Active Matter focuses on systems composed by self-driven units, also called active particles, that are capable of converting free energy into movement. While an unified framework to describe the phenomenology of the active matter is still missing, different approaches converge on the importance of the density fluctuations that result to be long-lived leading to non-Boltzmann stationary states with no vanishing probability currents.
In order to stabilize the spontaneous currents, environment and confinement play a crucial role: in recent years, it has been shown that the density fluctuations of active baths can produce unidirectional flux in asymmetric environments [1], sustain spontaneous flow in confined geometry [2], move micro gears [3,4], exert effective attractive forces [5], and deliver passive colloids [6].
We focus our attention on run-and-tumble particles, i. e., a model that captures the dynamics of low Reynolds number swimming organisms such as E. coli, embedded into (i) confining geometries[7] and (ii) subjected to external random fields[8]. The results obtained by mean of numerical simulations can been experimentally studied by mean of (i) microfluidic devices and (ii) speckle fields.

References

[1] P. Galajda et al., J. Bacteriol. 189, 1033 (2007).
[2] T. Sanchez, et al., Nature 491, 431 (2012).
[3] R. Di Leonardo, et al., Proc. Natl. Acad. Sci. 107, 9541 (2010).
[4] A. Sokolov, et al., Proc. Natl. Acad. Sci. U.S.A. 107, 969 (2010).
[5] L Angelani, et al., Phys. Rev. Lett. 107, 138302 (2011).
[6] N. Koumakis, et al., Nature Communications, 4, 2588 (2013).
[7] M. Paoluzzi, et al. http://arxiv.org/abs/1412.1131 (2014).
[8] M. Paoluzzi, et al. J. Phys.: Condens. Matter 26 375101 (2014).

Negative absolute temperatures emerge naturally from Boltzmann's definition of "surface" microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of negative absolute temperatures has been challenged, on account that only Gibbs "volume" entropy —and the strictly positive temperature thereof— would give rise to a consistent thermodynamics.
Here we focus on a discrete nonlinear model characterized by bounded energy densities, describing the propagation of light in arrays of coupled waveguides. We present analytical and numerical evidence that Boltzmann microcanonical entropy provides a consistent thermometry for both signs of the temperature. In particular, we show that Boltzmann (negative) temperature allows the description of phase transitions occurring at high energy densities, at variance with Gibbs temperature. Our results are relevant also to ultracold gases trapped in optical lattices.

The possibility of having mechanically isolated systems with negative absolute temperatures is one of the most fascinating results of statistical mechanics: however such a possibility dramatically depends upon the choice of the definition of entropy. In systems with unbounded phase-space, the two common definitions of entropy as the logarithm of the phase space volume (Gibbs entropy) or surface (Boltzmann entropy) are equivalent in the thermodynamic limit; this equivalence breaks down in some particular systems where the Boltzmann definition can lead to temperatures with negative sign. In the recent past, many authors affirmed that the Boltzmann definitions of entropy and temperature cannot be accepted since they are not consistent with thermodynamics: nonetheless, we want to emphasize that such a temperature gives a very strong characterization of the statistical features of the system. We have studied the dynamics of a chain of coupled rotators: in this simple system we can show, with direct numerical computations, the differences between the situation at positive and negative absolute temperature. In particular, by measuring the time averages of some observable quantities, we are able to show the crucial role of the Boltzmann temperature in the statistical description of the system.

The phase of a harmonically driven undamped pendulum undergoes strong anomalous diffusion due to the mixed nature of its phase space, with hierarchies of regular islands surrounded by the chaotic sea. A stochastic model that reproduces most properties of the original Hamiltonian system is explicitly built, and the connection between deterministic chaos, anomalous transport and fractal properties of the phase space is demonstrated in this paradigmatic case study.

In a random sequence of heads or tails, with a fair coin, every subsequence appears evenly. However, given a sequence, there is always another one that appears first, statistically. Betting on subsequences is a non-transitive game, like rock-paper-scissors. The analysis of non-transitivity can be extended to any Markov process, and also used for analysing real data. We found that there is a phase transition in the degree of non-transitivity for unfair coins, and that in general this degree depends on certain properties of the Markov process, in particular we analyzed diffusion processes on graphs. We finally started applying this concept to the analysis of DNA sequences.

In collaboration with F. Bagnoli and D. Fanelli

The matching problem is a long standing problem in combinatorial optimization that has attracted many attentions in the disordered systems community. In the Euclidean version of the problem the cost matrix is given by the distances among points randomly distributed in the d-dimensional box. Here we present a simple approximation for the Euclidean bipartite matching, based on the Poisson equation, that leads to several prediction on the exact limit value of the average optimal cost.

Understanding the relation between functional anatomy and structural substrates is a major challenge in neuroscience. To study at the aggregate level the interplay between structural brain networks and functional brain networks, a new method will be described; it provides an optimal brain partition —emerging out of a hierarchical clustering analysis— and maximizes the “cross-modularity” index, leading to large modularity for both networks as well as a large within-module similarity between them . The brain modules found by this approach will be compared with the classical Resting State Networks, as well as with anatomical parcellations in the Automated Anatomical Labeling atlas and with the Broadmann partition.

We consider pulse-coupled leaky integrate-and-fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level. Our main aim is to mimic the effect of the dilution as a noise source acting on the dynamics of a globally coupled nonchaotic system. Indeed, the evolution of a diluted neural network can be well approximated as a fully pulse-coupled network, where each neuron is driven by a mean synaptic current plus additive noise. These terms represent the average and the fluctuations of the synaptic currents acting on the single neurons in the diluted system. The main microscopic and macroscopic dynamical features can be retrieved with this stochastic approximation. Furthermore, the microscopic stability of the diluted network can be also reproduced, as demonstrated from the almost coincidence of the measured Lyapunov exponents in the deterministic and stochastic cases for an ample range of system sizes. Our results strongly suggest that the fluctuations in the synaptic currents are responsible for the emergence of chaos in this class of pulse-coupled networks.

Although the brain has been an object of study since long time, it is still largely unknown. Its highly non-trivially connected structure shapes a functional network whose activation and synchronization mechanisms still represent a major challenge for scientists belonging to the different fields, from neuroscience to complex system theory. This talk represents a contribution to the study of the brain from the perspective of complex network theory. In particular, a data set corresponding to the neuronal activity of 41 mice brains in a resting state, collected via the fMRI technique, has been analysed by applying a range of procedures (as data clustering, community detection, percolation analysis and others), in order to gain insight into the collective activity of brain areas. Our results indicate that a statistically significant signal of collective neuronal activity is detectable even in a resting state, thus allowing us to identify functionally-related areas. Indirectly, this also proves that the analytical tools provided by network theory may indeed provide a non-trivial insight into the structure of the brain, highlighting functional correlations between different areas.

In collaboration with: Giampiero Bardella, Angelo Bifone, Andrea Gabrielli.