Browsing by Subject "Fractals"
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Item A clubhouse facility for Meadowbrook Municipal Golf Course, Mackenzie State Park, Lubbock, Texas(Texas Tech University, 1995-05) Ulm, Trenton J.To generate an Architecture that is an intigrated whole within its environment through the application of the systems view of nature and fractal geometry.Item A fractal characterization of speech waveform graphs(Texas Tech University, 1989-05) Rao, GiridharThe thrust of this thesis is to investigate the applicability of the fractal dimension as a parameter in some speech recognition applications. Almost no work has been done in this area; we would like to see how well fractals can be used in speech analysis. This thesis is a report of preliminary investigations done in attempting to combine these two seemingly diverse fields in an attempt to lead us one step closer to the ultimate goal of fully automatic speech recognition.Item Analysis of gas differential diffusion through porous media using prompt gamma activation analysis(2013-12) Rios-Perez, Carlos Alfredo, 1981-; Deinert, MarkAccurate estimates for the molecular transport coefficients are critical to predicting the movement of gases in geological media. Here I present a novel methodology for using prompt gamma activation analysis to measure the effective diffusivity of noble gases in a porous medium. I also present a model to estimate the connectivity parameter of a soil from measurements of its saturated conductivity, macro porosity, and pore volume and pore surface fractal dimensions. Experiments with argon or xenon diffusing through a nitrogen saturated geological media were conducted. The noble gas concentration variations at its source were measured using prompt gamma activation analysis and later compared to a numerical diffusion model to estimate the effective diffusion coefficient. Numerical simulations using the estimated diffusivity and the experimental argon data produced results with a correlation parameter R² = 0.98. However, neglecting transport mechanisms other than diffusion largely under-predicted the xenon depletion rates observed during the first hours of experiment. To explain these results, a second model was developed which included the effect of pressure gradients and bulk convection that might arise from the faster molecular migration of the light species in a non-equimolar system and gravitational currents. Finally, the fractal model developed for this dissertation was used to estimate the connectivity parameters and walking fractal dimension of a group of geological samples that were previously characterized. This model successfully predicted positive connectivity factors and walking fractal dimensions between two and three for every sample analyzed.Item Discrete deterministic chaos(2010-08) Newton, Joshua Benjamin; Armendáriz, Efraim P.; Daniels, Mark L.In the course Discrete Deterministic Chaos, Dr. Mark Daniels introduces students to Chaos Theory and explores many topics within the field. Students prove many of the key results that are discussed in class and work through examples of each topic. Connections to the secondary mathematics curriculum are made throughout the course, and students discuss how the topics in the course could be implemented in the classroom. This paper will provide an overview of the topics covered in the course, Discrete Deterministic Chaos, and provide additional discussion on various related topics.Item Image recovery and segmentation using the fractal dimension(Texas Tech University, 1998-12) Pallemoni, Sharath CIt has been observed that real world objects are inherently composed of complex, rough and jumbled surfaces while current representational schemes use generalized cylinders or splines to describe natural surfaces. Therefore, there is a need to have a model for describing all naturally occurring surfaces. Alex Pentland [8] has shown that the fractal dimension is a representation, capable of succinctly describing the surfaces of natural objects, such as mountains, trees, clouds etc. His paper describes a method of computing the fractal dimension. In this work, Alex Pentland's [8] algorithm for evaluating the fractal dimension was applied to a set of images. The results of this algorithm when studied, reveal a distinct distribution of smooth edges such as the texture of the shirt in Figure 2, the facial variations in the same image, the surface variations of the road in the Figure 3 and the varied distribution of regions with people and houses in Figure 4. In addition to obtaining Sun Raster images for the fractal dimension using Pentland's [8] algorithm, this work also included evaluating the hard edges present in the images using the Sobel operator edge-detection scheme. On applying the Sobel operator method to Figure 3, the resultant image distinctly indicated the hard-edges in the original image by clearing bringing out the outlines of different people and the outlines of other objects present in the image. The Sobel edge-detected image had all the sharp edges represented by sudden variations of homogeneous regions in the original image (Figure 3). Finally, the results obtained using the fractal dimension and those obtained using the Sobel operator were logically OR-ed to capture both hard and soft edges. The test images used for this logical OR operation were the results of the fractal dimension algorithm and the Sobel operator edge-detection technique on Figure 3. As can be seen from the final result (Figure 49), both the soft edge distribution of the fractal dimension image (Figure 47) and the hard edges found in the Sobel operator image (Figure 48) were successfully captured in the logically OR-ed image. The final results of this work were thus able to represent up to a degree, a previously non-existent model which attempted to integrate the results of Alex Pentland's [8] work using the fractal dimension for evaluating soft edges and results obtained from the Sobel operator for hard edge detection. This work indicates mixed results in coming up with the new model suggested and definitely has potential for improvement.Item Time-series analysis using orthogonal polynomials(Texas Tech University, 2003-05) Vittal, Vinay AchalanandAdvances in the study of non-linear dynamics have encouraged the construction of models and simulators of non-linear time-series. Researchers in the field of both science and statistics have come up with innovative methods that are useful in extracting information from systems that exhibit non-linear dynamics. Time-series, as we all know, is the sequence x1, x2, x3,…x11 observed in time. Time-series analysis depends on the fact that data points taken over time may have internal structure such as autocorrelation, trend or seasonal variation. It is these properties that make model construction possible. As part of this research, the Measure Based approach to reconstruction, proposed by Giona [1], is investigated. This method is based on the Fourier expansion of the polynomial system 11 orthonormal to the invariant measures. Programs have been written based on the MB approach and these programs were tested on various one dimensional time-series like the sine map, the tent map and the logistic map. This approach to reconstruction furnishes good results when applied to chaotic one dimensional time-series.