HYBRID LINEAR AND QUADRATIC FINITE ELEMENT MODELS FOR 3D HELMHOLTZ PROBLEMS

In this paper, linear and quadratic finite element models are devised for the three- dimensional Helmholtz problem by using a hybrid variational functional. In each element, contin- uous and discontinuous Helmholtz fields are defined with their equality enforced over the element boundary in a weak sense. The continuous field is based on the C° nodal interpolation and the discontinuous field can be condensed before assemblage. Hence, the element can readily be in- corporated seamlessly into the standard finite element program framework. Discontinuous fields constructed by the plane-wave, Bessel and singular spherical-wave solutions are attempted. Nu- merical tests demonstrate that some of the element models are consistently and considerably more accurate than their conventional counterparts.     

A Comparative Study of Finite Element and Finite Difference Methods for Two-Dimensional Space-Fractional Advection-Dispersion Equation

The paper makes a comparative study of the finite element method (FEM) and the finite difference method (FDM) for two-dimensional fractional advection-dispersion equation (FADE) which has recently been considered a promising tool in modeling non-Fickian solute transport in groundwater. Due to the non-local property of integro-differential operator of the space-fractional derivative, numerical solution of FADE is very challenging and little has been reported in literature, especially for high-dimensional case. In order to effectively apply the FEM and the FDM to the FADE on a rectangular domain, a backward-distance algorithm is presented to extend the triangular elements to generic polygon elements in the finite element analysis, and a variable-step vector Grünwald formula is proposed to improve the solution accuracy of the conventional finite difference scheme. Numerical investigation shows that the FEM compares favorably with the FDM in terms of accuracy and convergence rate whereas the latter enjoys less computational effort.     

Time-resolved resonance Raman observation of the 2-fluorenylnitrenium ion reaction with guanosine to form a C8 intermediate

Time-resolved resonance Raman spectroscopy was used to directly observe the reaction of the 2-fluorenylnitrenium ion with guanosine to produce a C8 intermediate species. Comparison of the Raman spectra with results of density functional theory calculations indicates the C8 intermediate forms two C=N conjugated bonds in ring 1 of the guanosine moiety.     

The influence of a radial magnetic field on current-voltage characteristics of toroidal glow discharge

The present paper deals with the influence of a radial magnetic field on different regions of the toroidal glow discharge and with the subsequent changes of the current-voltage characteristics. From the above it is clear that when studying the influence of a transverse magnetic field on the glow discharge it is necessary to understand that the discharge is not a homogeneous unit and the change of current-voltage characteristics involves the total sum of changes of the properties in different regions of the discharge.     

Stoichiometric and catalytic reductive aldol cyclizations of alkynediones induced by Stryker's reagent

Conjugate reduction of alkynones by stoichiometric [(Ph(3)P)CuH](6) or catalytic [(Ph(3)P)CuH](6) and polymethyl-hydrosiloxane proceeds to cyclization by an aldol reaction with tethered ketones to generate [small beta]-hydroxyenones with good diastereoselectivity.     

Ultrafast holographic Stokesmeter for polarization imaging in real time

We propose an ultrafast holographic Stokesmeter using a volume holographic substrate with two sets of two orthogonal gratings to identify all four Stokes parameters of the input beam. We derive the Mueller matrix of the proposed architecture and determine the constraints necessary for reconstructing the complete Stokes vector. The speed of this device is determined primarily by the channel spectral bandwidth (typically 100 GHz), corresponding to a few picoseconds.