Manifold Elements Research Articles

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second-order displacement and the first-order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.

Theoretical study of three-dimensional numerical manifold method

The three-dimensional numerical manifold method(NMM) is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.

Graphical analysis of angular momentum for collision products

The complexity of atomic and nuclear structures and their collision processes involves conservation laws, bearing mainly on angular momenta; indeed angular momentum treatments prove most laborious. The analytic treatments, preferably carried out in Racah’s calculus, combine initially independent elements stepwise into structures branching out into resulting products. Graphical procedures that ensure phase and amplitude control of their manifold elements, illustrate these sequential steps and provide their results. The present report should familiarize readers with these procedures through examples of reactions of increasing complexity, bearing of course on structure calculations as well. The report has thus two aims: (i) computing correlation functions for reactions yielding several emitted particles (hence of arbitrary complexity) in terms of a novel method of computation, and (ii), describing the mathematical techniques relevant to solve high-complexity angular momentum problems, including the computation of many-body systems’ bound states. The complexity reflects the symmetries of the reaction products, and, more generally, of many-body system. The basic mathematical tool for such treatments is the Racah calculus which employs recoupling transformations, thus avoiding the many summations required by expansions in terms of vector coupling coefficients. The application of the Racah calculus is greatly aided by appropriate definitions and graphical procedures ensuring phase and amplitude control of their manifold elements, as well as illustrating the physical content. Beginning with photon absorption by discrete states, our examples progress to an Auger process yielding a correlation function with seven direction and polarization parameters.

A duality-like transformation in WZNW models inspired by dual riemannian globally symmetric spaces

We investigate transformations on the group manifold element and gauged fields on two different kinds of gauged WZNW models and thus obtain a duality-like transformation between chiral- and vector-gauged WZNW models with null gauged subgroups that exactly converts the chiral-gauged WZNW action to vector-gauged WZNW action and vice versa. These duality-like transformations correspond to the duality in Riemannian globally symmetric spaces.

Interpretation of gas oscillations in multicylinder fluid machinery manifolds by using lumped parameter descriptions

Fluid pressure oscillations are complicated in multicylinder positive displacement machinery manifolds because of the cylinder interactions due to (i) the kinematic arrangements between cylinders and (ii) the inter-connected manifold elements. In practice, manifolds possess irregular shapes and geometries. These are difficult to analyze by using a continuous parameters approach; however, the manifold components can be discretized easily and described by acoustic lumped parameters. Additionally, this approach is more suitable for developing design guidelines, which is the primary aim of the present paper. The multicylinder interaction problem is formulated in the frequency domain. Mass flow rates, with proper crank phase relationships, are considered excitation sources. Manifold components are described as acoustic elements. The equations of acoustic motion are solved for the eigenvalues and the natural modes of gas oscillation, and these are used to provide the forced acoustic response. The formulations are then applied to a two-cylinder compressor discharge system. The computed results compare well with measurements.