Radon concentration in caves is known to vary within an extremely wide range. Here the distribution of the average values of radon concentration is examined and a power law describing is identified, i.e. radon concentration has a fractal dimension D=1.26. This fact means that concentrations are not grouped around a mean value, a characteristic common to many other phenomena. Introduction Radon ...

We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates t, the exponent for the power law distribution of avalanche sizes, to D, the fractal dimension of an avalanche cluster. We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean-field ex...

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...

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 ...

A fractal is an object or a structure that is self-similar in all length scales. Fractal geometry is an excellent mathematical tool used in the study of irregular geometric objects. The concept of the fractal dimension, D, as a measure of complexity is defined. The concept of fractal geometry is closely linked to scale invariance, and it provides a framework for the analysis of natural phenomen...

The fractal Weyl law connects the asymptotic level number with the fractal dimension of the chaotic repeller. We provide the first test for the fractal Weyl law for a three-dimensional open scattering system. For the four-sphere billiard, we investigate the chaotic repeller and discuss the semiclassical quantization of the system by the method of cycle expansion with symmetry decomposition. We ...

It has been demonstrated that there is a geometrical order in text structures. Fractal geometry, as a modern mathematical approach and a new geometrical standpoint on natural objects including both processes and structures, is here employed for textual analysis. For this first study, the works of William Shakespeare were chosen as the most important items in Western literature. By counting the ...

Air conditioners have great potential to participate in power system frequency control. This paper proposes a control strategy to facilitate the active participation of air conditioners. For each air conditioner, a decentralized control law is designed to adjust its temperature set point in response to the system frequency deviation. The decentralized control law accounts for the user’s thermal...

In this paper, the characterization of catchments extracted from multiscale digital elevation models (DEMs) is performed. First, the lifting scheme is employed to generate multiscale DEMs. The catchments extracted from the generated multiscale DEMs are then characterized based on their numbers. A power law relationship is derived between the number of extracted catchments and the kernel size. T...

It was demonstrated that there is a geometrical order in the structure of literature. Fractal geometry as a modern mathematical approach and a new geometrical viewpoint on natural objects including both processes and structures was employed for analysis of literature. As the first study, the works of William Shakespeare were chosen as the most important items in western literature. By counting ...