Interference theory

Dhillon, B. S. 1980 Mechanical Reliability Interference Theory Models. In Proceedings Annual Reliability and Maintainability Symposium, 462-467. 

Disney, R. L., Sneth, N. J. and Lipson, C. 1968 The DeteiTnination of Probability of Failure by Stress/Strength Interference Theory. In Proceedings of Annual Symposium on Reliability, 417-422. 

In much of the interference theory of the acoustic microscope, and especially the theory of how the contrast varies with defocus, it is assumed that the microscope is perfectly monochromatic. Of course, the monochromatic theory could be summed over a frequency spectrum actually used in a given... 

J. C. Lewis. Intercollisional Interference - theory and experiment. In Phenomena Induced by Intermodular Interactions, G. Birnbaum, ed., p. 215, Plenum Press, New York, 1985. 

The succession of theoretical notions may be shown by using the corresponding principle for consideration of the chemical interference theory as a more general concept of interrelated and interacting reactions. The correspondence principle applied to the interference of chemical reactions must represent a postulate, which in the marginal case of the determinant (D —> v) requires the coincidence of its chemical consequences with yields of usual chemical reactions, e.g. classical stoichiometric reaction. 

The thicknesses 2v x) of craze and crack opening are given by basic interference theory... 

The procedure of Debye and Prins is still more exact. Here, relying on the strict relations of the interference theory, a mathematical connection is devised between the scattered intensity I as function of the angle of deviation and a distribution W as function of r, which indicates the degree of probability that, on proceeding from a given initial atom in any direction in space, another atom appears after traveling the distance r. 

The different day/night operating powers are designed to provide each AM station with a specified coverage area that is free from interference. Theory rarely translates into practice insofar as coverage is concerned, however, because of the increased interference that all AM stations suffer at nighttime. 

The obvious defect of classical trajectories is that they do not describe quantum effects. The best known of these effects is tunnelling tln-ough barriers, but there are others, such as effects due to quantization of the reagents and products and there are a variety of interference effects as well. To circumvent this deficiency, one can sometimes use semiclassical approximations such as WKB theory. WKB theory is specifically for motion of a particle in one dimension, but the generalizations of this theory to motion in tliree dimensions are known and will be mentioned at the end of this section. More complete descriptions of WKB theory can be found in many standard texts [1, 2, 3, 4 and 5, 18]. 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

The Rayleigh scattering theory which culminates in Eq. (10.60) as its most pertinent form for our purposes is based on the explicit assumption that interference effects are absent. The objective of the present section is to correct the Rayleigh theory to allow for interference effects. There are several assumptions-limitations that are implied by our approach ... 

We assume that the observed interference is the cumulative effect of the contributions of the individual polymer molecules and that solute-solute interactions do not enter the picture. This effectively limits the model to dilute solutions. This restriction is not particularly troublesome, since our development of the Rayleigh theory also assumes dilute solutions. 

We assume that there exists a function which we represent by P(0)-in recognition of the fact that it is angle dependent-which can be multiplied by the scattered intensity as predicted by the Rayleigh theory to give the correct value for i, even in the presence of interference. That is. 

In applying the Rayleigh theory to large polymer molecules, we had to extrapolate results measured at different 0 s to 0 = 0 to eliminate the interference effect. 

The theory is concerned with the problem of determining the probability of failure of a part which is subjected to a loading stress, L, and which has a strength, S. It is assumed that both L and S are random variables with known PDFs, represented by f S) and f L) (Disney et al., 1968). The probability of failure, and hence the reliability, can then be estimated as the area of interference between these stress and strength functions (Murty and Naikan, 1997). 

Reiiabiiity estimates - determined from the appropriate faiiure mode and faiiure theory using Stress-Strength Interference (SSI) analysis (Stage 3)... 

Sundararajan, C. and Witt, F.J. 1995 Stress-Strength Interference Method. In Sundararajan, C. (ed.). Probabilistic Structural Mechanics Handbook theory and industrial applications. NY Chapman Hall. 

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