Toroidal bubbles

Toroidal bubbles with circulation in ideal hydrodynamics: a variational approach.

Incompressible, inviscid, irrotational, unsteady flows with circulation Gamma around a distorted toroidal bubble are considered. A general variational principle that determines the evolution of the bubble shape is formulated. For a two-dimensional (2D) cavity with a constant area A, exact pseudodifferential equations of motion are derived, based on variables that determine a conformal mapping o...

Magnetic axis safety factor of finite b spheromaks and transition from spheromaks to toroidal magnetic bubbles

The value of the safety factor on the magnetic axis of a finite-beta spheromak is shown to be a function of beta in contrast to what was used in Bellan, Phys. Plasmas 9, 3050 (2002); this dependence on beta substantially reduces the gradient of the safety factor compared to the previous calculation. The method for generating finite-beta spheromak equilibria is extended to generate equilibria de...

Magnetic axis safety factor of finite β spheromaks and transition from spheromaks to toroidal magnetic bubbles

Abstract The value of the safety factor on the magnetic axis of a finite-beta spheromak is shown to be a function of beta in contrast to what was used in P. M. Bellan, Phys. Plasmas 9, 3050 (2002); this dependence on beta substantially reduces the gradient of the safety factor compared to the previous calculation. The method for generating finite-beta spheromak equilibria is extended to generat...

Minimum Tenacity of Toroidal graphs

The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connec...

Bubbles In Tehran Stock Exchange