Effects of Long-Range Coupling on Aggregation

TL;DR

This paper investigates how long-range coupling influences the transition from dense to multibranched fractal growth in pattern formation, using numerical simulations of the biharmonic equation as an alternative to Poisson growth models.

Contribution

It introduces a novel approach by analyzing long-range coupling effects through biharmonic equation simulations, providing new insights into fractal aggregate growth patterns.

Findings

Long-range coupling causes a transition from dense to multibranched growth.

Numerical simulations of the biharmonic equation effectively model pattern formation.

The study offers an alternative to traditional Poisson growth models.

Abstract

Alternative to the Poisson growth model, numerical simulations of the two-dimensional biharmonic equation $\nabla^{2*2} u =0$ show that a transition from dense to multibranched growth is a consequence of the different coupling between displacements on the pattern formation of fractal aggregates.