Let X be a smooth, projective and geometrically connected curve defined over a finite field ${\mathbb {F}}_q$ of characteristic p different from $2$ and $S\subseteq X$ a subset of closed points. Let $\overline {X}$ and $\overline {S}$ be their base changes to an algebraic closure of ${\mathbb {F}}_q$. We study the number of $\ell $-adic local systems $(\ell \neq p)$ in rank $2$ over $\overline {X}-\overline {S}$ with all possible prescribed tame local monodromies fixed by k-fold iterated action of Frobenius endomorphism for every $k\geq 1$. In all cases, we confirm conjectures of Deligne predicting that these numbers behave as if they were obtained from a Lefschetz fixed point formula. In fact, our counting results are expressed in terms of the numbers of some Higgs bundles.

Active flow control based on reinforcement learning has received much attention in recent years. Indeed, the requirement for substantial data for trial-and-error in reinforcement learning policies has posed a significant impediment to their practical application, which also serves as a limiting factor in the training of cross-case agents. This study proposes an in-context active flow control policy learning framework grounded in reinforcement learning data. A transformer-based policy improvement operator is set up to model the process of reinforcement learning as a causal sequence and autoregressively give actions with sufficiently long context on new unseen cases. In flow separation problems, this framework demonstrates the capability to successfully learn and apply efficient flow control strategies across various airfoil configurations. Compared with general reinforcement learning, this learning mode without the need for updating the network parameter has even higher efficiency. This study presents an effective novel technique in using a single transformer model to address the flow separation active flow control problem on different airfoils. Additionally, the study provides an innovative demonstration of incorporating reinforcement-learning-based flow control with aerodynamic shape optimization, leading to collective enhancement in performance. This method efficiently lessens the training burden of the new flow control policy during shape optimization, and opens up a promising avenue for interdisciplinary intelligent co-design of future vehicles.

An additional distant wall is known to highly alter the jetting scenarios of wall-proximal bubbles. Here, we combine high-speed photography and axisymmetric volume of fluid (VoF) simulations to quantitatively describe its role in enhancing the micro-jet dynamics within the directed jet regime (Zeng et al., J. Fluid Mech., vol. 896, 2020, A28). Upon a favourable agreement on the bubble and micro-jet dynamics, both experimental and simulation results indicate that the micro-jet velocity increases dramatically as $\eta$ decreases, where $\eta =H/R_{max}$ is the distance between two walls $H$ normalized by the maximum bubble radius $R_{max}$. The mechanism is related to the collapsing flow, which is constrained by the distant wall into a reverse stagnation-point flow that builds up pressure near the bubble's top surface and accelerates it into micro-jets. We further derive an equation expressing the micro-jet velocity $U_{jet}=87.94\gamma ^{0.5}(1+(1/3)(\eta -\lambda ^{1.2})^{-2})$, where ${\gamma =d/R_{max}}$ is the stand-off distance to the proximal wall with $d$ the distance between the initial bubble centre and the wall, $\lambda =R_{y,m}/R_{max}$ with $R_{y,m}$ the distance between the top surface and the proximal wall at the bubble's maximum expansion. Viscosity has a minimal impact on the jet velocity for small $\gamma$, where the pressure buildup is predominantly influenced by geometry.

NEWMOD®, developed by R.C. Reynolds, Jr., has been an important tool for evaluating quantitatively X-ray diffraction (XRD) patterns from interstratified clay minerals for more than 20 years. However, a significant drawback to the NEWMOD® approach is that analyses are done by forward simulation, making results sensitive to user input and starting-model assumptions. In the present study, a reverse-fitting procedure was implemented in a new program, FITMOD, which automatically minimizes the differences between experimental and simulated XRD patterns. The differences are minimized by varying model parameters (such as Reichweite, crystal-size distribution, cation content, type of disorder, etc.) using the downhill simplex method. The downhill simplex method is a non-linear optimization technique for determining minima of functions. This method does not require calculation of the derivatives of the functions being minimized, an important consideration with many of the parameters in NEWMOD- type simulations. Instead, the downhill simplex method calculates pseudo-derivatives by evaluating sufficient points to define a derivative for each independent variable. The performance of FITMOD was evaluated by fitting a series of synthetic XRD patterns generated by NEWMOD+, yielding agreement factors, Rwp, of <0.3%. As long as the correct interstratified system was specified (e.g. illite-smectite), excellent fits were obtained irrespective of the starting parameters for the simulations. FITMOD was also tested using experimental XRD patterns, which gave very good fits, in agreement with previously published results. The optimization routine yields good fits for both synthetic and experimental XRD profiles in a reasonable time, with the possibility of varying all important structural parameters. FITMOD automatically provides optimum fits to experimental XRD data without operator bias, and fitting efficiency and accuracy were, therefore, significantly improved.

Diffraction effects from interstratified phyllosilicates have been studied extensively, and several computer programs such as NEWMOD© are available to facilitate interpretation of X-ray diffraction (XRD) profiles. However, accurate quantification of samples containing multiple interstratified phyllosilicate minerals is difficult due to the generally subjective nature of interpretations. More recent automated fitting interpretations require extensive computational effort, involving numerous calculations of profiles with different fitting-parameter values. Computational cost in time per calculation is the key factor influencing the overall efficiency of automated profile fitting. In general, the matrix methodology developed by Kakinoki and Komura is more efficient than the NEWMOD© architecture. A new matrix methodology was developed that reduces the number of matrix operations such as multiplication and addition, and these modifications improve calculation efficiency by up to a factor of three, with even greater improvement for small crystallite sizes (< 20 layers). A new computer program, ClayStrat, based on the modified matrix methodology, was developed to calculate one-dimensional XRD profiles from interstratified phyllosilicates along the Z direction.

NEWMOD was developed by R.C. Reynolds, Jr., for the study of two-component interstratifications of clay minerals. One-dimensional X-ray diffraction (XRD) profiles of an interstratified system of two clay minerals can be simulated using NEWMOD, given a set of parameters that describes instrumental factors, the chemical composition of the system (e.g. the concentration of Fe and interlayer cations), and structural parameters (e.g. proportions of the two components, the nature of ordering, and crystallite size distribution). NEWMOD has served as the standard method for quantitatively evaluating interstratified clay minerals for >20 y. However, the efficiency and accuracy of quantitative analysis using NEWMOD have been limited by the graphical user interface (GUI), by the lack of quantitative measures of the goodness-of-fit between the experimental and simulated XRD patterns, and by inaccuracies in some structure models used in NEWMOD. To overcome these difficulties, NEWMOD+ was coded in Visual C++ using the NEWMOD architecture, incorporating recent progress in the structures of clay minerals into a more user-friendly GUI, greatly facilitating efficient and accurate fitting. Quantitative fitting parameters (unweighted R-factor, Rp, weighted R-factor, Rwp, expected R-factor, Rexp, and chisquare, χ2) are included, along with numerous other features such as a powerful series generator, which greatly simplifies the generation of multiple simulations and makes NEWMOD+ particularly valuable for teaching.

We study systematically the cavitation-induced wall shear stress on rigid boundaries as a function of liquid viscosity $\mu$ and stand-off distance $\gamma$ using axisymmetric volume of fluid (VoF) simulations. Here, $\gamma =d/R_{max}$ is defined with the initial distance of bubble centre from the wall $d$ and the bubble equivalent radius at its maximum expansion $R_{max}$. The simulations predict accurately the overall bubble dynamics and the time-dependent liquid film thickness between the bubble and the wall prior to the collapse. The spatial and temporal wall shear stress is discussed in detail as a function of $\gamma$ and the inverse Reynolds number $1/Re$. The amplitude of the wall shear stress is investigated over a large parameter space of viscosity and stand-off distance. The inward stress is caused by the shrinking bubble and its maximum value $\tau _{mn}$ follows $\tau _{mn} Re^{0.35}=-70\gamma +110$ (kPa) for $0.5<\gamma <1.4$. The expanding bubble and jet spreading on the boundary produce an outward-directed stress. The maximum outward stress is generated shortly after impact of the jet during the early spreading. We find two scaling laws for the maximum outward stress $\tau _{mp}$ with $\tau _{mp} \sim \mu ^{0.2} h_{jet}^{-0.3} U_{jet}^{1.5}$ for $0.5\leq \gamma \leq 1.1$ and $\tau _{mp} \sim \mu ^{-0.25} h_{jet}^{-1.5} U_{jet}^{1.5}$ for $\gamma \geq 1.1$, where $U_{jet}$ is the jet impact velocity and $h_{jet}$ is the distance between lower bubble interface and wall prior to impact.

A triazine-based graphite carbon nitride (tri-C3N4) was successfully prepared using a solid and mild method, and modified through concentrated acid and the hydrothermal method. Interestingly, the modified tri-C3N4 (tri-HC3N4) showed good water stability and excellent fluorescence property. Meanwhile, tri-HC3N4 was successfully used to construct a high-sensitive and selective fluorescence sensor to Ag+. The as-prepared fluorescence sensor showed a fast response and a low detection limit as 0.4046 μM. Moreover, the possible quenching mechanisms were discussed based on the photoinduced electron transfer and the formation of new complex between tri-HC3N4 and Ag+ with the help of the related characterizations. This study does not only provide a new tri-HC3N4 for a high efficiency fluorescence sensor, but also show the potential application in biological sciences.

During the detection of industrial hazardous gases, like formaldehyde (HCHO), the selectivity is still a challenging issue. Herein, an alternative HCHO chemosensor that based on the tin oxide nanoparticles is proposed, which was obtained through a facile hydrothermal method. Gas sensing performances showed that the optimal working temperature located at only 180 °C, the response value of 79 via 50 ppm HCHO was much higher than that of 35 at 230 °C. However, the compromised test temperature was selected as 230 °C, taking into account the faster response/recovery speeds than 180 °C, named 20/23versus 53/60 s, respectively. The response (35) of the SnO2 nanoparticles-based sensor to 50 ppm of HCHO is about 400% higher than that of bulk SnO2 sensor (9), especially when the gas concentration is 1 ppm, SnO2 nanoparticles also has a higher sensitivity which may possibly result from more exposed active sites and small size effect for nanoparticles than for bulk ones. The gas sensor based on SnO2 nanoparticles can be utilized as a promising candidate for practical low-temperature detectors of HCHO due to its higher gas response, excellent response–recovery properties, and perfect selectivity.

To reduce the seed length while maintaining the advantages of the cuboid KDP-type crystal, a long-seed KDP crystal with size $471~\text{mm}\times 480~\text{mm}\times 400~\text{mm}$ is rapidly grown. With almost the same high cutting efficiency to obtain third harmonic generation oriented samples, this long-seed KDP-type crystal can be grown with a shorter seed than that of the cuboid KDP-type crystal. The full width at half maximum of the high-resolution X-ray diffraction of the (200) crystalline face is 28.8 arc seconds, indicating that the long-seed KDP crystal has good crystalline quality. In the wavelength range of 377–1022 nm, the transmittance of the long-seed KDP crystal is higher than 90%. The fluence for the 50% probability of laser-induced damage (LID) is $18.5~\text{J}/\text{cm}^{2}$ (3 ns, 355 nm). Several test points survive when the laser fluence exceeds $30~\text{J}/\text{cm}^{2}$ (3 ns, 355 nm), indicating the good LID performance of the long-seed KDP crystal. At present, the growth of a long-seed DKDP crystal is under way.

NASA's Operation IceBridge mission flew over the Ross Sea, Antarctica (20 and 27 November 2013) and collected data with Airborne Topographic Mapper (ATM) and Digital Mapping System (DMS). Using the DMS and reflectivity of ATM L1B, leads are detected to define local sea level height. The total freeboard is then obtained and converted to ice thickness. The estimated mean sea-ice thickness values are found to be in the 0.48–0.99 m range. Along the N-S track, sea ice was thinner southward rather than northward of the fluxgate, resulting in two peaks of modal thickness: 0.35 m (south) and 0.7 m (north). This supports that new ice produced in coastal polynyas is transported northward by katabatic winds off the ice-shelf. The lowest (2%) elevation method used for freeboard retrieval for ICESat is also tested for ATM data. It is found that the lowest elevation method tends to overestimate freeboard, but mean values are less affected than mode values. Using mean thickness values of ICESat and ATM along the ‘fluxgate’, separating the shelf from the deep ocean, the exported ice volume at this ‘fluxgate’ is found to be higher during the ICESat years (2003–2008) than during the IceBridge year (2013).

In inertial confinement fusion experiments that involve short-laser pulses such as fast ignition (FI), diagnosis of neutrons is usually very challenging because high-intensity γ rays generated by short-laser pulses would mask the much weaker neutron signal. In this paper, fast-response scintillators with low afterglow and gated microchannel plate photomultiplier tubes are combined to build neutron time-of-flight (nTOF) spectrometers for such experiments. Direct-drive implosion experiments of deuterium-gas-filled capsules were performed at the Shenguang-II Upgrade (SG-II-UP) laser facility to study the compressed fuel areal density (〈ρR〉) and evaluate the performance of such nTOF diagnostics. Two newly developed quenched liquid scintillator detectors and a gated ultrafast plastic scintillator detector were used to measure the secondary DT neutrons and primary DD neutrons, respectively. The secondary neutron signals were clearly discriminated from the γ rays from (n, γ) reactions, and the compressed fuel areal density obtained with the yield-ratio method agrees well with the simulations. Additionally, a small scintillator decay tail and a clear DD neutron signal were observed in an integrated FI experiment as a result of the low afterglow of the oxygen-quenched liquid scintillator.

The ZnO/g-C3N4 binary heterostructures were formed by two steps, then the firm connection between ZnO NRs and lamellar g-C3N4 was characterized through powder XRD, FESEM with EDS, TEM, XPS, and Thermogravimetric analysis. Then the gas sensing performances of ZnO/g-C3N4 nanoheterostructures were analyzed systematically by using ethanol as a molecular probe. The results revealed that the fabricated compositive sensor not only exhibited quick response/recovery characteristics in the whole operating temperature (OT) range of 200–300 °C but also got a maximum response of 14.29 toward 100 ppm of ethanol at the optimal OT of only 260 °C. Moreover, such heterostructures also demonstrated good selectivity and superb reproducibility to acetone among all the tested toxic gases, especially higher response and faster response–recovery speeds than the pristine ZnO sensor. The above ZnO/g-C3N4 heterostructures may also supply other novel applications in the aspects of lithium-ion batteries, photocatalysis, optical devices, and so on.

Envisat Advanced Synthetic Aperture Radar (ASAR) Wide Swath Mode (WSM) images are used to derive C-band HH-polarization normalized radar cross sections (NRCS). These are compared with ice-core analysis and visual ship-based observations of snow and ice properties observed according to the Antarctic Sea Ice Processes and Climate (ASPeCt) protocol during two International Polar Year summer cruises (Oden 2008 and Palmer 2009) in West Antarctica. Thick first-year (TFY) and multi-year (MY) ice were the dominant ice types. the NRCS value ranges between –16.3 ± 1.1 and –7.6 ± 1.0 dB for TFY ice, and is –12.6 ± 1.3 dB for MY ice; for TFY ice, NRCS values increase from –~15 dB to –9 dB from December/January to mid-February. In situ and ASPeCt observations are not, however, detailed enough to interpret the observed NRCS change over time. Co-located Advanced Microwave Scanning Radiometer–Earth Observing System (AMSR-E) vertically polarized 37 GHz brightness temperatures (TB37V), 7 day and 1 day averages as well as the TB37V difference between ascending and descending AMSR-E overpasses suggest the low NRCS values (–15 dB) are associated with snowmelt being still in progress, while the change towards higher NRCS values (–9 dB) is caused by commencement of melt– refreeze cycles after about mid-January.

Antarctic Sea Ice Processes and Climate (ASPeCt) ship-based ice observations, conducted during the Sea Ice Mass Balance in the Antarctic (SIMBA) and Sea Ice Physics and Ecosystem eXperiment (SIPEX) International Polar Year (IPY) cruises (September–October 2007), are used to validate remote-sensing measurements of ice extent and concentration. Observations include varied sea-ice types at and inside the ice edge of West (~90˚ W) and East (~120˚ E) Antarctica. Time series of Advanced Microwave Scanning Radiometer–Earth Observing System (AMSR-E) ice extents and US National Ice Center (NIC) ice edges were obtained for the 2007–08 periods bracketing the period these cruises were conducted. A comparison between passive microwave satellite imagery and ASPeCt observations of sea-ice concentration during two cruises was also performed. In 90˚W regions, the concentrated pack ice indicated good correlation between ship observations and passive microwave estimates of the ice concentration (R2 = 0.80). In the marginal zone of West Antarctica and over nearly the entire sea-ice zone of East Antarctica, correlation dropped to R2 < 0.60. These findings are consistent with other studies comparing passive microwave and ship observations and further verify that the East Antarctic sea-ice zone is more marginal in character. There are significant ice-edge differences between AMSR-E and NIC between late November 2007 and early March 2008 such that the AMSR-E sea-ice extent estimate is 1–2 × 106 km2 less than the NIC estimate.

We examine the role of ocean heat flux (OHF) in Antarctic sea-ice growth and melt using data from autonomous ice mass-balance buoys deployed on pack ice in the Bellingshausen Sea and on fast ice in the Amundsen Sea during the spring/summer (October-December 2007) and summer/ autumn (February-March 2009) transitions, respectively. OHFs are derived using two methods that examine changes in (1) sub-ice ocean water properties (OHF1) and (2) ice thickness (OHF2), the latter only applying to thick snow-covered ice (i.e. a near-zero temperature gradient near the ice bottom). Good agreement is found between the time-averaged estimates of OHF1 and OHF2. Average OHF measured was 8 ± 2 W m-2 under the pack ice and 17 ± 2 W m-2 under the landfast ice. Some short-term OHF values (OHF1) in both seas exceeded 55 W m-2. The spring OHF variations in the Bellingshausen Sea were periodic and controlled by semi-diurnal ice velocity fluctuations. Larger temperature fluctuations in the summer Amundsen Sea, originating from incursions of warm deep water masses, contributed to the OHF being twice as high as in the Bellingshausen Sea and also accounted for the irregular OHF variability there.

This article compares the Australian and Chinese adult guardianship systems, and considers whether there is potential for drawing on some (or many) aspects of the Australian model for the Chinese legal framework. Australia has a well-developed guardianship framework that provides mechanisms for making healthcare decisions when an adult is no longer able to do so. This framework has evolved over many years and, in some cases, individuals can decide about medical treatment in advance of the situation arising, or who should be the decision-maker if he or she later loses capacity. The current Chinese legal framework, on the other hand, is a fragmented one and comprises laws that were not designed to deal with how healthcare decisions can be made for a person without capacity. This article outlines the legal framework in both jurisdictions and considers whether, having regard to the fact that these two countries have different values and cultures, there are features of the Australian guardianship system that could inform the development of Chinese law.