My work on growing spaces falls into two categories. The first concerns the behaviour of models from statistical physics on growing surfaces. This is the content of the first three examples below. The second, less developed category, is trying to understand why systems grow. I approach this problem from a computational perspective, specifically in terms of compressibility and algorithmic complexity.
Disordered packing
Disordered packing is a ubiquitous phenomenon and many variants exist, but what happens when disordered packing is on a growing surface? The short answer is that it gives rise to an unexpected state of matter. Click here to find out more.
Spots and stripes
What happens if we make surface growth nonuniform? In this example we look at a two-species model, representing a bacteria population, and demonstrate how surface growth is a control parameter for a phase transition. Click here to find out more.
Controlling competion outcome
During embryogenesis populations of proliferating cells migrate around the developing embryo to form various tisses. This means there are motile, proliferative cell populations on growing surfaces. How does surface growth affect the outcome of such cell populations? In this example we show that growth can cause symmetry breaking (or not), and in doing so determine competition outcome. Click here to find out more.
Travelling waves
Following the pandemic most of us probably understand what is meant by a close-contact network. We also know that we can change our contact network by changing our behaviour. If we want to grow it we go out and talk to people we have not met before. If we want to shrink it we stay at home and read a book. In this example we study a model that connects network growth and behaviour. The result is travelling waves and compressibility. Click here to find out more.
Algorithms in growing spaces
Are there processes that are more efficient if they are in a growing space? Or problems that are easier to solve? One way of addressing this question is to study how growth affects the computationally efficiency of an algorithm. To do so, we studied fixation times in a growing 1D voter model. More information regarding this work can be found here.