9,069 research outputs found
Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration
We present simulations of the non-linear evolution of streaming instabilities
in protoplanetary disks. The two components of the disk, gas treated with grid
hydrodynamics and solids treated as superparticles, are mutually coupled by
drag forces. We find that the initially laminar equilibrium flow spontaneously
develops into turbulence in our unstratified local model. Marginally coupled
solids (that couple to the gas on a Keplerian time-scale) trigger an upward
cascade to large particle clumps with peak overdensities above 100. The clumps
evolve dynamically by losing material downstream to the radial drift flow while
receiving recycled material from upstream. Smaller, more tightly coupled solids
produce weaker turbulence with more transient overdensities on smaller length
scales. The net inward radial drift is decreased for marginally coupled
particles, whereas the tightly coupled particles migrate faster in the
saturated turbulent state. The turbulent diffusion of solid particles, measured
by their random walk, depends strongly on their stopping time and on the
solids-to-gas ratio of the background state, but diffusion is generally modest,
particularly for tightly coupled solids. Angular momentum transport is too weak
and of the wrong sign to influence stellar accretion. Self-gravity and
collisions will be needed to determine the relevance of particle overdensities
for planetesimal formation.Comment: Accepted for publication in ApJ (17 pages). Movies of the simulations
can be downloaded at http://www.mpia.de/~johansen/research_en.ph
Terrestrial planets across space and time
The study of cosmology, galaxy formation and exoplanets has now advanced to a
stage where a cosmic inventory of terrestrial planets may be attempted. By
coupling semi-analytic models of galaxy formation to a recipe that relates the
occurrence of planets to the mass and metallicity of their host stars, we trace
the population of terrestrial planets around both solar-mass (FGK type) and
lower-mass (M dwarf) stars throughout all of cosmic history. We find that the
mean age of terrestrial planets in the local Universe is Gyr for FGK
hosts and Gyr for M dwarfs. We estimate that hot Jupiters have
depleted the population of terrestrial planets around FGK stars by no more than
, and that only of the terrestrial planets at the
current epoch are orbiting stars in a metallicity range for which such planets
have yet to be confirmed. The typical terrestrial planet in the local Universe
is located in a spheroid-dominated galaxy with a total stellar mass comparable
to that of the Milky Way. When looking at the inventory of planets throughout
the whole observable Universe, we argue for a total of and terrestrial planets around FGK and M
stars, respectively. Due to light travel time effects, the terrestrial planets
on our past light cone exhibit a mean age of just Gyr. These
results are discussed in the context of cosmic habitability, the Copernican
principle and searches for extraterrestrial intelligence at cosmological
distances.Comment: 11 pages, 8 figures. v.2: Accepted for publication in ApJ. Some
changes in quantitative results compared to v.1, mainly due to differences in
IMF assumption
Analysis of the phenomenon of speculative trading in one of its basic manifestations: postage stamp bubbles
We document and analyze the empirical facts concerning one of the clearest
evidence of speculation in financial trading as observed in the postage
collection stamp market. We unravel some of the mechanisms of speculative
behavior which emphasize the role of fancy and collective behavior. In our
conclusion, we propose a classification of speculative markets based on two
parameters, namely the amplitude of the price peak and a second parameter that
measures its ``sharpness''. This study is offered to anchor modeling efforts to
realistic market constraints and observations.Comment: 9 pages, 5 figures and 2 tables, in press in Int. J. Mod. Phys.
Stock mechanics: predicting recession in S&P500, DJIA, and NASDAQ
An original method, assuming potential and kinetic energy for prices and
conservation of their sum is developed for forecasting exchanges. Connections
with power law are shown. Semiempirical applications on S&P500, DJIA, and
NASDAQ predict a coming recession in them. An emerging market, Istanbul Stock
Exchange index ISE-100 is found involving a potential to continue to rise.Comment: 14 pages, 4 figure
Products of Random Matrices
We derive analytic expressions for infinite products of random 2x2 matrices.
The determinant of the target matrix is log-normally distributed, whereas the
remainder is a surprisingly complicated function of a parameter characterizing
the norm of the matrix and a parameter characterizing its skewness. The
distribution may have importance as an uncommitted prior in statistical image
analysis.Comment: 9 pages, 1 figur
Decay dynamics of quantum dots influenced by the local density of optical states of two-dimensional photonic crystal membranes
We have performed time-resolved spectroscopy on InAs quantum dot ensembles in
photonic crystal membranes. The influence of the photonic crystal is
investigated by varying the lattice constant systematically. We observe a
strong slow down of the quantum dots' spontaneous emission rates as the
two-dimensional bandgap is tuned through their emission frequencies. The
measured band edges are in full agreement with theoretical predictions. We
characterize the multi-exponential decay curves by their mean decay time and
find enhancement of the spontaneous emission at the bandgap edges and strong
inhibition inside the bandgap in good agreement with local density of states
calculations.Comment: 9 pages (preprint), 3 figure
Rapid planetesimal formation in turbulent circumstellar discs
The initial stages of planet formation in circumstellar gas discs proceed via
dust grains that collide and build up larger and larger bodies (Safronov 1969).
How this process continues from metre-sized boulders to kilometre-scale
planetesimals is a major unsolved problem (Dominik et al. 2007): boulders stick
together poorly (Benz 2000), and spiral into the protostar in a few hundred
orbits due to a head wind from the slower rotating gas (Weidenschilling 1977).
Gravitational collapse of the solid component has been suggested to overcome
this barrier (Safronov 1969, Goldreich & Ward 1973, Youdin & Shu 2002). Even
low levels of turbulence, however, inhibit sedimentation of solids to a
sufficiently dense midplane layer (Weidenschilling & Cuzzi 1993, Dominik et al.
2007), but turbulence must be present to explain observed gas accretion in
protostellar discs (Hartmann 1998). Here we report the discovery of efficient
gravitational collapse of boulders in locally overdense regions in the
midplane. The boulders concentrate initially in transient high pressures in the
turbulent gas (Johansen, Klahr, & Henning 2006), and these concentrations are
augmented a further order of magnitude by a streaming instability (Youdin &
Goodman 2005, Johansen, Henning, & Klahr 2006, Johansen & Youdin 2007) driven
by the relative flow of gas and solids. We find that gravitationally bound
clusters form with masses comparable to dwarf planets and containing a
distribution of boulder sizes. Gravitational collapse happens much faster than
radial drift, offering a possible path to planetesimal formation in accreting
circumstellar discs.Comment: To appear in Nature (30 August 2007 issue). 18 pages (in referee
mode), 3 figures. Supplementary Information can be found at 0708.389
Holomorphic Currents and Duality in N=1 Supersymmetric Theories
Twisted supersymmetric theories on a product of two Riemann surfaces possess
non-local holomorphic currents in a BRST cohomology. The holomorphic currents
act as vector fields on the chiral ring. The OPE's of these currents are
invariant under the renormalization group flow up to BRST-exact terms. In the
context of electric-magnetic duality, the algebra generated by the holomorphic
currents in the electric theory is isomorphic to the one on the magnetic side.
For the currents corresponding to global symmetries this isomorphism follows
from 't Hooft anomaly matching conditions. The isomorphism between OPE's of the
currents corresponding to non-linear transformations of fields of matter
imposes non-trivial conditions on the duality map of chiral ring. We consider
in detail the SQCD with matter in fundamental and adjoint
representations, and find agreement with the duality map proposed by Kutasov,
Schwimmer and Seiberg.Comment: 19 pages, JHEP3 LaTex, typos correcte
Synchronization and Coarsening (without SOC) in a Forest-Fire Model
We study the long-time dynamics of a forest-fire model with deterministic
tree growth and instantaneous burning of entire forests by stochastic lightning
strikes. Asymptotically the system organizes into a coarsening self-similar
mosaic of synchronized patches within which trees regrow and burn
simultaneously. We show that the average patch length grows linearly with
time as t-->oo. The number density of patches of length L, N(L,t), scales as
^{-2}M(L/), and within a mean-field rate equation description we find
that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for
x-->oo. In one dimension, we develop an event-driven cluster algorithm to study
the asymptotic behavior of large systems. Our numerical results are consistent
with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR
Construction and validation of a low cost paediatric pelvis phantom
PURPOSE: Imaging phantoms can be cost prohibitive, therefore a need exists to produce low cost alternatives which are fit for purpose. This paper describes the development and validation of a low cost paediatric pelvis phantom based on the anatomy of a 5-year-old child.
METHODS: Tissue equivalent materials representing paediatric bone (Plaster of Paris; PoP) and soft tissue (Poly methyl methacrylate; PMMA) were used. PMMA was machined to match the bony anatomy identified from a CT scan of a 5-year-old child and cavities were created for infusing the PoP. Phantom validation comprised physical and visual measures. Physical included CT density comparison between a CT scan of a 5-year old child and the phantom and Signal to Noise Ratio (SNR) comparative analysis of anteroposterior phantom X-ray images against a commercial anthropomorphic phantom. Visual analysis using a psychometric image quality scale (face validity).
RESULTS: CT density, the percentage difference between cortical bone, soft tissue and their equivalent tissue substitutes were -4.7 to -4.1% and -23.4%, respectively. For SNR, (mAs response) there was a strong positive correlation between the two phantoms (r>0.95 for all kVps). For kVp response, there was a strong positive correlation between 1 and 8 mAs (r=0.85), this then decreased as mAs increased (r=-0.21 at 20 mAs). Psychometric scale results produced a Cronbachâs Alpha of almost 0.8.
CONCLUSIONS: Physical and visual measures suggest our low-cost phantom has suitable anatomical characteristics for X-ray imaging. Our phantom could have utility in dose and image quality optimisation studies.
Keywords: Pelvis phantom, low-cost, dose optimisation, validation, development
- âŠ