Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme

We describe a method that serves to simultaneously determine the topological configuration of the intersection curve of two parametric surfaces and generate compatible decompositions of their parameter domains, that are amenable to the application of existing perturbation schemes ensuring exact topological consistency of the trimmed surface representations. To illustrate this method, we begin with the simpler problem of topology resolution for a planar algebraic curve F(x,y)=0 in a given domain, and then extend concepts developed in this context to address the intersection of two tensor-product parametric surfaces p(s,t) and q(u,v) defined on (s,t)∈[0,1]² and (u,v)∈[0,1]². The algorithms assume the ability to compute, to any specified precision, the real solutions of systems of polynomial equations in at most four variables within rectangular domains, and proofs for the correctness of the algorithms under this assumption are given. Mathematics subject classification (2000)  65D17     

Excited‐State Dynamics of Isolated DNA Bases: A Case Study of Adenine

We present a summary of recent advances in the understanding of the UV photophysics of the isolated DNA base adenine, emphasizing a discussion of the mechanisms behind the ultrafast relaxation following excitation to the ππ* band. Drawing on our femtosecond time‐resolved photoelectron spectroscopy experiments, we discuss differences in the ultrafast relaxation of adenine and 9‐methyladenine and consider the relative merits of the various proposed mechanisms.     

不重叠型Schwarz交替法的加速收敛

Matsokin与Nepomnyaschikh所提出的不重叠型S交替法的算法中不含有松弛因子，我们知道它有与h无关的几何收敛速度，但由于不含算法参数，该算法不能根据具体的情况加速收敛，本文提出加速收敛算法，我们在原算法的基础上引入两个松弛因子θ2，θ2并证明了除了例外均可实现加速收敛，θ1=θ^-1，θ2=θ^-2是满足均衡条件的最佳松弛因子，最后的算例表明该加速算法的有效性。     

Stable intersections of affine cantor sets

We construct open sets of pairs of affine Cantor sets (K, K′) with the simplest possible combinatorics (i. e., defined by two affine increasing maps) which have stable intersection, while the product of lateral thicknesses τ_R(K) • τ_L (K′) is smaller than one. Thus, in a strong form, the converse to the following classic result due to Newhouse is not true: if the product of the thicknesses of two Cantor sets is bigger than one then there are translations of them which have stable intersection. We also describe the topological structure of K—K′ for typical pairs (K, K′) in this open set.     

Discrete Spectrum of the Deficit Angle and the Differential Structure of a Cosmic String

Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior of the cosmic string space-time and that they loose this property at the singular boundary except for the cosmic string space-times with the following deficit angles: Δ=2π(1−1/n), n=1,2,… . A connection between smoothness of fields at the conical singularity and the scalar and electromagnetic conical bremsstrahlung is discussed. It is also argued that the smoothness assumption of fields at the singularity is equivalent to the Aliev and Gal’tsov “quantization” condition leading to the above mentioned discrete spectrum of the deficit angle.     

On the quantum dynamics of a point particle in conical space

A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a δ-function potential, which appear naturally in the model. These pathological potentials are treated with the self-adjoint extension method which yields the correct boundary condition (not necessarily a null wavefunction) at the origin. We show that the usual boundary condition requiring that the wavefunction vanishes at the origin is arbitrary and drastically reduces the number of bound states if used. The situation studied here is closely related to the problem of a dipole moving in conical space.