We prove two rigidity results for complete Riemannian threemanifolds of higher rank. Complete three-manifolds have higher spherical rank if and only if they are spherical space forms. Complete finite volume threemanifolds have higher hyperbolic rank if and only if they are finite volume hyperbolic space forms.

The properties of statistical ensembles with abelian charges close to the thermodynamic limit are discussed. The finite volume corrections to the probability distributions and particle density moments are calculated. Results are obtained for statistical ensembles with both exact and average charge conservation. A new class of variables (semi–intensive variables) which differ in the thermodynami...

Low frequency pulsatile flow of an incompressible viscous fluid has been numerically investigated in a rigid 90° bend of circular cross-section, using the finite-volume method. The governing parameters are as follows : amplitude ratio of 1.25, Womersley

We consider here second-order finite volume methods for onedimensional scalar conservation laws. We give a method to determine a slope reconstruction satisfying all the exact numerical entropy inequalities. It avoids inhomogeneous slope limitations and, at least, gives a convergence rate of ∆x1/2. It is obtained by a theory of second-order entropic projections involving values at the nodes of t...

In this paper, thermal effects of laser irradiance on biological tissue is investigated using computer simulations. Earlier attempts in this field made use of finite difference and finite element techniques. Here a novel approach is adopted to improve the results. The effect of our implicit approach on the convergence procedure and accuracy of results, with different timing steps, is explor...

there are different methods to reduce drag in high speed hulls. one of these methods is a change in the shape of the body by adding longitudinal side tunnels. in this paper it has been attempted to determine the influence of the tunnel height on hydrodynamic characteristics of the hull to achieving an optimum shape for the tunnel. to achieve this purpose, numerical simulation of the problem has...

We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, finite volume, mixed finite element, and conforming and nonconforming finite element methods in space and the backward Euler scheme in time. Our estimates are based on a H-conforming reconstruction of the potential, continuous and piec...

1. Poisson Equation 1 2. Outline of Topics 3 2.1. Finite Difference Method 3 2.2. Finite Element Method 3 2.3. Finite Volume Method 3 2.4. Sobolev Spaces and Theory on Elliptic Equations 3 2.5. Iterative Methods: Conjugate Gradient and Multigrid Methods 3 2.6. Nonlinear Elliptic Equations 3 2.7. Fast Multiple Method 3 3. Physical Examples 4 3.1. Gauss’ law and Newtonian gravity 4 3.2. Electrost...

A numerical method for the reconstruction of interfaces in finite volume schemes for multiphase flows is presented. The computation of the triple-point at the intersection of three materials in two dimensions of space is addressed. The determination of the normal vectors between pairs of materials is obtained with a finite element approximation. A numerical method for the localization of a trip...