On Sasaki-Einstein manifolds in dimension five

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde

Hydrodynamic reductions of the heavenly equation

We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.Comment: 14 page

Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect

The formulae for Planck length, Hawking temperature and Unruh-Davies temperature are derived by using only laws of classical physics together with the Heisenberg principle. Besides, it is shown how the Hawking relation can be deduced from the Unruh relation by means of the principle of equivalence; the deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure

Understanding the production of dual BEC with sympathetic cooling

We show, both experimentally and theoretically, that sympathetic cooling of $^{87}$Rb atoms in the $|F=2,m_F=2>$ state by evaporatively cooled atoms in the $|F=1,m_F=-1>$ state can be precisely controlled to produce dual or single condensate in either state. We also study the thermalization rate between two species. Our model renders a quantitative account of the observed role of the overlap between the two clouds and points out that sympathetic cooling becomes inefficient when the masses are very different. Our calculation also yields an analytical expression of the thermalization rate for a single species.Comment: 3 figure

On the nature of the most obscured C-rich AGB stars in the Magellanic Clouds

The stars in the Magellanic Clouds with the largest degree of obscuration are used to probe the highly uncertain physics of stars in the asymptotic giant branch (AGB) phase of evolution. Carbon stars in particular, provide key information on the amount of third dredge-up (TDU) and mass loss. We use two independent stellar evolution codes to test how a different treatment of the physics affects the evolution on the AGB. The output from the two codes are used to determine the rates of dust formation in the circumstellar envelope, where the method used to determine the dust is the same for each case. The stars with the largest degree of obscuration in the LMC and SMC are identified as the progeny of objects of initial mass $2.5-3~M_{\odot}$ and $\sim 1.5~M_{\odot}$, respectively. This difference in mass is motivated by the difference in the star formation histories of the two galaxies, and offers a simple explanation of the redder infrared colours of C-stars in the LMC compared to their counterparts in the SMC. The comparison with the Spitzer colours of C-rich AGB stars in the SMC shows that a minimum surface carbon mass fraction $X(C) \sim 5\times 10^{-3}$ must have been reached by stars of initial mass around $1.5~M_{\odot}$. Our results confirm the necessity of adopting low-temperature opacities in stellar evolutionary models of AGB stars. These opacities allow the stars to obtain mass-loss rates high enough ($\gtrsim 10^{-4}M_{\odot}/yr$) to produce the amount of dust needed to reproduce the Spitzer coloursComment: 14 pages, 5 figures, 1 table; accepted for publication in MNRAS Main Journa

Homogeneous heterotic supergravity solutions with linear dilaton

I construct solutions to the heterotic supergravity BPS-equations on products of Minkowski space with a non-symmetric coset. All of the bosonic fields are homogeneous and non-vanishing, the dilaton being a linear function on the non-compact part of spacetime.Comment: 36 pages; v2 conclusion updated and references adde