On the Geometric Principles of Surface Growth

TL;DR

This paper introduces a new geometric-based equation for surface growth that captures key behaviors like mound formation and mass conservation, linking physical principles with renormalization group analysis.

Contribution

It presents a novel geometric variational equation for epitaxial growth, bridging microscopic physics with continuum models and expanding understanding of surface evolution.

Findings

Reproduces mound formation and mass conservation behaviors.

Connects geometric principles with dynamic renormalization group analysis.

Provides a new framework for modeling surface growth phenomena.

Abstract

We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also able to reproduce the critical behavior already observed, mound formation and mass conservation, but however does not fit a divergence form as the most commonly spread models of conserved surface growth. This formulation allows us to connect the results of the dynamic renormalization group analysis with intuitive geometric principles, whose generic character may well allow them to describe surface growth and other phenomena in different areas of physics.