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Sep 19, 2013
09/13

by
C. Giardina'; R. Livi

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The problem of the existence of a Strong Stochasticity Threshold in the FPU-beta 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 temporal autocorrelation functions locate the threshold at a finite value of the energy density, that results to be indipendent of the...

Source: http://arxiv.org/abs/chao-dyn/9709015v1

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104

Jul 20, 2013
07/13

by
A. Lippi; R. Livi

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The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two different numerical approaches based on nonequilibrium and equilibrium simulations provide consistent indications in favour of a logarithmic divergence in "ergodic", i.e. highly chaotic, dynamical regimes. Analytical estimates obtained in the framework of linear-response theory confirm this...

Source: http://arxiv.org/abs/chao-dyn/9910034v1

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35

Sep 22, 2013
09/13

by
M. Bezzi; R. Livi

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A deterministic cellular automaton rule defined on the Moore neighbourhood is studied as a model of epidemic propagation. The directed nature of the interaction between cells allows one to introduce the dependence on a disorder parameter that determines the fraction of ``in-phase'' cells. Phase-disorder is shown to produce peculiar changes in the dynamical and statistical properties of the different evolution regimes obtained by varying the infection and the immunization periods. In particular,...

Source: http://arxiv.org/abs/cond-mat/9805044v1

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Sep 23, 2013
09/13

by
R. Collina; R. Livi; A. Mazzino

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The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. In virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure...

Source: http://arxiv.org/abs/physics/0312099v1

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Sep 21, 2013
09/13

by
L. Baroni; R. Livi; A. Torcini

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Synchronization is shown to occur in spatially extended systems under the effect of additive spatio-temporal noise. In analogy to low dimensional systems, synchronized states are observable only if the maximum Lyapunov exponent $\Lambda$ is negative. However, a sufficiently high noise level can lead, in map with finite domain of definition, to nonlinear propagation of information, even in non chaotic systems. In this latter case the transition to synchronization is ruled by a new ingredient :...

Source: http://arxiv.org/abs/chao-dyn/9907005v1

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28

Sep 23, 2013
09/13

by
M. Belushkin; R. Livi; G. Foffi

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The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the probabilities of observing entropy-producing and entropy-consuming fluctuations measured over a finite volume and time span in terms of the rate of entropy production in the system, the measurement volume and time. We study the fluctuation theorem in computer...

Source: http://arxiv.org/abs/1105.0311v1

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39

Sep 18, 2013
09/13

by
F. Piazza; S. Lepri; R. Livi

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We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localised vibrations dramatically slows down dissipation and gives rise to quasi-stationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension (1D), strong enough on--site coupling may yield stretched--exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism...

Source: http://arxiv.org/abs/cond-mat/0210027v1

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38

Sep 19, 2013
09/13

by
F. Ginelli; R. Livi; A. Politi

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Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime, denoted as ``stable chaos'', has been so far mainly characterized by numerical studies. In this manuscript we investigate the mechanisms that are at the basis of this form of unpredictable evolution generated by a nonlinear information flow through the...

Source: http://arxiv.org/abs/nlin/0102005v1

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Sep 18, 2013
09/13

by
F. Piazza; S. Lepri; R. Livi

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We investigate the energy relaxation process produced by thermal baths at zero temperature acting on the boundary atoms of chains of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit solution of the harmonic problem: even in such a simple system nontrivial features emerge from the interplay of the different decay rates of Fourier modes. In particular, a crossover from an exponential to an inverse-square-root law occurs on a time scale...

Source: http://arxiv.org/abs/nlin/0105028v1

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Sep 18, 2013
09/13

by
H. Kunz; R. Livi; A. Suto

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The overdamped dynamics of a charged particle driven by an uniform electric field through a random sequence of scatterers in one dimension is investigated. Analytic expressions of the mean velocity and of the velocity power spectrum are presented. These show that above a threshold value of the field normal diffusion is superimposed to ballistic motion. The diffusion constant can be given explicitly. At the threshold field the transition between conduction and localization is accompanied by an...

Source: http://arxiv.org/abs/nlin/0202029v1

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Sep 19, 2013
09/13

by
F. Cecconi; R. Livi; A. Politi

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A coupled-map lattice showing complex behavior in presence of a fully negative Lyapunov spectrum is considered. A phase transition from ordered to disordered evolution upon changing diffusive coupling is studied in detail. Various indicators provide a coherent description of the scenario: the existence of an intermediate transition region characterized by an irregular alternancy of periodic and chaotic evolution.

Source: http://arxiv.org/abs/chao-dyn/9709016v1

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Sep 19, 2013
09/13

by
H. Kunz; R. Livi; A. Suto

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Thermodynamical properties of the helix-coil transition were successfully described in the past by the model of Lifson, Poland and Sheraga. Here we compute the corresponding structure factor and show that it possesses a universal scaling behavior near the transition point, even when the transition is of first order. Moreover, we introduce a dynamical version of this model, that we solve numerically. A Langevin equation is also proposed to describe the dynamics of the density of hydrogen bonds....

Source: http://arxiv.org/abs/cond-mat/0701405v1

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32

Sep 20, 2013
09/13

by
R. Collina; R. Livi; A. Mazzino

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The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure...

Source: http://arxiv.org/abs/physics/0410148v1

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39

Sep 19, 2013
09/13

by
H. Hinrichsen; R. Livi; D. Mukamel; A. Politi

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We report a detailed account of the phase diagram of a recently introduced model for non-equilibrium wetting in 1+1 dimensions [Phys. Rev. Lett. 79, 2710 (1997)]. A mean field approximation is shown to reproduce the main features of the phase diagram, while providing indications for the behaviour of the wetting transition in higher dimensions. The mean field phase diagram is found to exhibit an extra transition line which does not exist in 1+1 dimensions. The line separates a phase in which the...

Source: http://arxiv.org/abs/cond-mat/0304357v1

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Sep 18, 2013
09/13

by
L. Delfini; S. Lepri; R. Livi; A. Politi

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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 localized with power-law tails. Numerical studies show that such a representation applies also to a purely deterministic model, the quartic...

Source: http://arxiv.org/abs/0806.4303v1

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Sep 18, 2013
09/13

by
F. Ginelli; R. Livi; A. Politi; A. Torcini

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We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs to the directed percolation (DP) universality class. The analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold. We find the existence of a critical...

Source: http://arxiv.org/abs/cond-mat/0212454v1

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3.0

Jun 29, 2018
06/18

by
S. Iubini; S. Lepri; R. Livi; A. Politi

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Steady non-equilibrium states are investigated in a one-dimensional setup in the presence of two thermodynamic currents. Two paradigmatic nonlinear oscillators models are investigated: an XY chain and the discrete nonlinear Schr\"odinger equation. Their distinctive feature is that the relevant variable is an angle in both cases. We point out the importance of clearly distinguishing between energy and heat flux. In fact, even in the presence of a vanishing Seebeck coefficient, a coupling...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1603.06847

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86

Jul 20, 2013
07/13

by
S. Iubini; S. Lepri; R. Livi; A. Politi

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Suitable Langevin thermostats are introduced which are able to control both the temperature and the chemical potential of a one-dimensional lattice of nonlinear Schr\"odinger oscillators. The resulting non-equilibrium stationary states are then investigated in two limit cases (low temperatures and large particle densities), where the dynamics can be mapped onto that of a coupled-rotor chain with an external torque. As a result, an effective kinetic definition of temperature can be...

Source: http://arxiv.org/abs/1304.5071v1

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70

Sep 22, 2013
09/13

by
L. Delfini; S. Lepri; R. Livi; A. Politi

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In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario to accomodate the known results obtained so far for this problem. More precisely, we conjecture that the universality class is determined by the leading order of the nonlinear interaction potential. Moreover, our analysis allows us determining the memory...

Source: http://arxiv.org/abs/cond-mat/0603129v1

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48

Sep 22, 2013
09/13

by
R. Zillmer; R. Livi; A. Politi; A. Torcini

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The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like 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-locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox...

Source: http://arxiv.org/abs/cond-mat/0603154v2

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127

Jul 20, 2013
07/13

by
C. Giardina'; R. Livi; A. Politi; M. Vassalli

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We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1d nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the...

Source: http://arxiv.org/abs/chao-dyn/9910023v1

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29

Sep 23, 2013
09/13

by
W. J. Freeman; R. Livi; M. Obinata; G. Vitiello

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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, electric, chemical, thermal produced and used by the brain. In this paper, we discuss the microscopic dynamics underlying the mesoscopic...

Source: http://arxiv.org/abs/1110.3677v1

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41

Sep 22, 2013
09/13

by
L. Bongini; L. Casetti; R. Livi; A. Politi; A. Torcini

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A method for reconstructing the energy landscape of simple polypeptidic chains is described. We show that we can construct an equivalent representation of the energy landscape by a suitable directed graph. Its topological and dynamical features are shown to yield an effective estimate of the time scales associated with the folding and with the equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph,...

Source: http://arxiv.org/abs/0811.3148v1

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38

Sep 18, 2013
09/13

by
F. Ginelli; H. Hinrichsen; R. Livi; D. Mukamel; A. Torcini

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A class of non-local contact processes is introduced and studied using mean-field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest particle. It is found that the transition into the absorbing state is continuous and is characterized by continuously varying critical exponents. This model differs from the previously studied non-local directed percolation model, where particles are created by...

Source: http://arxiv.org/abs/cond-mat/0606450v3

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43

Sep 21, 2013
09/13

by
F. Ginelli; H. Hinrichsen; R. Livi; D. Mukamel; A. Politi

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It is argued that some phase--transitions observed in models of non-equilibrium wetting phenomena are related to contact processes with long-range interactions. This is investigated by introducing a model where the activation rate of a site at the edge of an inactive island of length $\ell$ is $1+a\ell^{-\sigma}$. Mean--field analysis and numerical simulations indicate that for $\sigma>1$ the transition is continuous and belongs to the universality class of directed percolation, while for $0

Source: http://arxiv.org/abs/cond-mat/0407635v2

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9.0

Jun 28, 2018
06/18

by
M. di Volo; R. Burioni; M. Casartelli; R. Livi; A. Vezzani

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We study the dynamics of networks with inhibitory and excitatory leaky-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a Heterogeneous Mean-Field approximation, that allows to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, that give rise to a rich dynamical phase-diagram as a...

Topics: Neurons and Cognition, Quantitative Biology, Disordered Systems and Neural Networks, Condensed...

Source: http://arxiv.org/abs/1507.08183

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28

Jul 20, 2013
07/13

by
S. Iubini; R. Franzosi; R. Livi; G. -L. Oppo; A. Politi

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We explore the statistical behavior of the discrete nonlinear Schroedinger equation. We find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature. Such a state is metastable but the convergence to equilibrium occurs on astronomical time scales and becomes increasingly slower as a result of a coarsening processes. Stationary negative-temperature states can be experimentally generated via boundary dissipation or from...

Source: http://arxiv.org/abs/1203.4162v1

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58

Sep 21, 2013
09/13

by
F. Ginelli; P. Poggi; A. Turchi; H. Chaté; R. Livi; A. Politi

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A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows 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 have localization properties and spatial Fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the...

Source: http://arxiv.org/abs/0706.0510v1

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29

Sep 23, 2013
09/13

by
G. Basile; L. Delfini; S. Lepri; R. Livi; S. Olla; A. Politi

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After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this "conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity kappa(L) ~ L^alpha in the limit of small noise and...

Source: http://arxiv.org/abs/0801.3789v1

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Sep 22, 2013
09/13

by
L. Delfini; S. Denisov; S. Lepri; R. Livi; P. K. Mohanty; A. Politi

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We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit is nevertheless exceptional in that...

Source: http://arxiv.org/abs/cond-mat/0702212v1

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37

Sep 19, 2013
09/13

by
F. Ginelli; V. Ahlers; R. Livi; D. Mukamel; A. Pikovsky; A. Politi; A. Torcini

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A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behaviour observed along the transition line changes from a directed-percolation to a multiplicative-noise type. Numerical simulations allow for a quantitative study of the multicritical point separating the two regions, Mean-field arguments and the mapping on a yet simpler model provide some further...

Source: http://arxiv.org/abs/cond-mat/0302588v2