Glossary Cluster Clusters are sets of occupied neighbouring sites. Critical exponents At a critical point or second-order phase transition, many quantities diverge or vanish with a power law of the distance from this critical point; the critical exponent is the exponent for this power law. Fractals Fractals have a mass varying with some power of their linear dimension. The exponent of this powe...

Both natural scenes and visual art are often perceived as esthetically pleasing. It is therefore conceivable that the two types of visual stimuli share statistical properties. For example, natural scenes display a Fourier power spectrum that tends to fall with spatial frequency according to a power-law. This result indicates that natural scenes have fractal-like, scale-invariant properties. In ...

We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of nonlocal particle-particle interactions. We derive a self-similar linear wave operator describing the dynamics of a quasicontinuous linear chain of infinite ...

We have studied the presence of long-range correlations in the complete genomes of ten different dsDNA viruses and Saccharomyces cerevisiae (bakers' yeast) chromosome I. We have also studied the correlation between the distribution of the gene length and the domain of "1/f region" of their genomes. Linear regression analysis was done for the power-law region of these organisms and the slope val...

[1] Distributional analysis of river discharge time series is an important task in many areas of hydrological engineering, including optimal design of water storage and drainage networks, management of extreme events, risk assessment for water supply, and environmental flow management, among many others. Having diverging moments, heavy-tailed power law distributions have attracted widespread at...

In this study, a fractal, Y-shaped dual-mode resonator bandpass filter (BPF) with input-output cross-coupling is introduced. A parallel-coupling feed structure with a cross coupling has been used to generate two transmission zeroes (TZs) near the lower and upper cutoff frequency that can effectively improve the passband edge selectivity. Also, a fractal shaped based on conventional diamond and ...

The application of the spectral representation method in generating Gaussian and non-Gaussian fractal rough surfaces is studied this work. characteristics simulated by conventional Fast Fourier transform filtering are compared. Furthermore, these two methods compared simulation contact lubrication problems. Next, influence low high cutoff frequencies on normality investigated with roll-off powe...

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of t...

An accurate solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of Functionally Graded Sandwich (FGS) plates is presented. Since no assumptions on stresses and displacements have been employed, it can be applied to the free vibration analysis of plates with arbitrary thickness. The two-constituent FGS plate consists of ceramic and metal graded thr...

In anesthetized cats with cervical spinal cord transection, Fano factor analysis was used to test for timescale invariant (fractal) fluctuations in spike counts of single preganglionic cervical sympathetic neurons (PSNs) and putative sympathetic premotor neurons located in the rostral ven-trolateral medulla (RVLM) and caudal medullary raphe. The medullary neurons exhibited cardiac-related activ...