Boundary conditions coupled conical

Neumann boundary conditions, electronic states, adiabatic-to-diabatic transformation, two-state system, 304-309 Newton-Raphson equation, conical intersection location locations, 565 orthogonal coordinates, 567 Non-Abelian theory, molecular systems, Yang-Mills fields nuclear Lagrangean, 250 pure vs. tensorial gauge fields, 250-253 Non-adiabatic coupling ... 

As described in the introduction, submicrometer disk electrodes are extremely useful to probe local chemical events at the surface of a variety of substrates. However, when an electrode is placed close to a surface, the diffusion layer may extend from the microelectrode to the surface. Under these conditions, the equations developed for semi-infinite linear diffusion are no longer appropriate because the boundary conditions are no longer correct [97]. If the substrate is an insulator, the measured current will be lower than under conditions of semi-infinite linear diffusion, because the microelectrode and substrate both block free diffusion to the electrode. This phenomena is referred to as shielding. On the other hand, if the substrate is a conductor, the current will be enhanced if the couple examined is chemically stable. For example, a species that is reduced at the microelectrode can be oxidized at the conductor and then return to the microelectrode, a process referred to as feedback. This will occur even if the conductor is not electrically connected to a potentiostat, because the potential of the conductor will be the same as that of the solution. Both shielding and feedback are sensitive to the diameter of the insulating material surrounding the microelectrode surface, because this will affect the size and shape of the diffusion layer. When these concepts are taken into account, the use of scanning electrochemical microscopy can provide quantitative results. For example, with the use of a 30-nm conical electrode, diffusion coefficients have been measured inside a polymer film that is itself only 200 nm thick [98]. 

Jensen Webb (Ref 43) examined the data predicting the extent of afterburning in fuel-rich exhausts of metal-modified double-base proplnt rocket motors so as to determine the amt of an individual metal which is required to suppress this afterburning. The investigatory means they used consisted of a series of computer codes. First, an equilibrium chemistry code to calculate conditions at the nozzle throat then a nonequilibrium code to derive nozzle plane exit compn, temp and velocity and, finally, a plume prediction code which incorporates fully coupled turbulent kinetic energy boundary-layer and nonequilibrium chemical reaction mechanisms. Used for all the code calcns were the theoretical environment of a static 300 N (67-lb) thrust std research motor operating at a chamber press of S.SMNm 2 (500psi), with expansion thru a conical nozzle to atm press and a mass flow rate... 

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