A NEW APPROACH TO THE EQUATIONS FOR THE STEADY STATE CURRENTS AT MICROELECTRODES:EC'PROCESSES(SECOND ORDER REACTION)

With a new approach,the general current expressions of two typical second order catalytic reactions at microelectrodes are obtained.This allows the study of fast chemical reactions and systems where the reactants are present in similar concentrations.

THE VERIFICATION OF THE CURRENT TRANSIENT EQUATION AT TUBULAR ELECTRODES IN A FLOWING FLUID UNDER POTENTIAL STEP

The equation derived for the response of the current transients in the flowing fluid is verified experimentally.

Numerical Simulation for Refraction-Diffraction of Waves in Water of Slowly Varying Current and Topography

A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice.

The equation of chronoamperometric current on an oblate hemispheroid microelectrode and its verification

With the aspect of equivalent diffusion layer an analytical chronoamperometric current equation on an oblate hemispheroid microelectrode for reversible electrochemical condition is derived. To verify this equation the chronoammograms have been obtained with benzoquinone in McIlvaine buffer solution (pH 7.0) at a mercury oblate hemispheroid microelectrode. The experimental results agree with the theoretical conclusions.

CONVERGENCE OF ADAPTIVE EDGE ELEMENT METHODS FOR THE 3D EDDY CURRENTS EQUATIONS

We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.

Bosonic Operator Realization of Hamiltonian for a Superconducting QuantumInterference Device

Based on the appropriate bosonic phase operator diagonalized in the entangled state representation we construct the Hamiltonian operator model for a superconducting quantum interference device. The current operator and voltage operator equations are derived.

NUMERICAL SIMULATION OF A MATHEMATICAL MODEL FOR WAVE PROPAGATION ON NON-UNIFORM CURRENT AND DEPTH

A water wave evolution equation is developed from the combinedrefraction-diffraction equation on non-uniform current in water of slowly varying topography byusing the perturbation method. A numerical model is presented with the governing equationdiscretized with an improved Alternating Direction Impicit (ADI) method involving a relaxationfactor which can improve convergent rate. The calculation results show that the model caneffectively reflect the effects of current on wave propagation.

daptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems

We develop and analyze an adaptive hybridized Interior Penalty Discontinuous Galerkin(IPDG-H)method for H(curl)-elliptic boundary value problems in 2D or 3D arising from a semi-discretization of the eddy currents equations.The method can be derived from a mixed formulation of the given boundary value problem and involves a Lagrange multiplier that is an approximation of the tangential traces of the primal variable on the interfaces of the underlying triangulation of the computational domain.It is shown that the IPDG-H technique can be equivalently formulated and thus implemented as a mortar method.The mesh adaptation is based on a residual-type a posteriori error estimator consisting of element and face residuals.Within a unified framework for adaptive finite element methods,we prove the reliability of the estimator up to a consistency error.The performance of the adaptive symmetric IPDG-H method is documented by numerical results for representative test examples in 2D.

The Grad-Shafranov reconstruction in twenty years: 1996–2016

We review and summarize the applications of the Grad-Shafranov(GS) reconstruction technique to space plasma structures in the Earth's magnetosphere and in the interplanetary space. We organize our presentations following the branches of the "academic family tree" rooted on Prof. Bengt U. ? Sonnerup, the inventor of the GS method. Special attentions are paid to validations of the GS reconstruction results via(1) the direct validation by co-spatial in-situ measurements among multiple spacecraft, and(2) indirect validation by implications and interpretations of the physical connection between the structures reconstructed and other related processes. For the latter, the inter-comparison and interconnection between the large-scale magnetic flux ropes(i.e., Magnetic Clouds) in the solar wind and their solar source properties are presented. In addition, we also summarize various GS-type(or-like) reconstruction and an extension of the GS technique to toroidal geometry. In particular,we point to a possible advancement with added complexity of "helical symmetry" and mixed helicity, in the hope of stimulating interest in future development. We close by offering some thoughts on appreciating the scientific merit of GS reconstruction in general.