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The University of Southampton
International Summer School

Scale Invariance in the Real World

A system is said to be scale invariant if changing the scale does not change the system's properties. One of the best known examples of scale invariance is a fractal: if you zoom into a fractal it looks the same. Scale invariance is present in many important systems in the real world, and this invariance can be used to understand how the systems evolve with time.

Scale invariance in the real world
Scale invariance in the real world

This course will introduce the mathematical and statistical physics concepts used to describe scale invariance. We will explore the role of scale invariance in several real world systems, ranging from financial data to flocking phenomena. Remarkably, the migration of a flock of birds spontaneously develops scale invariance, which can be used to predict the motion of the birds.

Please note to take this topic you will need a familiarity with calculus - differentiation of functions, including functions of more than one variable.

The academic organising this topic is Professor Marika Taylor, Professor of Theoretical Physics.

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