3,935 research outputs found
On the densest packing of polycylinders in any dimension
Using transversality and a dimension reduction argument, a result of A.
Bezdek and W. Kuperberg is applied to polycylinders , showing that the optimal packing density is in
any dimension.Comment: Edited to reflect acknowledgements in the published versio
Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children's intuitive reasoning
This is an author-created version of this article. The original source of publication is Psychon Bull Rev. 2006 Dec;13(6):935-53
The final publication is available at www.springerlink.com
Published version: http://dx.doi.org/10.3758/BF0321390
Geometric Permutations of Non-Overlapping Unit Balls Revisited
Given four congruent balls in that have disjoint
interior and admit a line that intersects them in the order , we show
that the distance between the centers of consecutive balls is smaller than the
distance between the centers of and . This allows us to give a new short
proof that interior-disjoint congruent balls admit at most three geometric
permutations, two if . We also make a conjecture that would imply that
such balls admit at most two geometric permutations, and show that if
the conjecture is false, then there is a counter-example of a highly degenerate
nature
Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two
We consider the billiard dynamics in a non-compact set of R^d that is
constructed as a bi-infinite chain of translated copies of the same
d-dimensional polytope. A random configuration of semi-dispersing scatterers is
placed in each copy. The ensemble of dynamical systems thus defined, one for
each global realization of the scatterers, is called `quenched random Lorentz
tube'. Under some fairly general conditions, we prove that every system in the
ensemble is hyperbolic and almost every system is recurrent, ergodic, and
enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure
Cutting sequences on translation surfaces
We analyze the cutting sequences associated to geodesic flow on a large class
of translation surfaces, including Bouw-Moller surfaces. We give a
combinatorial rule that relates a cutting sequence corresponding to a given
trajectory, to the cutting sequence corresponding to the image of that
trajectory under the parabolic element of the Veech group. This extends
previous work for regular polygon surfaces to a larger class of translation
surfaces. We find that the combinatorial rule is the same as for regular
polygon surfaces in about half of the cases, and different in the other half.Comment: 30 pages, 19 figure
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