Shear-dependent apparent slip on hydrophobic surfaces: The Mattress Model

Recent experiments (Zhu & Granick (2001) Phys. Rev. Lett. 87 096105) have measured a large shear dependent fluid slip at partially wetting fluid-solid surfaces. We present a simple model for such slip, motivated by the recent observations of nanobubbles on hydrophobic surfaces. The model considers the dynamic response of bubbles to change in hydrodynamic pressure due to the oscillation of a solid surface. Both the compression and diffusion of gas in the bubbles decrease the force on the oscillating surface by a ``leaking mattress'' effect, thereby creating an apparent shear-dependent slip. With bubbles similar to those observed by atomic force microscopy to date, the model is found to lead to force decreases consistent with the experimental measurements of Zhu & Granick

Conformally flat manifolds with nonnegative Ricci curvature

revised version, added reference to previous paper by S. Zhu on the same subjectInternational audienceWe show that complete conformally flat manifolds of dimension n>2 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to flat space or to a spherical spaceform. This extends previous works by Q.-M. Cheng, M.H. Noronha, B.-L. Chen and X.-P. Zhu, and S. Zhu

Comparing the Tsallis distribution with and without thermodynamical description in p+p collisions

We compare two types of Tsallis distribution, i.e., with and without thermodynamical description, using the experimental data from the STAR, PHENIX, ALICE and CMS Collaborations on the rapidity and energy dependence of the transverse momentum spectra in p+p collisions. Both of them can give us the similar fitting power to the particle spectra. We show that the Tsallis distribution with thermodynamical description gives lower temperatures than the ones without it. The extra factor $m_T$ (transverse mass) in the Tsallis distribution with thermodynamical description plays an important role in the discrepancies between the two types of Tsallis distribution. But for the heavy particles, the choice to use the $m_T$ or $E_T$ (transverse energy) in the Tsallis distribution becomes more crucial.Comment: 9 pages, 5 figure