5,792 research outputs found
Importance-sampling computation of statistical properties of coupled oscillators
We introduce and implement an importance-sampling Monte Carlo algorithm to
study systems of globally-coupled oscillators. Our computational method
efficiently obtains estimates of the tails of the distribution of various
measures of dynamical trajectories corresponding to states occurring with
(exponentially) small probabilities. We demonstrate the general validity of our
results by applying the method to two contrasting cases: the driven-dissipative
Kuramoto model, a paradigm in the study of spontaneous synchronization; and the
conservative Hamiltonian mean-field model, a prototypical system of long-range
interactions. We present results for the distribution of the finite-time
Lyapunov exponent and a time-averaged order parameter. Among other features,
our results show most notably that the distributions exhibit a vanishing
standard deviation but a skewness that is increasing in magnitude with the
number of oscillators, implying that non-trivial asymmetries and states
yielding rare/atypical values of the observables persist even for a large
number of oscillators.Comment: 11 pages, 4 figures; v2: minor changes, close to the published
version, title changed to conform to PRE guideline
Effect of noise in open chaotic billiards
We investigate the effect of white-noise perturbations on chaotic
trajectories in open billiards. We focus on the temporal decay of the survival
probability for generic mixed-phase-space billiards. The survival probability
has a total of five different decay regimes that prevail for different
intermediate times. We combine new calculations and recent results on noise
perturbed Hamiltonian systems to characterize the origin of these regimes, and
to compute how the parameters scale with noise intensity and billiard openness.
Numerical simulations in the annular billiard support and illustrate our
results.Comment: To appear in "Chaos" special issue: "Statistical Mechanics and
Billiard-Type Dynamical Systems"; 9 pages, 5 figure
Sampling motif-constrained ensembles of networks
The statistical significance of network properties is conditioned on null
models which satisfy spec- ified properties but that are otherwise random.
Exponential random graph models are a principled theoretical framework to
generate such constrained ensembles, but which often fail in practice, either
due to model inconsistency, or due to the impossibility to sample networks from
them. These problems affect the important case of networks with prescribed
clustering coefficient or number of small connected subgraphs (motifs). In this
paper we use the Wang-Landau method to obtain a multicanonical sampling that
overcomes both these problems. We sample, in polynomial time, net- works with
arbitrary degree sequences from ensembles with imposed motifs counts. Applying
this method to social networks, we investigate the relation between
transitivity and homophily, and we quantify the correlation between different
types of motifs, finding that single motifs can explain up to 60% of the
variation of motif profiles.Comment: Updated version, as published in the journal. 7 pages, 5 figures, one
Supplemental Materia
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
We investigate chaos in mixed-phase-space Hamiltonian systems using time
series of the finite- time Lyapunov exponents. The methodology we propose uses
the number of Lyapunov exponents close to zero to define regimes of ordered
(stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The
dynamics is then investigated looking at the consecutive time spent in each
regime, the transition between different regimes, and the regions in the
phase-space associated to them. Applying our methodology to a chain of coupled
standard maps we obtain: (i) that it allows for an improved numerical
characterization of stickiness in high-dimensional Hamiltonian systems, when
compared to the previous analyses based on the distribution of recurrence
times; (ii) that the transition probabilities between different regimes are
determined by the phase-space volume associated to the corresponding regions;
(iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure
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