The onset of thermal convection in a rapidly rotating spherical shell is studied by linear stability analysis based on the fully compressible Navier–Stokes equations. Compressibility is quantified by the number of density scale heights $N_{\unicode[STIX]{x1D70C}}$ , which measures the intensity of density stratification of the motionless, polytropic base state. The nearly adiabatic flow with polytropic index $n=1.499<n_{a}=1.5$ is considered, where $n_{a}$ is the adiabatic polytropic index. By investigating the stability of the base state with respect to the disturbance of specified wavenumber, the instability process is found to be sensitive to the Prandtl number $Pr$ and to $N_{\unicode[STIX]{x1D70C}}$ . For large $Pr$ and small $N_{\unicode[STIX]{x1D70C}}$ , the quasi-geostrophic columnar mode loses stability first; while for relatively small $Pr$ a new quasi-geostrophic compressible mode is identified, which becomes unstable first under strong density stratification. The inertial mode can also occur first for relatively small $Pr$ and a certain intensity of density stratification in the parameter range considered. Although the Rayleigh numbers $Ra$ for the onsets of the quasi-geostrophic compressible mode and columnar mode are different by several orders of magnitude, we find that they follow very similar scaling laws with the Taylor number. The critical $Ra$ for convection onset is found to be always positive, in contrast with previous results based on the widely used anelastic model that convection can occur at negative $Ra$ . By evaluating the relative magnitude of the time derivative of density perturbation in the continuity equation, we show that the anelastic approximation in the present system cannot be applied in the small- $Ra$ and large- $N_{\unicode[STIX]{x1D70C}}$ regime.

Penetrative turbulent Rayleigh–Bénard convection which depends on the density maximum of water near $4^{\circ }\text{C}$ is studied using two-dimensional and three-dimensional direct numerical simulations. The working fluid is water near $4\,^{\circ }\text{C}$ with Prandtl number $Pr=11.57$ . The considered Rayleigh numbers $Ra$ range from $10^{7}$ to $10^{10}$ . The density inversion parameter $\unicode[STIX]{x1D703}_{m}$ varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thicknesses ( $F_{\unicode[STIX]{x1D706}}=\unicode[STIX]{x1D706}_{t}^{\unicode[STIX]{x1D703}}/\unicode[STIX]{x1D706}_{b}^{\unicode[STIX]{x1D703}}$ ) increases with increasing $\unicode[STIX]{x1D703}_{m}$ , and the relationship between $F_{\unicode[STIX]{x1D706}}$ and $\unicode[STIX]{x1D703}_{m}$ seems to be independent of $Ra$ . The centre temperature $\unicode[STIX]{x1D703}_{c}$ is enhanced compared to that of Oberbeck–Boussinesq cases, as $\unicode[STIX]{x1D703}_{c}$ is related to $F_{\unicode[STIX]{x1D706}}$ with $1/\unicode[STIX]{x1D703}_{c}=1/F_{\unicode[STIX]{x1D706}}+1$ , $\unicode[STIX]{x1D703}_{c}$ is also found to have a universal relationship with $\unicode[STIX]{x1D703}_{m}$ which is independent of $Ra$ . Both the Nusselt number $Nu$ and the Reynolds number $Re$ decrease with increasing $\unicode[STIX]{x1D703}_{m}$ , the normalized Nusselt number $Nu(\unicode[STIX]{x1D703}_{m})/Nu(0)$ and Reynolds number $Re(\unicode[STIX]{x1D703}_{m})/Re(0)$ also have universal relationships with $\unicode[STIX]{x1D703}_{m}$ which seem to be independent of both $Ra$ and the aspect ratio $\unicode[STIX]{x1D6E4}$ . The scaling exponents of $Nu\sim Ra^{\unicode[STIX]{x1D6FC}}$ and $Re\sim Ra^{\unicode[STIX]{x1D6FD}}$ are found to be insensitive to $\unicode[STIX]{x1D703}_{m}$ despite of the remarkable change of the flow organizations.

Teachers are burdened by high work pressure, suggesting the need for an effective stress coping system to support them. The present study evaluated the effectiveness of coping strategies currently utilized by teachers and explored the potential contribution of group sandplay to coping. The study was led by a group of experienced therapists and sandplay practitioners. Two hundred teachers served as participants, equally divided into two groups: An experimental sandplay group (EG) and control group. Both groups received a 3-hour tutorial on the psychological pressure at work, reactions to it, and physical/mental symptoms resulting from overwhelming pressure, and were introduced to the working principles and process of sandplay. EG participants then engaged in group sandplay for three consecutive days. The Simplified Coping Style Questionnaire was used as an objective measure of participants’ coping styles. Therapists’ and practitioners’ observations were used as subjective information, including the scenes and themes created by participants, individual performance during sandplay activities, and feedback regarding changes to stress coping strategies. We compared participants’ pre-and post-test stress coping strategies. The results revealed a significant improvement in the EG sample at the shift from passive coping (pre-test M = 1.94, 95% CI [1.83–2.05]; post-test M = 0.96, 95% CI [0.92–1.00]) to active coping (pre-test M = 1.76, 95% CI [1.69–1.83]; post-test M = 2.41, 95% CI [2.29–2.53]). Overall, our findings support the conclusion that group sandplay effectively improved Chinese teachers’ overall stress coping abilities.

There is a dearth of data on the iodine balance studies of Chinese population. In the present study, we aimed to explore the appropriate recommended nutrient intake (RNI) of iodine based on healthy Chinese women. A 4-week study was conducted in twenty-five Chinese euthyroid women. Uniform diets with different iodine contents were provided in two different periods, in which non-iodised salt was given in the first 3 weeks, followed by 1 week of iodised salt administration. The total iodine intake from diet, water and air as well as the total iodine excretion through urine, faeces and respiration were monitored and determined. The sweat iodine loss was also considered. Moreover, the regression curve model was established between the 24 h iodine intake and 24 h iodine excretion. The 24 h iodine intake in the two periods was 194·8 (sd 62·9) and 487·1 (sd 177·3) μg/d, respectively. The 24 h iodine excretion was 130·9 (sd 39·5) and 265·4 (sd 71·8) μg/d, respectively. Both 24 h iodine intake and 24 h iodine excretion of the two periods were significantly different (all P<0·05). The iodised salt contributed approximately 62·7 % of the total daily iodine intake. Moreover, 92·3 % (277/300) of samples were in positive balance, while twenty-three cases were in negative balance. Our data show that the estimated average requirement for iodine was 110·5 μg/d. Therefore, the RNI for iodine to non-pregnant, non-lactating Chinese women was 154·7 μg/d.

We present the design and experiment of a broadband optical parametric chirped-pulse amplifier (OPCPA) which provides high conversion efficiency and good beam quality at 808 nm wavelength. Using a three-dimensional spatial and temporal numerical model, several design considerations necessary to achieve high conversion efficiency, good beam quality and good output stability are discussed. To improve the conversion efficiency and broaden the amplified signal bandwidth simultaneously, the nonlinear crystal length and OPCPA parameters are analyzed and optimized with the concept of dissipating amplified idler between optical parametric amplification (OPA) of two crystals configuration. In the experiment, an amplifier consisting of two OPCPA stages of ‘L’ type configuration was demonstrated by using the optimized parameters. An amplified signal energy of 160 mJ was achieved with a total pump-to-signal efficiency of 35% (43% efficiency for the OPCPA stage 2). The output bandwidth of signal pulse reached 80 nm and the signal pulse was compressed to 24 fs. The energy stability reached 1.67% RMS at 3% pump energy variation. The optimized OPCPA amplifier operates at a repetition rate of 1 Hz and is used as a front-end injection for the main amplifier of SG-II 5PW laser facility.

A high-precision line-of-sight extraction technique is essential for autonomous optical navigation during the Mars approach phase. To support future Mars exploration missions, an optical image simulation system is a necessary ground verification facility for Mars image generation and line-of-sight extraction algorithm tests. In this paper, an optical image generation procedure is first developed according to projection relationships, reference flight profiles and camera parameters. Next, a hybrid image processing and subpixel-level line-of-sight extraction algorithm is proposed through modification of moment-based sub-pixel edge detection and improvement of direct least-square fitting approaches. Finally, an optical image simulation system is established, and the experimental results show that the proposed procedure can effectively simulate the optical image in the field-of-view of a Mars spacecraft, and the hybrid extraction algorithm can obtain high-precision Mars centroid information.

The influence of tilt on flow reversals in two-dimensional thermal convection in rectangular cells with two typical aspect ratios, $\unicode[STIX]{x1D6E4}=\text{width/height}=1$ and 2, are investigated by means of direct numerical simulations. For $\unicode[STIX]{x1D6E4}=1$ , tilt tends to suppress flow reversals. However, it is found that flow reversals characterized by two main rolls are promoted by tilt for $\unicode[STIX]{x1D6E4}=2$ , which are even observed for some cases of small Prandtl numbers ( $Pr$ ) and large tilt angles ( $\unicode[STIX]{x1D6FD}$ ). Different from level cases where the four corner rolls all have opportunities to grow and trigger a flow reversal, the reversals in an anticlockwise tilted cell with $\unicode[STIX]{x1D6E4}=2$ are always led by the growth of the bottom-right or the top-left corner roll. Tilt is favourable for the growth of the bottom-right or the top-left corner roll and thus for breaking the balance between the two main rolls and triggering a flow reversal. The mode decomposition analysis shows that the appearance of the intermediate single-roll mode is crucial for reversals, and flow reversals in a tilted cell with $\unicode[STIX]{x1D6E4}=2$ can be viewed as a mode competition process between single-roll mode and horizontally adjacent double-roll mode. They can only occur in a limited range of $\unicode[STIX]{x1D6FD}$ where the two modes have comparable strength. Furthermore, the Nusselt numbers at the hot plate $Nu_{h}$ and at the cold plate $Nu_{c}$ behave differently during a flow reversal for $\unicode[STIX]{x1D6E4}=2$ due to the preference of single corner roll growth.

We present a recent progress of the SG-II 5PW facility, which designed a multi-petawatt ultrashort pulse laser based on optical parametric chirped-pulse amplification (OPCPA). The prior two optical parametric amplifiers have been accomplished and chirped pulses with an energy of 49.7 J and a full-width-at-half-maximum (FWHM) spectrum bandwidth of 85 nm have been achieved. In the PW-scale optical parametric amplification (OPA), with the pump pulse that has an energy of 118 J from the second harmonic generation of the SG-II 7th beam, the pump-to-signal conversion efficiency is up to 41.9%, which to the best of our knowledge is the highest among all of the reported values for OPCPA systems. The compressed pulse is higher than 37 J in 21 fs (1.76 PW), and the focal spot is ${\sim}10~\unicode[STIX]{x03BC}\text{m}$ after the closed-loop corrections by the adaptive optics. Limited by the repetition of the pump laser, the SG-II 5PW facility operates one shot per hour. It has successfully been employed for high energy physics experiments.

Mastery of strengthening strategies to achieve high-capacity anodes for lithium-ion batteries can shed light on understanding the nature of diffusion-induced stress and offer an approach to use submicro-sized materials with an ultrahigh capacity for large-scale batteries. Here, we report solute strengthening in a series of silicon (Si)–germanium (Ge) alloys. When the larger solute atom (Ge) is added to the solvent atoms (Si), a compressive stress is generated in the vicinity of Ge atoms. This local stress field interacts with resident dislocations and subsequently impedes their motion to increase the yield stress in the alloys. The addition of Ge into Si substantially improves the capacity retention, particularly in Si0.50Ge0.50, aligning with literature reports that the Si/Ge alloy showed a maximum yield stress in Si0.50Ge0.50. In situ X-ray diffraction studies on the Si0.50Ge0.50 electrode show that the phase change undergoes three subsequent steps during the lithiation process: removal of surface oxide layer, formation of cluster-size Lix(Si,Ge), and formation of crystalline Li15(Si,Ge)4. Furthermore, the lithiation process starts from higher index facets, i.e., (220) and (311), then through the low index facet (111), suggesting the orientation-dependence of the lithiation process in the Si0.50Ge0.50 electrode.