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Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to simple mathematical models consisting of coupled oscillators on a lattice. The role of lattice dimensionality on the… (More)

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors… (More)

- Rüdiger Zillmer, Roberto Livi, Antonio Politi, Alessandro Torcini
- Physical review. E, Statistical, nonlinear, and…
- 2006

The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochasticlike regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase… (More)

The formation of amplitude modulated and phase modulated assemblies of neurons is observed in the brain functional activity. The study of the formation of such structures requires that the analysis has to be organized in hierarchical levels, microscopic, mesoscopic, macroscopic, each with its characteristic space-time scales and the various forms of energy,… (More)

- Rüdiger Zillmer, Roberto Livi, Antonio Politi, Alessandro Torcini
- Physical review. E, Statistical, nonlinear, and…
- 2007

The stability of the dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of globally coupled leaky integrate-and-fire neurons. This is done by reducing the set of differential equations to a map that is investigated in the limit of large network size. We show that the stability of the splay state depends crucially… (More)

- Luca Delfini, Stefano Lepri, Roberto Livi, Antonio Politi
- Physical review letters
- 2008

We provide an explicit representation of the nonequilibrium invariant measure for a chain of harmonic oscillators with conservative noise in the presence of stationary heat flow. By first determining the covariance matrix, we are able to express the measure as the product of Gaussian distributions aligned along some collective modes that are spatially… (More)

The problem of the existence of a Strong Stochasticity Threshold in the FPU-β model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding… (More)

- Simona Olmi, Roberto Livi, Antonio Politi, Alessandro Torcini
- Physical review. E, Statistical, nonlinear, and…
- 2010

We investigate the onset of collective oscillations in a excitatory pulse-coupled network of leaky integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O. V. Popovych, Phys. Rev. E 71… (More)

- Francesco Piazza, Stefano Lepri, Roberto Livi
- Chaos
- 2003

We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localized vibrations dramatically slows down dissipation and gives rise to quasistationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension, strong… (More)

- Fabio Cecconi, Carlo Guardiani, Roberto Livi
- Biophysical journal
- 2006

The WW domain of the human Pin1 protein for its simple topology and large amount of experimental data is an ideal candidate to assess theoretical approaches to protein folding. The purpose of this work is to compare the reliability of the chemically based Sorenson/Head-Gordon (SHG) model and a standard native centric model in reproducing, through molecular… (More)