L-Visibility Drawings of IC-planar Graphs

An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is an L-shape, and every edge is either a horizontal or vertical segment. As a byproduct of our drawing technique, we prove that an IC-plane graph has a RAC drawing in quadratic area with at most two bends per edge

Visibility Representations of Boxes in 2.5 Dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane $z=0$ and edges are unobstructed lines of sight parallel to the $x$- or $y$-axis. We prove that: $(i)$ Every complete bipartite graph admits a 2.5D-BR; $(ii)$ The complete graph $K_n$ admits a 2.5D-BR if and only if $n \leq 19$; $(iii)$ Every graph with pathwidth at most $7$ admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an $n$-vertex graph that admits a 2.5D-GBR has at most $4n - 6 \sqrt{n}$ edges and this bound is tight. Finally, we prove that deciding whether a given graph $G$ admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR $\Gamma$ is the set of bottom faces of the boxes in $\Gamma$.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

3D Visibility Representations of 1-planar Graphs

We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities between pairs of rectangles. In addition, the constructed representation is such that there is a plane that intersects all the rectangles, and this intersection defines a bar 1-visibility representation of G.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Downward pumping of magnetic flux as the cause of filamentary structures in sunspot penumbrae

The structure of a sunspot is determined by the local interaction between magnetic fields and convection near the Sun's surface. The dark central umbra is surrounded by a filamentary penumbra, whose complicated fine structure has only recently been revealed by high-resolution observations. The penumbral magnetic field has an intricate and unexpected interlocking-comb structure and some field lines, with associated outflows of gas, dive back down below the solar surface at the outer edge of the spot. These field lines might be expected to float quickly back to the surface because of magnetic buoyancy, but they remain submerged. Here we show that the field lines are kept submerged outside the spot by turbulent, compressible convection, which is dominated by strong, coherent, descending plumes. Moreover, this downward pumping of magnetic flux explains the origin of the interlocking-comb structure of the penumbral magnetic field, and the behaviour of other magnetic features near the sunspot

Persistence of magnetic field driven by relativistic electrons in a plasma

The onset and evolution of magnetic fields in laboratory and astrophysical plasmas is determined by several mechanisms, including instabilities, dynamo effects and ultra-high energy particle flows through gas, plasma and interstellar-media. These processes are relevant over a wide range of conditions, from cosmic ray acceleration and gamma ray bursts to nuclear fusion in stars. The disparate temporal and spatial scales where each operates can be reconciled by scaling parameters that enable to recreate astrophysical conditions in the laboratory. Here we unveil a new mechanism by which the flow of ultra-energetic particles can strongly magnetize the boundary between the plasma and the non-ionized gas to magnetic fields up to 10-100 Tesla (micro Tesla in astrophysical conditions). The physics is observed from the first time-resolved large scale magnetic field measurements obtained in a laser wakefield accelerator. Particle-in-cell simulations capturing the global plasma and field dynamics over the full plasma length confirm the experimental measurements. These results open new paths for the exploration and modelling of ultra high energy particle driven magnetic field generation in the laboratory

Theory of disk accretion onto supermassive black holes

Accretion onto supermassive black holes produces both the dramatic phenomena associated with active galactic nuclei and the underwhelming displays seen in the Galactic Center and most other nearby galaxies. I review selected aspects of the current theoretical understanding of black hole accretion, emphasizing the role of magnetohydrodynamic turbulence and gravitational instabilities in driving the actual accretion and the importance of the efficacy of cooling in determining the structure and observational appearance of the accretion flow. Ongoing investigations into the dynamics of the plunging region, the origin of variability in the accretion process, and the evolution of warped, twisted, or eccentric disks are summarized.Comment: Mostly introductory review, to appear in "Supermassive black holes in the distant Universe", ed. A.J. Barger, Kluwer Academic Publishers, in pres

Foundations of Black Hole Accretion Disk Theory

This review covers the main aspects of black hole accretion disk theory. We begin with the view that one of the main goals of the theory is to better understand the nature of black holes themselves. In this light we discuss how accretion disks might reveal some of the unique signatures of strong gravity: the event horizon, the innermost stable circular orbit, and the ergosphere. We then review, from a first-principles perspective, the physical processes at play in accretion disks. This leads us to the four primary accretion disk models that we review: Polish doughnuts (thick disks), Shakura-Sunyaev (thin) disks, slim disks, and advection-dominated accretion flows (ADAFs). After presenting the models we discuss issues of stability, oscillations, and jets. Following our review of the analytic work, we take a parallel approach in reviewing numerical studies of black hole accretion disks. We finish with a few select applications that highlight particular astrophysical applications: measurements of black hole mass and spin, black hole vs. neutron star accretion disks, black hole accretion disk spectral states, and quasi-periodic oscillations (QPOs).Comment: 91 pages, 23 figures, final published version available at http://www.livingreviews.org/lrr-2013-

Search for rare quark-annihilation decays, B --> Ds(*) Phi

We report on searches for B- --> Ds- Phi and B- --> Ds*- Phi. In the context of the Standard Model, these decays are expected to be highly suppressed since they proceed through annihilation of the b and u-bar quarks in the B- meson. Our results are based on 234 million Upsilon(4S) --> B Bbar decays collected with the BABAR detector at SLAC. We find no evidence for these decays, and we set Bayesian 90% confidence level upper limits on the branching fractions BF(B- --> Ds- Phi) Ds*- Phi)<1.2x10^(-5). These results are consistent with Standard Model expectations.Comment: 8 pages, 3 postscript figues, submitted to Phys. Rev. D (Rapid Communications