Singular surfaces, theory

In this section the classical heat and mass transfer theories are examined. The singular surface jump conditions for the primitive quantities, as derived in the framework of the standard averaging procedures, are approximated by the classical chemical engineering stagnant film theory normally used in chemical reactor models. The relevant transport phenomena solutions and the classical theories on heat and mass transfer considering both low- and high mass transfer rates are summarized in the subsequent subsections. 

The entire differential theory of singular surfaces grows from the application of modified Hadamard s lemma to... 

As indicated, an implicit assumption of the JKR theory is that there are no interactions outside the contact radius. More specifically, the energy arguments used in the development of the JKR theory do not allow specific locations of the adhesion forces to be determined except that they must be associated with the contact line where the two surfaces of the particle and substrate become joined. Adhesion-induced stresses act at the surface and not a result of action-at-a-distance interatomic forces. This results in a stress singularity at the circumference of the contact radius [41]. The validity of this assumption was first questioned by Derjaguin et al. [42], who proposed an alternative model of adhesion (commonly referred to as the DMT theory ). Needless to say, the predictions of the JKR and DMT models are vastly different, as discussed by Tabor [41]. 

Rapid flame spread. As we know, radiant preheating of a material can cause its surface temperature to approach its piloted ignition temperature. This causes a singularity in simple flame spread theory that physically means that a premixed mixture at its lower flammability limit occurs ahead of the surface flame. Hence, a rapid spread results in the order of 1 m/s. 

The purpose of the lectures was to discuss various properties of the Hilbert schemes of points on surfaces. Although it was not noticed until recently, the Hilbert schemes have relationship with many other branch of mathematics, such as topology, hyper-Kahler geometry, symplectic geometry, singularities, and representation theory. This is reflected to this note each chapter, which roughly corresponds to one lecture, discusses different topics. 

As for the theory of this phenomenon, it was first observed by Onsager [27a] that, since in the limit a — 0 an LCD a is expected to yield a singularity of the type —surface potential, the statistical-mechanical phase integral for counterions should diverge for a greater than some critical value, characteristic of a given valency. Indeed consider a counterion (for definiteness anion) of valency z. The appropriate phase integral is of the form... 

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