2,125 research outputs found
On the resolvent condition in the Kreiss matrix theorem
The Kreiss Matrix Theorem asserts the uniform equivalence over all N x N matrices of power boundedness and a certain resolvent estimate. It is shown that the ratio of the constants in these two conditions grows linearly with N, and the optimal proportionality factor is obtained up to a factor of 2. Analogous results are also given for the related problem involving matrix exponentials. The proofs make use of a lemma that may be of independent interest, which bounds the arch length of the image of a circle in the complex plane under a rational function
Fourier analysis of the SOR iteration
The SOR iteration for solving linear systems of equations depends upon an overrelaxation factor omega. It is shown that for the standard model problem of Poisson's equation on a rectangle, the optimal omega and corresponding convergence rate can be rigorously obtained by Fourier analysis. The trick is to tilt the space-time grid so that the SOR stencil becomes symmetrical. The tilted grid also gives insight into the relation between convergence rates of several variants
Information Theoretic Operating Regimes of Large Wireless Networks
In analyzing the point-to-point wireless channel, insights about two
qualitatively different operating regimes--bandwidth- and power-limited--have
proven indispensable in the design of good communication schemes. In this
paper, we propose a new scaling law formulation for wireless networks that
allows us to develop a theory that is analogous to the point-to-point case. We
identify fundamental operating regimes of wireless networks and derive
architectural guidelines for the design of optimal schemes.
Our analysis shows that in a given wireless network with arbitrary size,
area, power, bandwidth, etc., there are three parameters of importance: the
short-distance SNR, the long-distance SNR, and the power path loss exponent of
the environment. Depending on these parameters we identify four qualitatively
different regimes. One of these regimes is especially interesting since it is
fundamentally a consequence of the heterogeneous nature of links in a network
and does not occur in the point-to-point case; the network capacity is {\em
both} power and bandwidth limited. This regime has thus far remained hidden due
to the limitations of the existing formulation. Existing schemes, either
multihop transmission or hierarchical cooperation, fail to achieve capacity in
this regime; we propose a new hybrid scheme that achieves capacity.Comment: 12 pages, 5 figures, to appear in IEEE Transactions on Information
Theor
Numerical Simulation of the Hydrodynamical Combustion to Strange Quark Matter
We present results from a numerical solution to the burning of neutron matter
inside a cold neutron star into stable (u,d,s) quark matter. Our method solves
hydrodynamical flow equations in 1D with neutrino emission from weak
equilibrating reactions, and strange quark diffusion across the burning front.
We also include entropy change due to heat released in forming the stable quark
phase. Our numerical results suggest burning front laminar speeds of 0.002-0.04
times the speed of light, much faster than previous estimates derived using
only a reactive-diffusive description. Analytic solutions to hydrodynamical
jump conditions with a temperature dependent equation of state agree very well
with our numerical findings for fluid velocities. The most important effect of
neutrino cooling is that the conversion front stalls at lower density (below
approximately 2 times saturation density). In a 2-dimensional setting, such
rapid speeds and neutrino cooling may allow for a flame wrinkle instability to
develop, possibly leading to detonation.Comment: 5 pages, 3 figures (animations online at
http://www.capca.ucalgary.ca/~bniebergal/webPHP/research.php
Existence and approximation of probability measure solutions to models of collective behaviors
In this paper we consider first order differential models of collective
behaviors of groups of agents based on the mass conservation equation. Models
are formulated taking the spatial distribution of the agents as the main
unknown, expressed in terms of a probability measure evolving in time. We
develop an existence and approximation theory of the solutions to such models
and we show that some recently proposed models of crowd and swarm dynamics fit
our theoretic paradigm.Comment: 31 pages, 1 figur
Curative pelvic exenteration for recurrent cervical carcinoma in the era of concurrent chemotherapy and radiation therapy. A systematic review
International audienceOBJECTIVE: Pelvic exenteration requires complete resection of the tumor with negative margins to be considered a curative surgery. The purpose of this review is to assess the optimal preoperative evaluation and surgical approach in patients with recurrent cervical cancer to increase the chances of achieving a curative surgery with decreased morbidity and mortality in the era of concurrent chemoradiotherapy. METHODS: Review of English publications pertaining to cervical cancer within the last 25 years were included using PubMed and Cochrane Library searches. RESULTS: Modern imaging (MRI and PET-CT) does not accurately identify local extension of microscopic disease and is inadequate for preoperative planning of extent of resection. Today, only half of pelvic exenteration procedures obtain uninvolved surgical margins. CONCLUSION: Clear margins are required for curative pelvic exenterations, but are poorly predictable by pre-operative assessment. More extensive surgery, i.e. the infra-elevator exenteration with vulvectomy, is a logical surgical choice to increase the rate of clear margins and to improve patient survival following surgery for recurrent cervical carcinoma
Dynamics of Three Agent Games
We study the dynamics and resulting score distribution of three-agent games
where after each competition a single agent wins and scores a point. A single
competition is described by a triplet of numbers , and denoting the
probabilities that the team with the highest, middle or lowest accumulated
score wins. We study the full family of solutions in the regime, where the
number of agents and competitions is large, which can be regarded as a
hydrodynamic limit. Depending on the parameter values , we find six
qualitatively different asymptotic score distributions and we also provide a
qualitative understanding of these results. We checked our analytical results
against numerical simulations of the microscopic model and find these to be in
excellent agreement. The three agent game can be regarded as a social model
where a player can be favored or disfavored for advancement, based on his/her
accumulated score. It is also possible to decide the outcome of a three agent
game through a mini tournament of two-a gent competitions among the
participating players and it turns out that the resulting possible score
distributions are a subset of those obtained for the general three agent-games.
We discuss how one can add a steady and democratic decline rate to the model
and present a simple geometric construction that allows one to write down the
corresponding score evolution equations for -agent games
Projected SO(5) Hamiltonian for Cuprates and Its Applications
The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and
superconducting fluctuations of underdoped cuprates in terms of four bosons
moving on a coarse grained lattice. A simple mean field approximation can
explain some key feautures of the experimental phase diagram: (i) The Mott
transition between antiferromagnet and superconductor, (ii) The increase of T_c
and superfluid stiffness with hole concentration x and (iii) The increase of
antiferromagnetic resonance energy as sqrt{x-x_c} in the superconducting phase.
We apply this theory to explain the ``two gaps'' problem found in underdoped
cuprate Superconductor-Normal- Superconductor junctions. In particular we
explain the sharp subgap Andreev peaks of the differential resistance, as
signatures of the antiferromagnetic resonance (the magnon mass gap). A critical
test of this theory is proposed. The tunneling charge, as measured by shot
noise, should change by increments of Delta Q= 2e at the Andreev peaks, rather
than by Delta Q=e as in conventional superconductors.Comment: 3 EPS figure
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