Agglomeration/aggregation and chaotic behaviour in d-dimensional spatio-temporal matter rearrangements. Number-theoretic aspects

TL;DR

This paper explores how matter organizes into clusters at mesoscopic scales, exhibiting chaotic behavior influenced by temperature, dimension, and mechanical stresses, and provides a comprehensive model of d-dimensional matter rearrangements.

Contribution

It introduces a novel framework linking structural rearrangements, chaos, and number-theoretic aspects in d-dimensional matter formation.

Findings

Cluster formations depend on temperature and space dimension.

Rearrangements exhibit Verhulst-like saturation and frustration.

Chaotic behavior manifests in both space and time domains.

Abstract

Matter gets organized at several levels of structural rearrangements. At mesoscopic level one can distinguish between two types of rearrangements, conforming to different close-packing or densification conditions, appearing during different evolution stages. The cluster formations appear to be temperature- and space-dimension dependent. They suffer a type of Verhulst-like saturation (frustration) when one couples the growing (instability) and mechanical stress relaxation modes together. They manifest a chaotic behavior both in space and time domains. We pretend to offer a comprehensive and realistic picture of a material or megacluster formation in d-dimension.