Bundle theory

I. Topological Basis for Higher-Symmetry Electrodynamics II. Basis in Fiber Bundle Theory... 

In summary of this introduction therefore, we develop a novel theory of electrodynamics based on vacuum topology that gives self-consistent descriptions of empirical data where an electrodynamics based on a U(l) vacuum fails. It turns out that 0(3) electrodynamics does not incorporate a monopole, as a material point particle, because it is a theory based on the topology of the vacuum. The next section provides foundational justification for gauge field theory using fiber bundle theory. 

The possibilities of the Poiseuille equation for explaining capillary phenomena in soils have had a certain amount of appeal to soil physicists. The theory of capillarity is so simple and so well established that if suitable soil parameters to express a bundle of capillaries could be found, the problem would be solved in the most direct fashion. Unfortunately, however, there has as yet been no completely satisfactory formula for the capillary bundle theory, although it has often given results of the proper magnitude in certain instances. We shall here develop the Poiseuille equation for special capillary conditions and point out the fallacies of this approach. 

Using the tube bundle theory and the concept of hydraulic radius, Blake (1922) proposed the following equation for the average velocity of fluid flowing in a porous medium of porosity e ... 

Proof. This is a standard argument in fiber bundle theory. We refer, for example, to [SteSl] for details. ... 

Petlyuk, F. B., Danilov, R. Yu. (2001). Few-Step Iterative Methods for Distillation Process Design Using the Trajectory Bundle Theory Algorithm Structure. Theor. Round. Chem. Eng., 35,229-236. 

Calculation investigations (Petlyuk, 1978 Petlyuk Vinogradova, 1980 Shafir et al., 1984) determined the conditions under which saddle and saddle-node stationary points of sections trajectory bundles at finite reflux arise inside the concentration simplex, but not only at its boundary elements, promoted the development of this trajectory bundles theory. 

The development of distillation traj ectory bundles theory at finite reflux showed that the task of minimum reflux mode calculation for nonideal zeotropic and azeotropic mixtures can be solved in another statement at set composition xf and thermal state q of feeding, it is necessary to determine minimum reflux number i min for the set product compositions xd and xb of sharp separation and set permissible concentrations of admixtures in the products. 

Bundle theory becomes most interesting when we think about a particular way of dealing with materials substituting new materials for others of high value. This was a major project, across a wide range of sciences during the eighteenth century there were powerful economic and political rationales for substitution, in the hope of... 

Allegra G, Meille SV (1999) The bundle theory for polymer crystallisation. Phys Chem Chem Phys 1(22) 5179 5188... 

JACKSON, J.D. and HALL, W.B., Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent condition . Turbulent Forced Convection in Channels and Bundles Theory and Applications to Heat Exchangers and Nuclear Reactors, 2, Advanced Study Institute Book (eds. Kakac, S. and Spalding, D.B.), 613-640, (1979). 

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