The Universality Concept as a Tool to Simplify Numerical Simulations

Abstract

A number of physical systems exhibit naturally self-similar features, characterized by power-law correlations over some spatial and/or temporal domain. Critical or self-organized critical systems are general examples, and they appear in all fields of physics dealing with N interacting constituents. The powerful renormalization-group theory is able to answer many precise questions concerning these systems. But by for the most important consequence of the theory is the concept of the universality class. This fundamental concept can be used to simplify dramatically the numerical simulations of such systems, leading to the exact values of the relevant physical quantities—those who are related to the long-range correlations. In this paper, we develop the general method with the practical steps to apply it to concrete physical situations. We then focus on the particular case of the aggregates of colloidal particles.

Keywords:

• Self-similarity
• Colloidal aggregates
• Fractals
• Critical systems