From the viewpoint of grain boundary structure a small-angle symmetric tilt boundary can be considered a boundary that is symmetrically mis-oriented by a small angle from a perfect Σ=1 boundary. The misoriention in these boundaries occurs during the re-crystallization period when annealing of the deformed material helps to develop the boundary. The development of the boundary occurs mainly by t...

Context-free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power, both for generating sets of graphs and for generating sets of hypergraphs. Arbitrary boundary graph grammars have more graph generating power than context-free hypergraph grammars, but they have the same hypergraph generating power. To obtain these results, several normal forms for bo...

Given a surface triangulation T of and a subset X of its vertex set V (T ), we define a restricted edge contraction as a contraction of an edge connecting X and V (T )−X. Boundary vertices in V (T ) − X are only allowed to be contracted to the boundary vertices in X adjacent through boundary edges. In this paper, we prove that if a triangulation T of the sphere with boundary satisfies some conn...

This paper is concerned with an investigation into the localized instability of a thin elastic orthotropic semi-infinite plate. In this study, a semi-infinite plate, simply supported on two edges and under different boundary conditions of clamped, hinged, sliding contact and free on the other edge, is studied. A mathematical model is used and a general solution is presented. The conditions unde...

Data previously obtained for the X-33 in the NASA Langley Research Center 20-Inch Mach 6 Air Tunnel have been reanalyzed to compare methods for determining boundary layer edge conditions for use in transition correlations. The experimental results were previously obtained utilizing the phosphor thermography technique to monitor the status of the boundary layer downstream of discrete roughness e...

This paper deals with the basic approximation properties of the h-p version of the boundary element method (BEM) in IR 3. We extend the results on the exponential convergence of the h-p version of the boundary element method on geometric meshes from problems in polygonal domains to problems in polyhedral domains. In 2D elliptic boundary value problems the solutions have only corner singularitie...

Conventionally, edges are treated as either scalar or vector quantities. This paper presents a novel framework which treats edges as directional dipoles that induce the eld around themselves. An analogy can be made between this concept and the interaction of magnetic dipoles with the magnetic eld. The dipoles interact with the eld and align themselves into a smooth contour connguration. This pa...