A theory of hyperfinite sets

We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS and present some applications.Comment: 28 page

On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities

We demonstrate a close analogy between a viscoelastic medium and an electrically conducting fluid containing a magnetic field. Specifically, the dynamics of the Oldroyd-B fluid in the limit of large Deborah number corresponds to that of a magnetohydrodynamic (MHD) fluid in the limit of large magnetic Reynolds number. As a definite example of this analogy, we compare the stability properties of differentially rotating viscoelastic and MHD flows. We show that there is an instability of the Oldroyd-B fluid that is physically distinct from both the inertial and elastic instabilities described previously in the literature, but is directly equivalent to the magnetorotational instability in MHD. It occurs even when the specific angular momentum increases outwards, provided that the angular velocity decreases outwards; it derives from the kinetic energy of the shear flow and does not depend on the curvature of the streamlines. However, we argue that the elastic instability of viscoelastic Couette flow has no direct equivalent in MHD.Comment: 21 pages, 3 figures, to be published in J. Fluid Mec

On charged impurity structures in liquid helium

The thermoluminescence spectra of impurity-helium condensates (IHC) submerged in superfluid helium have been observed for the first time. Thermoluminescence of impurity-helium condensates submerged in superfluid helium is explained by neutralization reactions occurring in impurity nanoclusters. Optical spectra of excited products of neutralization reactions between nitrogen cations and thermoactivated electrons were rather different from the spectra observed at higher temperatures, when the luminescence due to nitrogen atom recombination dominates. New results on current detection during the IHC destruction are presented. Two different mechanisms of nanocluster charging are proposed to describe the phenomena observed during preparation and warmup of IHC samples in bulk superfluid helium, and destruction of IHC samples out of liquid helium

Acceleration Of Protons To Above 6 MeV Using H2O >Snow> Nanowire Targets

A scheme is presented for using H2O >snow> nanowire targets for the generation of fast protons. This novel method may relax the requirements for very high laser intensities, thus reducing the size and cost of laser based ion acceleration system.Physic

Enhanced Molecular Orientation Induced by Molecular Anti-Alignment

We explore the role of laser induced anti-alignment in enhancing molecular orientation. A field-free enhanced orientation via anti-alignment scheme is presented, which combines a linearly polarized femtosecond laser pulse with a half-cycle pulse. The laser pulse induces transient anti-alignment in the plane orthogonal to the field polarization, while the half-cycle pulse leads to the orientation. We identify two qualitatively different enhancement mechanisms depending on the pulse order, and optimize their effects using classical and quantum models both at zero and non-zero temperature