a baseline geometry. Unfortunately layout design spaces are inherently large and the key contributing analysis i.e. collision detection, can be very expensive as well. Even when an appropriate baseline geometry has been identified, another hurdle i.e. vehicle scaling has to be overcome. Through the design of a notional Cessna C-172R powered by a liquid hydrogen Proton Exchange Membrane (PEM) fuel cell, it has been demonstrated that the various forms of vehicle scaling i.e. photographic and historical-data-based scaling can result in highly sub-optimal results even for very small O(10-3) scale factors. There is therefore a need for higher fidelity vehicle scaling laws especially since emergent technologies tend to be volumetrically and/or gravimetrically constrained when compared to incumbents. The Configuration-space Exploration and Scaling Methodology (CESM) is postulated herein as a solution to the above-mentioned challenges. This bottom-up methodology entails the representation of component or sub-system geometries as matrices of points in 3D space. These typically large matrices are reduced using minimal convex sets or convex hulls. This reduction leads to significant gains in collision detection speed at minimal approximation expense. (The Gilbert-Johnson-Keerthi algorithm is used for collision detection purposes in this methodology.) Once the components are laid out, their collective convex hull (from here on out referred to as the super-hull) is used to approximate the inner mold line of the minimum enclosing envelope of the vehicle concept. A sectional slicing algorithm is used to extract the sectional dimensions of this envelope. An offset is added to these dimensions in order to come up with the sectional fuselage dimensions. Once the lift and control surfaces are added, vehicle level objective functions can be evaluated and compared to other designs. For each design, changes in the super-hull dimensions in response to perturbations in requirements can be tracked and regressed to create custom geometric scaling laws. The regressions are based on dimensionally consistent parameter groups in order to come up with dimensionally consistent and thus physically meaningful laws. CESM enables the designer to maintain design freedom by portably carrying multiple designs deeper into the design process. Also since CESM is a bottom-up approach, all proposed baseline concepts are implicitly volumetrically feasible. Furthermore the scaling laws developed from custom data for each concept are subject to less design noise than say, regression based approaches. Through these laws, key physics-based characteristics of vehicle subsystems such as energy density can be mapped onto key system level metrics such as fuselage volume or take-off gross weight. These laws can then substitute some historical-data based analyses thereby improving the fidelity of the analyses and reducing design time.