Analytical model of brittle destruction based on hypothesis of scale similarity

TL;DR

This paper presents an analytical model linking brittle destruction to scale similarity, explaining dust particle size distributions in nuclear fusion devices through fractal theory and power law relationships.

Contribution

It introduces a novel analytical model connecting brittle destruction with fractal theory, deriving size distribution laws from scale similarity assumptions.

Findings

Size distribution follows a power law with exponent between -4 and -1.

The power exponent relates to the fractal dimension of fragments.

Destruction laws can be inferred from measured size distributions.

Abstract

The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys the power law with the exponent between -4 and -1. The model of destruction has much in common with the fractal theory. The power exponent can be expressed in terms of the fractal dimension. Reasonable assumptions on the shape of fragments concretize the power exponent, and vice versa possible destruction laws can be inferred on the basis of measured size distributions.