11,874 research outputs found
Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group
Let denote the group of unipotent upper-triangular matrices
over a fixed finite field \FF_q, and let U_\cP denote the pattern subgroup
of corresponding to the poset \cP. This work examines the superclasses
and supercharacters, as defined by Diaconis and Isaacs, of the family of normal
pattern subgroups of . After classifying all such subgroups, we describe
an indexing set for their superclasses and supercharacters given by set
partitions with some auxiliary data. We go on to establish a canonical
bijection between the supercharacters of U_\cP and certain \FF_q-labeled
subposets of \cP. This bijection generalizes the correspondence identified by
Andr\'e and Yan between the supercharacters of and the \FF_q-labeled
set partitions of . At present, few explicit descriptions appear
in the literature of the superclasses and supercharacters of infinite families
of algebra groups other than \{U_n : n \in \NN\}. This work signficantly
expands the known set of examples in this regard.Comment: 28 page
Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups
Let be a classical root system and be a field of sufficiently
large characteristic. Let be the classical group over with the root
system , be its maximal unipotent subgroup and be the
Lie algebra of . Let be an orthogonal subset of and be a
coadjoint orbit of associated with . We construct a polarization of
at the canonical form on . We also find the dimension of
in terms of the Weyl group of . As a corollary, we determine all
possible dimensions of irreducible complex represenations of the group for
the case of finite field .Comment: 11 page
Terrestrial Planet Formation Constrained by Mars and the Structure of the Asteroid Belt
Reproducing the large Earth/Mars mass ratio requires a strong mass depletion
in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack
model invokes a specific migration history of the giant planets to remove most
of the mass initially beyond 1 AU and to dynamically excite the asteroid belt.
However, one could also invoke a steep density gradient created by inward drift
and pile-up of small particles induced by gas-drag, as has been proposed to
explain the formation of close-in super Earths. Here we show that the asteroid
belt's orbital excitation provides a crucial constraint against this scenario
for the Solar System. We performed a series of simulations of terrestrial
planet formation and asteroid belt evolution starting from disks of
planetesimals and planetary embryos with various radial density gradients and
including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with
shallow density gradients reproduce the dynamical excitation of the asteroid
belt by gravitational self-stirring but form Mars analogs significantly more
massive than the real planet. In contrast, a disk with a surface density
gradient proportional to reproduces the Earth/Mars mass ratio but
leaves the asteroid belt in a dynamical state that is far colder than the real
belt. We conclude that no disk profile can simultaneously explain the structure
of the terrestrial planets and asteroid belt. The asteroid belt must have been
depleted and dynamically excited by a different mechanism such as, for
instance, in the Grand Tack scenario.Comment: Accepted for publication in MNRA
Energy efficiency of mmWave massive MIMO precoding with low-resolution DACs
With the congestion of the sub-6 GHz spectrum, the interest in massive
multiple-input multiple-output (MIMO) systems operating on millimeter wave
spectrum grows. In order to reduce the power consumption of such massive MIMO
systems, hybrid analog/digital transceivers and application of low-resolution
digital-to-analog/analog-to-digital converters have been recently proposed. In
this work, we investigate the energy efficiency of quantized hybrid
transmitters equipped with a fully/partially-connected phase-shifting network
composed of active/passive phase-shifters and compare it to that of quantized
digital precoders. We introduce a quantized single-user MIMO system model based
on an additive quantization noise approximation considering realistic power
consumption and loss models to evaluate the spectral and energy efficiencies of
the transmit precoding methods. Simulation results show that
partially-connected hybrid precoders can be more energy-efficient compared to
digital precoders, while fully-connected hybrid precoders exhibit poor energy
efficiency in general. Also, the topology of phase-shifting components offers
an energy-spectral efficiency trade-off: active phase-shifters provide higher
data rates, while passive phase-shifters maintain better energy efficiency.Comment: Published in IEEE Journal of Selected Topics in Signal Processin
Presupernova Evolution of Rotating Massive Stars and the Rotation Rate of Pulsars
Rotation in massive stars has been studied on the main sequence and during
helium burning for decades, but only recently have realistic numerical
simulations followed the transport of angular momentum that occurs during more
advanced stages of evolution. The results affect such interesting issues as
whether rotation is important to the explosion mechanism, whether supernovae
are strong sources of gravitational radiation, the star's nucleosynthesis, and
the initial rotation rate of neutron stars and black holes. We find that when
only hydrodynamic instabilities (shear, Eddington-Sweet, etc.) are included in
the calculation, one obtains neutron stars spinning at close to critical
rotation at their surface -- or even formally in excess of critical. When
recent estimates of magnetic torques (Spruit 2002) are added, however, the
evolved cores spin about an order of magnitude slower. This is still more
angular momentum than observed in young pulsars, but too slow for the collapsar
model for gamma-ray bursts.Comment: 10 pages, 2 figures, to appear in Proc. IAU 215 "Stellar Rotation
Non-Unitary Neutrino Propagation From Neutrino Decay
Neutrino propagation in space-time is not constrained to be unitary if very
light states - lighter than the active neutrinos - exist into which neutrinos
may decay. If this is the case, neutrino flavor-change is governed by a handful
of extra mixing and "oscillation" parameters, including new sources of
CP-invariance violation. We compute the transition probabilities in the two-
and three-flavor scenarios and discuss the different phenomenological
consequences of the new physics. These are qualitatively different from other
sources of unitarity violation discussed in the literature.Comment: 8 pages, no figure
Resonantly enhanced pair production in a simple diatomic model
A new mechanism for the production of electron-positron pairs from the
interaction of a laser field and a fully stripped diatomic molecule in the
tunneling regime is presented. When the laser field is turned off, the Dirac
operator has resonances in both the positive and the negative energy continua
while bound states are in the mass gap. When this system is immersed in a
strong laser field, the resonances move in the complex energy plane: the
negative energy resonances are pushed to higher energies while the bound states
are Stark shifted. It is argued here that there is a pair production
enhancement at the crossing of resonances by looking at a simple 1-D model: the
nuclei are modeled simply by Dirac delta potential wells while the laser field
is assumed to be static and of finite spatial extent. The average rate for the
number of electron-positron pairs produced is evaluated and the results are
compared to the single nucleus and to the free cases. It is shown that
positrons are produced by the Resonantly Enhanced Pair Production (REPP)
mechanism, which is analogous to the resonantly enhanced ionization of
molecular physics. This phenomenon could be used to increase the number of
pairs produced at low field strength, allowing the study of the Dirac vacuum.Comment: 11 pages, 4 figure
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