Correction to Euler's equations and elimination of the closure problem in turbulence

It has been demonstrated that the Euler equations of inviscid fluid are incomplete: according to the principle of release of constraints, absence of shear stresses must be compensated by additional degrees of freedom, and leads to Reynolds-type multivalued velocity field. however unlike the Reynolds equations, the enlarged Euler's (EE) model provides additional equations for fluctuations, and that eliminates the closure problem. Therefore the (EE) equations are applicable to fully developed turbulent motions where the physical viscosity is vanishingly small compare to the turbulent viscosity, as well as to superfluids and atomized fluids.Analysis of coupled mean/fluctuation EE equations shows that fluctuations stabilize the whole system generating elastic shear waves and increasing speed of sound. Those turbulent motions that originated from instability of underlying laminar motions can be described by the modified Euler's equation with the closure provided by the stabilization principle: driven by instability of laminar motions, fluctuations grow until the new state attains a neutral stability in the enlarged (multivalued) class of functions, and those fluctuations can be taken as boundary conditions for the EE model. The approach is illustrated by an example.Comment: 12 pages,1 figur

Critique [of Some Symbols of Identity of Byzantine Catholics]

Two primary assumptions appear to inform this descriptive article about Byzantine Catholic communities in the United States: (1) old traditions are maintained in new environments through “syncretism”; and (2) the symbols that emerge in those syncretisms are reflective of the world view of the ethnic group that created them

Magnetic translation groups as group extension

Extensions of a direct product T of two cyclic groups Z_n1 and Z_n2 by an Abelian (gauge) group G with the trivial action of T on G are considered. All possible (nonequivalent) factor systems are determined using the Mac Lane method. Some of resulting groups describe magnetic translation groups. As examples extensions with G=U(1) and G=Z_n are considered and discussed.Comment: 10 page