4,997 research outputs found
Modelling the magnetosphere of Mercury
A model magnetosphere for Mercury is presented using an upstream image-dipole and nightside 2-dimensional tail current sheet method. The tail field is represented by an analytical formulation. Magnetic field data from the Mercury 1 encounter by Mariner 10 in March 1974 are used to determine quantitative parameters of the model magnetosphere, using the method of least squares. The magnetopause crossing points directly observed are used to determine the size of the magnetosphere, and the solar wind conditions are used to determine the magnetospheric field at the stagnation point. The model produces a magnetosphere-like region with planetary field lines that are confined in nearly circular cross-sections transverse to the sun-planet line. Results are used to show geometry, field line configuration, and contours of constant field intensity inside the magnetosphere
Capacity of Compound MIMO Gaussian Channels with Additive Uncertainty
This paper considers reliable communications over a multiple-input
multiple-output (MIMO) Gaussian channel, where the channel matrix is within a
bounded channel uncertainty region around a nominal channel matrix, i.e., an
instance of the compound MIMO Gaussian channel. We study the optimal transmit
covariance matrix design to achieve the capacity of compound MIMO Gaussian
channels, where the channel uncertainty region is characterized by the spectral
norm. This design problem is a challenging non-convex optimization problem.
However, in this paper, we reveal that this problem has a hidden convexity
property, which can be exploited to map the problem into a convex optimization
problem. We first prove that the optimal transmit design is to diagonalize the
nominal channel, and then show that the duality gap between the capacity of the
compound MIMO Gaussian channel and the min-max channel capacity is zero, which
proves the conjecture of Loyka and Charalambous (IEEE Trans. Inf. Theory, vol.
58, no. 4, pp. 2048-2063, 2012). The key tools for showing these results are a
new matrix determinant inequality and some unitarily invariant properties.Comment: 8 pages, submitted to IEEE Transactions on Information Theor
X-ray accretion signatures in the close CTTS binary V4046 Sgr
We present Chandra HETGS observations of the classical T Tauri star (CTTS)
V4046 Sgr. The He-like triplets of O VII, Ne IX, and Si XIII are clearly
detected. Similar to the CTTS TW Hya and BP Tau, the forbidden lines of O VII
and Ne IX are weak compared to the intercombination line, indicating high
plasma densities in the X-ray emitting regions. The Si XIII triplet, however,
is within the low-density limit, in agreement with the predictions of the
accretion funnel infall model with an additional stellar corona. V4046 Sgr is
the first close binary exhibiting these features. Together with previous
high-resolution X-ray data on TW Hya and BP Tau, and in contrast to T Tau, now
three out of four CTTS show evidence of accretion funnels.Comment: 5 pages, 5 figure
Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation
Bistable systems present two degenerate metastable configurations separated
by an energy barrier. Thermal or quantum fluctuations can promote the
transition between the configurations at a rate which depends on the dynamical
properties of the local environment (i.e., a thermal bath). In the case of
classical systems, strong system-bath interaction has been successfully
modelled by the Generalised Langevin Equation (GLE) formalism. Here we show
that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014)
can be extended to include some crucial aspects of the quantum fluctuations. In
particular, the expected isotopic effect is observed along with the convergence
of the quantum and classical transition rates in the strong coupling limit.
Saturation of the transition rates at low temperature is also retrieved, in
qualitative, yet not quantitative, agreement with the analytic predictions. The
discrepancies in the tunnelling regime are due to an incorrect sampling close
to the barrier top. The domain of applicability of the quasiclassical GLE is
also discussed.Comment: 21 pages, 5 figures. Presented at the NESC16 conference: Advances in
theory and simulation of non-equilibrium system
Applications of the Generalised Langevin Equation: towards a realistic description of the baths
The Generalised Langevin Equation (GLE) method, as developed in Ref. [Phys.
Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of
systems described at the atomic level. The GLE scheme goes beyond the commonly
used bilinear coupling between the central system and the bath, and permits us
to have a realistic description of both the dissipative central system and its
surrounding bath. We show how to obtain the vibrational properties of a
realistic bath and how to convey such properties into an extended Langevin
dynamics by the use of the mapping of the bath vibrational properties onto a
set of auxiliary variables. Our calculations for a model of a Lennard-Jones
solid show that our GLE scheme provides a stable dynamics, with the
dissipative/relaxation processes properly described. The total kinetic energy
of the central system always thermalises toward the expected bath temperature,
with appropriate fluctuation around the mean value. More importantly, we obtain
a velocity distribution for the individual atoms in the central system which
follows the expected canonical distribution at the corresponding temperature.
This confirms that both our GLE scheme and our mapping procedure onto an
extended Langevin dynamics provide the correct thermostat. We also examined the
velocity autocorrelation functions and compare our results with more
conventional Langevin dynamics.Comment: accepted for publication in PR
Efficient Beam Alignment in Millimeter Wave Systems Using Contextual Bandits
In this paper, we investigate the problem of beam alignment in millimeter
wave (mmWave) systems, and design an optimal algorithm to reduce the overhead.
Specifically, due to directional communications, the transmitter and receiver
beams need to be aligned, which incurs high delay overhead since without a
priori knowledge of the transmitter/receiver location, the search space spans
the entire angular domain. This is further exacerbated under dynamic conditions
(e.g., moving vehicles) where the access to the base station (access point) is
highly dynamic with intermittent on-off periods, requiring more frequent beam
alignment and signal training. To mitigate this issue, we consider an online
stochastic optimization formulation where the goal is to maximize the
directivity gain (i.e., received energy) of the beam alignment policy within a
time period. We exploit the inherent correlation and unimodality properties of
the model, and demonstrate that contextual information improves the
performance. To this end, we propose an equivalent structured Multi-Armed
Bandit model to optimally exploit the exploration-exploitation tradeoff. In
contrast to the classical MAB models, the contextual information makes the
lower bound on regret (i.e., performance loss compared with an oracle policy)
independent of the number of beams. This is a crucial property since the number
of all combinations of beam patterns can be large in transceiver antenna
arrays, especially in massive MIMO systems. We further provide an
asymptotically optimal beam alignment algorithm, and investigate its
performance via simulations.Comment: To Appear in IEEE INFOCOM 2018. arXiv admin note: text overlap with
arXiv:1611.05724 by other author
The construction and evaluation of a test on the concepts of informal geometry
Thesis (Ed.M.)--Boston UniversityThe primary purpose of
constructing a test on informal geometry is to provide the
eighth-grade mathematics teacher with an objective means
of measuring the achievement of his students in geometry.
A secondary purpose is to explore the possibility that
this test alone, or in conjunction with other criteria, might
have value in predicting the degree of success of a student
in demonstrative geometry
Scheduling of Multicast and Unicast Services under Limited Feedback by using Rateless Codes
Many opportunistic scheduling techniques are impractical because they require
accurate channel state information (CSI) at the transmitter. In this paper, we
investigate the scheduling of unicast and multicast services in a downlink
network with a very limited amount of feedback information. Specifically,
unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs)
to a base station, and multicast users only report infrequent ACKs to avoid
feedback implosion. We consider the use of physical-layer rateless codes, which
not only combats channel uncertainty, but also reduces the overhead of ACK
feedback. A joint scheduling and power allocation scheme is developed to
realize multiuser diversity gain for unicast service and multicast gain for
multicast service. We prove that our scheme achieves a near-optimal throughput
region. Our simulation results show that our scheme significantly improves the
network throughput over schemes employing fixed-rate codes or using only
unicast communications
Nonequilibrium processes from Generalised Langevin Equations: realistic nanoscale systems connected to two thermal baths
We extend the Generalised Langevin Equation (GLE) method [Phys. Rev. B 89,
134303 (2014)] to model a central classical region connected to two realistic
thermal baths at two different temperatures. In such nonequilibrium conditions
a heat flow is established, via the central system, in between the two baths.
The GLE-2B (GLE two baths) scheme permits us to have a realistic description of
both the dissipative central system and its surrounding baths. Following the
original GLE approach, the extended Langevin dynamics scheme is modified to
take into account two sets of auxiliary degrees of freedom corresponding to the
mapping of the vibrational properties of each bath. These auxiliary variables
are then used to solve the non-Markovian dissipative dynamics of the central
region. The resulting algorithm is used to study a model of a short Al nanowire
connected to two baths. The results of the simulations using the GLE-2B
approach are compared to the results of other simulations that were carried out
using standard thermostatting approaches (based on Markovian Langevin and
Nose-Hoover thermostats). We concentrate on the steady state regime and study
the establishment of a local temperature profile within the system. The
conditions for obtaining a flat profile or a temperature gradient are examined
in detail, in agreement with earlier studies. The results show that the GLE-2B
approach is able to treat, within a single scheme, two widely different thermal
transport regimes, i.e. ballistic systems, with no temperature gradient, and
diffusive systems with a temperature gradient.Comment: present version accepted for publication in Phys. Rev. B (Apr 2016
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