On the boundary-value problems and the validity of the Post constraint in modern electromagnetism

We recall that the theory of electromagnetism consists of three building blocks: (a) the inhomogeneous Maxwell equations for the electric and magnetic excitations (D,H) (which reflects charge conservation), (b) the homogeneous Maxwell equations for the electric and magnetic field strengths (E,B) (which reflects flux conservation), and (c) the constitutive relation between (D,H) and (E,B). In the recent paper [A. Lakhtakia, Boundary-value problems and the validity of the Post constraint in modern electromagnetism, Optik 117 (2006) 188-192], Lakhtakia proposed to change the standard boundary conditions in electrodynamics in order to exclude certain constitutive parameters. We show that this is inadmissible both from the macroscopic and the microscopic points of view.     

An Assessment of Evans’ Unified Field Theory II

Evans attempted to develop a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for a theory that implements some of the ideas that have been (imprecisely) indicated by Evans and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans’ unified field theory, collapses to an ordinary Einstein equation.     

Can cosmic rotation explain an apparently periodic universe?

We demonstrate a possible explanation of the observed periodicity of the large-scale distribution of galaxies as an effect of the global rotation of the universe.     

Counterion phase transitions in dilute polyelectrolyte solutions

In dilute solutions of rodlike polyelectrolytes some counterions are distributed far from polyions while others are located in their vicinity in the regions of cylindrical symmetry of the electrostatic potential. For these cylindrical regions around rodlike polyelectrolytes we find an exact solution of the nonlinear Poisson-Boltzmann equation for the case of nonzero net charge in these regions. This exact solution implies three qualitatively different phases of counterion distribution around the polyions with second order phase transitions between these phases.     

Spin, gravity, and inertia

The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze the nonrelativistic limit of the theory. The new term describing the specific spin (gravitational moment) interaction effect is recovered in the Hamiltonian. The comparison of the true gravitational coupling with the purely inertial case demonstrates that the spin relativistic effects do not violate the equivalence principle for the Dirac fermions.     

Algebras of Symmetry Operators of the Klein–Gordon–Fock Equation for Groups Acting Transitively on Two-Dimensional Subspaces of a Space-Time Manifold

Russian Physics Journal - All external electromagnetic fields are found in which the Klein–Gordon–Fock equation for a charged test particle admits first-order symmetry operators...     

Asymptotic Theory of Anisotropic Classical Diffusion in Inhomogeneous Media

Journal of Experimental and Theoretical Physics - An asymptotic theory of classical anisotropic diffusion in inhomogeneous media has been developed based on the differential geometry formalism...