1,721,203 research outputs found
One-dimensional lattice of oscillators coupled through power-law interactions: Continuum limit and dynamics of spatial Fourier modes
No full textWe study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and is normalized by a size-dependent constant. The exponent ? of the power law is taken in the range 0??<1. The oscillator frequency distribution is symmetric about its mean (taken to be zero) and is nonincreasing on [0,?). In the continuum limit, the local density of oscillators evolves in time following the continuity equation that expresses the conservation of the number of oscillators of each frequency under the dynamics. This equation admits as a stationary solution the unsynchronized state uniform both in phase and over the space of the lattice. We perform a linear stability analysis of this state to show that when it is unstable, different spatial Fourier modes of fluctuations have different stability thresholds beyond which they grow exponentially in time with rates that depend on the Fourier modes. However, numerical simulations show that at long times all the nonzero Fourier modes decay in time, while only the zero Fourier mode (i.e., the “mean-field” mode) grows in time, thereby dominating the instability process and driving the system to a synchronized state. Our theoretical analysis is supported by extensive numerical simulations.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin
Ensemble inequivalence in systems with long-range interactions
No full textEnsemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions. We display a connection between such behaviour and a mean-field like structure of the partition function. Since short-range models cannot display this kind of behaviour, this strongly suggests that such systems are necessarily non-mean field in the sense indicated here. We illustrate our results showing an application to the Blume-Emery-Griffiths model. We further show that a broad class of systems with non-integrable interactions are indeed of mean-field type in the sense specified, so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble
Microcanonical solution of the mean-field phi(4) model: Comparison with time averages at finite size
No full textWe study the mean-field phi(4) model in an external magnetic field in the microcanonical ensemble using two different methods
Chaos suppression in the large size limit for long-range systems
No full textWe consider the class of long-range Hamiltonian systems first introduced by Anteneodo and Tsallis and called the alpha -XY model. This involves N classical rotators on a d-dimensional periodic lattice interacting all to all with an attractive coupling whose strength decays as r(-alpha), r being the distance between sites. Using a recent geometrical approach, we estimate for any d-dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N, as a function of a in the large energy regime where rotators behave almost freely. We find that the LLE vanishes as N-kappa, with kappa = 1/3 for 0 less than or equal to alpha /d less than or equal to 1/2 and kappa = 2/3(1 - alpha /d) for 1/2 less than or equal to alpha /d < 1. These analytical results present a nice agreement with numerical results obtained by Campa et al, including deviations at small N
The Italian faunal Provinces.
No full textMemorie del Museo Civico di Storia Naturale di Verona 2. serie - Sezione Scienze della Vita 1
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