Non-linear phenomena exhibit extreme variability over a wide range of scales and intensities. In multifractal processes, variability increases algebraically with resolution: as we approach the small scale limit, we develop a highly singular field of diverging and vanishing densities. Even over a finite range of scales, the variability can readily exceed the finite signal-response range capabilities of measuring devices. In face of such extreme behavior, one can no longer consider the problems of observing such processes as "merely" experimental ones. / Detectors will rarely be capable of handling the full dynamic range of intensities, missing either the extreme events or the small input signal. Therefore it is of fundamental importance to understand what multifractals "look like" when observed through a detector having only a finite dynamic range. / Limitations on the observable dynamic range affect intensities at nearby scales, breaking the scale invariance and imposing a limit on the range of scales over which scaling behaviour can be observed. / A simple model of a threshold-type problem, in which a detector has a (finite) minimum detectable signal level, is solved in the multifractal framework. Results include a breaking of the scaling symmetry for scales particularly close to the scale corresponding to the resolution of the detector. The scaling improves as we as we degrade further to lower resolutions. It also improves as we move to higher moment statistics. / Rainfall time series from time scales of 180 years to 5 minutes are analysed, revealing, in particular, a break in the spectral scaling behavior near 2.4 hours. Some of the theoretical results are used to show that this break is likely to be caused by instrumental problems at low signal intensities. The correct scaling behavior is successfully recovered from the low resolution information.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.22752 |
| Date | January 1995 |
| Creators | Larnder, Chris |
| Contributors | Lovejoy, S. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001460746, proquestno: MM05575, Theses scanned by UMI/ProQuest. |
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