High-Reynolds number flow over tree-like fractals is considered, with emphasis on the drag forces produced. Fractal objects display large scale-disparity and complexity while being amenable to a simple and standardized description. Hence, they offer an elegant idealization of the actual boundaries in practical applications where turbulence interacts with boundaries that are characterized by mul...

A fundamental aspect of harmonic analysis on Euclidean spaces deals with various classes of real or complex-valued functions, such as the C classes of functions which are continuous and continuously differentiable up to order k, where k is a nonnegative integer. If k = 0, this simply means that the function is continuous. Of course continuity of a function makes sense on any metric space, or on...

In a colloidal suspension with attractive interaction, particles form aggregates that settle to the bottom of the container. As the concentration of particles is increased, the overlapping of the aggregates (flocs) produces a continuous network throughout the suspension before settling occurs and a colloidal gel is formed. Colloidal gels may be divided into hard gels and soft gels. 1 Hard gels ...

Fractal, which means broken or irregular fragments, was originally coined by Dr B. Mandelbrot in the year the 1970. Fractals describe a family of complex shapes that possess an inherent self-similarity in their geometrical structure usually in nature, since the pioneering work of Mandelbrot and others, a wide variety of applications for fractals has been found in many branches of science and en...

The most significant aspect of a geochemical exploration program is to define and separate the anomalous values from the background. In the past decades, geochemical anomalies have been identified by means of various methods. Most of the conventional statistical methods aiming at defining the geochemical concentration thresholds for separating anomalies from the background have limited the effi...

Resources/reserves classification is crucial for block model creation utilised in mine planning and feasibility study. Selection of estimation methods is an essential part of mineral exploration and mining activities. In other word, resources classification is an issue for mining companies, investors, financial institutions and authorities, but it remains subject to some confusion. The aim of t...

Orthodontic tooth movement (OTM) is a dynamic process of bone modeling involving osteoclast-driven resorption on the compression side. Consequently, to estimate the influence of various situations on tooth movement, experimental studies need to analyze this cell. Objectives The aim of this study was to test and validate a new method for evaluating osteoclastic activity stimulated by mechanical ...

Fractal phenomena are a source of geometric detail that can be difficult to harness for general purpose shape modeling. We present a method for modeling surfaces by warping a fractal onto a given mesh. The warp is specified by the user as a coarse displacement field and interpolated by triharmonic radial basis functions. Efficient methods for rendering the warped fractal by ray tracing and isos...