Simultaneous displacement method

Repeated application of this equation constitutes the point-simultaneous relaxation method, also known as the point Jacobi method or the method of simultaneous displacements. 

In the sandwich method, the skin component is injected first which forms the solidifying layer in accordance to the "fountain flow principle, followed by the core component in the fluid core , simultaneously displacing the skin component. 

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

The effects of adsorbed inhibitors on the individual electrode reactions of corrosion may be determined from the effects on the anodic and cathodic polarisation curves of the corroding metaP . A displacement of the polarisation curve without a change in the Tafel slope in the presence of the inhibitor indicates that the adsorbed inhibitor acts by blocking active sites so that reaction cannot occur, rather than by affecting the mechanism of the reaction. An increase in the Tafel slope of the polarisation curve due to the inhibitor indicates that the inhibitor acts by affecting the mechanism of the reaction. However, the determination of the Tafel slope will often require the metal to be polarised under conditions of current density and potential which are far removed from those of normal corrosion. This may result in differences in the adsorption and mechanistic effects of inhibitors at polarised metals compared to naturally corroding metals . Thus the interpretation of the effects of inhibitors at the corrosion potential from applied current-potential polarisation curves, as usually measured, may not be conclusive. This difficulty can be overcome in part by the use of rapid polarisation methods . A better procedure is the determination of true polarisation curves near the corrosion potential by simultaneous measurements of applied current, corrosion rate (equivalent to the true anodic current) and potential. However, this method is rather laborious and has been little used. 

It is also feasible to measure both droplet size and velocity simultaneously with the holographic method. Such a measurement system has been developed by Murakami and Ishikawa. 65()l They used two pulse lasers of different wavelengths to record two holograms on two different films, separated by an appropriate time interval. The displacements of moving particles were measured on a superimposed picture of the two films to determine the velocities of the particles. 

Bimetallic metal particles are important materials because their characteristics, especially their catalytic properties, are often quite different from those of pure metal particles. Dendrimer-encapsulated bimetallic clusters can be synthesized by any of three methods (Fig. 17) (1) partial displacement of the dendrimer-encapsidated cluster, (2) simultaneous co-complexation of two different metal ions followed by reduction, or (3) sequential loading and reduction of two different metal ions. 

Kraak et al. (38) reported the first ACE application to study drug binding to a plasma protein. They used the model system warfarin-human serum albumin (HSA) to compare the suitability of the Hummel-Dreyer, frontal analysis, and vacancy peak methods. A more methodologically intended paper from Erim and Kraak (39) used VACE to study the displacement of warfarin from bovine serum albumin (BSA) by furosemide and phenylbutazone. They concluded that VACE is especially suited to examining competitive properties of simultaneously administered compounds toward a given protein-drug system. 

Ames and Ribeira (75JCS(Pl)1390) described a method for the preparation of thieno[2,3-c]pyridin-7-ones (Scheme 68). The sodium salt of 3-bromothiophene-2-carboxylic acid reacts with carbanions in the presence of copper or copper(II) acetate to give condensation products (274) by displacement of bromide ion, often with simultaneous deacetylation. Cyclization of (274) provides a convenient route to thieno[2,3-c]pyridin-7-ones. Thieno[2,3-c]pyridin-4-ones and thieno[3,2-c]pyridin-7-ones have been prepared by Friedel-Crafts cyclization of AT-(2-thenyl)- and A-(3-thenyl)-glycine derivatives (81H(l6)127l). 

Optical methods can also be utilized to track the displacement of samples surfaces. Various types of interferometers have been employed for measurements of this type, yielding accuracy in the surface displacement between 0.1 and 10-5 A [6,9,15]. Both single and double beam versions have been developed for measuring the d33 coefficient of bulk samples. Cubic samples can avoid some of the difficulties associated with sample flexure on actuation [9], In some cases, one of the probing beams can also be brought to the side of the sample, so that lateral and tangential displacements can be tracked simultaneously [15]. 

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