Search results for " Singularity"
showing 10 items of 203 documents
Complete, exact, and efficient computations with cubic curves
2004
The Bentley-Ottmann sweep-line method can be used to compute thearrangement of planar curves provided a number of geometricprimitives operating on the curves are available. We discuss themathematics of the primitives for planar algebraic curves of degreethree or less and derive efficient realizations. As a result, weobtain a complete, exact, and efficient algorithm for computingarrangements of cubic curves. Conics and cubic splines are specialcases of cubic curves. The algorithm is complete in that it handles all possibledegeneracies including singularities. It is exact in that itprovides the mathematically correct result. It is efficient in thatit can handle hundreds of curves with a quart…
Real Line Arrangements and Surfaces with Many Real Nodes
2008
A long standing question is if the maximum number μ(d) of nodes on a surface of degree d in P( ) can be achieved by a surface defined over the reals which has only real singularities. The currently best known asymptotic lower bound, μ(d) 5 12 d, is provided by Chmutov’s construction from 1992 which gives surfaces whose nodes have non-real coordinates. Using explicit constructions of certain real line arrangements we show that Chmutov’s construction can be adapted to give only real singularities. All currently best known constructions which exceed Chmutov’s lower bound (i.e., for d = 3, 4, . . . , 8, 10, 12) can also be realized with only real singularities. Thus, our result shows that, up t…
The indirect force method
1990
Abstract It is known that the matrix force method shows some advantages over the displacement method for certain classes of problems, particularly in optimization and in the stress concentration analysis. Notwithstanding this, few efforts have been made to employ this method in engineering problems. In this paper, within the elastic analysis of frames and trusses, the indirect force method, utilizing beam-node type finite elements, is proposed. This method is based on the kinematical and mechanical study of nodes and of beams, the latter connected with the nodes by their first extremes according to a preliminary arrangement. In this formulation kinematical singularities are included, in the…
Mappings of finite distortion: Removable singularities for locally homeomorphic mappings
2004
Let f be a locally homeomorphic mapping of finite distortion in dimension larger than two. We show that when the distortion of f satisfies a certain subexponential integrability condition, small sets are removable. The smallness is measured by a weighted modulus.
Mappings of finite distortion: Removable singularities
2003
We show that certain small sets are removable for bounded mappings of finite distortion for which the distortion function satisfies a suitable subexponential integrability condition. We also give an example demonstrating the sharpness of this condition.
Vacuum Casimir energy densities and field divergences at boundaries
2014
We consider and review the emergence of singular energy densities and field fluctuations at sharp boundaries or point-like field sources in the vacuum. The presence of singular energy densities of a field may be relevant from a conceptual point of view, because they contribute to the self-energy of the system. They should also generate significant gravitational effects. We first consider the case of the interface between a metallic boundary and the vacuum, and obtain the structure of the singular electric and magnetic energy densities at the interface through an appropriate limit from a dielectric to an ideal conductor. Then, we consider the case of a point-like source of the electromagneti…
Singularity tracking for Camassa-Holm and Prandtl's equations
2006
In this paper we consider the phenomenon of singularity formation for the Camassa-Holm equation and for Prandtl's equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.
Large-photon-number limit and the essential singularity in finite quantum electrodynamics
1976
It is shown that the essential singularity in finite quantum electrodynamics can be located by considering only those diagrams with a large number of photons exchanged in the single-fermion loop, without photons emitted and absorbed on a fermion line. (AIP)
Critical behavior of short range Potts glasses
1993
We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T−2), and an algebraic singularity atT…
Self-dual modules over local rings of curve singularities
2006
Abstract Let C be a reduced curve singularity. C is called of finite self-dual type if there exist only finitely many isomorphism classes of indecomposable, self-dual, torsion-free modules over the local ring of C . In this paper it is shown that the singularities of finite self-dual type are those which dominate a simple plane singularity.