The map equation

Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature, researchers would benefit from some guidelines about which of the so-called community detection algorithms are most appropriate for the structures they are studying and the questions they are asking. Here we show that different methods highlight different aspects of a network's structure and that the the sort of information that we seek to extract about the system must guide us in our decision. For example, many community detection algorithms, including the popular modularity maximization approach, infer module assignments from an underlying model of the network formation process. However, we are not always as interested in how a system's network structure was formed, as we are in how a network's extant structure influences the system's behavior. To see how structure influences current behavior, we will recognize that links in a network induce movement across the network and result in system-wide interdependence. In doing so, we explicitly acknowledge that most networks carry flow. To highlight and simplify the network structure with respect to this flow, we use the map equation. We present an intuitive derivation of this flow-based and information-theoretic method and provide an interactive on-line application that anyone can use to explore the mechanics of the map equation. We also describe an algorithm and provide source code to efficiently decompose large weighted and directed networks based on the map equation.Comment: 9 pages and 3 figures, corrected typos. For associated Flash application, see http://www.tp.umu.se/~rosvall/livemod/mapequation

Warped and eccentric discs around black holes

Accretion discs around black holes in X-ray binary stars are warped if the spin axis of the black hole is not perpendicular to the binary orbital plane. They can also become eccentric through an instability involving a resonance with the binary orbit. Depending on the thickness of the disc and the efficiency of dissipative processes, these global deformations may be able to propagate into the innermost part of the disc in the form of stationary bending or density waves. We describe the solutions in the linear regime and discuss the conditions under which a warp or eccentricity is likely to produce significant activity in the inner region, which may include the excitation of quasi-periodic oscillations.Comment: 6 pages, 3 figures; accepted for inclusion in the proceedings of "Cool Discs, Hot Flows: The Varying Faces of Accreting Compact Objects," ed. M. Axelsson (New York: AIP

Excitation of trapped oscillations in discs around black holes

High-frequency quasi-periodic oscillations detected in the light curves of black hole candidates can, according to one model, be identified with hydrodynamic oscillations of the accretion disc. We describe a non-linear coupling mechanism, suggested by Kato, through which inertial waves trapped in the inner regions of accretion discs around black holes are excited. Global warping and/or eccentricity of the disc have a fundamental role in this coupling: they combine with trapped modes, generating negative energy waves, that are damped as they approach the inner edge of the disc or their corotation resonance. As a result of this damping, inertial oscillations are amplified. We calculate the resulting eigenfunctions and their growth rates.Comment: 6 pages, 2 figures; accepted for inclusion in the proceedings of "Cool Discs, Hot Flows: The Varying Faces of Accreting Compact Objects," ed. M. Axelsson (New York: AIP

Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi

We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\infty})-functional calculus on these spaces. This provides a new way of proving functional calculus of (A) on the Bochner spaces (L^p(\R^n;X)) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when (X=\C), our approach gives refined (p)-dependent versions of known results.Comment: 28 pages; submitted for publicatio

CFD investigation of a complete floating offshore wind turbine

This chapter presents numerical computations for floating offshore wind turbines for a machine of 10-MW rated power. The rotors were computed using the Helicopter Multi-Block flow solver of the University of Glasgow that solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. Hydrodynamic loads on the support platform were computed using the Smoothed Particle Hydrodynamics method. This method is mesh-free, and represents the fluid by a set of discrete particles. The motion of the floating offshore wind turbine is computed using a Multi-Body Dynamic Model of rigid bodies and frictionless joints. Mooring cables are modelled as a set of springs and dampers. All solvers were validated separately before coupling, and the loosely coupled algorithm used is described in detail alongside the obtained results

Measuring energy dependent polarization in soft gamma-rays using Compton scattering in PoGOLite

Linear polarization in X- and gamma-rays is an important diagnostic of many astrophysical sources, foremost giving information about their geometry, magnetic fields, and radiation mechanisms. However, very few X-ray polarization measurements have been made, and then only mono-energetic detections, whilst several objects are assumed to have energy dependent polarization signatures. In this paper we investigate whether detection of energy dependent polarization from cosmic sources is possible using the Compton technique, in particular with the proposed PoGOLite balloon-experiment, in the 25-100 keV range. We use Geant4 simulations of a PoGOLite model and input photon spectra based on Cygnus X-1 and accreting magnetic pulsars (100 mCrab). Effective observing times of 6 and 35 hours were simulated, corresponding to a standard and a long duration flight respectively. Both smooth and sharp energy variations of the polarization are investigated and compared to constant polarization signals using chi-square statistics. We can reject constant polarization, with energy, for the Cygnus X-1 spectrum (in the hard state), if the reflected component is assumed to be completely polarized, whereas the distinction cannot be made for weaker polarization. For the accreting pulsar, constant polarization can be rejected in the case of polarization in a narrow energy band with at least 50% polarization, and similarly for a negative step distribution from 30% to 0% polarization.Comment: 11 pages, 12 figures; updated to match version accepted for publication in Astroparticle Physics (only minor changes

Crossing the Dripline to 11N Using Elastic Resonance Scattering

The level structure of the unbound nucleus 11N has been studied by 10C+p elastic resonance scattering in inverse geometry with the LISE3 spectrometer at GANIL, using a 10C beam with an energy of 9.0 MeV/u. An additional measurement was done at the A1200 spectrometer at MSU. The excitation function above the 10C+p threshold has been determined up to 5 MeV. A potential-model analysis revealed three resonance states at energies 1.27 (+0.18-0.05) MeV (Gamma=1.44 +-0.2 MeV), 2.01(+0.15-0.05) MeV, (Gamma=0.84 +-$0.2 MeV) and 3.75(+-0.05) MeV, (Gamma=0.60 +-0.05 MeV) with the spin-parity assignments I(pi) =1/2+, 1/2- and 5/2+, respectively. Hence, 11N is shown to have a ground state parity inversion completely analogous to its mirror partner, 11Be. A narrow resonance in the excitation function at 4.33 (+-0.05) MeV was also observed and assigned spin-parity 3/2-.Comment: 14 pages, 9 figures, twocolumn Accepted for publication in PR