Non-linear dynamics of Kelvin-Helmholtz unstable magnetized jets: three-dimensional effects

A numerical study of the Kelvin-Helmholtz instability in compressible magnetohydrodynamics is presented. The three-dimensional simulations consider shear flow in a cylindrical jet configuration, embedded in a uniform magnetic field directed along the jet axis. The growth of linear perturbations at specified poloidal and axial mode numbers demonstrate intricate non-linear coupling effects. The physical mechanims leading to induced secondary Kelvin-Helmholtz instabilities at higher mode numbers are identified. The initially weak magnetic field becomes locally dominant in the non-linear dynamics before and during saturation. Thereby, it controls the jet deformation and eventual breakup. The results are obtained using the Versatile Advection Code [G. Toth, Astrophys. Lett. Comm. 34, 245 (1996)], a software package designed to solve general systems of conservation laws. An independent calculation of the same Kelvin-Helmholtz unstable jet configuration using a three-dimensional pseudo-spectral code gives important insights into the coupling and excitation events of the various linear mode numbers.Comment: 10 (+7) pages, 6 figures, accepted for Phys. Plasmas 6, to appear 199

Notions of denseness

The notion of a completely saturated packing [Fejes Toth, Kuperberg and Kuperberg, Highly saturated packings and reduced coverings, Monats. Math. 125 (1998) 127-145] is a sharper version of maximum density, and the analogous notion of a completely reduced covering is a sharper version of minimum density. We define two related notions: uniformly recurrent and weakly recurrent dense packings, and diffusively dominant packings. Every compact domain in Euclidean space has a uniformly recurrent dense packing. If the domain self-nests, such a packing is limit-equivalent to a completely saturated one. Diffusive dominance is yet sharper than complete saturation and leads to a better understanding of n-saturation.Comment: Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol4/paper9.abs.htm

‘In volumine Longobardo’ New Light on the Date and Origin of the Latin Translation of St Anthony’s Seven Letters

The seven letters of St Antony of Egypt, after the ground-breaking study of Samuel Rubenson, have been revealed to be one of our earliest sources for Egyptian monastic and ascetic theology of the fourth century. However, the letters, except for some fragments, are not extant in their original Coptic version and the most reliable source we have is a Georgian translation of the seven letters and a complete Latin translation first published in 1516. This Latin version is usually considered by scholarship as a humanist translation made on the basis of a lost Greek original. This view has remained ever since accepted in later scholarship. A deeper examination of the Latin text and its transmission, however, reveals a completely different story and the Latin translation has turned out to be much earlier than it was previously assumed and it should be regarded as an early composition, made sometimes between the fifth and seventh centuries which, beside the fifth century Syriac translation of Anthony’s first letter, makes it one of the earliest extant witnesses to Antony’s letters

Another generalization of the gcd-sum function

We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that the asymptotic properties of this function are closely connected to the Piltz divisor function. A generalization of Menon's identity is also considered.Comment: 9 page