We report finite-size numerical investigations and mean-field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine, for a gaussian distribution of the frequencies, the transition from incoherence to coherence for increasingly large system size and inertia. For sufficiently large inertia the transition is hysteretic, and within the hysteretic region clusters of locked oscillators of various sizes and different levels of synchronization coexist. A modification of the mean-field theory developed by Tanaka, Lichtenberg, and Oishi [Physica D 100, 279 (1997)] allows us to derive the synchronization curve associated to each of these clusters. We have also investigated numerically the limits of existence of the coherent and of the incoherent solutions. The minimal coupling required to observe the coherent state is largely independent of the system size, and it saturates to a constant value already for moderately large inertia values. The incoherent state is observable up to a critical coupling whose value saturates for large inertia and for finite system sizes, while in the thermodinamic limit this critical value diverges proportionally to the mass. By increasing the inertia the transition becomes more complex, and the synchronization occurs via the emergence of clusters of whirling oscillators. The presence of these groups of coherently drifting oscillators induces oscillations in the order parameter. We have shown that the transition remains hysteretic even for randomly diluted networks up to a level of connectivity corresponding to a few links per oscillator. Finally, an application to the Italian high-voltage power grid is reported, which reveals the emergence of quasiperiodic oscillations in the order parameter due to the simultaneous presence of many competing whirling clusters.
The lifetime of a metastable state in the transient dynamics of an overdamped Brownian particle is analyzed, both in terms of the mean first passage time and by means of the mean growth rate coefficient. Both quantities feature nonmonotonic behaviors as a function of the noise intensity, and are independent signatures of the noise enhanced stability effect. They can therefore be alternatively used to evaluate and estimate the presence of this phenomenon, which characterizes metastability in nonlinear physical systems.
Abstract. In this article we address the problem of distinguishing between two different geodynamical histories using a geometrical description of the fault system in the Ethiopian Rift. The regional distribution of structures has been characterized by the estimation of the generalized fractal dimensions for the whole system as well as for the subsets of faults oriented along two different directions, using the importance sampling approach. Results show that the two subsets are monofra•tal with different dimensions, providing an independent indication that different dynamical processes have been responsible for the fault generation of this area.
We introduce a characteristic time of a classical chaotic dynamics, represented by the coherence time of the local maximum expansion direction. For a quantum system whose classical limit follows the above chaotic dynamics, the ratio between this time and the decorrelation time ͑of the order of the reciprocal of the maximum Liapunov exponent͒ rules the ratio between nonclassical ͑Moyal͒ and classical ͑Liouville͒ terms in the evolution of the density matrix. We show that such a ratio does not provide a complete criterion for quantumclassical correspondence.PACS number͑s͒: 05.45.ϩb, 03.65.BzThe problem of the correspondence between the classical and the quantum evolution of a Hamiltonian system has been recently considered ͓1-7͔ in various situations. A quantumclassical correspondence ͑QCC͒ implies an answer to the question of the limitations imposed by the quantum nature of the system to the measuring process ͓8͔.In particular, recent papers ͓9͔ have shown that the ratio between nonclassical and classical terms in the evolution equation of the phase space density diverges for an unstable motion, whereas it decays to zero if one accounts for a coupling with the environment, and that decay was taken as a definition of QCC.In this paper we present a relevant case whereby ͑i͒ that ratio remains confined to very small values even for an isolated system ͑i.e., in the absence of the environment͒, because of the intrinsic spread of the chaotic motion, and yet ͑ii͒ a QCC, defined more rigorously as the absence of appreciable differences between classical and quantum phase space densities, is not achieved, since for long times the quantum phase space density shows appreciable deviations from the classical one. Claim ͑i͒ is based on the introduction of a chaotic indicator, not considered previously in classical chaos; claim ͑ii͒ is supported by numerical evidence. Precisely, we refer to a classically chaotic nonautonomous system ͑i.e., with a time dependent forcing term͒, which models a Hydrogen atom in a Rydberg state excited by a microwave field ͓10͔.The quantum evolution is described by the quasiprobability Wigner function ͓11͔where is the density operator of the system, p and q are the conjugate variables and ͗ . . . ͘ stays for the expectation value. The Wigner function can take negative values, thus it is not a probability function ͓11͔; however, it represents a good tool for inspecting the classical or quantum nature of the system. Indeed, its time evolution is ruled by Ẇ ϭ͕H,W͖ PB ϩ ͚ nу1
The dynamics of an assembly of cardiac cells is modeled by a simple cellular automaton that reduces to a single variable the two variable competition of the standard models of excitable media. Furthermore, a short superexcitability period is introduced, as suggested by the dynamics of the single cardiac miocyte. The model reproduces several pathological cardiac behaviors as, e.g., the fast transition from normal behavior to fibrillation, showing how this latter one can either occur over the whole spatial domain or can be confined within a limited region.
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