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Dissertation
Fractal concepts in the analysis of dispersion/relaxation processes
Doctor of Philosophy (Ph.D.), Drexel University
Jun 1987
DOI:
https://doi.org/10.17918/00010000
Abstract
The frequency spectra of randomly structured dispersion/relaxation systems often exhibit a fractional power function dependence on frequency, i.e. a fractional slope on the log-log scale. In this thesis, such systems are identified as 'fractal systems' and a new formalism based on fractal concepts is proposed to model their phenomenological behavior in terms of both the global and local properties. The transient response of dispersion/relaxation systems consists of a collection of decaying real exponentials indicating a distributed relaxation process. The 'singularity structure' analysis is introduced to model the corresponding singularity structure; the pattern of singularities exhibits the statistical properties which can be equivalently studied by the corresponding distribution of relaxation times. The method emphasizes, therefore, the relationship between the underlying processes as opposed to techniques which fit the model to the actual physical behavior by minimizing an error function. The singularity structure of a fractal system is self-similarly constructed, thus the system can be modeled using a proper 'structure base' according to the 'view base' chosen for observation. Finally, the study is extended to the onset of the nonlinear behavior, i.e. within the region of reversibility; the change in the singularity structure as a function of perturbations is advanced as a possible analysis technique. Algorithms to implement the theory of singularity structure analysis are introduced and the experimental results are discussed.
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Details
- Title
- Fractal concepts in the analysis of dispersion/relaxation processes
- Creators
- Yuan Ying Tsao
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- vi, 96 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Engineering (1970-2026); Drexel University
- Other Identifier
- 991021889095204721