Aspect ratio dependence of heat transport by turbulent Rayleigh-B\'{e}nard convection in rectangular cells

We report high-precision measurements of the Nusselt number $Nu$ as a function of the Rayleigh number $Ra$ in water-filled rectangular Rayleigh-B\'{e}nard convection cells. The horizontal length $L$ and width $W$ of the cells are 50.0 cm and 15.0 cm, respectively, and the heights $H=49.9$, 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios $(\Gamma_x\equiv L/H,\Gamma_y\equiv W/H)=(1,0.3)$, $(2,0.6)$, $(4,1.2)$, $(7.3,2.2)$, $(14.3,4.3)$, and $(20.8,6.3)$. The measurements were carried out over the Rayleigh number range $6\times10^5\lesssim Ra\lesssim10^{11}$ and the Prandtl number range $5.2\lesssim Pr\lesssim7$. Our results show that for rectangular geometry turbulent heat transport is independent of the cells' aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where $Nu$ is found to be in general a decreasing function of $\Gamma$, at least for $\Gamma=1$ and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of $Nu_{\infty}$ for plates with perfect conductivity. The local scaling exponents $\beta_l$ of $Nu_{\infty}\sim Ra^{\beta_l}$ are calculated and found to increase from 0.243 at $Ra\simeq9\times10^5$ to 0.327 at $Ra\simeq4\times10^{10}$.Comment: 15 pages, 7 figures, Accepted by Journal of Fluid Mechanic

Bearing fault diagnosis based on Shannon entropy and wavelet package decomposition

A new feature extraction method based on WPD and Entropy is proposed in this paper. Firstly, WPD is utilized to decompose the signal into different frequency bands to obtain different frequency sub-signal. Secondly, root-mean-squire (RMS) value, kurtosis (K) and peak factor (PF) parameters are extracted from each sub-signal to obtain the fault feature vector. Thirdly the Entropy of each feature vector is calculated to realize the bearing fault diagnosis. Finally, experimental results indicate that the bearing fault diagnosis method proposed in this paper is effective

BsB_s Semileptonic Decays to DsD_s and Ds∗D_s^* in Bethe-Salpeter Method

Using the relativistic Bethe-Salpeter method, the electron energy spectrum and the semileptonic decay widths of $B^0_s\to D^-_s \ell^+{\nu_\ell}$ and $B^0_s\to D_s^{*-}\ell^+{\nu_\ell}$ are calculated. We obtained large branching ratios, $Br(B_s\to D_se\nu_e)=(2.85\pm0.35)$ and $Br (B_s\to D_s^*e\nu_e)=(7.09\pm0.88)$, which can be easily detected in the future experiment.Comment: 3 pages, 3 figures

1,3-Bis(chloro­meth­yl)-2-methyl-5-nitro­benzene

The title compound, C9H9Cl2NO2, is a natural product isolated from the endophytic fungus No. B77 of the mangrove tree from the South China Sea coast. In the crystal structure, the mol­ecules lie on twofold axes and form offset stacks through face-to-face π–π inter­actions. Adjacent mol­ecules in each stack are related by a centre of inversion and have an inter­planar separation of 3.53 (1) Å, with a centroid–centroid distance of 3.76 (1) Å. Between stacks, there are C—H⋯O inter­actions to the nitro groups and Cl⋯Cl contacts of 3.462 (1) Å

3-Hydroxy­meth­yl-6,8-dimeth­oxy-2H-chromen-2-one

The asymmetric unit of the title compound, C12H12O5, contains four independent mol­ecules. In the crystal structure, inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into one-dimensional infinite chains. They are arranged in a nearly parallel fashion along the b axis and stabilized by π–π inter­actions [3.443 (2) Å]