973 research outputs found
On The Possibility of Enrichment and Differentiation in Gas Giants During Birth by Disk Instability
We investigate the coupling between rock-size solids and gas during the
formation of gas giant planets by disk fragmentation in the outer regions of
massive disks. In this study, we use three-dimensional radiative hydrodynamics
simulations and model solids as a spatial distribution of particles. We assume
that half of the total solid fraction is in small grains and half in large
solids. The former are perfectly entrained with the gas and set the opacity in
the disk, while the latter are allowed to respond to gas drag forces, with the
back reaction on the gas taken into account. To explore the maximum effects of
gas-solid interactions, we first consider 10cm-size particles. We then compare
these results to a simulation with 1 km-size particles, which explores the
low-drag regime. We show that (1) disk instability planets have the potential
to form large cores due to aerodynamic capturing of rock-size solids in spiral
arms before fragmentation; (2) that temporary clumps can concentrate tens of
of solids in very localized regions before clump disruption; (3)
that the formation of permanent clumps, even in the outer disk, is dependent on
the grain-size distribution, i.e., the opacity; (4) that nonaxisymmetric
structure in the disk can create disk regions that have a solids-to-gas ratio
greater than unity; (5) that the solid distribution may affect the
fragmentation process; (6) that proto-gas giants and proto-brown dwarfs can
start as differentiated objects prior to the H collapse phase; (7) that
spiral arms in a gravitationally unstable disk are able to stop the inward
drift of rock-size solids, even redistributing them to larger radii; and, (8)
that large solids can form spiral arms that are offset from the gaseous spiral
arms. We conclude that planet embryo formation can be strongly affected by the
growth of solids during the earliest stages of disk accretion.Comment: Accepted by ApJ. 55 pages including 24 figures. In response to
comments from the referee, we have included a new simulation with km-size
objects and have revised some discussions and interpretations. Major
conclusions remain unchanged, and new conclusions have been added in response
to the new ru
Classification and reduction of pilot error
Human error is a primary or contributing factor in about two-thirds of commercial aviation accidents worldwide. With the ultimate goal of reducing pilot error accidents, this contract effort is aimed at understanding the factors underlying error events and reducing the probability of certain types of errors by modifying underlying factors such as flight deck design and procedures. A review of the literature relevant to error classification was conducted. Classification includes categorizing types of errors, the information processing mechanisms and factors underlying them, and identifying factor-mechanism-error relationships. The classification scheme developed by Jens Rasmussen was adopted because it provided a comprehensive yet basic error classification shell or structure that could easily accommodate addition of details on domain-specific factors. For these purposes, factors specific to the aviation environment were incorporated. Hypotheses concerning the relationship of a small number of underlying factors, information processing mechanisms, and error types types identified in the classification scheme were formulated. ASRS data were reviewed and a simulation experiment was performed to evaluate and quantify the hypotheses
Chemistry in a gravitationally unstable protoplanetary disc
Until now, axisymmetric, alpha-disc models have been adopted for calculations
of the chemical composition of protoplanetary discs. While this approach is
reasonable for many discs, it is not appropriate when self-gravity is
important. In this case, spiral waves and shocks cause temperature and density
variations that affect the chemistry. We have adopted a dynamical model of a
solar-mass star surrounded by a massive (0.39 Msun), self-gravitating disc,
similar to those that may be found around Class 0 and early Class I protostars,
in a study of disc chemistry. We find that for each of a number of species,
e.g. H2O, adsorption and desorption dominate the changes in the gas-phase
fractional abundance; because the desorption rates are very sensitive to
temperature, maps of the emissions from such species should reveal the
locations of shocks of varying strengths. The gas-phase fractional abundances
of some other species, e.g. CS, are also affected by gas-phase reactions,
particularly in warm shocked regions. We conclude that the dynamics of massive
discs have a strong impact on how they appear when imaged in the emission lines
of various molecular species.Comment: 10 figures and 3 tables, accepted for publication in MNRA
On the accuracy of solving confluent Prony systems
In this paper we consider several nonlinear systems of algebraic equations
which can be called "Prony-type". These systems arise in various reconstruction
problems in several branches of theoretical and applied mathematics, such as
frequency estimation and nonlinear Fourier inversion. Consequently, the
question of stability of solution with respect to errors in the right-hand side
becomes critical for the success of any particular application. We investigate
the question of "maximal possible accuracy" of solving Prony-type systems,
putting stress on the "local" behavior which approximates situations with low
absolute measurement error. The accuracy estimates are formulated in very
simple geometric terms, shedding some light on the structure of the problem.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
Clumps in the Outer Disk by Disk Instability: Why They are Initially Gas Giants and the Legacy of Disruption
We explore the initial conditions for fragments in the extended regions
( AU) of gravitationally unstable disks. We combine analytic
estimates for the fragmentation of spiral arms with 3D SPH simulations to show
that initial fragment masses are in the gas giant regime. These initial
fragments will have substantial angular momentum, and should form disks with
radii of a few AU. We show that clumps will survive for multiple orbits before
they undergo a second, rapid collapse due to H dissociation and that it is
possible to destroy bound clumps by transporting them into the inner disk. The
consequences of disrupted clumps for planet formation, dust processing, and
disk evolution are discussed. We argue that it is possible to produce
Earth-mass cores in the outer disk during the earliest phases of disk
evolution.Comment: Accepted for publication in Icarus. The arguments have been greatly
expanded (from v1) to address comments by the referee
Gravitational instabilities in a protosolar-like disc - I. Dynamics and chemistry
MGE gratefully acknowledges a studentship from the European Research Council (ERC; project PALs 320620). JDI gratefully acknowledges funding from the European Union FP7-2011 under grant agreement no. 284405. ACB's contribution was supported, in part, by The University of British Columbia and the Canada Research Chairs program. PC and TWH acknowledge the financial support of the European Research Council (ERC; project PALs 320620).To date, most simulations of the chemistry in protoplanetary discs have used 1 + 1D or 2D axisymmetric α-disc models to determine chemical compositions within young systems. This assumption is inappropriate for non-axisymmetric, gravitationally unstable discs, which may be a significant stage in early protoplanetary disc evolution. Using 3D radiative hydrodynamics, we have modelled the physical and chemical evolution of a 0.17 M⊙ self-gravitating disc over a period of 2000 yr. The 0.8 M⊙ central protostar is likely to evolve into a solar-like star, and hence this Class 0 or early Class I young stellar object may be analogous to our early Solar system. Shocks driven by gravitational instabilities enhance the desorption rates, which dominate the changes in gas-phase fractional abundances for most species. We find that at the end of the simulation, a number of species distinctly trace the spiral structure of our relatively low-mass disc, particularly CN. We compare our simulation to that of a more massive disc, and conclude that mass differences between gravitationally unstable discs may not have a strong impact on the chemical composition. We find that over the duration of our simulation, successive shock heating has a permanent effect on the abundances of HNO, CN and NH3, which may have significant implications for both simulations and observations. We also find that HCO+ may be a useful tracer of disc mass. We conclude that gravitational instabilities induced in lower mass discs can significantly, and permanently, affect the chemical evolution, and that observations with high-resolution instruments such as Atacama Large Millimeter/submillimeter Array (ALMA) offer a promising means of characterizing gravitational instabilities in protosolar discs.Publisher PDFPeer reviewe
Simulated Observations of Young Gravitationally Unstable Protoplanetary Discs
The formation and earliest stages of protoplanetary discs remain poorly
constrained by observations. ALMA will soon revolutionise this field.
Therefore, it is important to provide predictions which will be valuable for
the interpretation of future high sensitivity and high angular resolution
observations. Here we present simulated ALMA observations based on radiative
transfer modelling of a relatively massive (0.39 M_solar) self-gravitating disc
embedded in a 10 M_solar dense core, with structure similar to the pre-stellar
core L1544. We focus on simple species and conclude that C17O 3-2, HCO+ 3-2,
OCS 26-25 and H2CO 404-303 lines can be used to probe the disc structure and
kinematics at all scales.Comment: 12 pages, 15 figures, Accepted by MNRA
Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness
Convex optimization has become ubiquitous in most quantitative disciplines of
science, including variational image processing. Proximal splitting algorithms
are becoming popular to solve such structured convex optimization problems.
Within this class of algorithms, Douglas--Rachford (DR) and alternating
direction method of multipliers (ADMM) are designed to minimize the sum of two
proper lower semi-continuous convex functions whose proximity operators are
easy to compute. The goal of this work is to understand the local convergence
behaviour of DR (resp. ADMM) when the involved functions (resp. their
Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when
both of the two functions (resp. their conjugates) are partly smooth relative
to their respective manifolds, we show that DR (resp. ADMM) identifies these
manifolds in finite time. Moreover, when these manifolds are affine or linear,
we prove that DR/ADMM is locally linearly convergent. When and are
locally polyhedral, we show that the optimal convergence radius is given in
terms of the cosine of the Friedrichs angle between the tangent spaces of the
identified manifolds. This is illustrated by several concrete examples and
supported by numerical experiments.Comment: 17 pages, 1 figure, published in the proceedings of the Fifth
International Conference on Scale Space and Variational Methods in Computer
Visio
Algorithmic fault tolerance using the Lanczos method
We consider the problem of algorithm-based fault tolerance, and make two major contributions. First, we show how very general sequences of polynomials can be used to generate the checksums, so as to reduce the chance of numerical overows. Second, we show how the Lanczos process can be applied in the error location and correction steps, so as to save on the amount of work and to facilitate actual hardware implementation
- …