Renormalization-group for amplitude equations in cellular pattern formation with and without conservation law

TL;DR

This paper introduces a refined renormalization-group approach to derive amplitude equations for striped pattern formation, effectively preserving conservation laws and symmetries unlike traditional methods.

Contribution

It presents a novel renormalization-group scheme that maintains physical symmetries and conservation laws in amplitude equations for pattern formation.

Findings

Preserves conservation law in amplitude equations

Maintains rotational invariance of the system

Contrasts with traditional perturbation methods

Abstract

A proper version of the proto renormalization-group scheme is presented to derive amplitude equations in striped pattern formation with conserved and nonconserved order parameter. In the conserved case, the result preserves the conservation law as well as the rotational invariance of the physical system. This makes a great contrast with existing singular perturbation theories such as the multiple-scales method, in which the perturbation expansion truncated at any finite order destroys those symmetries.