6,645 research outputs found
Post-Impact Thermal Evolution of Porous Planetesimals
Impacts between planetesimals have largely been ruled out as a heat source in
the early Solar System, by calculations that show them to be an inefficient
heat source and unlikely to cause global heating. However, the long-term,
localized thermal effects of impacts on planetesimals have never been fully
quantified. Here, we simulate a range of impact scenarios between planetesimals
to determine the post-impact thermal histories of the parent bodies, and hence
the importance of impact heating in the thermal evolution of planetesimals. We
find on a local scale that heating material to petrologic type 6 is achievable
for a range of impact velocities and initial porosities, and impact melting is
possible in porous material at a velocity of > 4 km/s. Burial of heated
impactor material beneath the impact crater is common, insulating that material
and allowing the parent body to retain the heat for extended periods (~
millions of years). Cooling rates at 773 K are typically 1 - 1000 K/Ma,
matching a wide range of measurements of metallographic cooling rates from
chondritic materials. While the heating presented here is localized to the
impact site, multiple impacts over the lifetime of a parent body are likely to
have occurred. Moreover, as most meteorite samples are on the centimeter to
meter scale, the localized effects of impact heating cannot be ignored.Comment: 38 pages, 9 figures, Revised for Geochimica et Cosmochimica Acta
(Sorry, they do not accept LaTeX
Shockley model description of surface states in topological insulators
We show that the surface states in topological insulators can be understood
based on a well-known Shockley model, a one-dimensional tight-binding model
with two atoms per elementary cell, connected via alternating tunneling
amplitudes. We generalize the one-dimensional model to the three-dimensional
case corresponding to the sequence of layers connected via the amplitudes,
which depend on the in-plane momentum p = (p_x,p_y). The Hamiltonian of the
model is described a (2 x 2) Hamiltonian with the off-diagonal element t(k,p)
depending also on the out-of-plane momentum k. We show that the complex
function t(k,p) defines the properties of the surface states. The surface
states exist for the in-plane momenta p, where the winding number of the
function t(k,p) is non-zero as k is changed from 0 to 2pi. The sign of the
winding number defines the sublattice on which the surface states are
localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional
momentum space. The projection of the vortex line on the two-dimensional
momentum p space encircles the domain where the surface states exist. We
illustrate how our approach works for a well-known TI model on a diamond
lattice. We find that different configurations of the vortex lines are
responsible for the "weak" and "strong" topological insulator phases. The phase
transition occurs when the vortex lines reconnect from spiral to circular form.
We discuss the Shockley model description of Bi_2Se_3 and the applicability of
the continuous approximation for the description of the topological edge
states. We conclude that the tight-binding model gives a better description of
the surface states.Comment: 18 pages, 17 figures; version 3: Sections I-IV revised, Section VII
added, Refs. [33]-[35] added; Corresponds to the published versio
Following microscopic motion in a two dimensional glass-forming binary fluid
The dynamics of a binary mixture of large and small discs are studied at
temperatures approaching the glass transition using an analysis based on the
topology of the Voronoi polygon surrounding each atom. At higher temperatures
we find that dynamics is dominated by fluid-like motion that involves particles
entering and exiting the nearest-neighbour shells of nearby particles. As the
temperature is lowered, the rate of topological moves decreases and motion
becomes localised to regions of mixed pentagons and heptagons. In addition we
find that in the low temperature state particles may translate significant
distances without undergoing changes in their nearest neig hbour shell. These
results have implications for dynamical heterogeneities in glass forming
liquids.Comment: 12 pages, 7 figure
Focussing quantum states
Does the size of atoms present a lower limit to the size of electronic
structures that can be fabricated in solids? This limit can be overcome by
using devices that exploit quantum mechanical scattering of electron waves at
atoms arranged in focussing geometries on selected surfaces. Calculations
reveal that features smaller than a hydrogen atom can be obtained. These
structures are potentially useful for device applications and offer a route to
the fabrication of ultrafine and well defined tips for scanning tunneling
microscopy.Comment: 4 pages, 4 figure
Techniques for QCD calculations by numerical integration
Calculations of observables in quantum chromodynamics are typically performed
using a method that combines numerical integrations over the momenta of final
state particles with analytical integrations over the momenta of virtual
particles. I describe the most important steps of a method for performing all
of the integrations numerically.Comment: 36 pages with 16 postscript figure
Community Detection and Classification Guarantees Using Embeddings Learned by Node2Vec
Embedding the nodes of a large network into an Euclidean space is a common
objective in modern machine learning, with a variety of tools available. These
embeddings can then be used as features for tasks such as community
detection/node clustering or link prediction, where they achieve state of the
art performance. With the exception of spectral clustering methods, there is
little theoretical understanding for other commonly used approaches to learning
embeddings. In this work we examine the theoretical properties of the
embeddings learned by node2vec. Our main result shows that the use of k-means
clustering on the embedding vectors produced by node2vec gives weakly
consistent community recovery for the nodes in (degree corrected) stochastic
block models. We also discuss the use of these embeddings for node and link
prediction tasks. We demonstrate this result empirically, and examine how this
relates to other embedding tools for network data
Double non-equivalent chain structure on vicinal Si(557)-Au surface
We study electronic and topographic properties of the vicinal Si(557)-Au
surface using scanning tunneling microscopy and reflection of high energy
electron diffraction technique. STM data reveal double wire structures along
terraces. Moreover behavior of the voltage dependent STM tip - surface distance
is different in different chains. While the one chain shows oscillations of the
distance which are sensitive to the sign of the voltage bias, the oscillations
in the other chain remain unchanged with respect to the positive/negative
biases. This suggests that one wire has metallic character while the other one
- semiconducting. The experimental results are supplemented by theoretical
calculations within tight binding model suggesting that the observed chains are
made of different materials, one is gold and the other one is silicon chain.Comment: 9 pages, 12 figures, accepted for publication in Phys. Rev.
Matching parton showers to NLO computations
We give a prescription for attaching parton showers to next-to-leading order
(NLO) partonic jet cross sections in electron-positron annihilation. Our method
effectively extends to NLO the scheme of Catani, Krauss, Kuhn, and Webber for
matching between m hard jets and (m+1) hard jets. The matching between parton
splitting as part of a shower and parton splitting as part of NLO matrix
elements is based on the Catani-Seymour dipole subtraction method that is
commonly used for removing the singularities from the NLO matrix elements.}Comment: 45 pages, new introduction, more detailed discussion of the Sudakov
reweightin
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