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  • Print publication year: 2020
  • Online publication date: March 2020

10 - Dimensional Analysis, Chaos and Self-Organised Criticality

from Case Study III - Mechanics and Dynamics: Linear and Non-linear

Summary

The majority of physics problems are impossible to solve by analytic means. Various strategies have been developed to cope with the highly non-linear nature of many of these problems. Dimensional analysis provides a powerful tool for addressing many complex problems, suggesting the form the solutions must have. Examples include the non-linear pendulum, explosions, flow at high Reynolds number and the law of corresponding states. The study of chaotic phenomena became feasible with the development of high speed computers and revealed regularities despite the apparent unpredictability of the systems. Scaling laws for extremely complex and non-linear problems lead to the concept of self-organised criticality, illustrated by the model computations for rice and sand piles.