Fractal Dimension Of Boundary Research Articles

A SCALING LAW RELATING THE RATE OF DESTRUCTION OF A SOLID TUMOR AND THE FRACTAL DIMENSION OF ITS BOUNDARY

In this paper, we investigate the scaling law relating the size of the boundary of a solid tumor and the rate at which it is lysed by a cell population of non-infiltrating cytotoxic lymphocytes. We do it in the context of enzyme kinetics through geometrical, analytical and numerical arguments. Following the Koch island fractal model, a scale-dependent function that describes the constant rate of the decay process and the fractal dimension is obtained. Then, in silico experiments are accomplished by means of a stochastic hybrid cellular automaton model. This model is used to grow several tumors with varying morphology and to test the power decay law when the cell-mediated immune response is effective, confirming its validity.

Development of a new machine vision algorithm to estimate potato's shape and size based on support vector machine

AbstractDevelopment of a new machine vision‐based algorithm, to estimate potato's shape and size, will have great significance to agricultural industry in developing countries. Machine vision, one of hot technique, uses machines to execute measurement, calculating, and judgment instead of human eyes. In this study, a new machine vision algorithm, based on support vector machine, was proposed for estimating potato's shape and size. After captured the square RGB image with 512 × 512 pixels, the original image was processed by gray scale and linear transformation, filtering, entity, and boundary detecting. Then, geometric characteristics, image wavelet moment, and fractal dimension of boundary were extracted for marking the potato's characteristic. In addition, the effect of four kind of support vector machine (SVM) kernel function was comparing by several experiments with 64 potato samples. By experimental confirmation, SVM based on the polynomial kernel is more suitable for discriminating potato's shape with an accuracy of 88.89%; SVM based on the linear kernel is more suitable for estimating potato's size with an accuracy of 87.41%.Practical applicationsPotato is a high‐yield, nutrient‐rich crop with high nutritional value. This study proposes a potato shape and size estimation algorithm based on machine vision. Through experimental verification, the detection accuracy of the algorithm initially meets the actual engineering application. The shape and size of potatoes can be detected to classify potatoes. In the process of food processing such as potato chips, the classification of potatoes is conducive to improving the quality of food processing.

Fractal dimension of cluster boundaries in porous polycrystalline HTSC materials

The fractal dimension of the boundaries of clusters formed by pores and granules in polycrystalline materials is shown to be determined by the sample density and crystallite sizes. The dependence of the fractal dimension on the density has a maximum. It is shown that the maximum diamagnetic response can be obtained in a porous high-temperature superconductor with a porosity of 50–60% and small crystallite sizes.

Study of current–voltage characteristics of Bi-based high-temperature superconductors with fractal cluster structure

We study the effect of the structure on critical currents and current–voltage characteristics (CVC’s) of foamed bismuth-based polycrystalline high-temperature superconductors (HTSC). The fractal cluster structure of superconducting foams has been observed and the fractal dimension of boundaries between superconducting and normal clusters has been determined. Based on the magnetic and transport properties of the foamed polycrystalline superconductors, we have shown that the initial parts of CVC’s of the superconducting foams are described well by the model that accounts the magnetic flux trapping in fractal clusters of a normal phase.