Cylindrical smoothed particle hydrodynamics simulations of water entry

This paper presents a smoothed particle hydrodynamics (SPH) modeling technique based on the cylindrical coordinates for axisymmetrical hydrodynamic applications, thus to avoid a full three-dimensional (3D) numerical scheme as required in the Cartesian coordinates. In this model, the governing equations are solved in an axisymmetric form and the SPH approximations are modified into a two-dimensional cylindrical space. The proposed SPH model is first validated by a dam-break flow induced by the collapse of a cylindrical column of water with different water height to semi-base ratios. Then, the model is used to two benchmark water entry problems, i.e., cylindrical disk and circular sphere entry. In both cases, the model results are favorably compared with the experimental data. The convergence of model is demonstrated by comparing with the different particle resolutions. Besides, the accuracy and efficiency of the present cylindrical SPH are also compared with a fully 3D SPH computation. Extensive discussions are made on the water surface, velocity, and pressure fields to demonstrate the robust modeling results of the cylindrical SPH

Υ(nS)\Upsilon(nS) and χb(nP)\chi_b(nP) production at hadron colliders in nonrelativistic QCD

$\Upsilon(nS)$ and $\chi_b(nP)$ (n=1,2,3) production at the LHC is studied at next-to-leading order in $\alpha_s$ in nonrelativistic QCD. Feeddown contributions from higher $\chi_b$ and $\Upsilon$ states are all considered for lower $\Upsilon$ cross sections and polarizations. The long distance matrix elements (LDMEs) are extracted from the yield data, and then used to make predictions for the $\Upsilon(nS)$ polarizations, which are found to be consistent with the measured polarization data within errors. In particular, the $\Upsilon(3S)$ polarization puzzle can be understood by a large feeddown contribution from $\chi_b(3P)$ states. Our results may provide a good description for both cross sections and polarizations of prompt $\Upsilon(nS)$ and $\chi_b(nP)$ production at the LHC.Comment: The text and abstract are substantially changed due to the change in the fitting procedure: we now extract LDMEs of $\Upsilon(nS)$ and $\chi_b{nP}$ by fitting the yield data of the LHC (including cross sections measured by ATLAS, CMS, and LHCb), and then make predictions for the polarizations of $\Upsilon(nS)