We present novel enhanced finite element methods for the Darcy problem starting from the non stable continuous P1/P0 finite element space enriched with multiscale functions. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with functions based on residuals of the strong equations in each element and edge partition. The strategy le...

Article history: Received 12 October 2011 Received in revised form 8 December 2011 Accepted 9 December 2011 Available online 13 December 2011 Communicated by F. Porcelli The Hamiltonian structures of the incompressible ideal fluid, including entropy advection, and magnetohydrodynamics are investigated by making use of Dirac’s theory of constrained Hamiltonian systems. A Dirac bracket for these ...

We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially considered as independent fields, in contrast to the conventional Ostrogradski method, where only the velocity is turned into an independent field variable. Th...

In this article, we consider hypersurfaces moving with normal velocity depending on the timespace coordinates and on the normal to the hypersurface. We naturally define a measure associated to this hypersurface. This measure is defined on a suitable space/unit normal/curvature configuration space. We show that, while the hypersurface stays smooth, then the measure is a solution to a linear tran...

A model reference adaptive control formulation is presented that uses the dynamical structure of the state space descriptions of a large class of systems. Of particular interest, the formulations enable the imposition of exact kinematic differential equation constraints upon the adaptation process that compensates for model errors and disturbances at the acceleration level. The resulting closed...

The incompressible fluid dynamics is reformulated as dynamics of closed loops C in coordinate space. This formulation allows to derive explicit functional equation for the generating functional Ψ[C] in inertial range of spatial scales, which allows the scaling solutions. The requirement of finite energy dissipation rate leads then to the Kolmogorov index. We find an exact steady solution of the...

The formulation of the relativistic spinless path integral on the general affine space is presented. For the one dimensional space, the Duru-Kleinert (DK) method and the δ-function perturbation technique are applied to solve the relativistic path integrals of the smooth potential and the Dirichlet boundary condition problems, respectively. Let us first consider a point particle of mass M moving...

The effect of replacing hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) by octahydro-1,3,5,7-tetranitro-1,3,5,7tetrazocine (HMX) in HTPB-binder on the performance, sensitivity, thermal, and mechanical properties of the sheet explosive formulation has been studied. The maximum loading of HMX was achieved up to 78 per cent in HTPB-binder system. The velocity of detonation (VOD) of HMX-based sheet e...

Abstract Modeling solute transport in heterogeneous porous media faces two challenges: scale dependence of dispersion and reproducing mixing separately from spreading. Both are crucial since real applications may require km scales whereas reactions, often controlled by mixing, occur at the pore scale. Methods have been developed response to these challenges, but none has satisfactorily characte...

We develop a mixed finite element method for the coupled problem arising in interaction between free fluid governed by Stokes equations and flow deformable porous medium modeled Biot system of poroelasticity. Mass conservation, balance stress, Beavers–Joseph–Saffman condition are imposed on interface. consider fully formulation based weakly symmetric stress-displacement-rotation elasticity Darc...