Chaotic Self Avoiding Walks of Multiple Atoms
a.k.a. Rabbits and Wolves; a.k.a. the Game of Knots
Our recent experimental observations show motion of subcellular structures (also called atom or specie in different contexts) that avoid certain regions of the cell and also some parts of the cell wall. We hence developed a new theoretical framework to explain such behviours. We have made successful models for 1 specie (atom or structure) systems in 2D and now aim to develop this unique model to n-species in 3D.
Your Research
Developing a new class of dynamical systems where two species avoid each other and interact with boundaries in an odd way. This is a project at the boundaries of pure & applied mathematics and soft matter physics, and you will be involved in the numerical (billiards and chaos) and analytical (geometry and topology) calculations to explain complex systems with possible applications in biological or active systems, quantum chaos and soft matter theory/polymer physics.
Research Question:
How does a self avoiding system with more than 1 species behave?
When an ensemble of self-avoiding walkers become chaotic?
Methods involved
Theory: pen & paper, python programming
Keywords:
Chaos, Billiards, Self-avoiding walks, Quantum Chaology