Microscopically-informed active field theories
Objectives
Active field theories (M3) are widely used to study collective effects in driven systems at all levels of organisation (L1-4), allowing instabilities to pattern formation to be identified [1]. Most commonly such theories are phenomenological, built by identifying the dominant terms consistent with symmetries and conservation laws that are present [2,3]. It is difficult in this approach to connect to underlying microscopic processes, such as the rate at which a microscopic constituent (be that a motor protein, a cell or a higher organism) consumes energy. In this project, our aim is to build on previous success [4] in constructing a stochastic field theory from first principles that features multiplicative noise, and where quantitative agreement with a particle-based model (T1) is achieved in one spatial dimension with a numerical algorithm (T10) that employs non-Gaussian stochastic increments. We aim to extend this approach to more complex models in higher-dimensions, thereby creating new microscopically-informed field-theories for dry active matter. This could be used to predict phase transitions driven by changes in behaviour at the microscopic scale.
Activities of the Doctoral Candidate
Following [4], we will construct active field theories for particles undergoing self-propulsion, alignment, attraction and repulsion. These model bird flocks or fish schools in more than one dimension. Blythe’s model-building expertise (T1) will generate new field theories (T3) and numerical integration methods (T10). Maggi will contribute parallel computing expertise [5] to implement these algorithms on high-end GPUs. This will allow efficient parameter space scanning, validation against particle-based simulations (T9) and study of collective effects and phase transitions. Models will also be applied to 3d tracking data of fish schooling (L4) collected by the Rome group [6]. There is also an opportunity to model swimming sperm which exhibit collective motion at high speeds, applying to data provided by Dyneval.
Facilities Provided
TBC.
Employment Contract
TBC.
Period of Doctorate and Funding
TBC.
References
[1] Cates, ME (2022) in Active Matter and Nonequilibrium Statistical Physics (OUP) [2] Toner, J, & Tu, Y. (1995) Phys Rev Lett 75:4326 [3] Wittkowsi. R, et al. (2014) Nat Comm 5:4351 (2014) [4] Ó Laighléis, E, et al. (2018) Phys Rev E 98:062127 [5] Maggi, C, et al (2021) Soft Matter 17:3807 [6] sites.google.com/view/claudio-maggi-cnr/projects