We investigate the nature of entropy generation for natural convection in a twodimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Bo...

Contents Introduction 3 1 Finite volume discretization of balance laws 4 1.

Voxelisation is the term given to the process of converting data from one source type into a three dimensional volume of data values. The techniques known collectively as volume visualisation can then be applied to the data in order to produce a graphical representation of the object. This paper gives a new practical approach to the voxelisation of data which fills the entire volume. Its use is...

We compute the L-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds.

Abstract: We investigate the nature of heat transfer and entropy generation for natural convection in a two-dimensional circular section enclosure. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Where...

We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f . We show, for instance, that if an X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurfac...

In this paper we will show that on any complete noncompact Riemannian manifold with a finite volume there exist geodesic loops of arbitrarily small length.

Introduction We consider a Riemannian manifold M n with a positive density function Ψ (x) used to weight volume and hypersurface area. In terms of the underlying Riemannian volume dV 0 and area dA 0 , the new, weighted volume and area are given by

We show that if L is a codimension-one lamination in a finite volume hyperbolic 3-manifold such that the principal curvatures of each leaf of L are all in the interval (−δ, δ) for a fixed δ ∈ [0, 1) and no complimentary region of L is an interval bundle over a surface, then each boundary leaf of L has a nontrivial fundamental group. We also prove existence of a fixed constant δ0 > 0 such that i...

In this paper, we prove that every closed nil 3-manifold is diffeomorphic to a cusp cross-section of a finite volume complex hyperbolic 2-orbifold.