Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators Γ to SL(2,C). In this note we extend Bowditch’s result by giving ...

An industrial scheme, to simulate the two compressible phase flow in porous media, consists in a finite volume method together with a phase-by-phase upstream scheme. The implicit finite volume scheme satisfies industrial constraints of robustness. We show that the proposed scheme satisfy the maximum principle for the saturation, a discrete energy estimate on the pressures and a function of the ...

Article history: Received 12 July 2011 Received in revised form 30 January 2012 Accepted 2 February 2012 Available online 6 February 2012

An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as compared to standard front tracking methods. The resulting algorithm is also more efficient than exis...

in this work a numerical study of thermal and fluid dynamics behavior of natural air convection in a square cavity in a laminar flow is presented, by finite volume method. the square cavity has two walls heated with different temperatures and two isolated walls. the numerical simulation is made up of several rayleigh numbers to . flow and isotherm lines are presented and analyzed. the numerical...

unglazed transpired solar collectors are widely used for heating outside air directly, these days. pre-heating ventilation air for large spaces and heating air for crop drying, are some of the applications of these kinds of collectors. the outside air is drawn straight from ambient, uniformly through the whole surface of a perforated absorber (transpired, dark-colored plate) exposed to the sun....

We study the L-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M = Γ\X with finite volume and arithmetic fundamental group Γ whose universal covering X is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.

Let X be a quasiprojective manifold given by the complement of a divisor D with normal crossings in a smooth projective manifold X. Using a natural compactification of X by a manifold with corners e X, we describe the full asymptotic behavior at infinity of certain complete Kähler metrics of finite volume on X. When these metrics evolve according to the Ricci flow, we prove that such asymptotic...

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...