11,514 research outputs found
From Dust to Planetesimals: Criteria for Gravitational Instability of Small Particles in Gas
Dust particles sediment toward the midplanes of protoplanetary disks, forming
dust-rich sublayers encased in gas. What densities must the particle sublayer
attain before it can fragment by self-gravity? We describe various candidate
threshold densities. One of these is the Roche density, which is that required
for a strengthless satellite to resist tidal disruption by its primary. Another
is the Toomre density, which is that required for de-stabilizing self-gravity
to defeat the stabilizing influences of pressure and rotation. We show that for
sublayers containing aerodynamically well-coupled dust, the Toomre density
exceeds the Roche density by many (up to about 4) orders of magnitude. We
present 3D shearing box simulations of self-gravitating, stratified, dust-gas
mixtures to test which of the candidate thresholds is relevant for collapse.
All our simulations indicate that the larger Toomre density is required for
collapse. This result is sensible because sublayers are readily stabilized by
pressure. Sound-crossing times for thin layers are easily shorter than
free-fall times, and the effective sound speed in dust-gas suspensions
decreases only weakly with the dust-to-gas ratio (as the inverse square root).
Our findings assume that particles are small enough that their stopping times
in gas are shorter than all other timescales. Relaxing this assumption may
lower the threshold for gravitational collapse back down to the Roche
criterion. In particular, if the particle stopping time becomes longer than the
sound-crossing time, sublayers may lose pressure support and become
gravitationally unstable.Comment: 19 pages, 13 figures, and 5 tables. ApJ accepte
Gravito-Turbulent Disks in 3D: Turbulent Velocities vs. Depth
Characterizing turbulence in protoplanetary disks is crucial for
understanding how they accrete and spawn planets. Recent measurements of
spectral line broadening promise to diagnose turbulence, with different lines
probing different depths. We use 3D local hydrodynamic simulations of cooling,
self-gravitating disks to resolve how motions driven by "gravito-turbulence"
vary with height. We find that gravito-turbulence is practically as vigorous at
altitude as at depth: even though gas at altitude is much too rarefied to be
itself self-gravitating, it is strongly forced by self-gravitating
overdensities at the midplane. The long-range nature of gravity means that
turbulent velocities are nearly uniform vertically, increasing by just a factor
of 2 from midplane to surface, even as the density ranges over nearly three
orders of magnitude. The insensitivity of gravito-turbulence to height
contrasts with the behavior of disks afflicted by the magnetorotational
instability (MRI); in the latter case, non-circular velocities increase by at
least a factor of 15 from midplane to surface, with various non-ideal effects
only magnifying this factor. The distinct vertical profiles of
gravito-turbulence vs. MRI turbulence may be used in conjunction with
measurements of non-thermal linewidths at various depths to identify the source
of transport in protoplanetary disks.Comment: Accepted to Ap
Gravito-turbulence in irradiated protoplanetary discs
Using radiation hydrodynamics simulations in a local stratified shearing box
with realistic equations of state and opacities, we explored the outcome of
self-gravity at 50 AU in a protoplanetary disc irradiated by the central star.
We found that gravito-turbulence is sustained for a finite range of the surface
density, from to 250 gcm. The disk is laminar below the
range while fragments above it. In the range of gravito-turbulence, the Toomre
parameter decreases monotonically from to as the surface
density increases while an effective cooling time is almost constant at in terms of the inverse of the orbital frequency. The turbulent motions are
supersonic at all heights, which dissipates through both shock waves and
compressional heating. The compressional motions, occurring near the midplane,
create upward flows, which not only contribute to supporting the disc but also
to transporting the dissipated energy to the disc surfaces. The irradiation
does not affect much the gravito-turbulence near the midplane unless the
grazing angle is larger than 0.32. We also show that a simple cooling function
with a constant cooling time does not approximate the realistic cooling.Comment: accepted for publication in MNRA
Nonlinear outcome of gravitational instability in an irradiated protoplanetary disc
Using local three dimensional radiation hydrodynamics simulations, the
nonlinear outcome of gravitational instability in an irradiated protoplanetary
disc is investigated in a parameter space of the surface density and
the radius . Starting from laminar flow, axisymmetric self-gravitating
density waves grow first. Their self-gravitating degree becomes larger when
is larger or the cooling time is shorter at larger radii. The density
waves eventually collapse owing to non-axisymmetric instability, which results
in either fragmentation or gravito-turbulence after a transient phase. The
boundaries between the two are found at AU as well as at the
that corresponds to the initial Toomre's parameter of . The
former boundary corresponds to the radius where the cooling time becomes short,
approximating unity. Even when gravito-turbulence is established around the
boundary radius, such a short cooling time inevitably makes the fluctuation of
large enough to trigger fragmentation. On the other hand, when
is beyond the latter boundary (i.e. the initial Toomre's parameter is
less than ), the initial laminar flow is so unstable against
self-gravity that it evolves into fragmentation regardless of the radius or,
equivalently, the cooling time. Runaway collapse follows fragmentation when the
mass concentration at the centre of a bound object is high enough that the
temperature exceeds the H dissociation temperature.Comment: accepted for publication in MNRA
Quantum phase transition and entanglement in Li atom system
In this paper we study the quantum phase transition and entanglement in
s1=1/2 and s2=1 spin pair system by the exact diagonalization method. We show
that, for this exactly solvable quantum bi-spin system, entanglement appears
before quantum phase transition and disappears after it. Moreover, we show that
the von Neumann entropy, as a measure of entanglement, can reveal quantum phase
transition in this system.Comment: 5 pages, 2 figure
Charmonium dissociation in collision with phi meson in hadronic matter
The phi-charmonium dissociation reactions in hadronic matter are studied.
Unpolarised cross sections for 12 reactions are calculated in the Born
approximation, in the quark-interchange mechanism and with a
temperature-dependent quark potential. The potential leads to remarkable
temperature dependence of the cross sections. With the cross sections and the
phi distribution function we calculate the dissociation rates of the charmonia
in the interactions with the phi meson in hadronic matter. The dependence of
the rates on temperature and charmonium momentum is meaningful to the influence
of phi mesons on charmonium suppression.Comment: 21 pages, 12 figure
Three Dimensional MHD Simulation of Circumbinary Accretion Disks -2. Net Accretion Rate
When an accretion disk surrounds a binary rotating in the same sense, the
binary exerts strong torques on the gas. Analytic work in the 1D approximation
indicated that these torques sharply diminish or even eliminate accretion from
the disk onto the binary. However, recent 2D and 3D simulational work has shown
at most modest diminution. We present new MHD simulations demonstrating that
for binaries with mass ratios of 1 and 0.1 there is essentially no difference
between the accretion rate at large radius in the disk and the accretion rate
onto the binary. To resolve the discrepancy with earlier analytic estimates, we
identify the small subset of gas trajectories traveling from the inner edge of
the disk to the binary and show how the full accretion rate is concentrated
onto them.Comment: updated to ApJ accepted versio
How Empty are Disk Gaps Opened by Giant Planets?
Gap clearing by giant planets has been proposed to explain the optically thin
cavities observed in many protoplanetary disks. How much material remains in
the gap determines not only how detectable young planets are in their birth
environments, but also how strong corotation torques are, which impacts how
planets can survive fast orbital migration. We determine numerically how the
average surface density inside the gap, sigma_gap, depends on planet-to-star
mass ratio q, Shakura-Sunyaev viscosity parameter alpha, and disk
height-to-radius aspect ratio h/r. Our results are derived from our new
GPU-accelerated Lagrangian hydrodynamical code PEnGUIn, and are verified by
independent simulations with ZEUS90. For Jupiter-like planets, we find
sigma_gap \propto q^-2.2 alpha^1.4 (h/r)^6.6, and for near brown dwarf masses,
sigma_gap \propto q^-1 alpha^1.3 (h/r)^6.1. Surface density contrasts inside
and outside gaps can be as large as 10^4, even when the planet does not
accrete. We derive a simple analytic scaling, sigma_gap \propto q^-2 alpha^1
(h/r)^5, that compares reasonably well to empirical results, especially at low
Neptune-like masses, and use discrepancies to highlight areas for progress.Comment: Accepted to Ap
Optimal Throughput--Outage Analysis of Cache-Aided Wireless Multi-Hop D2D Networks -- Derivations of Scaling Laws
Cache-aided wireless device-to-device (D2D) networks have demonstrated
promising performance improvement for video distribution compared to
conventional distribution methods. Understanding the fundamental scaling
behavior of such networks is thus of paramount importance. However, existing
scaling laws for multi-hop networks have not been found to be optimal even for
the case of Zipf popularity distributions (gaps between upper and lower bounds
are not constants); furthermore, there are no scaling law results for such
networks for the more practical case of a Mandelbrot-Zipf (MZipf) popularity
distribution. We thus in this work investigate the throughput-outage
performance for cache-aided wireless D2D networks adopting multi-hop
communications, with the MZipf popularity distribution for file requests and
users distributed according to Poisson point process. We propose an achievable
content caching and delivery scheme and analyze its performance. By showing
that the achievable performance is tight to the proposed outer bound, the
optimal scaling law is obtained. Furthermore, since the Zipf distribution is a
special case of the MZipf distribution, the optimal scaling law for the
networks considering Zipf popularity distribution is also obtained, which
closes the gap in the literature.Comment: A condensed version of this paper will be submitted to IEEE
Transactions on Communication
Series expansion in fractional calculus and fractional differential equations
Fractional calculus is the calculus of differentiation and integration of
non-integer orders. In a recently paper (Annals of Physics 323 (2008)
2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted.
Based on this theorem, in this paper we introduce fractional series expansion
method to fractional calculus. We define a kind of fractional Taylor series of
an infinitely fractionally-differentiable function. Further, based on our
definition we generalize hypergeometric functions and derive corresponding
differential equations. For finitely fractionally-differentiable functions, we
observe that the non-infinitely fractionally-differentiability is due to more
than one fractional indices. We expand functions with two fractional indices
and display how this kind of series expansion can help to solve fractional
differential equations.Comment: 15 pages, no figur
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