Superburst oscillations: ocean and crustal modes excited by Carbon-triggered Type I X-ray bursts

Accreting neutron stars (NS) can exhibit high frequency modulations in their lightcurves during thermonuclear X-ray bursts, known as burst oscillations. The frequencies can be offset from the spin frequency of the NS by several Hz, and can drift by 1-3 Hz. One possible explanation is a mode in the bursting ocean, the frequency of which would decrease (in the rotating frame) as the burst cools, hence explaining the drifts. Most burst oscillations have been observed during H/He triggered bursts, however there has been one observation of oscillations during a superburst; hours' long Type I X-ray bursts caused by unstable carbon burning deeper in the ocean. This paper calculates the frequency evolution of an oceanic r-mode during a superburst. The rotating frame frequency varies during the burst from 4-14 Hz, and is sensitive to the background parameters, in particular the temperature of the ocean and ignition depth. This calculation is compared to the superburst oscillations observed on 4U-1636-536. The predicted mode frequencies ($\sim$ 10 Hz) would require a spin frequency of $\sim$ 592 Hz to match observations; 6 Hz higher than the spin inferred from an oceanic r-mode model for the H/He triggered burst oscillations. This model also over-predicts the frequency drift during the superburst by 90 %.Comment: Accepted for publication in MNRA

The onset of low Prandtl number thermal convection in thin spherical shells

This study considers the onset of stress-free Boussinesq thermal convection in rotating spherical shells with aspect ratio $\eta=r_i/r_o=0.9$ ($r_i$ and $r_o$ being the inner and outer radius), Prandtl numbers ${\rm Pr} \in[10^{-4},10^{-1}]$, and Taylor numbers ${\rm Ta}\in[10^{4},10^{12}]$. We are particularly interested in the form of the convective cell pattern that develops, and in its time scales, since this may have observational consequences. For a fixed ${\rm Ta}<10^{9}$ and by decreasing ${\rm Pr}$ from 0.1 to $10^{-4}$ a transition between spiralling columnar (SC) and equatorially-attached (EA) modes, and a transition between EA and equatorially antisymmetric or symmetric polar (AP/SP) weakly multicellular modes are found. The latter modes are preferred at very low ${\rm Pr}$. Surprisingly, for ${\rm Ta}>3\times 10^{9}$ the unicellular polar modes become also preferred at moderate ${\rm Pr}\sim10^{-2}$ because two new transition curves between EA and AP/SP and between AP/SP and SC modes are born at a triple-point bifurcation. The dependence on ${\rm Pr}$ and ${\rm Ta}$ of the transitions is studied to estimate the type of modes, and their critical parameters, preferred at different stellar regimes.Comment: Accepted for publication in Physical Review Fluids. Contains 17 pages, 8 figures and 3 tables. Added brief erratum correcting values used for estimates of neutron star ocean viscosit

Polar waves and chaotic flows in thin rotating spherical shells

Convection in rotating spherical geometries is an important physical process in planetary and stellar systems. Using continuation methods at low Prandtl number, we find both strong equatorially asymmetric and symmetric polar nonlinear rotating waves in a model of thermal convection in thin rotating spherical shells with stress-free boundary conditions. For the symmetric waves convection is confined to high latitude in both hemispheres but is only restricted to one hemisphere close to the pole in the case of asymmetric waves. This is in contrast to what is previously known from studies in the field. These periodic flows, in which the pattern is rotating steadily in the azimuthal direction, develop a strong axisymmetric component very close to onset. Using stability analysis of periodic orbits the regions of stability are determined and the topology of the stable/unstable oscillatory flows bifurcated from the branches of rotating waves is described. By means of direct numerical simulations of these oscillatory chaotic flows, we show that these three-dimensional convective polar flows exhibit characteristics, such as force balance or mean physical properties, which are similar to flows occuring in planetary atmospheres. We show that these results may open a route to understanding unexplained features of gas giant atmospheres, in particular for the case of Jupiter. These include the observed equatorial asymmetry with a pronounced decrease at the equator (the so-called dimple), and the coherent vortices surrounding the poles recently observed by the Juno mission.Comment: Published in Physical Review Fluids (2019). Contains 2 tables and 8 figure

Scaling Behaviour of Developing and Decaying Networks

We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barab\'{a}si and Albert in the particular case of growing networks. The networks considered here evolve according to the following rules: (i) Each instant a new site is added, the probability of its connection to old sites is proportional to their connectivities. (ii) In addition, (a) new links between some old sites appear with probability proportional to the product of their connectivities or (b) some links between old sites are removed with equal probability.Comment: 7 pages (revtex

Small world effect in an epidemiological model

A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered systems, there is a fluctuating endemic state of low infection. At a finite value of the disorder of the network, we find a transition to self-sustained oscillations in the size of the infected subpopulation

Theory of Networked Minority Games based on Strategy Pattern Dynamics

We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. The novel feature of the present formalism is its focus on the dynamical pattern of strategy rankings, and its careful treatment of the strategy ties which arise during the system's temporal evolution. We apply it to the Minority Game (MG) with connected populations. Expressions for the mean success rate among the agents and for the mean success rate for agents with $k$ neighbors are derived. We also use the theory to estimate the value of connectivity $p$ above which the Binary-Agent-Resource system with high resource level goes into the high-connectivity state.Comment: 24 pages, 3 figures, submitted to PR

Instability of scale-free networks under node-breaking avalanches

The instability introduced in a large scale-free network by the triggering of node-breaking avalanches is analyzed using the fiber-bundle model as conceptual framework. We found, by measuring the size of the giant component, the avalanche size distribution and other quantities, the existence of an abrupt transition. This test of strength for complex networks like Internet is more stringent than others recently considered like the random removal of nodes, analyzed within the framework of percolation theory. Finally, we discuss the possible implications of our results and their relevance in forecasting cascading failures in scale-free networks.Comment: 4 pages, 4 figures, final version to be published in Europhys. Let

Clustering and Synchronization of Oscillator Networks

Using a recently described technique for manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson and scale-free degree distributions. For both types of network, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, scale-free networks show an additional, advanced transition instead of a single synchronization threshold. This cluster-enhanced synchronization of hubs may be relevant to the brain with its scale-free and highly clustered structure.Comment: Submitted to Phys. Rev.

Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model

We generalize the Barab\'{a}si--Albert's model of growing networks accounting for initial properties of sites and find exactly the distribution of connectivities of the network $P(q)$ and the averaged connectivity $\bar{q}(s,t)$ of a site $s$ in the instant $t$ (one site is added per unit of time). At long times $P(q) \sim q^{-\gamma}$ at $q \to \infty$ and $\bar{q}(s,t) \sim (s/t)^{-\beta}$ at $s/t \to 0$, where the exponent $\gamma$ varies from 2 to $\infty$ depending on the initial attractiveness of sites. We show that the relation $\beta(\gamma-1)=1$ between the exponents is universal.Comment: 4 pages revtex (twocolumn, psfig), 1 figur