Geometry factors

The term r Vf in Equation (3.71) can be interpreted as a reduced fiber-volume fraction. The word reduced is used because q 1. Moreover, it is apparent from Equation (3.72) that r is affected by the constituent material properties as well as by the reinforcement geometry factor To further assist in gaining appreciation of the Halpin-Tsai equations, the basic equation. Equation (3.71), is plotted in Figure 3-39 as a function of qV,. Curves with intermediate values of can be quickly generated. Note that all curves approach infinity as qVf approaches one. Obviously, practical values of qV, are less than about. 6, but most curves are shown in Figure 3-39 for values up to about. 9. Such master curves for various vaiues of can be used in design of composite materiais. 

Similarly, for the frictional resistive force, Ff, lumping the geometry factors into a constant, c, and letting a = friction coefficient ... 

The area exposed to heat is given by the geometry factors provided with Equation 9-36 ... 

The number of ions i" produced from a gas in the ion source is proportional to the emission current i, to the specific ionization Sggj, to a geometry factor f representing the ionization path inside the ionization source, to the relative ionization probability RlPgaj. and to the partial pressure Pggj. This number of ions produced is, by definition, made equal to the sensitivity Egas times the partial pressure Pg ... 

GROSSWENDT, B. (1991). The angular dependence and irradiation geometry factor for the dose equivalent for photons in slab phantoms of tissue-equivalent material and PMMA, Radiat. Prot. Dosim. 35, 221-235. 

Thermal conductivity can also be measured in a cylindrical geometry. This arrangement makes it much easier to avoid other losses of heat besides conduction through the gas. The equation for heat transfer in a cylindrical geometry is the same as above, except that the dimensions (A/x) in Equation 5.1 are replaced by a geometry factor, G ... 

The strength a of a brittle material is proportional to the fracture toughness KIC and indirectly proportional to the square root of the highest defect size Vfl in the loaded volume a =Y -Kic/yfa (Y is a geometry factor). For optimisation a must be reduced and KIC increased. Whilst the reduction of a is possible by optimising all the processing steps (Sect. 5), an improvement of KIC is mainly possible by microstructural engineering (Sect. 6). 

Let E[GRj be the expected value of the geometry factor G multiplied by the reflectance R,. Both can be considered as independent random variables, as there is no correlation between the shape and the color of an object. Let us assume that the reflectances are uniformly distributed, i.e. many different colors are present in the scene and each color is equally likely. Therefore, the reflectance can be considered to be a random variable drawn from the range [0, 1]. We obtain (Johnson and Bhattacharyya 2001)... 

If we have narrow-band sensors where each sensor responds to a single wavelength X, with i e r, g, b, then the intensity /, measured by the sensor is simply the product of a geometry factor G, the illuminant L,(x, y) at the corresponding object location (x, y) and the reflectance R at this location. 

After we have estimated the illuminant, we can use this information to calculate the reflectances of the objects in view. In Chapter 3 we have seen that, for the given assumptions, pixel intensity c is given by the product of a geometry factor G, the object reflectance R, and the illuminant L. For a nonuniform illuminant, we obtain... 

Therefore, the product between the geometry factor G and the reflectances can be calculated... 

G geometry factor, intensity of the green color channel, Gaussian... 

Geometry Factors. To overcome the inherent first-order release behavior with continuously diminishing release rate from matrix systems, geometry factors have been utilized to compensate for the increasing diffusional distance and decreasing area at the penetrating diffusion front generally encountered in matrix systems. 

Kodym, R., Bergmann M.E.H. and Bouzek, K. (2005) First results of modelling geometry factors in electrolysis cells for direct drinking water disinfection. Proceedings 56th Annual Meeting of the International Society of Electrochemistry, September 26-30, Busan/Korea, p. 896. 

---