Periodic Reporting for period 1 - RG.BIO (Renormalization group approach to the collective behaviour of strongly correlated biological systems)
Reporting period: 2018-10-01 to 2020-03-31
Collective biological systems are correlated to a degree which is unusually strong and which would require fine tuning at the physical level. Strong correlations are at the same time the mystery of collective behaviour and the key to unlock this mystery. On the one hand, we do not fully understand why correlations are so strong, and conjectures about collective response and fluctuation-dissipation relations are to be proved. On the other hand, strong correlations allow us to study and compare through the same theoretical looking glass systems as diverse as bird flocks, insect swarms and cell colonies: when correlations extend beyond all microscopic length scales of the system, we are led to believe that details cannot matter a lot. In absence of any empirical backup, this may look like wishful thinking. But an empirical backup does exist, in the form of scaling laws, which have been found to hold both at the static and at the dynamic level. This scenario suggests that the current landscape of scattered concepts (correlation, universality, scaling) can be brought to a theoretical closure through the main tool that physics developed half a century ago exactly to this aim, namely the renormalization group.
By conducting innovative experimental observations on bird flocks (starlings, swifts), insect swarms (midges, mosquitoes) and cell colonies, and building on the statistical physics concepts of correlation and scaling, RG.BIO aims at developing a novel renormalization group approach to strongly correlated biological systems, with the purpose of classifying into new universality classes the collective phenomena of life.
THEORY. One of the central ideas inspiring my theoretical understanding of biological collective behaviour, is that the social forces appearing into the equations of motion cannot act directly on the velocities of the animals, but have to be mediated by the spin, namely the generator of the rotations of the velocity itself. This change of perspective allowed our lab to reconcile theory with experiments regarding the propagation of information in bird flocks and the shape of the dynamical correlation functions in insect swarms. In the light of this, our first theoretical effort within RG.BIO has been to perform an RG calculation of a model in which non-dissipative terms coupling the velocity and the spin modes coexisted with the dissipative terms typical of any biological system. We discovered that for low enough dissipation, or small enough groups, dissipation is ineffective, so that the critical exponent ruling the dynamics has a value much closer to the experimental one than previous estimates. We are now studying how these mode-coupling terms impact on hydrodynamics theories with explicit terms of self-propulsion. Finally, we have developed a new marginal field theory, able to explain the scale-free correlations of the speed found in bird flocks as a phenomenon due to the vicinity to a zero temperature critical point, hence avoiding the need to tune any parameter to criticality.
THEORY. The central theoretical idea of RG.BIO is that the only way to develop a predictive theoretical physics of biological collective phenomena is through a novel renormalization group (RG) approach. The long-term objective of the project is to develop a new RG perturbative theory based on separation of time scales, using correlations and scaling laws as empirical anchors of theoretical work. These results will be tested against the experimental arm of the project, exploring the validity of an RG classification of collective biological phenomena into universality classes. Quantitatively accurate, and possibly parameter-free matching between theory and experiment, in the theoretical physics tradition, will be a major concern of RG.BIO.