Novel universality classes in polar active fluids using nonperturbative renormalization group methods
File(s)
Author(s)
Jentsch, Patrick
Type
Thesis
Abstract
The compressible Toner-Tu equations are investigated with respect to novel universality classes, describing the structure of its phase diagram. This is achieved using the nonperturbative functional renormalization group. In particular, the ordered flocking phase and a multicritical region, where the critical order-disorder and critical phase-separation points coincide, are studied. The flocking phase is studied in two levels of approximation. In the incompressible limit, it is confirmed that the scaling exponents, previously obtained using perturbative methods, are indeed exact also within a nonperturbative approximation. Further, this work revealed an active Goldstone regime, where novel scaling laws for the previously neglected parallel and longitudinal modes emerge. In a second approximation, compressibility effects are taken into account using a simplified model, where density fluctuations are only minimally coupled. In dimensions d < 11/3, this model is described by a novel compressible universality class, which in two and three dimensions matches state-of-the-art simulation results of the celebrated Vicsek model. I therefore believe to have uncovered the universality class describing the flocking phase of the Vicsek model, a question that has remained unanswered since the early beginnings of active matter. Around the multicritical point, three novel fixed points are discovered, including the one describing generically the scaling behaviour of the multicritical point. All three universality classes carry the hallmarks of a nonequilibrium universality class.
Version
Open Access
Date Issued
2024-07-31
Date Awarded
01/01/2025
Advisor
Lee, Chiu Fan
Publisher Department
Bioengineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)