Gamma Methods

Bums, S., 2007, Sterilization New gamma methods increase options for allograft materials, Med. Dev. Diagn. Lnd. 29(3) 82-92. 

If we choose to use one of FFF 2-5 for all components in both phases, then we have the gamma-gamma method. Invariably, the same FFF is used for both phases, so there are four common versions of this method but in principle, we could use any of the four fugacity formulae 2-5 for each phase, so that for two-phase equilibrium, we have ten possible versions of the method. At low pressures, the FFF 2-5 are equivalent, and the gamma-gamma method simplifies to this one form... 

Liquid-solid equilibria are attacked with the gamma-gamma method in the same general way as liquid-liquid systems however, the two applications differ in how the standard-state fugacities are treated. We still start from the equality of fugacities. 

Figure 10.3 Liquid-liquid equilibrium comjnited from the gamma-gamma method for a binary mixture at fixed T and P. Top Fugadty of component 2. Bottom Fugacity of component 1. The fugacities were computed from the low-pressure form of FFF 2 using Porter s equations with A = 2.4. Broken horizontal lines are tie lines.

The gamma-phi and gamma-gamma methods involve activity coefficients, which measure how component fugacities in a real mixture deviate from those in an ideal solution. Many kinds of ideal solutions are available, and yet all have one common attribute every ideal solution has each fugacity linear in its mole fraction. 

The gamma-gamma method ( 10.1.3) is commonly applied to low-pressure, liquid-liquid equilibrium calculations. Recall that at low pressures, FFF 2-5 are all equivalent, so the gamma-gamma method reduces to (10.1.5). Then if we choose the same standard state for both liquid phases, (10.1.5) simplifies to... 

Figure 11.4 Rachford-Rice algorithm applied to the gamma-gamma method for solving multi-component liquid-liquid equilibrium problems...

The methods presented in previous sections can be combined to attack multiphase equilibrium problems. To illustrate, we combine the gamma-phi method wi the gamma-gamma method to solve three-phase, vapor-liquid-liquid problems. We again choose to pose these problems as analogies to isothermal flash calculations, as in 11.1.5. Then such problems are well-posed when we have specified values for T independent properties, where T is given by (9.1.12) with S = 0,... 

Figure 11.6 Double Rachford-Rice algorithm for using the combined gamma-phi and gamma-gamma methods to solve multicomponent (C > 3) vapor-Uquid-Uquid equilibrium problems. This method fails for binary mixtures (C = 2).

Figure 12.8 Correlation of solid-solid equilibria for binary alloys of nickel -i- gold. Points are experimental data from the collection of Hansen [1]. Line was computed via the gamma-gamma method using the Margules equation with each Margules parameter fit to the data via a...

The Gamma Method Bending Resistance of Bipartite Beam with an Elastic... 

Figure 1. The Gamma-method for a bipartite beam with an elastic shear connection The external bending moment Mg on the composite beam comprises three component moments Mi, M2 and My, which induce the stresses in the two members as shown above.

The Gamma method is named after the caitical factor Gamma y, which describes the relative stiffness of the elastic shear connection between the two members which form the bipartite beam. In a normal glulam beam, where the laminates are connected together with very stiff adhesive layers, y is 1.0 where there is no adhesive at all, and the two laminates are in no way connected to each other, y is zero. Our calculations indicate that the bipartite beam will attain the above optimal bending resistance only if the y value of the connection between the two members attains the corresponding ideal value ... 

The requisite slope for the adhesive layer can be calculated with the rules of the Gamma method. The procedure is based on essentially simple rules, but it involves operations with some rather long equations. The final solution for an elastic adhesive layer is well documented in [5,6] . K ei = 60 N/mm. 

An important finding was that instead of an elastic adhesive layer as required by the Gamma method, a plastic adhesive layer could also lead to the same final strength enhancement of about 20% in comparison to conventional glulam. The calculations for the ideal plastic adhesive layer are documented in Donze [6]. The adhesive layer would need to exhibit a yield point at a shear stress below 1 N/mm, but it is very important that it would fail only after a very large shear deformation (Fig. 5). 

The above value is exactly equal to the value predicted by the calculation model by integration . The approximate Gamma method had predicted a value of 1.19. 

Gamma methods are effective only when a measurable amount of gamma photons are able to penetrate the package to be measured. It presents the advantage to identify munerous radionuclides. It presents also some difficulties such as the high impact to heavy density matrix on the measurement and the low capability to detect actinides mixed with fission products. Very low energy gamma photons (X-rays) or beta and alpha emitters cannot be detected directly by this method. In function of the nature of the matrices, the number of the radionuclides able to measure is different, three case are commonly discusses, (i) measurements on transuranics in a solution without Fission Products, (ii) measurements on Fission Products in a solution without transuranics or a (iii) mixed solution (cf Table 2). 

Khusnullin, M.K., 1973. Application of gamma method for determination of waterflooded strata. Geol. Nefti. I Gaza 12, 63-67. December. 

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