Response to perturbations in active matter systems

Flocking, the collective motion displayed by large groups of birds in the absence of an obvious leader, is one of the most spectacular examples of emergent collective behavior in nature and has fascinated inquiring minds for a long time. Flocking, is not only restricted to birds, but can be observed in an extremely wide range of active matter systems - systems composed by "active particles" able to extract and dissipate energy from their surroundings to produce systematic and coherent motion -- as diverse as fish schools, vertebrate herds, bacteria colonies, insect swarms, active macromolecules in living cells and even driven granular matter.

While our knowledge of collective motion has greatly advanced in recent years thanks to the study of minimal models of self propelled particles (SPP) and hydrodynamic continuum theories, as well as the development of the first quantitative experiments, little is known concerning the response of moving groups to perturbations, a question of both theoretical interest (fluctuation-response in out-of-equilibrium physics) and of great ethological importance (biological significance of group response, spatio-temporal mechanisms of information propagation in cases of alert).

Protection from external threats is thought to be one of the most important factors in the evolution towards collective behavior, and there is indeed evidence that certain collective properties observed in animal groups cannot be understood in the context of unperturbed theories. Experimental observations in starlings, for instance, have revealed that flocks are much more internally correlated, and thus have a more efficient collective response mechanism than expected from standard unperturbed flocking theories.

Our working hypothesis, supported by preliminary results in simple spin systems, is that certain properties of collectively moving animal groups can only be understood in terms of the system response to localized, dynamical perturbations. We will characterize the response of flocks to such perturbations, devoting particular attention to the role of information transmission from the boundaries to the bulk of a finite system. We will also address the origin of such perturbations. They may be exogenous, due to environmental stimuli such as attacking predators or the perception of non-homogeneous landscapes. But perturbations may also be endogenous: even in the absence of external stimuli, individuals may suddenly switch their behavioral patterns so that the group sets itself constantly into a state of dynamical excitation, possibly because this behavior enhances collective response when true perturbations strike.

We will consider finite perturbations, which induce a nonlinear response in flocks, but also the limit of infinitesimal perturbations, which may allow for a deeper theoretical analysis of linear response by extension of the fluctuation-dissipation relation (FDR) to flocking systems (out-of-equilibrium generalization of the FDR are already known, but flocking systems remain largely unexplored). This is an issue of great interest for the study of animal group behavior, since it could provide relevant information (at least at the linear level) concerning the response to perturbations starting only from the knowledge of unperturbed fluctuations. It is our goal to extend and test a generalized FDR to flocking systems.

This project aims at a well-defined advance in the scientific knowledge and will have direct impact on the academic communities of out-of-equilibrium statistical mechanics and group animal behavior. On a longer time scale, however, a better understanding of emergent collective phenomena in living matter could beneficially impact a number of important fields ranging from biotechnologies (subcellular dynamics of protein filaments, swarming nanorobots) to environmental resources conservation and management (animal group behavior, animal populations response to environmental changes).

This proposal regards a theoretical approach to out-of equilibrium collective motion in living matter and other active matter systems. It falls naturally within the physics challenges highlighted by EPSRC: Understanding emergence in real systems, understanding physical phenomena far from equilibrium, and understanding the physics of life, have been recently listed among the "Physics grand challenges" in a document produced by the EPSRC (Outputs from EPSRC Physics Grand Challenge Surveys, 2011) as a result of a survey study conducted among UK scientists. Such document explicitly states: "Understanding and eventually predicting emergent states, is a central challenge for the physics community. This challenge would be wide ranging, across phase/scale boundaries" and "This fundamental work will be driven by the ever-present possibility that emergent states may provide the foundations for the technologies of the future".

Although the main impact of this project is within the (national and international) academic environment, on a decennial timescale, a better understanding of emergent collective phenomena in living matter could beneficially impact a number of important fields ranging from biotechnologies (subcellular dynamics of protein filaments, swarming nanorobots) to environmental resources conservation and management (animal group behavior, animal populations response to environmental changes), as clarified by the two following simple examples:

i) Future medical applications, for instance, consider scenarios where a swarm of nanorobots is launched from a starting point into the human body to perform group tasks, such as searching particular places in the human body for effective drug delivery. Due to miniaturization issues, global view or external coordination would not be possible, and the group should rely on self-organized flocking due to local communications only. Understanding collective response mechanisms to external stimuli is a required step towards the realization of such nanorobot swarms.
ii) Marine ecosystem knowledge and conservation, on the other hand, could not leave aside a better understanding of large oceanic fish shoals collective behavior (and their response to external perturbations and stimuli), as they provide a vital link in the ocean and human food chain.

We should also not dismiss the impact of this project on the training and education of a young scientist, the RA, who will work on a highly interdisciplinary subject at the crossover between statistical physics and biology and learn new methodologies in a growing developing research field. As a consequence, we expect that, in the end of the project, the RA will have further advanced towards academic independence.

Animal collective behavior, moreover, is a fascinating subject particularly well suited for dissemination towards the general public, and we will take every possible effort (participation to café scientifiques and other divulgation initiatives, creation of a website to popularize project results and demos of our model to the inquiring minds) to increase the general public awareness towards the emergent complexity of animal group behavior in particular and the complexity of our ecosystem at large.