Building general Langevin models from discrete data sets
F. Ferretti, V. Chardès, T. Mora, A. M. Walczak and I. Giardina
Experiments revealed inertial signatures in the effective dynamics of natural flocks of starlings and swarms of midges at their observational space-time scales. A quantitative assessment of the damping regime in which these systems operate may bring relevant information for the understanding of their dynamic properties and function. Learning from empirical observations is a long-standing goal in physics, but even today it can be often harder than expected. Building a stochastic model with memory from discrete time series is a challenging task, due to the non-Markovian character of the observed process. In the search for a robust inference method for our birds’ data, we developed a novel maximum likelihood scheme for non-Markovian dynamics with linear dissipation. Its potential application is not restricted to simple underdamped equilibrium models, but it can be implemented also in out-of-equilibrium and large size systems.
Dynamical Renormalization Group approach to the collective behavior of swarms
A.Cavagna, L. Di Carlo, I. Giardina, L. Grandinetti, T. S. Grigera, G. Pisegna
The dynamical scaling hypothesis states that, for systems at the critical point the correlation length is linked to the characteristic relaxation time through the dynamic critical exponent z. Experimental results show that swarms of insects satisfy this property exhibiting an exponent z ≈1.2. Searching for a model able to reproduce this result, we study the critical properties of model with non-dissipative couplings. Using the Dynamical Renormalization Group technique, and working in the fixed network approximation, we find a crossover from a non-dissipative fixed point (z=d/2) to a dissipative ( z=2) fixed point. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system. The value z=d/2 in 3d is significantly closer to the experimental value, then the value found numerically in fully dissipative models z =1.7. This result suggests that mode coupling interaction is a key ingredient to build a theory of natural swarms close to the experiments. Further investigations including the self-propelled nature of the particles are necessary to embed the out-of-equilibrium essence of these biological systems.
Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks
A.Cavagna, A. Culla, L. Di Carlo, I. Giardina, T.S. Grigera
We introduced and studied a novel ferromagnetic model, suitable to reproduce a fascinating statistical property of starlings speeds in their flocking phase. From experimental data one finds that, in a strongly polarized flock, speed’s fluctuations are correlated on a characteristic length that is proportional to the system’s size, i.e. speed correlations are scale-free. We show that, using our “marginal” model, it is possible to reproduce this specific and unusual phenomenology, even in the equilibrium case. The key idea is to consider a bounding potential for the single-particle speed that has zero curvature. A novel zero-temperature critical point emerges and the model develops divergent susceptibility and correlation length of the modulus of the microscopic degrees of freedom, in analogy with experimental data of natural flocks.
Our tasks now are many: first of all, we will investigate more deeply the nature of the “marginal” scale-free behaviour of the model, extracting, in a numerical and a rigorous way, the critical exponents. Then, we will closely compare the statistical field theory, built from our microscopic model, to the experimental data.