The coupled modeling of the flow of two immiscible fluid phases in a heterogeneous, elastic, porous material is formulated in a manner analogous to that for a single fluid phase. An asymptotic technique, valid when the heterogeneity is smoothly varying, is used to derive equations for the phase velocities of the various modes of propagation. A cubic equation is associated with the phase velocit...

This paper is concerned with the Cubic Interpolation scheme CIP proposed by T. Yabe for the Galerkin Characteristic Method and the possibility of improving the precision of PDE solvers when the differentiated form of the equation is used. For convection diffusion equations a Lagrangian treatment of the convective term is analyzed for various approximations of the projection operator. It is foun...

Earth-observing satellites, such Landsat, provide many multitemporal images of earth, either water body or land. Using spectral water body characteristics and field measurement, bathymetry (water depth) of the study area can be calculated for each image recorded/acquired at different time. Four multitemporal spatial images were used for generating bathymetry images which were arranged as multil...

The present paper uses new approach and methodology to solve second order one dimensional hyperbolic telegraph equation numerically by B-spline collocation method. It is based on collocation of modified cubic B-spline basis functions over the finite elements. The given equation is decomposed into system of equations and modified cubic B-spline basis functions have been used for spatial variable...

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The dispersive shock wave (DSW) refraction due to its head-on collision with the centred rarefaction wave (RW) is considered in the frameworks of the one-dimensional defocusing nonlinear Schr...

An explicit projective embedding of the moduli space of marked cubic surfaces is given. This embedding is equivariant under the Weyl group of type E6. The image is defined by a system of linear and cubic equations. To express the embedding in a most symmetric way, the target would be 79-dimensional, however the image lies in a 9-dimensional linear subspace. 1 The moduli space of cubic surfaces ...

Geometric design of quadratic and cubic developable Be Âzier patches from two boundary curves is studied in this paper. The conditions for developability are derived geometrically from the de Casteljau algorithm and expressed as a set of equations that must be ful®lled by the Be Âzier control points. This set of equations allows us to infer important properties of developable Be Âzier patches t...

By using the Lie’s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. Starting from the equivalence generators we construct the differential invariants of order one. We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schrödinger equations whi...

In this paper, we find the exact solutions of some nonlinear evolution equations by using ( ′ G )expansion method. Four nonlinear models of physical significance i.e. the symmetric regularized longwave equation, the Klein-Gordon-Zakharov equations, the Burgers-Kadomtsev-Petviashvili equation and the nonlinear Schrödinger equation with a cubic nonlinearity are considered and obtained their exact...

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N = 2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between fiveand four-dimensio...