We prove that there is a unique convex non-collinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such central configuration posses a symmetry line and it is a kite shaped quadrilateral. We also show that there is exactly on...

For a manifold with an affine connection, we prove formulas which infinitesimally quantify the gap in certain naturally defined open geodesic quadrilateral associated to pair of tangent vectors u, v at point manifold. We show that first-order infinitesimal obstruction close is always zero, second-order $$-T(u,v)$$ , where T torsion tensor and if $$T = 0$$ then third-order $$(1/2)R(u,v)(u+v)$$ t...

In this paper, we describe the implementation of an open source code (Jaal) for producing a high quality, isotropic all-quadrilateral mesh for an arbitrary complex surface geometry. Two basic steps in this process are: (1) Triangle to quad mesh conversion using Suneeta Ramaswamy’s tree matching algorithm and (2) Global mesh cleanup operation using Guy Bunin’s one-defect remeshing to reduce irre...

This paper presents a new automated method of quadrilateral meshes with random line constraints which have not been fully considered in previous models. The authors developed a new looping scheme and a direct quadrilateral forming algorithm based on advanced front techniques. This generator overcomes the limitations of previous studies such as line constraint, unmeshed hole and mesh refinement....

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted r...

A general 2D-hp-adaptive Finite Element FE implementation in Fortran 90 is described. The implementation is based on an abstract data structure, which allows to incorporate the full hp-adaptivity of triangular and quadrilateral nite elements. The h-reenement strategies are based on h2-reenement of quadrilaterals and h4-reenement of triangles. For p-reenement we allow the approximation order to ...