14,574 research outputs found
Omniscopes: Large Area Telescope Arrays with only N log N Computational Cost
We show that the class of antenna layouts for telescope arrays allowing cheap
analysis hardware (with correlator cost scaling as N log N rather than N^2 with
the number of antennas N) is encouragingly large, including not only previously
discussed rectangular grids but also arbitrary hierarchies of such grids, with
arbitrary rotations and shears at each level. We show that all correlations for
such a 2D array with an n-level hierarchy can be efficiently computed via a
Fast Fourier Transform in not 2 but 2n dimensions. This can allow major
correlator cost reductions for science applications requiring exquisite
sensitivity at widely separated angular scales, for example 21cm tomography
(where short baselines are needed to probe the cosmological signal and long
baselines are needed for point source removal), helping enable future 21cm
experiments with thousands or millions of cheap dipole-like antennas. Such
hierarchical grids combine the angular resolution advantage of traditional
array layouts with the cost advantage of a rectangular Fast Fourier Transform
Telescope. We also describe an algorithm for how a subclass of hierarchical
arrays can efficiently use rotation synthesis to produce global sky maps with
minimal noise and a well-characterized synthesized beam.Comment: Replaced to match accepted PRD version. 10 pages, 9 fig
Investigation of the Initial State of the Moon-Forming Disk: Bridging SPH Simulations and Hydrostatic Models
According to the standard giant impact hypothesis, the Moon formed from a
partially vaporized disk generated by a collision between the proto Earth and a
Mars sized impactor. The initial structure of the disk significantly affects
the Moon forming process, including the Moons mass, its accretion time scale,
and its isotopic similarity to Earth. The dynamics of the impact event
determines the initial structure of a nearly hydrostatic Moon forming disk.
However, the hydrostatic and hydrodynamic models have been studied separately
and their connection has not previously been well quantified. Here, we show the
extent to which the properties of the disk can be inferred from Smoothed
Particle Hydrodynamic (SPH) simulations. By using entropy, angular momentum and
mass distributions of the SPH outputs as approximately conserved quantities, we
compute the two dimensional disk structure. We investigate four different
models: (a) standard, the canonical giant impact model, (b) fast spinning
Earth, a collision between a fast spinning Earth and a small impactor, (c) sub
Earths, a collision between two objects with half Earths mass, and (d)
intermediate, a collision of two bodies whose mass ratio is 7:3. Our SPH
calculations show that the initial disk has approximately uniform entropy. The
disks of the fast spinning Earth and sub Earths cases are hotter and more
vaporized (80-90% vapor) than the standard case (20%). The intermediate case
falls between these values. In the highly vaporized cases, our procedure fails
to establish a unique surface density profile of the disk because the disk is
unstable according to the Rayleigh criterion. In these cases, we estimate
non-unique disk models by conserving global quantities. We also develop a semi
analytic model for the thermal structure of the disk, which requires only two
inputs: the average entropy and the surface density of the disk.Comment: Accepted for publication in Icaru
Melting and Mixing States of the Earth's Mantle after the Moon-Forming Impact
The Earth's Moon is thought to have formed by an impact between the Earth and
an impactor around 4.5 billion years ago. This impact could have been so
energetic that it could have mixed and homogenized the Earth's mantle. However,
this view appears to be inconsistent with geochemical studies that suggest that
the Earth's mantle was not mixed by the impact. Another plausible outcome is
that this energetic impact melted the whole mantle, but the extent of mantle
melting is not well understood even though it must have had a significant
effect on the subsequent evolution of the Earth's interior and atmosphere. To
understand the initial state of the Earth's mantle, we perform giant impact
simulations using smoothed particle hydrodynamics (SPH) for three different
models: (a) standard: a Mars-sized impactor hits the proto-Earth, (b)
fast-spinning Earth: a small impactor hits a rapidly rotating proto-Earth, and
(c) sub-Earths: two half Earth-sized planets collide. We use two types of
equations of state (MgSiO3 liquid and forsterite) to describe the Earth's
mantle. We find that the mantle remains unmixed in (a), but it may be mixed in
(b) and (c). The extent of mixing is most extensive in (c). Therefore, (a) is
most consistent and (c) may be least consistent with the preservation of the
mantle heterogeneity, while (b) may fall between. We determine that the Earth's
mantle becomes mostly molten by the impact in all of the models. The choice of
the equations of state does not affect these outcomes. Additionally, our
results indicate that entropy gains of the mantle materials by a giant impact
cannot be predicted well by the Rankine-Hugoniot equations. Moreover, we show
that the mantle can remain unmixed on a Moon-forming timescale if it does not
become mixed by the impact.Comment: Accepted for publication in EPS
Geometric and combinatorial realizations of crystal graphs
For irreducible integrable highest weight modules of the finite and affine
Lie algebras of type A and D, we define an isomorphism between the geometric
realization of the crystal graphs in terms of irreducible components of
Nakajima quiver varieties and the combinatorial realizations in terms of Young
tableaux and Young walls. For affine type A, we extend the Young wall
construction to arbitrary level, describing a combinatorial realization of the
crystals in terms of new objects which we call Young pyramids.Comment: 34 pages, 17 figures; v2: minor typos corrected; v3: corrections to
section 8; v4: minor typos correcte
Combinatorial realizations of crystals via torus actions on quiver varieties
Consider Kashiwara's crystal associated to a highest weight representation of
a symmetric Kac-Moody algebra. There is a geometric realization of this object
using Nakajima's quiver varieties, but in many particular cases it can also be
realized by elementary combinatorial methods. Here we propose a framework for
extracting combinatorial realizations from the geometric picture: We construct
certain torus actions on the quiver varieties and use Morse theory to index the
irreducible components by connected components of the subvariety of torus fixed
points. We then discuss the case of affine sl(n). There the fixed point
components are just points, and are naturally indexed by multi-partitions.
There is some choice in our construction, leading to a family of combinatorial
models for each highest weight crystal. Applying this construction to the
crystal of the fundamental representation recovers a family of combinatorial
realizations recently constructed by Fayers. This gives a more conceptual proof
of Fayers' result as well as a generalization to higher level. We also discuss
a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some
references; v3: many small correction
Are U.S. and Seventh District business cycles alike?
This article explains the recent high levels of residential investment and rates of homeownership.Business cycles
A Theoretical Framework for R-parity Violation
We propose a theoretical framework for R-parity violation. It is realized by
a class of Calabi--Yau compactification of Heterotic string theory. Trilinear
R-parity violation in superpotential is either absent or negligibly small
without an unbroken symmetry, due to a selection rule based on charge counting
of a spontaneously broken U(1) symmetry. Although such a selection rule cannot
be applied in general to non-renormalizable operators in the low-energy
effective superpotential, it is valid for terms trilinear in low-energy degrees
of freedom, and hence can be used as a solution to the dimension-4 proton decay
problem in the minimal supersymmetric standard model. Bilinear R-parity
violation is generated, but there are good reasons why they are small enough to
satisfy its upper bounds from neutrino mass and washout of baryon/lepton
asymmetry. All R-parity violating dimension-5 operators can be generated. In
this theoretical framework, nucleons can decay through squark-exchange diagrams
combining dimension-5 and bilinear R-parity violating operators. B-L breaking
neutron decay is predicted
Weight Vectors of the Basic A_1^(1)-Module and the Littlewood-Richardson Rule
The basic representation of \A is studied. The weight vectors are
represented in terms of Schur functions. A suitable base of any weight space is
given. Littlewood-Richardson rule appears in the linear relations among weight
vectors.Comment: February 1995, 7pages, Using AMS-Te
Phase-Control of Photoabsorption in Optically Dense Media
We present a self-consistent theory, as well as an illustrative application
to a realistic system, of phase control of photoabsorption in an optically
dense medium. We demonstrate that, when propagation effects are taken into
consideration, the impact on phase control is significant. Independently of the
value of the initial phase difference between the two fields, over a short
scaled distance of propagation, the medium tends to settle the relative phase
so that it cancels the atomic excitation. In addition, we find some rather
unusual behavior for an optically thin layer.Comment: 5 pages, 3 figures, submitted to PR
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