Fragmentation is a complex phenomenon seen ubiquitously in nature, with the elucidation
of its complexity being one of the most popular subjects of the last century. It
arises across at a vast multitude of scales in a diverse range of fields such as geophysics
and materials, mineral processing, meteorological processes, astrophysics and nuclei
impacts - only to be limited by the fundamental units of matter itself.
This thesis establishes a new statistical basis for the evolution of particle fragmentation
and the resulting product population at all scales. It is informed by the
underlying physical processes and builds on the existing disconnected models of fragmentation,
mainly the time-continuous grinding and the universality of critical scaleinvariant
systems arising in geophysical systems.
By extending fractal theory into a temporal context and lifting the various limitations
posed by fractals, it provides a solution to the fragmentation problem via
a statistical approach which is verified and developed based on terrestrial data from
both artificial and natural fragmentation processes. It is then applied to model observations
from around the solar system as both an explanatory and predictive approach
to the evaluation of planetary surfaces, one of the major areas of study in planetary
sciences. Furthermore, a stochastic model for drilling in a planetary regolith is developed
both mathematically and through the synthesis of digital soil.