Magnetohydrodynamic drift equations : from Langmuir circulations to magnetohydrodynamic dynamo?

We derive the closed system of averaged magnetohydrodynamic (MHD) equations for general oscillating flows. The used small parameter of our asymptotic theory is the dimensionless inverse frequency, and the leading term for a velocity field is chosen to be purely oscillating. The employed mathematical approach combines the two timing method and the notion of a distinguished limit. The properties of commutators are used to simplify calculations. The derived averaged equations are similar to the original MHD equations, but surprisingly (instead of the commonly expected Reynolds stresses) a drift velocity plays a part of an additional advection velocity. In the special case of a vanishing magnetic field $h\equiv 0$, the averaged equations produce the Craik–Leibovich equations for Langmuir circulations (which can be called ‘vortex dynamo’). We suggest that, since the mathematical structure of the full averaged equations for $h\neq 0$ is similar to those for $h =0$, these full equations could lead to a possible mechanism of MHD dynamo, such as the generation of the magnetic field of the Earth

On self-propulsion of NN-sphere micro-robot

The aim of this paper is to describe the self-propulsion of a micro-robot (or micro-swimmer) consisting of $N$ spheres moving along a fixed line. The spheres are linked to each other by arms with the lengths changing periodically. For the derivation, we use the asymptotic procedure containing the two-timing method and a distinguished limit. We show that in the main approximation, the self-propulsion velocity appears as a linear combination of velocities of all possible triplets of spheres. Velocities and efficiencies of three-, four-, and five-swimmers are calculated. The paper is devoted to H.K.Moffatt, who initiated the author's interests in low-Reynolds-number fluid dynamics.Comment: 10 pages, 1 figur

The Stabilizing Role of Fiscal Policy: Theoretical Background and Empirical Evidence

Тhе study sheds light on the stabilizing role of government budget. It finds that in Bulgaria both taxes and government spending are negatively related to the real growth rate. This leads to the conclusion that budgetary expenditure influence output in a non-Keynesian fashion. The size of discretionary fiscal impulse is the main determinant of the non-Keynesian outcome. The results imply that although the balanced budget ensures the sustainability of public finances, it does not guarantee a growth-stimulating effect in case of a large government sector. Abstention from an active fiscal policy would allow the automatic stabilizers to operate freely and to counteract the negative shocks to the economy.government budget, stabilizing fiscal policy, Keynesian vs. non-Keynesian effects