Dual models for p-form mimetic gravity and their connection to perfect fluids consisting of (p+1)-branes

We propose an approach that allows one to reformulate $n$-dimensional $p$-form mimetic gravity (including usual mimetic gravity as particular case $p = 0$) as nonlinear $(n-p-1)$-form electrodynamics via electric-magnetic duality. The resulting dual Lagrangian density is just the square root of the ordinary quadratic Lagrangian density of $(n-p-1)$-form electrodynamics. By applying field transformation in the action, we show that for the arbitrary $p$ this dual theory transforms into the $(p+1)$-brane fluid: the model of the stack of the parallel $(p+1)$-branes foliating physical spacetime. As the structure of the field transformations depends on $p$, the sets of solutions in these models are related differently. We prove, that for $p = 0$ and $p = n-2$ dual mimetic models describe usual particle fluid with the potential flow and to the $(n-1)$-brane fluid respectively. For other values of $p$ not all mimetic solutions behave like that, in general, so we restrict ourselves only to the case $n = 4$, $p = 1$. In this case, we show, that mimetic formulation is dual to the well-known Nielsen-Olesen theory of "dual strings" and discuss the criterion indicating whether its solutions behave like string fluid.Comment: 12 page

Aspects of geometric calculation of the planetary gear train with intermediate rollers. Part 1

The paper presents the geometric calculation of the planetary gear train with intermediate rollers, where the number of intermediate rollers is greater or less than that of the teeth in the annular gear by one, the profile surface of the annular gear teeth being the same. The gear ratio is changed by both a value and a sign

Load analysis of the planetary gear train with intermediate rollers. Part 2

The paper presents the load analysis of the planetary gear train with intermediate rollers based on solving a statically indeterminate problem including contact area problems

Proximity effect model of ultra-narrow NbN strips

We show that narrow superconducting strips in superconducting (S) and normal (N) states are universally described by the model presenting them as lateral NSN proximity systems in which the superconducting central band is sandwiched between damaged edge-bands with suppressed superconductivity.The width of the superconducting band was experimentally determined from the value of magnetic field at which the band transits from the Meissner state to the static vortex state. Systematic experimental study of 4.9 nm thick NbN strips with widths in the interval from 50 nm to 20 ${\mu}$m, which are all smaller than the Pearl's length, demonstrates gradual evolution of the temperature dependence of the critical current with the change of the strip width