3,824 research outputs found
Aerodynamic influence coefficient method using singularity splines
A numerical lifting surface formulation, including computed results for planar wing cases is presented. This formulation, referred to as the vortex spline scheme, combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of loading function methods. The formulation employes a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfied all the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise. Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral. The current formulation uses the elementary horseshoe vortex as the basic singularity and is therefore restricted to linearized potential flow. As part of the study, a non planar development was considered, but the numerical evaluation of the lifting surface concept was restricted to planar configurations. Also, a second order sideslip analysis based on an asymptotic expansion was investigated using the singularity spline formulation
Positive configuration space
We define and study the totally nonnegative part of the Chow quotient of the
Grassmannian, or more simply the nonnegative configuration space. This space
has a natural stratification by positive Chow cells, and we show that
nonnegative configuration space is homeomorphic to a polytope as a stratified
space. We establish bijections between positive Chow cells and the following
sets: (a) regular subdivisions of the hypersimplex into positroid polytopes,
(b) the set of cones in the positive tropical Grassmannian, and (c) the set of
cones in the positive Dressian. Our work is motivated by connections to super
Yang-Mills scattering amplitudes, which will be discussed in a sequel.Comment: 46 pages; citations adde
Formal study of plane Delaunay triangulation
This article presents the formal proof of correctness for a plane Delaunay
triangulation algorithm. It consists in repeating a sequence of edge flippings
from an initial triangulation until the Delaunay property is achieved. To
describe triangulations, we rely on a combinatorial hypermap specification
framework we have been developing for years. We embed hypermaps in the plane by
attaching coordinates to elements in a consistent way. We then describe what
are legal and illegal Delaunay edges and a flipping operation which we show
preserves hypermap, triangulation, and embedding invariants. To prove the
termination of the algorithm, we use a generic approach expressing that any
non-cyclic relation is well-founded when working on a finite set
Isotopic Equivalence from Bezier Curve Subdivision
We prove that the control polygon of a Bezier curve B becomes homeomorphic
and ambient isotopic to B via subdivision, and we provide closed-form formulas
to compute the number of iterations to ensure these topological
characteristics. We first show that the exterior angles of control polygons
converge exponentially to zero under subdivision.Comment: arXiv admin note: substantial text overlap with arXiv:1211.035
Scaling and Universality in City Space Syntax: between Zipf and Matthew
We report about universality of rank-integration distributions of open spaces
in city space syntax similar to the famous rank-size distributions of cities
(Zipf's law). We also demonstrate that the degree of choice an open space
represents for other spaces directly linked to it in a city follows a power law
statistic. Universal statistical behavior of space syntax measures uncovers the
universality of the city creation mechanism. We suggest that the observed
universality may help to establish the international definition of a city as a
specific land use pattern.Comment: 24 pages, 5 *.eps figure
Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
We consider geometric instances of the Maximum Weighted Matching Problem
(MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000
vertices. Making use of a geometric duality relationship between MWMP, MTSP,
and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields
in near-linear time solutions as well as upper bounds. Using various
computational tools, we get solutions within considerably less than 1% of the
optimum.
An interesting feature of our approach is that, even though an FWP is hard to
compute in theory and Edmonds' algorithm for maximum weighted matching yields a
polynomial solution for the MWMP, the practical behavior is just the opposite,
and we can solve the FWP with high accuracy in order to find a good heuristic
solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental
Algorithms, 200
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