Francesco Ginellli is a physicist working on out-of-equilibrium statistical mechanics, nonlinear dynamics and complex systems. He graduated at the University of Milan, Italy, and received his PhD at the University of Florence under the supervision of R. Livi and A. Politi, with a thesis on spatiotemporal, analyzed with a combinations of tools from nonequilibrium statistical mechanics and nonlinear dynamics.
He has been a post doc at the department of Physics and Astronomy of the University of Wuerzburg, Germany, at the Service de Physique de l'Etat Condensée, CEA - Centre d'etudes de Saclay, France. He has served as a researcher for three yars at the Institut des Systemes Complexes, Paris Ile de France (CNRS), and he has been a researcher TD at the Complex System Institute, CNR, of Rome, Italy. He is currently Senior Lecturer in Physics at the Department of Physics and Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen.
I am a theoretician with a background in nonlinear dynamics, statistical physics and complex systems.
My research activity focuses on a number of theoretical soft-condensed matter and applied mathematics subjects, including: collective motion in active matter systems and collective animal behavior; Lyapunov analysis of chaotic systems; synchronization phenomena in spatiotemporal chaos. Non-equilibrium phase transitions and emergent phenomena.
In the last twenty years or so, statistical mechanics has become more and more involved with “biological matter”, that is collections of cells or more complex living organisms which are typically found in an out of equilibrium state. An extremely useful idealization to tackle this kind of systems is the concept of active particles. Active particles yield some unspecified internal degrees of freedom which allows them to extract and dissipate energy from their environment to move in a preferred direction. This could be due, for instance, to the effect of the complex biochemistry fueling living organisms, but it should be noted that this is not an exclusive characteristic of living organisms: vertically shaken granular rods, for instance, dissipate the energy of their upward bounces by friction with the substrate, resulting in a two dimensional motion, preferentially oriented along their major axis. This self-propulsion is strictly a non thermal phenomenon, as opposed, for instance, to Brownian moving particles. As a consequence, ensembles of active particles (active matter) are characterized by an out-of-equilibrium dynamics, which yields a number of extremely interesting phenomena, such as the occurrence of abnormal density fluctuations in the local particles number. Another phenomenon of great interest is the spontaneous symmetry breaking transition leading to order in several active particles systems (i.e. the particles synchronize their preferred direction of motion and tend to move in the same direction). The collective coherent motion of a large number of these self propelled particles (generally known as flocking) is indeed an ubiquitous phenomena in nature. Examples of large scale structures emerging in such systems range from bird flocks and fish schools to bacteria aggregates and segregation phenomena in a driven monolayer of elongated granular matter.
When dealing with active matter, it is the hope of a theoretical physics approach that, despite the many individual differences existing between these systems, it could be possible to classify them according to their symmetries and conservation laws and their corresponding universal behavior, thus delimiting broad universality classes. My research then concentrates on the study of simple agent-based models - which captures essential (universal) features in the simplest possible setup – and their coarse-grained mesoscopic description via stochastic partial differential equations which describe the long wavelength behavior of the relevant slow variables (typically the density and orientation fields).
In a collaborative effort with biologist interested in animal behavior, agent based models for collective motion are being employed to model and describe flocking behavior in animal groups such as fish schools, starling flocks or sheep herds.
Figure 1. Starling flocks over Rome. Their complex and dynamically changing three dimensional patterns (images a, b) can be reproduced by simple models of locally interacting agents (as indicated by some preliminary results, as the simulation of image c).
Characteryzing dynamics with covariant Lyapunov vectors
Recently, my research in nonlinear dynamical systems concentrated on Lyapunov vectors theory, to unambiguously define and compute a complete set of locally stable and unstable tangent space directions (i.e. “covariant Lyapunov vectors”) associated to exponential growth rates (the Lyapunov exponents). These vectors are norm independent, covariant with the dynamics and invariant under time reversal. They coincide with the stable and unstable manifold at each point in phase space. Furthermore, I have shown that they differ from the orthonormal vectors computed via the celebrated Benettin et al. algorithm. They allow to address fundamental questions -such as the degree of non-hyperbolicity of a dynamical system –and they could also prove as useful tool in practical applications, such as instability control algorithms (i.e. data assimilation) in atmospheric modeling. Moreover, covariant Lyapunov vectors can be employed to characterize spaziotemporal chaos (possibly via a hierarchical decomposition approach) and systems with many degrees of freedom, particularly for what regards the so called hydrodynamic Lyapunov modes in Hamiltonian extended systems or collective dynamics in globally coupled systems.
Finally, they can also be used to estimate the effective dimension in certain classes of chaotic dissipative partial differential equations.
Figure 2. Schematic representation of the strategy used to compute covariant Lyapunov vectors: first, the dynamics dx/dt = F(x) is iterated forward to generate a (sufficiently long) phase space trajectory (black line) between t0 and t1. Also a tangent space orthogonal base of Gram –Schmidt vectors (GSVs, red arrows) is generated at each sampled phase space point by linearized evolution and Gram-Schmidt orthogonalization. Orthonormalization coefficients are systematically stored in the upper triangular matrix Rt. The i-th covariant vector can be expressed as a linear combination of the first i GSVs. Moreover, it can be shown that their coefficients evolve according to the upper triangular matrix R: Ct+Δt = RtCt, where C is the coefficient matrix. By following the same trajectory backward (blue line), and backward iterating a generic upper triangular matrix A by the inverse of R, it will converge to the correct covariant vectors coefficient matrix for every time t sufficiently smaller then t1.
EPSRC Starting Grant: Response to perturbations in active matter systems
Fundings: 122.326 £
Dates: May 1st 2013 - January 31th 2015
Marie Curie Career Integration Grant: PIFS, Perturbations in Flocking Systems
Fundings: 100.000 EUR
Dates: August 1st 2013 - July 31th 2017
Marie Curie European Joint Doctorate (EJD) grant: Complex Oscillatory Systems: Modeling and analysis (COSMOS)
Fundings: 819.864 £
Dates: Jan 1st 2015 - December 31st 2018
Statistical Physics and Stochastic Systems (PX4012)
Analytical Mechanics and Elements of Relativity (PX4517)
- Further Info
Guest Editor, Journal of Physics A for the special issue:
Lyapunov analysis, from theory to applications.