Geometrical modeling of dendritic structures

TL;DR

This paper presents a geometric approach to modeling dendritic crystal growth, analyzing surface perturbations, symmetry, and topology, supported by computer simulations under various flow conditions.

Contribution

It introduces a novel geometric modeling method for dendritic structures, including topological analysis and computer simulations of growth in different fluid flow environments.

Findings

Surface perturbations lead to different equilibrium shapes.

Computer models simulate dendritic growth with and without convective flow.

Topological features of dendrites include surfaces of various genus, up to 270.

Abstract

Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the same equilibrium shape receiving of the same of crystal, are established. Fulfilled computer embodiment of such dendritic crystals which are growing both in conditions without convective flow and in the oncoming flow of liquid. Special attention is paid to topological characteristics of models with non-crystallographic point groups of symmetry. Surfaces of various genus, including 270, were investigated.