6,810 research outputs found
Tangent Graeffe Iteration
Graeffe iteration was the choice algorithm for solving univariate polynomials
in the XIX-th and early XX-th century. In this paper, a new variation of
Graeffe iteration is given, suitable to IEEE floating-point arithmetics of
modern digital computers. We prove that under a certain generic assumption the
proposed algorithm converges. We also estimate the error after N iterations and
the running cost. The main ideas from which this algorithm is built are:
classical Graeffe iteration and Newton Diagrams, changes of scale
(renormalization), and replacement of a difference technique by a
differentiation one. The algorithm was implemented successfully and a number of
numerical experiments are displayed
Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem
Jamming, or dynamical arrest, is a transition at which many particles stop
moving in a collective manner. In nature it is brought about by, for example,
increasing the packing density, changing the interactions between particles, or
otherwise restricting the local motion of the elements of the system. The onset
of collectivity occurs because, when one particle is blocked, it may lead to
the blocking of a neighbor. That particle may then block one of its neighbors,
these effects propagating across some typical domain of size named the
dynamical correlation length. When this length diverges, the system becomes
immobile. Even where it is finite but large the dynamics is dramatically
slowed. Such phenomena lead to glasses, gels, and other very long-lived
nonequilibrium solids. The bootstrap percolation models are the simplest
examples describing these spatio-temporal correlations. We have been able to
solve one such model in two dimensions exactly, exhibiting the precise
evolution of the jamming correlations on approach to arrest. We believe that
the nature of these correlations and the method we devise to solve the problem
are quite general. Both should be of considerable help in further developing
this field.Comment: 17 pages, 4 figure
Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition
The formal structure of glass singularities in the mode-coupling theory (MCT)
of supercooled liquids dynamics is closely related to that appearing in the
analysis of heterogeneous bootstrap percolation on Bethe lattices, random
graphs and complex networks. Starting from this observation one can build up
microscopic on lattice realizations of schematic MCT based on cooperative
facilitated spin mixtures. I discuss a microscopic implementation of the F13
schematic model including multiple glassy states and the glass-glass
transition. Results suggest that our approach is flexible enough to bridge
alternative theoretical descriptions of glassy matter based on the notions of
quenched disorder and dynamic facilitation.Comment: 4 pages, 2 figure
Is ALT control really necessary for routine ART monitoring in resource poor settings?
2006 AIDS Conference in Toront
Near-IR imaging of T Cha: evidence for scattered-light disk structures at solar system scales
T Chamaeleontis is a young star surrounded by a transitional disk, and a
plausible candidate for ongoing planet formation. Recently, a substellar
companion candidate was reported within the disk gap of this star. However, its
existence remains controversial, with the counter-hypothesis that light from a
high inclination disk may also be consistent with the observed data. The aim of
this work is to investigate the origin of the observed closure phase signal to
determine if it is best explained by a compact companion. We observed T Cha in
the L and K s filters with sparse aperture masking, with 7 datasets covering a
period of 3 years. A consistent closure phase signal is recovered in all L and
K s datasets. Data were fit with a companion model and an inclined
circumstellar disk model based on known disk parameters: both were shown to
provide an adequate fit. However, the absence of expected relative motion for
an orbiting body over the 3-year time baseline spanned by the observations
rules out the companion model. Applying image reconstruction techniques to each
dataset reveals a stationary structure consistent with forward scattering from
the near edge of an inclined disk.Comment: 6 pages, 3 figures, accepted for publication in MNRAS Letter
Assessment of experimental optical techniques for characterizing heat transfer using numerical simulations
This manuscript addresses the application of numerical simulations for assessing the error in the measurement of the bulk temperature along the laser beam of a 3D flow using a 2D Moiré deflectometry analysis. To analyze the effect of different flow parameters on the error, a 3D computational model of an experimental system was developed. The simulated domain represents the well-known solution of the backward facing step in a rectangular channel but includes a hot-plate at the bottom of the step to enhance the heat transfer effects. The geometry resembles that found in a general heat exchanger. The difference between the computed bulk temperature of the flow and the average temperature obtained via the 2D Moiré is analytically evaluated for various assumed general temperature profiles; the numerically computed profiles of temperature indicates that the error decreases with the channel aspect ratio. The use of CFD enables the determination of the flow topology and thus an evaluation of the 3D flow behavior that will cause the measurement error. A parametric study was performed for different flow conditions, namely, the aspect ratio of the channel, the inflow conditions (flow velocity or Reynolds number), and the temperature of the hot wall. The results indicate that the Moiré technique is suitable for evaluating the bulk temperature in typical heat exchange devices and flow conditions
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