Self-gravitating stringlike configurations from nonlinear electodynamics

We consider static, cylindrically symmetric configurations in general relativity coupled to nonlinear electrodynamics (NED) with an arbitrary gauge-invariant Lagrangian of the form $L_{em}= \Phi(F)$, $F =F_{mn}F^{mn}$. We study electric and magnetic fields with three possible orientations: radial (R), longitudinal (L) and azimuthal (A), and try to find solitonic stringlike solutions, having a regular axis and a flat metric at large $r$, with a possible angular defect. Assuming the function $\Phi(F)$ to be regular at small $F$, it is shown that a regular axis is impossible in R-fields if there is a nonzero effective electric charge and in A-fields if there is a nonzero effective electric current along the axis. Solitonic solutions are only possible for purely magnetic R-fields and purely electric A-fields, in cases when $\Phi(F)$ tends to a finite limit at large $F$. For both R- and A-fields, the desired large $r$ asymptotic is only possible with a non- Maxwell behaviour of $\Phi(F)$ at small $F$. For L-fields, solutions with a regular axis are easily obtained (and can be found by quadratures) whereas a desired large $r$ asymptotic is only possible in an exceptional solution; the latter gives rise to solitonic configurations in case \Phi(F) = \const \cdot \sqrt{F}. We give an explicit example of such a solution.Comment: 7 pages, Latex-2e,gc.sty, to appear in Grav. & Cosmo

Effect of boundary conditions on the character of ambipolar diffusion in electrolytes

PREInternational audienceWe discuss the details of ambipolar relaxation of the electric field in liquid asymmetric electrolytes to its stationary value. It is demonstrated that the account for finite boundary conditions modifies the existing concepts of this diffusion process. In particular, we succeeded to suggest a qualitatively correct explanation of the observed distribution of the electric fields over the bulk of the cuvette and its nonmonotonic behavior in measurements on the finite-size cuvette. We analyze the conditions of such an anomaly at the intermediate stages of the relaxation proces

Spatially self-similar locally rotationally symmetric perfect fluid models

Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system of differential equations is reduced as far as possible. The system is subsequently analyzed qualitatively for some of the models. The nature of the singularities occurring in the models is discussed.Comment: 27 pages, pictures available at ftp://vanosf.physto.se/pub/figures/ssslrs.tar.g