In a systematic study, we compare the density statistics in high resolution numerical experiments of supersonic isothermal turbulence, driven by the usually adopted solenoidal (divergence-free) forcing and by compressive (curl-free) forcing. We find that for the same rms Mach number, compressive forcing produces much stronger density enhancements and larger voids compared to solenoidal forcing....

We examine eleven open source software systems and present empirical evidence for the existence of fractal structures in software evolution. In our study, fractal structures are measured as power laws through the lifetime of a software system. We describe two specific power law related phenomena: the probability distribution of software changes decreases as a power function of change sizes; and...

The traditional methods of analysing heart rate variability based on means and variance are unable to detect subtle but potentially important changes in interbeat heart rate behaviour. This research was designed to evaluate the clinical applicability and prognostic significance of new dynamical methods of analysing heart rate behaviour derived from nonlinear mathematics. The study covered four ...

This paper presents a multi-fractal based approach for the classification of emphysema patterns by calculating the local singularity coefficients of an image using different intensity measures. One of the primary statistical measures of self-similarity used in the processing of tissue images is holder exponent (αvalue) that represents the power law which the intensity distribution satisfies in ...

The electromagnetic response of H-fractal structures, consisting of self-similar metallic lines or slits in metallic films deposited on silicon substrate, has been investigated in the terahertz region. The subwavelength fractal structure was observed to display electric resonances, with redshift in the resonant frequencies accompanying an increase in either the fractal level or the sample size....

Using top-end high fidelity computer simulations we demonstrate the existence of a mechanism present in turbulent flows generated by multiscale or fractal objects and which has its origin in the multiscale or fractal space-scale structure of such turbulent flow generators. As a result of this space-scale unfolding mechanism, fractal grids can enhance scalar transfer and turbulent diffusion by o...

Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one. The strength of the dependence obl...

In this paper, the fractal dimensions are proposed for characterizing the optical fiber corrosion sensors, which is applied to measure the steel corrosion based on Fe-C alloy film. Because corrosion was a complex random phenomenon and the corrosion surface of Fe-C alloy film of the optical fiber corrosion sensor possessed fractal characteristics, the image fractal dimensions is as a quantitativ...

Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from Ndimensional hypercomplex numbers (N a power of 2, and at least 4) can represent singularities and, as N → ∞, fractals – and thereby, scale-free networks. Any integer > 8 and not a power of 2 generates a meta-fractal or Sky when it is interpreted as the strut constant (S) of an ensemble of octahedral vertex figures called Box-Kite...

Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from Ndimensional hypercomplex numbers (N a power of 2, and at least 4) can represent singularities and, as N → ∞, fractals – and thereby, scale-free networks. Any integer > 8 and not a power of 2 generates a meta-fractal or Sky when it is interpreted as the strut constant (S) of an ensemble of octahedral vertex figures called Box-Kite...