Optimal global synchronization of partially forced Kuramoto oscillators.

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system.

Symmetries and synchronization in multilayer random networks.

In the light of the recently proposed scenario of asymmetry-induced synchronization (AISync), in which dynamical uniformity and consensus in a distributed system would demand certain asymmetries in the underlying network, we investigate here the influence of some regularities in the interlayer connection patterns on the synchronization properties of multilayer random networks. More specifically, by considering a Stuart-Landau model of complex oscillators with random frequencies, we report for multilayer networks a dynamical behavior that could be also classified as a manifestation of AISync. We show, namely, that the presence of certain symmetries in the interlayer connection pattern tends to diminish the synchronization capability of the whole network or, in other words, asymmetries in the interlayer connections would enhance synchronization in such structured networks.

Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach.

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function ω(T)Lω, where ω stands for the vector of the natural frequencies of the oscillators and L for the network Laplacian matrix.

Doughnut-shaped soap bubbles.

Soap bubbles are thin liquid films enclosing a fixed volume of air. Since the surface tension is typically assumed to be the only factor responsible for conforming the soap bubble shape, the realized bubble surfaces are always minimal area ones. Here, we consider the problem of finding the axisymmetric minimal area surface enclosing a fixed volume V and with a fixed equatorial perimeter L.

Explosive synchronization with partial degree-frequency correlation.

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of their corresponding vertices exhibit so-called explosive synchronization behavior, which is now under intensive investigation. Here we study and discuss explosive synchronization in a situation that has not yet been considered, namely when only a part, typically a small part, of the vertices is subjected to a degree-frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees.

Modeling the ATP production in mitochondria.

We revisit here the mathematical model for ATP production in mitochondria introduced recently by Bertram, Pedersen, Luciani, and Sherman (BPLS) as a simplification of the more complete but intricate Magnus and Keizer's model. We identify some inaccuracies in the BPLS original approximations for two flux rates, namely the adenine nucleotide translocator rate JANT and the calcium uniporter rate Juni. We introduce new approximations for such flux rates and then analyze some of the dynamical properties of the model.

Lyapunov statistics and mixing rates for intermittent systems.

We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a generic class of maps of the Pomeau-Manneville type. We show further that, typically, the decay properties of such tail probabilities do not provide significant information on key aspects of weakly chaotic dynamics such as ergodicity and instability regimes.

Alternative numerical computation of one-sided Lévy and Mittag-Leffler distributions.

We consider here the recently proposed closed-form formula in terms of the Meijer G functions for the probability density functions g(α)(x) of one-sided Lévy stable distributions with rational index α=l/k, with 0<α<1. Since one-sided Lévy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions ρ(α)(x) of the latter. We show, however, that the formula is computationally inviable for fractions with large denominators, being unpractical even for some modest values of l and k.

Ergodic transitions in continuous-time random walks.

We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent results presented in the literature. For the case where sojourn times are identically distributed independent random variables, our results shed some light on the recently proposed transitions between ergodic and weakly nonergodic regimes.

Relativistic Weierstrass random walks.

The Weierstrass random walk is a paradigmatic Markov chain giving rise to a Lévy-type superdiffusive behavior. It is well known that special relativity prevents the arbitrarily high velocities necessary to establish a superdiffusive behavior in any process occurring in Minkowski spacetime, implying, in particular, that any relativistic Markov chain describing spacetime phenomena must be essentially Gaussian. Here, we introduce a simple relativistic extension of the Weierstrass random walk and show that there must exist a transition time t{c} delimiting two qualitative distinct dynamical regimes: the (nonrelativistic) superdiffusive Lévy flights, for tt{c} .

Relativistic invariance of Lyapunov exponents in bounded and unbounded systems.

The study of chaos in relativistic systems has been hampered by the observer dependence of Lyapunov exponents (LEs) and of conditions, such as orbit boundedness, invoked in the interpretation of LEs as indicators of chaos. Here we establish a general framework that overcomes both difficulties and apply the resulting approach to address three fundamental questions: how LEs transform under Lorentz and Rindler transformations and under transformations to uniformly rotating frames. The answers to the first and third questions show that inertial and uniformly rotating observers agree on a characterization of chaos based on LEs.

Extracellular polymeric bacterial coverages as minimal area surfaces.

Surfaces formed by extracellular polymeric substances enclosing individual and some small communities of Acidithiobacillus ferrooxidans on plates of hydrophobic silicon and hydrophilic mica are analyzed by means of atomic force microscopy imaging. Accurate nanoscale descriptions of such coverage surfaces are obtained. The good agreement with the predictions of a rather simple but realistic theoretical model allows us to conclude that they correspond, indeed, to minimal area (constant mean curvature) surfaces enclosing a given volume associated with the encased bacteria.