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The force acting on a spinning sphere moving in a rarefied gas is calculated. It is found to have three contributions with different directions. The transversal contribution is of opposite direction compared to the so-called Magnus force normally exerted on a sphere by a dense gas. It is given by F=−ατξ23πR3mnω×v, where ατ is the accommodation coefficient of tangential momentum, R is the radius of the sphere, m is the mass of a gas molecule, n is the number density of the surrounding gas, ω is the angular velocity, and v is the velocity of the center of the sphere relative to the gas. The dimensionless factor ξ is close to unity, but depends on ω and κ, the heat conductivity of the body.

Streamer branching in liquid dielectrics is driven by stochastic and deterministic factors. The presence of stochastic causes of streamer branching such as inhomogeneities inherited from noisy initial states, impurities, or charge carrier density fluctuations is inevitable in any dielectric. A fully three-dimensional streamer model presented in this paper indicates that deterministic origins of branching are intrinsic attributes of streamers, which in some cases make the branching inevitable depending on shape and velocity of the volume charge at the streamer frontier. Specifically, any given inhomogeneous perturbation can result in streamer branching if the volume charge layer at the original streamer head is relatively thin and slow enough. Furthermore, discrete nature of electrons at the leading edge of an ionization front always guarantees the existence of a non-zero inhomogeneous perturbation ahead of the streamer head propagating even in perfectly homogeneous dielectric. Based on the modeling results for streamers propagating in a liquid dielectric, a gauge on the streamer head geometry is introduced that determines whether the branching occurs under particular inhomogeneous circumstances. Estimated number, diameter, and velocity of the born branches agree qualitatively with experimental images of the streamer branching. V

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