Geometry of solid

Duke, C.B. Determination of the atomic geometries of solid surfaces. Appl. Surf. Sci. 1982, 11-12, 1-19. 

Ferguson J.R., Fiard J.M., Herbin, R., 1996. Three-dimensional numerical simulation for various geometries of solid oxide fuel cells. Journal of Power Sources 58, 109-122. 

Acoustic streaming flow fields depend on acoustic wave properties, fluid properties, the geometry of solid boundaries, and presence of solid particles within the fluid. Depending on these factors, laminar, transitional, or turbulent flow with jets and vortices can be generated. The acoustic streaming effect is proportional to the sound pressure level and the square of the frequency of the pressure wave [1]. However, excessive heating... 

Standardization of Methods for Characterizing the Surface Geometry of Solids, Particle Particle Systems Characterization, 20 (2003) 5, p. 311-322. 

Figure 735 Tubular, monolithic and planar geometries of solid oxide fuel cells. Illustration courtesy of M. Muller (Muller, 2001).

Izotov, A. D., Balankin, A. S., Lazarev, V. B. (1993). Synergetics and Fractal Thermomechanics of Inorganic Materials, n. Fractal Geometry of Solids Fracture. Neor-ganicheskie Materialy, 29(7), 883-893. 

Tarski, 1926] A. Tarski. Foundations of the Geometry of Solids, trans. of original 1926 article... 

This rule means that the detailed geometry of solid part determines the detailed geometry of porous part and vice versa. 

Example Approximate calculation of the hardness of solids. This concept of shear yielding - where we ignore the details of the grains in our polycrystal and treat the material as a continuum - is useful in many respects. For example, we can use it to calculate the loads that would make our material yield for all sorts of quite complicated geometries. 

Before equations such as Eqs. 6, 7 and 8 can be used, values for the surface energies have to be obtained. While surface energies of liquids may be measured relatively easily by methods such as the du Nouy ring and Wilhelmy plate, those of solids present more problems. Three approaches will be briefly described. Two involve probing the solid surface with a liquid or a gas, the third relies on very sensitive measurement of the force required to separate two surfaces of defined geometry. All involve applying judicious assumptions to the experimental results. 

The elasticity approaches depend to a great extent on the specific geometry of the composite material as well as on the characteristics of the fibers and the matrix. The fibers can be hollow or solid, but are usually circular in cross section, although rectangular-cross-section fibers are not uncommon. In addition, fibeie rejjsuallyjsotropic, but can have more complex material behavior, e.g., graphite fibers are transversely isotropic. 

The solid-flame model can be used to overcome the inaccuracy of the point-source model. This model assumes that the fire can be represented by a solid body of a simple geometrical shape, and that all thermal radiation is emitted from its surface. To ensure that fire volume is not neglected, the geometries of the fire and target, as well as their relative positions, must be taken into account because a portion of the fire may be obscured as seen from the target. 

Fig. 2. Geometries calculated (solid lines) and observed (bold dashed lines) for 1-propanol in its a-cyclodextrin adduct. G3 and G6 denote the numbers of glucopyranose units of a-cyclodextrin. H3 and H5 refer to the hydrogen atoms located inside of the cyclodextrin cavity. The hydrogen atoms for the observed geometry of 1-propanol are not shown, since their atomic coordinates have not been determined. The observed 1-propanol is twofold disordered, with site a occupied 80%, site b 20%. Interatomic distances are shown in bold italics on fine dashed lines (nm). Reproduced with permission from the Chemical Society of Japan...

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