10,776 research outputs found
Reply to Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'
This is a Reply to Comment arXiv:0707.2642 by Hof et al. on Letter
arXiv:physics/0608292 which was subsequently published in Phys Rev Lett, 98,
014501 (2007).
In our letter it was reported that in pipe flow the median time for
relaminarisation of localised turbulent disturbances closely follows the
scaling . This conclusion was based on data from
collections of 40 to 60 independent simulations at each of six different
Reynolds numbers, Re. In the Comment, Hof et al. estimate differently
for the point at lowest Re. Although this point is the most uncertain, it forms
the basis for their assertion that the data might then fit an exponential
scaling , for some constant A, supporting Hof et al.
(2006) Nature, 443, 59. The most certain point (at largest Re) does not fit
their conclusion and is rejected. We clarify why their argument for rejecting
this point is flawed. The median is estimated from the distribution of
observations, and it is shown that the correct part of the distribution is
used. The data is sufficiently well determined to show that the exponential
scaling cannot be fit to the data over this range of Re, whereas the fit is excellent, indicating critical behaviour and supporting
experiments by Peixinho & Mullin 2006.Comment: 1 page, 1 figur
Assessing schematic knowledge of introductory probability theory
[Abstract]: The ability to identify schematic knowledge is an important goal for both assessment
and instruction. In the current paper, schematic knowledge of statistical probability theory is
explored from the declarative-procedural framework using multiple methods of assessment.
A sample of 90 undergraduate introductory statistics students was required to classify 10
pairs of probability problems as similar or different; to identify whether 15 problems
contained sufficient, irrelevant, or missing information (text-edit); and to solve 10 additional
problems. The complexity of the schema on which the problems were based was also
manipulated. Detailed analyses compared text-editing and solution accuracy as a function of
text-editing category and schema complexity. Results showed that text-editing tends to be
easier than solution and differentially sensitive to schema complexity. While text-editing and
classification were correlated with solution, only text-editing problems with missing
information uniquely predicted success. In light of previous research these results suggest
that text-editing is suitable for supplementing the assessment of schematic knowledge in
development
Optimization of the magnetic dynamo
In stars and planets, magnetic fields are believed to originate from the
motion of electrically conducting fluids in their interior, through a process
known as the dynamo mechanism. In this Letter, an optimization procedure is
used to simultaneously address two fundamental questions of dynamo theory:
"Which velocity field leads to the most magnetic energy growth?" and "How large
does the velocity need to be relative to magnetic diffusion?" In general, this
requires optimization over the full space of continuous solenoidal velocity
fields possible within the geometry. Here the case of a periodic box is
considered. Measuring the strength of the flow with the root-mean-square
amplitude, an optimal velocity field is shown to exist, but without limitation
on the strain rate, optimization is prone to divergence. Measuring the flow in
terms of its associated dissipation leads to the identification of a single
optimal at the critical magnetic Reynolds number necessary for a dynamo. This
magnetic Reynolds number is found to be only 15% higher than that necessary for
transient growth of the magnetic field.Comment: Optimal velocity field given approximate analytic form. 4 pages, 4
figure
Effects of the roller feed ratio on wrinkling failure in conventional spinning of a cylindrical cup
In this study, wrinkling failure in conventional spinning of a cylindrical cup has been investigated by using both finite element (FE) analysis and experimental methods. FE simulation models of a spinning experiment have been developed using the explicit finite element solution method provided by the software Abaqus. The severity of wrinkles is quantified by calculating the standard deviation of the radial coordinates of element nodes on the edge of the workpiece obtained from the FE models. The results show that the severity of wrinkles tends to increase when increasing the roller feed ratio. A forming limit study for wrinkling has been carried out and shows that there is a feed ratio limit beyond which the wrinkling failure will take place. Provided that the feed ratio is kept below this limit, the wrinkling failure can be prevented. It is believed that high compressive tangential stresses in the local forming zone are the causes of the wrinkling failure. Furthermore, the computational performance of the solid and shell elements in simulating the spinning process are examined and the tool forces obtained from wrinkling and wrinkle-free models are compared. Finally, the effects of the feed ratio on variations of the wall thickness of the spun cylindrical cup are investigated. </jats:p
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