4,164 research outputs found
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 ((CHOH)), glycolaldehyde (CHOHCHO) and methyl formate
(HCOOCH), 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 (CHOH), CHOHCHO and HCOOCH spatially
coexist, relative abundance ratios, HCOOCH/(CHOH), of 31 and 35 are
derived for G34.3+0.2 and W51/e2, respectively. CHOHCHO is not detected,
but the data provide lower limits to the HCOOCH/CHOHCHO abundance
ratios of 193 for G34.3+0.2 and 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/(CHOH)
and HCOOCH/CHOHCHO 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 (CHOH)/CH2OHCHO for G34.3+0.2 (6) and W51/e2
(16). This result confirms that a high (CHOH)/CHOHCHO
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
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 ), the reconnection outflows are dominated by thermal agitation instead of
bulk kinetic energy. (ii) At large inflow electron magnetization (), 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 , that
depends mostly on the inflow Alfv\'en speed and magnetization
of species , with for electrons to for increasing .
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
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