Linear scale-invariant system models for self-similar wireless traffic characterization

2000 ◽  
Author(s):  
Raghuveer M. Rao ◽  
S. Lee ◽  
Soheil A. Dianat ◽  
Athimootil V. Mathew
Keyword(s):  
Invariant System ◽  
Linear Scale ◽  
Scale Invariant ◽  
Traffic Characterization ◽  
System Models ◽  
Self Similar

scholarly journals On the fractal nature of complex syntax and the timescale problem

2020 ◽  
Vol 10 (4) ◽  
pp. 697-721
Author(s):  
D. Reid Evans
Keyword(s):  
Complex Systems ◽  
Dynamic Systems Theory ◽  
Self Similarity ◽  
Scale Invariant ◽  
Complex Dynamic Systems ◽  
Complex Syntax ◽  
Dynamic Relationship ◽  
Self Similar ◽  
Multiple Component ◽  
Dynamic Relationships

Fundamental to complex dynamic systems theory is the assumption that the recursive behavior of complex systems results in the generation of physical forms and dynamic processes that are self-similar and scale-invariant. Such fractal-like structures and the organismic benefit that they engender has been widely noted in physiology, biology, and medicine, yet discussions of the fractal-like nature of language have remained at the level of metaphor in applied linguistics. Motivated by the lack of empirical evidence supporting this assumption, the present study examines the extent to which the use and development of complex syntax in a learner of English as a second language demonstrate the characteristics of self-similarity and scale invariance at nested timescales. Findings suggest that the use and development of syntactic complexity are governed by fractal scaling as the dynamic relationship among the subconstructs of syntax maintain their complexity and variability across multiple temporal scales. Overall, fractal analysis appears to be a fruitful analytic tool when attempting to discern the dynamic relationships among the multiple component parts of complex systems as they interact over time.

Application of Fractal Geometry to Fracture Forensics, Research and Production

2006 ◽  
Vol 45 ◽  
pp. 1646-1651 ◽  
Author(s):  
J.J. Mecholsky Jr.
Keyword(s):  
Fractal Analysis ◽  
Fractal Geometry ◽  
Crack Size ◽  
Structural Parameter ◽  
New Materials ◽  
Scale Invariant ◽  
Prepared Material ◽  
Reasonable Approach ◽  
Self Similar ◽  
Production Problems

The fracture surface records past events that occur during the fracture process by leaving characteristic markings. The application of fractal geometry aids in the interpretation and understanding of these events. Quantitative fractographic analysis of brittle fracture surfaces shows that these characteristic markings are self-similar and scale invariant, thus implying that fractal analysis is a reasonable approach to analyzing these surfaces. The fractal dimensional increment, D*, is directly proportional to the fracture energy, γ, during fracture for many brittle materials, i.e., γ = ½ E a0 D* where E is the elastic modulus and a0 is a structural parameter. Also, D* is equal to the crack-size-to-mirror-radius ratio. Using this information can aid in identifying toughening mechanisms in new materials, distinguishing poorly fabricated from well prepared material and identifying stress at fracture for field failures. Examples of the application of fractal analysis in research, fracture forensics and solving production problems are discussed.

Breaking waves and the equilibrium range of wind-wave spectra

1997 ◽  
Vol 342 ◽  
pp. 377-401 ◽  
Author(s):  
S. E. BELCHER ◽  
J. C. VASSILICOS
Keyword(s):  
High Frequency ◽  
Wind Wave ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Wave Spectra ◽  
Scale Invariant ◽  
Self Similar ◽  
Dynamical Properties ◽  
Dynamical Balance ◽  
Equilibrium Range

When scaled properly, the high-wavenumber and high-frequency parts of wind-wave spectra collapse onto universal curves. This collapse has been attributed to a dynamical balance and so these parts of the spectra have been called the equilibrium range. We develop a model for this equilibrium range based on kinematical and dynamical properties of breaking waves. Data suggest that breaking waves have high curvature at their crests, and they are modelled here as waves with discontinuous slope at their crests. Spectra are then dominated by these singularities in slope. The equilibrium range is assumed to be scale invariant, meaning that there is no privileged lengthscale. This assumption implies that: (i) the sharp-crested breaking waves have self-similar shapes, so that large breaking waves are magnified copies of the smaller breaking waves; and (ii) statistical properties of breaking waves, such as the average total length of breaking-wave fronts of a given scale, vary with the scale of the breaking waves as a power law, parameterized here with exponent D.

Sign in / Sign up

Export Citation Format

Share Document