The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

in this study, the modeling of hydrogen production process in microreactors by methanol-steam reforming reaction is investigated. the catalytic reaction of methanol-steam reforming producing hydrogen is simulated considering a 3d geometry for the microreactor. to calculate diffusion among species, mixture average correlations are compared to stephan-maxwell equations. the reactions occurring in...

Macroscopic Einstein-Maxwell equations for a system of interacting particles to second-order accuracy in the interaction constan. Macroscopic Einstein-Maxwell equations for a system of interacting particles to second-order accuracy in the interaction constant. Abstract. In this paper the macroscopic Einstein and Maxwell equations for system, in which the electromagnetic interactions are dominat...

In this paper we propose and investigate some edge element approximations for three Maxwell systems in three dimensions: the stationary Maxwell equations, the time-harmonic Maxwell equations and the time-dependent Maxwell equations. These approximations have three novel features. First, the resulting discrete edge element systems can be solved by some existing preconditioned solvers with optima...

We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the familiar Maxwell equations as a special case but, in other cases, can predict birefringence, charge non-conservation, wave damping and other effects that the famili...

H. Akbar-Zadeh has recently proposed (J Geom Phys 17 (1995) 342) a new geometric formulation of Einstein–Maxwell system with source in terms of what are called “Generalized Einstein manifolds”. We show that, contrary to the claim, Maxwell equations have not been derived in this formulation and that, the assumed equations can be identified only as sourcefree Maxwell equations in the proposed geo...

We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations, Einstein-dilaton or Einstein-Maxwell equations. In four dimensions the field equations of the Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling p...

The Maxwell equations describe the interaction of electric and magnetic fields. Important applications are electric machines such as transformers or motors, or electromagnetic waves radiated from antennas or transmitted in optical fibres. To compute the solutions of real life problems on complicated geometries, numerical methods are required. In this lecture we formulate the Maxwell equations, ...