Young theory

It is mainly for these two reasons that this monograph should not be considered to be a comprehensive text on scheme theory. It is much more an attempt to present those concepts and results in scheme theory which seem to have the potential to convince the reader that scheme theory is a young theory the florescence of which is still to come. 

D. The Kosterlitz-Thouless-Halperin-Nelson-Young Theory of Two-Dimensional Melting... 

The wettability of an ideal solid surface (smooth, rigid, chemically homogeneous, insoluble, and nonreactive) depends only on the surface and interfacial tensions y. The relationship between the CA and the corresponding tensions is established by the Young theory [14] ... 

According to the Fowkes-Young theory for the interfacial tension and under the assumptions where = y, the Zisman plot is given by the equation ... 

POWDERS,HANDLING - DISPERSION OF POWDERS IN LIQUIDS] (Vol 19) Young-Helmholtz color-vision theory... 

Surface Area and Permeability or Porosity. Gas or solute adsorption is typicaUy used to evaluate surface area (74,75), and mercury porosimetry is used, ia coajuactioa with at least oae other particle-size analysis, eg, electron microscopy, to assess permeabUity (76). Experimental techniques and theoretical models have been developed to elucidate the nature and quantity of pores (74,77). These iaclude the kinetic approach to gas adsorptioa of Bmaauer, Emmett, and TeUer (78), known as the BET method and which is based on Langmuir s adsorption model (79), the potential theory of Polanyi (25,80) for gas adsorption, the experimental aspects of solute adsorption (25,81), and the principles of mercury porosimetry, based on the Young-Duprn expression (24,25). 

Adsorbed-Solution Theoiy The common thennodynamic approach to multicomponent adsorption treats adsorption equilibrium in a way analogous to fluid-fluid equilibrium. The theory has as its basis the Gibbs adsorption isotherm [Young and Crowell, gen. refs.], which is... 

This book may prove to be a boon to young engineers entering the field. With it they can compare the theory of their studies with application in the field. 

The formulations for the failure governing stress for most stress systems can be found in Young (1989). Using the variance equation and the parameters for the dimensional variation estimates and applied load, a statistical failure theory can be formulated for a probabilistic analysis of stress rupture. 

The JKR model predicts that the contact radius varies with the reciprocal of the cube root of the Young s modulus. As previously discussed, the 2/3 and — 1/3 power-law dependencies of the zero-load contact radius on particle radius and Young s modulus are characteristics of adhesion theories that assume elastic behavior. 

Another manifestation of a time dependence to particle adhesion involves the phenomenon of total engulfment of the particle by the substrate. It is recognized that both the JKR and MP theories of adhesion assume that the contact radius a is small compared to the particle radius R. Realistically, however, that may not be the case. Rather, the contact radius depends on the work of adhesion between the two materials, as well as their mechanical properties such as the Young s modulus E or yield strength Y. Accordingly, there is no fundamental reason why the contact radius cannot be the same size as the particle radius. For the sake of the present discussion, let us ignore some mathematical complexities and simply assume that both the JKR and MP theories can be simply expanded to include large contact radii. Let us further assume that, under conditions of no externally applied load, the contact and particle radii are equal, that is a(0) = R. Under these conditions, Eq. 29 reduces to... 

As previously discussed, the JKR theory predicts that the detachment force is independent of the Young s modulus. Yet despite that, when Gady et al. [117] measured the detachment force of polystyrene particles from two elastomeric substrates having Young s moduli of 3.8 and 320 MPa, respectively, they found that the detachment force from only the more compliant substrate agreed with the predicted value. The force needed to separate the particle from the more rigid substrate was about a factor of 20 lower. Estimates of the penetration depth revealed that the particles would penetrate into the more compliant substrate more deeply than the heights of the asperities. Thus, in that case, the spherical particle approximation would be reasonable. On the other hand, the penetration depth... 

Obviously, the assumptions involved in the foregoing derivation are not entirely consistent. A transverse strain mismatch exists at the boundary between the fiber and the matrix by virtue of Equation (3.8). Moreover, the transverse stresses in the fiber and in the matrix are not likely to be the same because v, is not equal to Instead, a complete match of displacements across the boundary between the fiber and the matrix would constitute a rigorous solution for the apparent transverse Young s modulus. Such a solution can be found only by use of the theory of elasticity. The seriousness of such inconsistencies can be determined only by comparison with experimental results. 

Having met Joule for the first time at the 1847 meeting of the British Association for the Advancement of Science in Oxford, Thomson initially accepted that Joule s experiments had shown that work converted into heat. Committed to Carnot s theory of the production of work from a fall of heat, however, he could not accept the converse proposition that work had been converted into heat could simply be recovered as useful work. Therefore, he could not agree to Joule s claim for mutual convertibility. By 1848 he had appropriated from the lectures of the late Thomas Young (reprinted in the mid-1840s) the term energy as a synonym for vis viva (the term in use at the time, traditionally measured as mtc) and its equivalent terms such as work, but as yet the term appeared only in a footnote. 

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