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Control of free length when coiling a helical spring
No full textThe problem of controlling the free-length of a helical spring while it is being
manufactured on an automatic coiling machine is examined. This is a disturbance rejection
problem, and the feedback system is designed to reject disturbances caused by variation of the
wire properties and disturbances generated by the coiler. Fixed, self-tuning and fuzzy self-tuning
control are used to reduce the variance of the coiled and free length of a helical spring. Friction
feedfonvard is proposed to compensate for the varying coefficients of friction of different
materials
Front propogation into an unstable state of reaction-transport system
No full textWe studied the propagation of traveling fronts into an unstable state of the reaction-transport systems involving integral transport. By using a hyperbolic scaling procedure and singular perturbation techniques, we determined a Hamiltonian structure of reaction-transport equations. This structure allowed us to derive asymptotic formulas for the propagation rate of a reaction front. We showed that the macroscopic dynamics of the front are “nonuniversal” and depend on the choice of the underlying random walk model for the microscopic transport process
On the minmal parabolic system related to the monster simple group
No full textAlmost all of the 26 sporadic finite simple groups possess systems of sub-
groups which, in several ways, resemble the parabolic systems of the finite
simple groups of Lie type. Many of these systems are catalogued in [RSt,
RSm]. Those in [RSt] mirror more closely the minimal parabolic systems
of a finite simple group of Lie type. In this paper the term minimal
parabolic system will be used in a broader sense, to be explained in a
moment.
Our interest here is in a very particular kind of (generalized) minimal
parabolic system, an example of which occurs in the Monster simple group,
and the object of this work is to derive ``local'' information about such a
minimal parabolic system. In order to state these results we need to intro-
duce some definitions and notation
Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem
Get PDFA standard method for solving
the symmetric definite generalized eigenvalue problem
,
where is symmetric and is symmetric positive definite,
is to compute a Cholesky factorization
(optionally with complete pivoting)
and solve the equivalent
standard symmetric eigenvalue problem C y = \l y where .
Provided that a stable eigensolver is used,
standard error analysis
says that the computed eigenvalues are exact for A+\dA and B+\dB with
\max( \normt{\dA}/\normt{A}, \normt{\dB}/\normt{B} )
bounded by a multiple of ,
where is the unit roundoff.
We take the Jacobi method as the eigensolver
and give a detailed error analysis that yields
backward error bounds potentially much smaller than
.
To show the practical utility of our bounds we describe a vibration problem
from structural engineering in which is ill conditioned yet
the error bounds are small.
We show how, in cases of instability,
iterative refinement based on Newton's method
can be used to produce eigenpairs with small backward errors.
Our analysis and experiments also give insight into the popular Cholesky--QR
method, in which the QR method is used as the eigensolver.
We argue that it is desirable to augment current implementations
of this method with pivoting in the Cholesky factorization
Hyperbolicity of the invariant set for the logistic map with
Get PDFClassic results due to Guckenheimer and Misiurewicz imply that the invariant set of the logistic map with µ in (4,2+\sqrt{5}] is hyperbolic. This is well known, but the only obvious reference in the literature uses relatively sophisticated ideas from complex variable theory.
This pedagogical note provides a brief, self-contained account of this result using only elementary real analysis. The method also gives a good estimate of the expansion rate on the invariant set
An OpenMP-like interface for parallel programming in Java
No full textThis paper describes the definition and implementation of an OpenMP-like set of directives and library routines for shared memory parallel programming in Java. A specification of the directives and routines is proposed and discussed. A prototype implementation, consisting of a compiler and a runtime library, both written entirely in Java, is presented, which implements most of the proposed specification. Some preliminary performance results are reported
Magnetic Fields in barred galaxies: II Dynamo models
Get PDFWe study the generation and maintenance of large-scale magnetic fields in barred galaxies. We take a velocity field (with strong noncircular components) from a published gas dynamical simulation of Athanassoula (1992), and use this as input to a galactic dynamo calculation. Our work is largely motivated by recent high quality VLA radio observations of the barred galaxy NGC 1097, and we compare our results in detail with the regular magnetic fields deduced from these observations. We are able to reproduce most of the conspicuous large-scale features of the observed regular field, including the field structure in the central regions, by using a simple mean-field dynamo model in which the intensity of interstellar turbulence (more precisely, the turbulent diffusivity) is enhanced by a factor of 2-6 in the dust lanes and near the circumnuclear ring. We argue that magnetic fields can be dynamically important, and therefore should be included in models of gas flow in barred galaxies
Spin-up of a two-layer rotating stratified fluid in a variable-depth container
No full textWe consider the spin-up of a two-layer, stably (density) stratified fluid in a rotating
container with an axisymmetric sloping base and cylindrical walls. Details of the spin-
up readjustment mechanisms are presented under the assumption of small impulsive
changes in the rotation rate of the container. It is shown that the relative positions
of the density interface and the discontinuity in wall slope determine the qualitative
large-time spin-up response of the fluid. The density interface leads to a spin-up
readjustment in each of the fluid layers that is essentially independent. However,
when the density interface is below the boundary-slope discontinuity, a sub-region
of the upper layer is predicted to readjust in an algebraic rather than exponential
manner. A detailed sequence of laboratory experiments have been performed to
confirm the predictions of the linear spin-up analysis