116,897 research outputs found
Accurately model the Kuramoto--Sivashinsky dynamics with holistic discretisation
Get PDFWe analyse the nonlinear Kuramoto--Sivashinsky equation to develop accurate
discretisations modeling its dynamics on coarse grids. The analysis is based
upon centre manifold theory so we are assured that the discretisation
accurately models the dynamics and may be constructed systematically. The
theory is applied after dividing the physical domain into small elements by
introducing isolating internal boundaries which are later removed.
Comprehensive numerical solutions and simulations show that the holistic
discretisations excellently reproduce the steady states and the dynamics of the
Kuramoto--Sivashinsky equation. The Kuramoto--Sivashinsky equation is used as
an example to show how holistic discretisation may be successfully applied to
fourth order, nonlinear, spatio-temporal dynamical systems. This novel centre
manifold approach is holistic in the sense that it treats the dynamical
equations as a whole, not just as the sum of separate terms.Comment: Without figures. See
http://www.sci.usq.edu.au/staff/aroberts/ksdoc.pdf to download a version with
the figure
Floyd-Thomas\u27s Making it Plain: Liberating Black Church History (Book Review)
Full text linkA Review of
Making it Plain: Liberating Black Church History, by Juan M. Floyd-Thomas. Nashville, TN: Abingdon Press, 2014. 163 pp. $17.99. ISBN 978067833275
Use the information dimension, not the Hausdorff
Get PDFMulti-fractal patterns occur widely in nature. In developing new algorithms
to determine multi-fractal spectra of experimental data I am lead to the
conclusion that generalised dimensions of order , including the
Hausdorff dimension, are effectively \emph{irrelevant}. The reason is that
these dimensions are extraordinarily sensitive to regions of low density in the
multi-fractal data. Instead, one should concentrate attention on generalised
dimensions for , and of these the information dimension
seems the most robustly estimated from a finite amount of data.Comment: 11 page
Kendall\u27s Connected: Christian Parenting in an Age of IM and MySpace (Book Review)
Full text linkA Review of
Connected: Christian Parenting in an Age of IM and MySpace, by Peggy Kendall. Valley Forge, PA: Judson Press, 2007. 123 pp. $12.00. ISBN 978081701516
Cowan and Wilder\u27s In Defense of the Bible: A Comprehensive Apologetic for the Authority of Scripture (Book Review)
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