5,466 research outputs found
Equations, inequations and inequalities characterizing the configurations of two real projective conics
Couples of proper, non-empty real projective conics can be classified modulo
rigid isotopy and ambient isotopy.
We characterize the classes by equations, inequations and inequalities in the
coefficients of the quadratic forms defining the conics.
The results are well--adapted to the study of the relative position of two
conics defined by equations depending on parameters.Comment: 31 pages. See also
http://emmanuel.jean.briand.free.fr/publications/twoconics/ Added references
to important prior work on the subject. The title changed accordingly. Some
typos and imprecisions corrected. To be published in Applicable Algebra in
Engineering, Communication and Computin
Topological Mixing with Ghost Rods
Topological chaos relies on the periodic motion of obstacles in a
two-dimensional flow in order to form nontrivial braids. This motion generates
exponential stretching of material lines, and hence efficient mixing. Boyland
et al. [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277
(2000)] have studied a specific periodic motion of rods that exhibits
topological chaos in a viscous fluid. We show that it is possible to extend
their work to cases where the motion of the stirring rods is topologically
trivial by considering the dynamics of special periodic points that we call
ghost rods, because they play a similar role to stirring rods. The ghost rods
framework provides a new technique for quantifying chaos and gives insight into
the mechanisms that produce chaos and mixing. Numerical simulations for Stokes
flow support our results.Comment: 13 pages, 11 figures. RevTeX4 format. (Final version
Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex
We develop topological methods for analyzing difference topology experiments
involving 3-string tangles. Difference topology is a novel technique used to
unveil the structure of stable protein-DNA complexes involving two or more DNA
segments. We analyze such experiments for the Mu protein-DNA complex. We
characterize the solutions to the corresponding tangle equations by certain
knotted graphs. By investigating planarity conditions on these graphs we show
that there is a unique biologically relevant solution. That is, we show there
is a unique rational tangle solution, which is also the unique solution with
small crossing number.Comment: 60 pages, 74 figure
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