The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, since the largest interior angles are subdivided. In this paper we specifically introduce a new local refinement for triangulations based on the longest-edge trisection, the 7-triangle longest-edge (7T-LE) local refinement algorithm. Each triangle to be refined is subdivided...

Many aspects of geophysical flows can be described compactly in terms of potential vorticity dynamics. Since potential temperature can fluctuate at boundaries, however, the boundary conditions for potential vorticity dynamics are inhomogeneous, which complicates considerations of potential vorticity dynamics when boundary effects are dynamically significant. A formulation of potential vorticity...

We consider an integral equation obtained by the “direct method” for the Neumann problem on a polygonal domain which may contain slits, i.e., interior angles of 2π. By using a Galerkin method with piecewise linear functions on a suitable graded mesh one can obtain the optimal convergence rate h3/2. Using a Gauss solver for the arising linear system would require C h−3 operations. We show that a...

An improved algorithm for two-dimensional triangular mesh generation in arbitrary polygonally bounded domains with holes and isolated interior points is presented. The algorithm is quad-tree based and follows the ideas of Bern, Eppstein and Gilbert 1]. Using a rhomboid structure of the quad-tree and a number of new ideas for warping and centering points and for shifting grids, we are able to ge...

Both collinear factorization theorem 1 and kT factorization theorem 2,3 are the fundamental tools of perturbative QCD (PQCD), where kT denotes parton transverse momenta. In these theorems the amplitude for an exclusive process can be calculated as an expansion of αs(Q) and Λ/Q with Q being a large momentum transfer and Λ a small hadronic scale. Similarly, in the heavy quark limit mb → ∞, mb bei...

1 Motivation The compliant walking models are often used for reproducing characteristic gait dynamics [1]. However, since they require the touchdown angles to be chosen independently, there is a limited explanation for the foot placement selection in relation to the state of the body. In this study, it is hypothesized that the foot placement is indicated by progression of the center of pressure...

In this paper we explore, from an algorithmic point of view, the extent to which the facial angles and combinatorial structure of a convex polyhedron determine the polyhedron—in particular the edge lengths and dihedral angles of the polyhedron. Cauchy’s rigidity theorem of 1813 states that the dihedral angles are uniquely determined. Finding them is a significant algorithmic problem which we ex...

A die angle is one of the most important parameters for a drawing process. It should be chosen in that way that a draw stress is low, a wire surface quality is satisfactory and die durability is high [1]. The temperature of a wire in deformation zone depends on amounts of heat generated during a drawing. This heat consists of two components; one is the work piece deformation and another is fric...

The μ(I)-rheology is a nonlinear viscous law, with a strain-rate invariant and pressure-dependent viscosity, that has proved to be effective at modelling dry granular flows in the intermediate range of the inertial number, I. This paper shows how to incorporate the rheology into depth-averaged granular avalanche models. To leading order, the rheology generates an effective basal friction, which...

Abstract This paper establishes new analytical results in the mathematical theory of brush tyre models. In first part, exact problem which considers large camber angles is analysed from perspective linear dynamical systems. Under assumption vanishing sliding, most salient properties model are discussed with some insights on concepts as existence and uniqueness solution. A comparison against cla...