6,971 research outputs found
Quadri-tilings of the plane
We introduce {\em quadri-tilings} and show that they are in bijection with
dimer models on a {\em family} of graphs arising from rhombus
tilings. Using two height functions, we interpret a sub-family of all
quadri-tilings, called {\em triangular quadri-tilings}, as an interface model
in dimension 2+2. Assigning "critical" weights to edges of , we prove an
explicit expression, only depending on the local geometry of the graph ,
for the minimal free energy per fundamental domain Gibbs measure; this solves a
conjecture of \cite{Kenyon1}. We also show that when edges of are
asymptotically far apart, the probability of their occurrence only depends on
this set of edges. Finally, we give an expression for a Gibbs measure on the
set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs
measures, and conjecture it to be that of minimal free energy per fundamental
domain.Comment: Revised version, minor changes. 30 pages, 13 figure
Planet formation around stars of various masses: Hot super-Earths
We consider trends resulting from two formation mechanisms for short-period
super-Earths: planet-planet scattering and migration. We model scenarios where
these planets originate near the snow line in ``cold finger'' circumstellar
disks. Low-mass planet-planet scattering excites planets to low periastron
orbits only for lower mass stars. With long circularisation times, these
planets reside on long-period eccentric orbits. Closer formation regions mean
planets that reach short-period orbits by migration are most common around
low-mass stars. Above ~1 Solar mass, planets massive enough to migrate to
close-in orbits before the gas disk dissipates are above the critical mass for
gas giant formation. Thus, there is an upper stellar mass limit for
short-period super-Earths that form by migration. If disk masses are
distributed as a power law, planet frequency increases with metallicity because
most disks have low masses. For disk masses distributed around a relatively
high mass, planet frequency decreases with increasing metallicity. As icy
planets migrate, they shepherd interior objects toward the star, which grow to
~1 Earth mass. In contrast to icy migrators, surviving shepherded planets are
rocky. Upon reaching short-period orbits, planets are subject to evaporation
processes. The closest planets may be reduced to rocky or icy cores. Low-mass
stars have lower EUV luminosities, so the level of evaporation decreases with
decreasing stellar mass.Comment: Accepted to ApJ. 13 pages of emulateap
The interaction of a gap with a free boundary in a two dimensional dimer system
Let be a fixed vertical lattice line of the unit triangular lattice in
the plane, and let \Cal H be the half plane to the left of . We
consider lozenge tilings of \Cal H that have a triangular gap of side-length
two and in which is a free boundary - i.e., tiles are allowed to
protrude out half-way across . We prove that the correlation function of
this gap near the free boundary has asymptotics ,
, where is the distance from the gap to the free boundary. This
parallels the electrostatic phenomenon by which the field of an electric charge
near a conductor can be obtained by the method of images.Comment: 34 pages, AmS-Te
Habituation to novel visual vestibular environments with special reference to space flight
The etiology of space motion sickness and the underlying physiological mechanisms associated with spatial orientation in a space environment were investigated. Human psychophysical experiments were used as the basis for the research concerning the interaction of visual and vestibular cues in the development of motion sickness. Particular emphasis is placed on the conflict theory in terms of explaining these interactions. Research on the plasticity of the vestibulo-ocular reflex is discussed
The discovery of a low mass, pre-main-sequence stellar association around gamma Velorum
We report the serendipitous discovery of a population of low mass, pre-main
sequence stars (PMS) in the direction of the Wolf-Rayet/O-star binary system
gamma^{2} Vel and the Vela OB2 association. We argue that gamma^{2} Vel and the
low mass stars are truly associated, are approximately coeval and that both are
at distances between 360-490 pc, disagreeing at the 2 sigma level with the
recent Hipparcos parallax of gamma^{2} Vel, but consistent with older distance
estimates. Our results clearly have implications for the physical parameters of
the gamma^{2} Vel system, but also offer an exciting opportunity to investigate
the influence of high mass stars on the mass function and circumstellar disc
lifetimes of their lower mass PMS siblings.Comment: Monthly Notices of the Royal Astronomical Society, Letters - in pres
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