2,113,740 research outputs found
Numerical Methods of Multifractal Analysis in Information Communication Systems and Networks
In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity
spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and
scaling functions, and methods used in their determination by means of Wavelet Transform Modulus
Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectrum
are presented. A method based on multifractal data analysis at network layer level by means of WTMM
is proposed for the detection of traffic anomalies in computer and telecommunication networks. The
chapter also introduces WTMM as the informative indicator to exploit the distinction of fractal dimen-
sions on various parts of a given dataset. A novel approach based on the use of multifractal spectrum
parameters is proposed for estimating queuing performance for the generalized multifractal traffic on
the input of a buffering device. It is shown that the multifractal character of traffic has significant impact
on queuing performance characteristics
Numerical Analysis
Acknowledgements: This article will appear in the forthcoming Princeton Companion to Mathematics, edited by Timothy Gowers with June Barrow-Green, to be published by Princeton University Press.\ud
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In preparing this essay I have benefitted from the advice of many colleagues who corrected a number of errors of fact and emphasis. I have not always followed their advice, however, preferring as one friend put it, to "put my head above the parapet". So I must take full responsibility for errors and omissions here.\ud
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With thanks to: Aurelio Arranz, Alexander Barnett, Carl de Boor, David Bindel, Jean-Marc Blanc, Mike Bochev, Folkmar Bornemann, Richard Brent, Martin Campbell-Kelly, Sam Clark, Tim Davis, Iain Duff, Stan Eisenstat, Don Estep, Janice Giudice, Gene Golub, Nick Gould, Tim Gowers, Anne Greenbaum, Leslie Greengard, Martin Gutknecht, Raphael Hauser, Des Higham, Nick Higham, Ilse Ipsen, Arieh Iserles, David Kincaid, Louis Komzsik, David Knezevic, Dirk Laurie, Randy LeVeque, Bill Morton, John C Nash, Michael Overton, Yoshio Oyanagi, Beresford Parlett, Linda Petzold, Bill Phillips, Mike Powell, Alex Prideaux, Siegfried Rump, Thomas Schmelzer, Thomas Sonar, Hans Stetter, Gil Strang, Endre Süli, Defeng Sun, Mike Sussman, Daniel Szyld, Garry Tee, Dmitry Vasilyev, Andy Wathen, Margaret Wright and Steve Wright
Parallel Factorizations in Numerical Analysis
In this paper we review the parallel solution of sparse linear systems,
usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is
based on the concept of parallel factorization of a (block) tridiagonal matrix.
This allows to obtain efficient parallel extensions of many known matrix
factorizations, and to derive, as a by-product, a unifying approach to the
parallel solution of ODEs.Comment: 15 pages, 5 figure
Numerical Analysis of Parallel Replica Dynamics
Parallel replica dynamics is a method for accelerating the computation of
processes characterized by a sequence of infrequent events. In this work, the
processes are governed by the overdamped Langevin equation. Such processes
spend much of their time about the minima of the underlying potential,
occasionally transitioning into different basins of attraction. The essential
idea of parallel replica dynamics is that the exit time distribution from a
given well for a single process can be approximated by the minimum of the exit
time distributions of independent identical processes, each run for only
1/N-th the amount of time.
While promising, this leads to a series of numerical analysis questions about
the accuracy of the exit distributions. Building upon the recent work in Le
Bris et al., we prove a unified error estimate on the exit distributions of the
algorithm against an unaccelerated process. Furthermore, we study a dephasing
mechanism, and prove that it will successfully complete.Comment: 37 pages, 4 figures, revised and new estimates from the previous
versio
Numerical Analysis of Black Hole Evaporation
Black hole formation/evaporation in two-dimensional dilaton gravity can be
described, in the limit where the number of matter fields becomes large, by
a set of second-order partial differential equations. In this paper we solve
these equations numerically. It is shown that, contrary to some previous
suggestions, black holes evaporate completely a finite time after formation. A
boundary condition is required to evolve the system beyond the naked
singularity at the evaporation endpoint. It is argued that this may be
naturally chosen so as to restore the system to the vacuum. The analysis also
applies to the low-energy scattering of -wave fermions by four-dimensional
extremal, magnetic, dilatonic black holes.Comment: 10 pages, 9 figures in separate uuencoded fil
Numerical aeroacoustic analysis of propeller designs
As propeller-driven aircraft are the best choice for short/middle-haul flights but their acoustic emissions may require improvements to comply with future noise certification standards, this work aims to numerically evaluate the acoustics of different modern propeller designs. Overall sound pressure level and noise spectra of various blade geometries and hub configurations are compared on a surface representing the exterior fuselage of a typical large turboprop aircraft. Interior cabin noise is also evaluated using the transfer function of a Fokker 50 aircraft. A blade design operating at lower RPM and with the span-wise loading moved inboard is shown to be significantly quieter without severe performance penalties. The employed Computational Fluid Dynamics (CFD) method is able to reproduce the tonal content of all blades and its dependence on hub and blade design features
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