Degree growth of meromorphic surface maps

We study the degree growth of iterates of meromorphic selfmaps of compact Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show that the degrees grow similarly to those of mappings that are algebraically stable on some birational model.Comment: 17 pages, final version, to appear in Duke Math Journa

Singular semipositive metrics in non-Archimedean geometry

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or plurisubharmonic) metrics on L, and prove the analogue of the following two basic results in the complex case: the set of semipositive metrics is compact modulo constants, and each semipositive metric is a decreasing limit of smooth semipositive ones. In particular, for continuous metrics our definition agrees with the one by S.-W. Zhang. The proofs use multiplier ideals and the construction of suitable models of X over the valuation ring of K, using toroidal techniques.Comment: 49 pages, 1 figure. Accepted in the Journal of Algebraic Geometr

Supersonic turbulence in 3D isothermal flow collision

Colliding supersonic bulk flows shape observable properties and internal physics of various astrophysical objects, like O-star winds, molecular clouds, galactic sheets, binaries, or gamma-ray bursts. Using numerical simulations, we show that the bulk flows leave a clear imprint on the collision zone, its mean properties and the turbulence it naturally develops. Our model setup consists of 3D head-on colliding isothermal hydrodynamical flows with Mach numbers between 2 and 43. Simulation results are in line with expectations from self-similarity: root mean square Mach numbers (Mrms) scale linearly with upstream Mach numbers, mean densities remain limited to a few times the upstream density. The density PDF is not log-normal. The turbulence is inhomogeneous: weaker in the zone center than close to the confining shocks. It is anisotropic: while Mrms is generally supersonic, Mrms transverse to the upstream flow is always subsonic. We argue that uniform, isothermal, head-on colliding flows generally disfavor isotropic, supersonic turbulence. The anisotropy carries over to other quantities like the density variance - Mach number relation. Structure functions differ depending on whether they are computed along a line-of-sight perpendicular or parallel to the upstream flow. We suggest that such line-of-sight effects should be kept in mind when interpreting turbulence characteristics derived from observations.Comment: 20 pages, 14 figures, 4 tables, accepted by Astronomy and Astrophysic

Tentative detection of ethylene glycol toward W51/e2 and G34.3+0.2

How complex organic - and potentially prebiotic - molecules are formed in regions of low- and high-mass star-formation remains a central question in astrochemistry. In particular, with just a few sources studied in detail, it is unclear what role environment plays in complex molecule formation. In this light, a comparison of relative abundances of related species between sources might be useful to explain observed differences. We seek to measure the relative abundance between three important complex organic molecules, ethylene glycol ((CH$_2$OH)$_2$), glycolaldehyde (CH$_2$OHCHO) and methyl formate (HCOOCH$_3$), toward high-mass protostars and thereby provide additional constraints on their formation pathways. We use IRAM 30-m single dish observations of the three species toward two high-mass star-forming regions - W51/e2 and G34.3+0.2 - and report a tentative detection of (CH2OH)2 toward both sources. Assuming that (CH$_2$OH)$_2$, CH$_2$OHCHO and HCOOCH$_3$ spatially coexist, relative abundance ratios, HCOOCH$_3$/(CH$_2$OH)$_2$, of 31 and 35 are derived for G34.3+0.2 and W51/e2, respectively. CH$_2$OHCHO is not detected, but the data provide lower limits to the HCOOCH$_3$/CH$_2$OHCHO abundance ratios of $\ge$193 for G34.3+0.2 and $\ge$550 for W51/e2. A comparison of these results to measurements from various sources in the literature indicates that the source luminosities may be correlated with the HCOOCH$_3$/(CH$_2$OH)$_2$ and HCOOCH$_3$/CH$_2$OHCHO ratios. This apparent correlation may be a consequence of the relative timescales each source spend at different temperatures-ranges in their evolution. Furthermore, we obtain lower limits to the ratio of (CH$_2$OH)$_2$/CH2OHCHO for G34.3+0.2 ($\ge$6) and W51/e2 ($\ge$16). This result confirms that a high (CH$_2$OH)$_2$/CH$_2$OHCHO abundance ratio is not a specific property of comets, as previously speculated.Comment: Accepted for publication by A&

Relativistic magnetic reconnection in collisionless ion-electron plasmas explored with particle-in-cell simulations

Magnetic reconnection is a leading mechanism for magnetic energy conversion and high-energy non-thermal particle production in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas (e.g., microquasars or AGNs) - a regime where first principle studies are scarce. We present 2D particle-in-cell (PIC) simulations of low $\beta$ ion-electron plasmas under relativistic conditions, i.e., with inflow magnetic energy exceeding the plasma rest-mass energy. We identify outstanding properties: (i) For relativistic inflow magnetizations (here $10 < \sigma_e < 360$), the reconnection outflows are dominated by thermal agitation instead of bulk kinetic energy. (ii) At large inflow electron magnetization ($\sigma_e > 80$), the reconnection electric field is sustained more by bulk inertia than by thermal inertia. It challenges the thermal-inertia-paradigm and its implications. (iii) The inflows feature sharp transitions at the entrance of the diffusion zones. These are not shocks but results from particle ballistic motions, all bouncing at the same location, provided that the thermal velocity in the inflow is far smaller than the inflow E cross B bulk velocity. (iv) Island centers are magnetically isolated from the rest of the flow, and can present a density depletion at their center. (v) The reconnection rates are slightly larger than in non-relativistic studies. They are best normalized by the inflow relativistic Alfv\'en speed projected in the outflow direction, which then leads to rates in a close range (0.14-0.25) thus allowing for an easy estimation of the reconnection electric field.Comment: Submitted to A&

The energetics of relativistic magnetic reconnection: ion-electron repartition and particle distribution hardness

Collisionless magnetic reconnection is a prime candidate to account for flare-like or steady emission, outflow launching, or plasma heating, in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas. But the fate of the initial magnetic energy in a reconnection event remains poorly known: what is the amount given to kinetic energy, the ion/electron repartition, and the hardness of the particle distributions? We explore these questions with 2D particle-in-cell simulations of ion-electron plasmas. We find that 45 to 75% of the total initial magnetic energy ends up in kinetic energy, this fraction increasing with the inflow magnetization. Depending on the guide field strength, ions get from 30 to 60% of the total kinetic energy. Particles can be separated into two populations that only weakly mix: (i) particles initially in the current sheet, heated by its initial tearing and subsequent contraction of the islands; and (ii) particles from the background plasma that primarily gain energy via the reconnection electric field when passing near the X-point. Particles (ii) tend to form a power-law with an index $p=-d\log n(\gamma)/d\log\gamma$, that depends mostly on the inflow Alfv\'en speed $V_A$ and magnetization $\sigma_s$ of species $s$, with for electrons $p=5$ to $1.2$ for increasing $\sigma_e$. The highest particle Lorentz factor, for ions or electrons, increases roughly linearly with time for all the relativistic simulations. This is faster, and the spectra can be harder, than for collisionless shock acceleration. We discuss applications to microquasar and AGN coronae, to extragalactic jets, and to radio lobes. We point out situations where effects such as Compton drag or pair creation are important.Comment: 15 pages, submitted to A&

Gait analysis of patients with knee osteoarthritis highlights a pathological mechanical pathway and provides a basis for therapeutic interventions

Knee osteoarthritis (OA) is a painful and incapacitating disease affecting a large portion of the elderly population, for which no cure exists. There is a critical need to enhance our understanding of OA pathogenesis, as a means to improve therapeutic options. Knee OA is a complex disease influenced by many factors, including the loading environment. Analysing knee biomechanics during walking - the primary cyclic load-bearing activity - is therefore particularly relevant. There is evidence of meaningful differences in the knee adduction moment, flexion moment and flexion angle during walking between non-OA individuals and patients with medial knee OA. Furthermore, these kinetic and kinematic gait variables have been associated with OA progression. Gait analysis provides the critical information needed to understand the role of ambulatory biomechanics in OA development, and to design therapeutic interventions. Multidisciplinary research is necessary to relate the biomechanical alterations to the structural and biological components of OA. Cite this article: Favre J, Jolles BM. Analysis of gait, knee biomechanics and the physiopathology of knee osteoarthritis in the development of therapeutic interventions. EFORT Open Rev 2016;1:368-374. DOI: 10.1302/2058-5241.1.000051

Apar-T: code, validation, and physical interpretation of particle-in-cell results

We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests: spectra from simulations of thermal plasmas, linear growth rates of the relativistic tearing instability and of the filamentation instability, and non-linear filamentation merging phase. For the filamentation instability we show that the effective growth rates measured on the total energy can differ by more than 50% from the linear cold predictions and from the fastest modes of the simulation. Second, we detail a new method for initial loading of Maxwell-J\"uttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. Third, we scrutinize the question of what description of physical plasmas is obtained by PIC models. These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p~10^10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e., quantities depending on p. They derive from the PIC plasma parameter Lambda^{PIC}, which we show to scale as 1/p. We explore two implications. One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p~10^10 smaller than in real plasmas. The other is that the level of electric field fluctuations scales as 1/Lambda^{PIC} ~ p. We provide a corresponding exact expression. Fourth, we compare the Vlasov-Maxwell theory, which describes a phase-space fluid with infinite Lambda, to the PIC model and its relatively small Lambda.Comment: 24 pages, 14 figures, accepted in Astronomy & Astrophysic