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

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

The Large Magellanic Cloud as a laboratory for Hot Bottom Burning in massive Asymptotic Giant Branch stars

We use Spitzer observations of the rich population of Asymptotic Giant Branch stars in the Large Magellanic Cloud (LMC) to test models describing the internal structure and nucleosynthesis of the most massive of these stars, i.e. those with initial mass above $\sim 4M_{\odot}$. To this aim, we compare Spitzer observations of LMC stars with the theoretical tracks of Asymptotic Giant Branch models, calculated with two of the most popular evolution codes, that are known to differ in particular for the treatment of convection. Although the physical evolution of the two models are significantly different, the properties of dust formed in their winds are surprisingly similar, as is their position in the colour-colour (CCD) and colour-magnitude (CMD) diagrams obtained with the Spitzer bands. This model independent result allows us to select a well defined region in the ($[3.6]-[4.5], [5.8]-[8.0]$) plane, populated by AGB stars experiencing Hot Bottom Burning, the progeny of stars with mass $M\sim 5.5M_{\odot}$. This result opens up an important test of the strength hot bottom burning using detailed near-IR (H and K bands) spectroscopic analysis of the oxygen-rich, high luminosity candidates found in the well defined region of the colour-colour plane. This test is possible because the two stellar evolution codes we use predict very different results for the surface chemistry, and the C/O ratio in particular, owing to their treatment of convection in the envelope and of convective boundaries during third dredge-up. The differences in surface chemistry are most apparent when the model stars reach the phase with the largest infrared emission.Comment: 11 pages, 14 figures, accepted for publication in MNRA

A thick shell Casimir effect

We consider the Casimir energy of a thick dielectric-diamagnetic shell under a uniform velocity light condition, as a function of the radii and the permeabilities. We show that there is a range of parameters in which the stress on the outer shell is inward, and a range where the stress on the outer shell is outward. We examine the possibility of obtaining an energetically stable configuration of a thick shell made of a material with a fixed volume

Coarsening in potential and nonpotential models of oblique stripe patterns

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as $t^{1/2}$. Further from onset, the characteristic lengths along the preferred directions $\hat{x}$ and $\hat{y}$ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and Model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results of electroconvection in nematics is presented.Comment: 13 pages, 13 figures. To appear in Phys. Rev.

The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence

We calculate the volumes of a large class of Einstein manifolds, namely Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones described by polynomial embedding relations in C^n. These volumes are important because they allow us to extend and test the AdS/CFT correspondence. We use these volumes to extend the central charge calculation of Gubser (1998) to the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These volumes also allow one to quantize precisely the D-brane flux of the AdS supergravity solution. We end by demonstrating a relationship between the volumes of these Einstein spaces and the number of holomorphic polynomials (which correspond to chiral primary operators in the field theory dual) on the corresponding affine cone.Comment: 25 pp, LaTeX, 1 figure, v2: refs adde

Spatial Attention to Social Cues is not a Monolithic Process

Social stimuli are a highly salient source of information, and seem to possess unique qualities that set them apart from other well-known categories. One characteristic is their ability to elicit spatial orienting, whereby directional stimuli like eyegaze and pointing gestures act as exogenous cues that trigger automatic shifts of attention that are difficult to inhibit. This effect has been extended to non-social stimuli, like arrows, leading to some uncertainty regarding whether spatial orienting is specialized for social cues. Using a standard spatial cueing paradigm, we found evidence that both a pointing hand and arrow are effective cues, but that the hand is encoded more quickly, leading to overall faster responses. We then extended the paradigm to include multiple cues in order to evaluate congruent vs. incongruent cues. Our results indicate that faster encoding of the social cue leads to downstream effects on the allocation of attention resulting in faster orientin

Casimir energy of a dilute dielectric ball with uniform velocity of light at finite temperature

The Casimir energy, free energy and Casimir force are evaluated, at arbitrary finite temperature, for a dilute dielectric ball with uniform velocity of light inside the ball and in the surrounding medium. In particular, we investigate the classical limit at high temperature. The Casimir force found is repulsive, as in previous calculations.Comment: 15 pages, 1 figur