a major concern of farmers is deterioration of the soil and water resources. soil management is the most direct way for mankind to interfere with natural processes that may either intensify or hinder soil degradation. fractal geometry has been widely used to describe heterogeneity in a wide range of natural processes, including physical systems of soil. in this study, the effects of different m...

The Ardabil geothermal area is located in the northwest of Iran, which hosts several hot springs. It is situated mostly around the Sabalan Mountain. The Sabalan geothermal area is now under investigation for the geothermal electric power generation. It is characterized by its high thermal gradient and high heat flow. In this study, our aim is to determine the fractal parameter and top and botto...

Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm re...

We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find bil-liard tables that generate these Teichmüller curves. We interprete some of ...

Jessica L. Green*, John Harte and Annette Ostling Department of Environmental Science and Policy, University of California, One Shields Avenue, Davis, CA 95616, USA Energy and Resources Group, University of California, Berkeley, CA 94720, USA *Correspondence: E-mail: [email protected] Abstract Although scaling relationships that characterize fractal species distributions offer an exciting pot...

We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface, which appears to be 2D SG fractal. The two-polymer system is modelled by two mutually cr...

RATIONALE Airway wall remodeling is an important aspect of asthma. It has proven difficult to assess quantitatively as it involves changes in several components of the airway wall. OBJECTIVE To develop a simple method for quantifying the overall severity of airway wall remodeling in asthmatic airways using fractal geometry. METHODS Negative-pressure silicone rubber casts of lungs were made ...

In this paper, a pilot study regarding carotid atherosclerotic plaque instability using B-mode ultrasound (US) images was carried out. The fractal dimension of plaques obtained from ten symptomatic subjects (i.e., subjects having experienced neurological symptoms) as well as from nine asymptomatic subjects, was estimated using a novel method, called the kth nearest neighbour (KNN) method. The r...

Given a Fuchsian group with at least one cusp, Deroin, Kleptsyn and Navas define a Lyapunov expansion exponent for a point on the boundary, and ask if it vanishes for almost all points with respect to Lebesgue measure. We give an affirmative answer to this question, by considering the behavior of the word metric along typical geodesic rays and their excursions into cusps. We also consider the b...

Fractals are a group of irregularly irregular geometric objects, first described by Mandelbrot.ln2 We have previously suggested that a patient’s distribution of ventricular premature contractions (VPCs) over time can be represented by a particular kind of fractal-the fractal dust.3 This makes it possible to measure dimension (D), a number that quantifies the uniformity or nonuniformity of that ...