Semileptonic decays of BcB_c meson to S-wave charmonium states in the perturbative QCD approach

Inspired by the recent measurement of the ratio of $B_c$ branching fractions to $J/\psi \pi^+$ and $J/\psi \mu^+\nu_{\mu}$ final states at the LHCb detector, we study the semileptonic decays of $B_c$ meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions $B_c\rightarrow P,V$, where $P$ and $V$ denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizing the light-cone wave function for $B_c$ meson. It is found that the predicted branching ratios range from $10^{-6}$ up to $10^{-2}$ and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions $\frac{\mathcal {BR}(B_c^+\rightarrow J/\Psi \pi^+)}{\mathcal {BR}(B_c^+\rightarrow J/\Psi \mu^+\nu_{\mu})}$ is in good agreement with the data. For $B_c\rightarrow V l \nu_l$ decays, the relative contributions of the longitudinal and transverse polarization are discussed in different momentum transfer squared regions. These predictions will be tested on the ongoing and forthcoming experiments.Comment: 12 pages, 3 figures, 5 table

RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned

Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure models continue to play important roles in industrial flow simulations. However, the commonly used linear eddy viscosity models are intrinsically unable to handle flows with non-equilibrium turbulence. Reynolds stress models, on the other hand, are plagued by their lack of robustness. Recent studies in plane channel flows found that even substituting Reynolds stresses with errors below 0.5% from direct numerical simulation (DNS) databases into RANS equations leads to velocities with large errors (up to 35%). While such an observation may have only marginal relevance to traditional Reynolds stress models, it is disturbing for the recently emerging data-driven models that treat the Reynolds stress as an explicit source term in the RANS equations, as it suggests that the RANS equations with such models can be ill-conditioned. So far, a rigorous analysis of the condition of such models is still lacking. As such, in this work we propose a metric based on local condition number function for a priori evaluation of the conditioning of the RANS equations. We further show that the ill-conditioning cannot be explained by the global matrix condition number of the discretized RANS equations. Comprehensive numerical tests are performed on turbulent channel flows at various Reynolds numbers and additionally on two complex flows, i.e., flow over periodic hills and flow in a square duct. Results suggest that the proposed metric can adequately explain observations in previous studies, i.e., deteriorated model conditioning with increasing Reynolds number and better conditioning of the implicit treatment of Reynolds stress compared to the explicit treatment. This metric can play critical roles in the future development of data-driven turbulence models by enforcing the conditioning as a requirement on these models.Comment: 35 pages, 18 figure

Pedestrian Attribute Recognition: A Survey

Recognizing pedestrian attributes is an important task in computer vision community due to it plays an important role in video surveillance. Many algorithms has been proposed to handle this task. The goal of this paper is to review existing works using traditional methods or based on deep learning networks. Firstly, we introduce the background of pedestrian attributes recognition (PAR, for short), including the fundamental concepts of pedestrian attributes and corresponding challenges. Secondly, we introduce existing benchmarks, including popular datasets and evaluation criterion. Thirdly, we analyse the concept of multi-task learning and multi-label learning, and also explain the relations between these two learning algorithms and pedestrian attribute recognition. We also review some popular network architectures which have widely applied in the deep learning community. Fourthly, we analyse popular solutions for this task, such as attributes group, part-based, \emph{etc}. Fifthly, we shown some applications which takes pedestrian attributes into consideration and achieve better performance. Finally, we summarized this paper and give several possible research directions for pedestrian attributes recognition. The project page of this paper can be found from the following website: \url{https://sites.google.com/view/ahu-pedestrianattributes/}.Comment: Check our project page for High Resolution version of this survey: https://sites.google.com/view/ahu-pedestrianattributes