On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev\'e equation

Using a simple operator-norm estimate we show that the solution to the second Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well defined region of the complex plane of the independent variable. The result is illustrated with several numerical examples.Comment: 8 pages, to appear in Nonlinearit

The PDEs of biorthogonal polynomials arising in the two-matrix model

The two-matrix model can be solved by introducing bi-orthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of bi-orthogonal polynomials (called "windows") satisfy polynomial ODEs as well as deformation equations (PDEs) and finite difference equations (Delta-E) which are all Frobenius compatible and define discrete and continuous isomonodromic deformations for the irregular ODE, as shown in previous works of ours. In the one matrix model an explicit and concise expression for the coefficients of these systems is known and it allows to relate the partition function with the isomonodromic tau-function of the overdetermined system. Here, we provide the generalization of those expressions to the case of bi-orthogonal polynomials, which enables us to compute the determinant of the fundamental solution of the overdetermined system of ODE+PDEs+Delta-E.Comment: 20 pages v1 18 Nov 2003; v2 9 Jan 2004: trivial Latex mistake correcte

Drop impact on spherical soft surfaces

The impact of water drops on spherical soft surfaces is investigated experimentally through high-speed imaging. The effect of a convex compliant surface on the dynamics of impacting drops is relevant to various applications, such as 3D ink-jet printing, where drops of fresh material impact on partially cured soft substrates with arbitrary shape. Several quantities which characterize the morphology of impacting drops are measured through image-processing, including the maximum and minimum spreading angles, length of the wetted curve, and dynamic contact angle. In particular, the dynamic contact angle is measured using a novel digital image-processing scheme based on a goniometric mask, which does not require edge fitting. It is shown that the surface with a higher curvature enhances the retraction of the spreading drop; this effect may be due to the difference of energy dissipation induced by the curvature of the surface. In addition, the impact parameters (elastic modulus, diameter ratio, and Weber number) are observed to significantly affect the dynamic contact angle during impact. A quantitative estimation of the deformation energy shows that it is significantly smaller than viscous dissipation

The impact of viscoplastic drops on a heated surface in the Leidenfrost regime

The impact morphology of viscoplastic drops on a heated surface in the Leidenfrost regime is investigated experimentally by high-speed imaging. In particular several important parameters which characterize the impact morphology (such as maximum spreading diameter, minimum retracting diameter and maximum bouncing height etc.) are measured by analysing the impact process, recorded using a high-speed camera. It is shown that as the yield stress grows, surface forces are no longer able to minimize the free surface of the drop, and the inertial deformation upon impact becomes permanent. For small values of the yield stress, the impact morphology of viscoplastic Leidenfrost drops is similar to that of Newtonian drops. These effects can be interpreted in terms of the Bingham–Capillary number, which compares the yield stress magnitude and the capillary (Laplace) pressure. These results suggest that the main contribution to drop rebound is due to surface forces, and not to the intrinsic elasticity of the vapour cushion between the drop and the surface, which is a major assumption in one of the existing models

Private school quality in Italy

Private school enrolment may lead to worse subsequent performance in further education or in the labour market. If students differ in their ability not only to pay but to take advantage of educational opportunities (“talent” for short), private schools attract a worse pool of students when publicly funded schools are better suited to foster progress by more talented students. In the data we analyze, the impact of observable talent proxies on educational and labour market outcomes is indeed more positive for students who (endogenously) choose to attend public schools than for those who choose to pay for private education

Mixed correlation function and spectral curve for the 2-matrix model

We compute the mixed correlation function in a way which involves only the orthogonal polynomials with degrees close to $n$, (in some sense like the Christoffel Darboux theorem for non-mixed correlation functions). We also derive new representations for the differential systems satisfied by the biorthogonal polynomials, and we find new formulae for the spectral curve. In particular we prove the conjecture of M. Bertola, claiming that the spectral curve is the same curve which appears in the loop equations.Comment: latex, 1 figure, 55 page

Possible Recovery of SN 1961V In Hubble Space Telescope Archival Images

SN 1961V in NGC 1058 was originally classified by Fritz Zwicky as a ``Type V'' supernova. However, it has been argued that SN 1961V was not a genuine supernova, but instead the superoutburst of an eta Carinae-like luminous blue variable star. In particular, Filippenko et al. (1995, AJ, 110, 2261) used pre-refurbishment HST WFPC images and the known radio position of SN 1961V to conclude that the star survived the eruption and is likely coincident with a V \~ 25.6 mag, V-I ~ 1.9 mag object. Recently, Stockdale et al. (2001, AJ, 122, 283) recovered the fading SN 1961V at radio wavelengths and argue that its behavior is similar that of some Type II supernovae. We have analyzed post-refurbishment archival HST WFPC2 data and find that the new radio position is still consistent with the Filippenko et al. object, which has not changed in brightness or color, but is also consistent with an adjacent, fainter (I ~ 24.3 mag) and very red (V-I > 1.0 mag) object. We suggest that this fainter object could be the survivor of SN 1961V. Forthcoming HST observations may settle this issue.Comment: 8 pages, 6 figures, to appear in the PASP (2002 July issue