Complex Phenomena in Simple Systems
Physics of the Everyday: Complex Phenomena in Simple Systems
Module convenor: Professor Patrick Royall
Duration: 10 hourly sessions
Start date: 12/01/2027
Tuesdays & Thursdays 10-11
Overview
Many everyday phenomena are characterised by collective behaviour of large numbers of interacting particles, for example freezing and melting. This course looks at how we understand such phenomena from the perspective of simple, generic, model systems. In particular we consider models of atoms and molecules that may be treated either with analytical theory or for large enough systems and long enough timescales computationally to access rare events. Such rare events can be relaxation in glassy materials or crystal nucleation in liquids. Where appropriate we emphasise the individuals who have developed the field.
Course Description
The course begins with a description of the models, such as the Lennard-Jones and Hard Sphere models of atoms and molecules. Colloids are introduced as experimental model systems suitable to probe microscopic time- and length-scales. The equilibrium phase behaviour is explored and key elements from liquid state physics are reviewed.
Our state of understanding of the glass transition, described by Nobel Laureate Philip Anderson as “the deepest problem in solid state physics” is discussed in some detail. Different theoretical approaches are outlined, and we review theoretical and experimental developments over the last decades including recent machine-learning approaches.
The second area that we address is crystal nucleation. Surprisingly, given that crystallisation is an everyday phenomenon and is important in industry and climate change modelling to give just two examples, it is all but impossible to predict the rate of formation of crystalline nuclei in a liquid. We discuss this challenge in the context of Classical Nucleation Theory and review recent developments in experiment and highlight the exciting potential of machine learning methods to produce much more accurate models than those currently available.
We then move on to the emergent field of Active Matter. In particular, by adding self-propulsion to the models we have discussed so far, they are enable to mimic the flocking, swarming and milling that are exhibited by groups of bacteria, insects, fish and even humans. We consider this collective behaviour through the lens of non-equilibrium phase transitions and draw analogies with phase transitions in physical systems.
Lectures
1. Introduction and Overview: what is Physics of the Everyday all about?
2. Models. The surprising accuracy of the Lennard-Jones model of atoms and molecules. Colloids as model atoms.
3. Overview of relevant liquid state theory. Equation of state. 2-point correlation functions. Equilibrium phase behaviour of simple models. Dynamics in liquids and colloids.
4. The glass transition I. Outline of the problem. Intuitive theoretical descriptions from a thermodynamic perspective. Adam-Gibbs theory. Random-First-Order Transition theory. Geometric Frustration.
5. The glass transition II. Mode Coupling Theory. The only quantitative first-principles theory of the glass transition; its success and failures.
6. The glass transition III. The Glass Transition as a Scientific Revolution: Dynamic Facilitation Theory and its incompatibility with other theories. Machine-Learning approaches to the glass transition.
7. Liquid-Liquid Transitions: nature of liquid-liquid transitions, their discovery and the “water wars”.
8. Crystallisation and Nucleation. Classical Nucleation Theory. The experimental challenges of measuring nucleation and recent developments. The computational challenges of predicting nucleation and the promise of machine learning techniques to solve the problem.
9. Collective Behaviour in Active Matter. Flocking, Swarming and Schooling in simple models and their analogy to phase transitions in physical systems. Active colloids as a synthetic testbed for biomimetic behaviour. Case study: multistate behaviour in zebrafish.
10. Summary and Future Directions for Physics of the Everyday.
Intended learning objectives
To understand and to be able to articulate the concepts discussed in the lecture series.
In particular to be able to explain the key systems. And to be able to discuss the challenges in the phenomena addressed, such as the glass transition and predicting nucleation rates.
Assessment
Assessment will be via a short perspective-style piece on a topic covered in the course, for example:
(i) Challenges in predicting nucleation rates
(ii) Success of different theoretical descriptions of the glass transition
(iii) The “water wars” and the liquid-liquid transition
Resources
A basic knowledge of Statistical Physics will be required.