Spelling suggestions: "subject:"fractal""
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New Statistical Methods to Get the Fractal Dimension of Bright Galaxies Distribution from the Sloan Digital Sky Survey DataWu, Yongfeng January 2007 (has links) (PDF)
No description available.
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Fractal solutions to the long wave equationsAjiwibowo, Harman 13 September 2002 (has links)
The fractal dimension of measured ocean wave profiles is found to be in the
range of 1.5-1.8. This non-integer dimension indicates the fractal nature of the
waves. Standard formulations to analyze waves are based on a differential
approach. Since fractals are non-differentiable, this formulation fails for waves with
fractal characteristics. Integral solutions for long waves that are valid for a non-differentiable
fractal surfaces are developed. Field observations show a positive
correlation between the fractal dimension and the degree of nonlinearity of the
waves, wave steepness, and breaking waves. Solutions are developed for a variety
of linear cases. As waves propagate shoreward and become more nonlinear, the
fractal dimension increases. The linear solutions are unable to reproduce the change
in fractal dimension evident in the ocean data. However, the linear solutions do
demonstrate a finite speed of propagation.
The correlation of the fractal dimension with the nonlinearity of the waves
suggests using a nonlinear wave equation. We first confirm the nonlinear behavior
of the waves using the finite difference method with continuous function as the
initial condition. Next, we solve the system using a Runge-Kutta method to
integrate the characteristics of the nonlinear wave equation. For small times, the
finite difference and Runge-Kutta solutions are similar. At longer times, however,
the Runge-Kutta solution shows the leading edge of the wave extending beyond the
base of the wave corresponding to over-steepening and breaking.
A simple long wave solution on multi-step bottom is developed in order to
calculate the reflection coefficient for a sloping beach. Multiple reflections and
transmissions are allowed at each step, and the resulting reflection coefficient is
calculated. The reflection coefficient is also calculated for model with thousands of
small steps where the waves are reflected and transmitted once over each step. The
effect of depth-limited breaking waves is also considered. / Graduation date: 2003
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Spectral Analysis of Laplacians on Certain FractalsZhou, Denglin January 2007 (has links)
Surprisingly, Fourier series on certain fractals can have better
convergence properties than classical Fourier series. This is a
result of the existence of gaps in the spectrum of the Laplacian. In
this work we prove a general criterion for the existence of gaps.
Most of the known examples on which the Laplacians admit spectral
decimation satisfy the criterion. Then we analyze the infinite
family of Vicsek sets, finding an explicit formula for the spectral
decimation functions in terms of Chebyshev polynomials. The
Laplacians on this infinite family of fractals are also shown to
satisfy our criterion and thus have gaps in their spectrum.
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Spectral Analysis of Laplacians on Certain FractalsZhou, Denglin January 2007 (has links)
Surprisingly, Fourier series on certain fractals can have better
convergence properties than classical Fourier series. This is a
result of the existence of gaps in the spectrum of the Laplacian. In
this work we prove a general criterion for the existence of gaps.
Most of the known examples on which the Laplacians admit spectral
decimation satisfy the criterion. Then we analyze the infinite
family of Vicsek sets, finding an explicit formula for the spectral
decimation functions in terms of Chebyshev polynomials. The
Laplacians on this infinite family of fractals are also shown to
satisfy our criterion and thus have gaps in their spectrum.
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Standard and nonstandard roughness - consequences for the physics of self-affine surfacesGheorghiu Ștefan, January 2000 (has links)
Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 87-91). Also available on the Internet.
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Fractal geometry of iso-surfaces of a passive scalar in a turbulent boundary layerSchuerg, Frank, January 2003 (has links) (PDF)
Thesis (M.S. in E.S.M.)--School of Civil and Environmental Engineering, Georgia Institute of Technology, 2004. Directed by Donald R. Webster. / Includes bibliographical references (leaves 118-121).
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Visualization tools for information exploration /Hong, Kam-kee, Kay. January 2001 (has links)
Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 119-122).
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Visualization tools for information exploration康錦琦, Hong, Kam-kee, Kay. January 2001 (has links)
published_or_final_version / Computer Science and Information Systems / Master / Master of Philosophy
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Fraktalinis vaizdų suspaudimo metodo tyrimas / Fractal image compressionŽemlo, Gražina 11 June 2004 (has links)
One of the images compression methods – fractal image compression is analyzed in the work. After work carried out, it is possible to state, that selecting parameters of method of fractal compression depends on user’s demands.
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A fractal theory of iterated Markov operators with applications to digital image codingJacquin, Arnaud E. 08 1900 (has links)
No description available.
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