Nonzero divergence application

The present chapter is devoted mainly to one of these new theories, in particular to its possible applications to photon physics and optics. This theory is based on the hypothesis of a nonzero divergence of the electric field in vacuo, in combination with the condition of Lorentz invariance. The nonzero electric field divergence, with an associated space-charge current density, introduces an extra degree of freedom that leads to new possible states of the electromagnetic field. This concept originated from some ideas by the author in the late 1960s, the first of which was published in a series of separate papers [10,12], and later in more complete forms and in reviews [13-20]. 

Figure 1. New features introduced by the concept of nonzero electric field divergence in vacuum space. The arrows point to possible areas of application.

The first line, /j(x), has a nonphysical behavior, if correlation of orientations is lacking (g = 1), since the susceptibility Xt(x) does not have an imaginary component in this case moreover, Xr(x) diverges at the rigorous resonance condition (x = 1), when %t = G(1 — x2) 1. These results mean that the correlation factor g should actually be nonzero and/or that the parabolic potential has a restricted applicability. 

Two traditional approaches to the closure of the Reynolds equation are outlined below. These approaches are based on Boussinesq s model of turbulent viscosity completed by Prandtl s or von Karman s hypotheses [276, 427]. For simplicity, we confine our consideration to the case of simple shear flow, where the transverse coordinate Y = Xi is measured from the wall (the results are also applicable to turbulent boundary layers). According to Boussinesq s model, the only nonzero component of the Reynolds turbulent shear stress tensor and the divergence of this tensor are defined as... 

---