Helicity, an invariant under ideal-fluid (Euler) evolution, has a topological interpretation in terms of writhe and twist for a closed vortex tube, but accurately quantifying twist is challenging in viscous flows. With a novel helicity decomposition, we present a framework to construct the differential twist that establishes the theoretical relation between the total twisting number and the local twist rate of each vortex surface. This framework can characterize coiling vortex lines and internal structures within a vortex – important in laminar–turbulence transition, and in vortex instability, reconnection and breakdown. As a typical example, we explore the dynamics of vortex rings with differential twist via direct numerical simulation (DNS) of the Navier–Stokes equations. Two twist waves with opposite chiralities propagate towards each other along the ring and then collide whence the local twist rate rapidly surges. Local vortex surfaces are squeezed into a disk-like dipole structure containing coiled vortex lines, leading to vortex bursting. We derive a Burgers-equation-like model to quantify this process, which predicts a bursting time that agrees well with DNS.

A target benefit plan (TBP) is a collective defined contribution (DC) plan that is growing in popularity in Canada. Similar to DC plans, TBPs have fixed contribution rates, but they also implement pooling of longevity and investment risk. In this paper, we formulate a multi-period model that incorporates two sources of risk – asset risk and labor income risk for active members. We present an optimal investment and retirement benefits schedule for TBP members with a fixed contribution rate. Using Australian data from 1965 to 2018, we evaluate the performance of the optimal TBP scheme and compare it to the optimal DC scheme. By adopting the benefit–investment strategy derived in this paper, we demonstrate the stability of benefit distribution over time for a TBP scheme in this stochastic formulation. To outperform the DC scheme’s benefit payment, careful consideration shall be given to the benefit target in the TBP scheme. A high target may not be achievable, while a low target can impede the accumulation momentum of the fund’s wealth in its early stages. Moreover, a TBP fund’s investment strategy is primarily influenced by the wealth target, with more aggressive investments in risky assets as the wealth target increases. This analysis may shed light on the possible improvements to retirement planning in Australia. Although the results are sensitive to the choice of model parameters, overall, the proposed TBP promotes system stability in various scenarios.

The predictive methods of tool wear are usually based on different algorithm predictors, different source data, and different sensing devices for remaining useful life (RUL). In general, it has challenges to model and ensure all of the cutting conditions that are suitable in the actual cutting process for sustainable manufacturing. In order to overcome the doing large amount of experimental data and predict different tool RULs, this study combines the analytical force modeling, the back-propagation neural network (BPNN) machine learning, and the current sensor which all are integrated in smart machine box (SMB) to realize the practical RUL prediction for on-line and real-time applications. The analytical model of the cutting force coefficients of shear and ploughing was established from average cutting forces, it could reduce the experimental number and predict the different cutting conditions. In general, the loading current of the cutting tool from a spindle motor is relatively easier acquired than the resultant forces. Thus, the loading currents of the spindle are used to train and predict the cutting forces using the BPNN model during intelligent manufacturing. The SMB architecture mainly performed the autonomous actions based on the edge layer, the fog layer, and the cloud layer via the TCP/IP, the MQTT protocol, and the unified communication library. Results showed that a predictive error for the ends of the tool life is about 3–10% that are based on the calculating of the cumulative current ratio.

Hand, foot and mouth disease (HFMD) is a common infection in the world, and its epidemics result in heavy disease burdens. Over the past decade, HFMD has been widespread among children in China, with Shanxi Province being a severely affected northern province. Located in the temperate monsoon climate, Shanxi has a GDP of over 2.5 trillion yuan. It is important to have a comprehensive understanding of the basic features of HFMD in those areas that have similar meteorological and economic backgrounds to northern China. We aimed to investigate epidemiological characteristics, identify spatial clusters and predict monthly incidence of HFMD. All reported HFMD cases were obtained from the Shanxi Center for Disease Control and Prevention. Overall HFMD incidence showed a significant downward trend from 2017 to 2020, increasing again in 2021. Children aged < 5 years were primarily affected, with a high incidence of HFMD in male patients (relative risk: 1.316). The distribution showed a seasonal trend, with major peaks in June and July and secondary peaks in October and November with the exception of 2020. Other enteroviruses were the predominant causative agents of HFMD in most years. Areas with large numbers of HFMD cases were primarily in central Shanxi, and spatial clusters in 2017 and 2018 showed a positive global spatial correlation. Local spatial autocorrelation analysis showed that hot spots and secondary hot spots were concentrated in Jinzhong and Yangquan in 2018. Based on monthly incidence from September 2021 to August 2022, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) of the long short-term memory (LSTM) and seasonal autoregressive integrated moving average (SARIMA) models were 386.58 vs. 838.25, 2.25 vs. 3.08, and 461.96 vs. 963.13, respectively, indicating that the predictive accuracy of LSTM was better than that of SARIMA. The LSTM model may be useful in predicting monthly incidences of HFMD, which may provide early warnings of HFMD epidemics.

This study aimed to explore the mediation effects of one-carbon metabolism (OCM) related nutrients on the association between MTHFR rs1801133 polymorphism and gestational diabetes mellitus (GDM). Folate, vitamin B12 and homocysteine (Hcy) were measured in the serum of 1254 pregnant women. Linear and logistic regressions were used to estimate the associations of OCM nutrients and MTHFR rs1801133 polymorphism with blood glucose levels and GDM risk. Mediation analysis was applied to test the mediation effects of folate, vitamin B12 and Hcy on the association of MTHFR rs1801133 polymorphism with blood glucose concentrations and GDM. Pregnant women with MTHFR rs1801133 CC genotype had higher serum folate (10·75 v. 8·90 and 9·40 ng/ml) and lower serum Hcy (4·84 v. 4·93 and 5·20 μmol/l) than those with CT and TT genotypes. Folate concentrations were positively associated with fasting plasma glucose (FPG), 1-h plasma glucose (1-h PG), 2-h plasma glucose (2-h PG) and GDM risk. Vitamin B12 levels were negatively correlated with FPG and GDM. Although no direct association was found between MTHFR rs1801133 genotypes and GDM, there were significant indirect effects of MTHFR rs1801133 CC genotype on FPG (β: 0·005; 95 % CI: 0·001, 0·013), 1-h PG (β: 0·006; 95 % CI: 0·001, 0·014), 2-h PG (β: 0·007; 95 % CI: 0·001, 0·015) and GDM (β: 0·006; 95 % CI: 0·001, 0·014) via folate. In conclusion, serum folate mediates the effect of MTHFR rs1801133 on blood glucose levels and GDM. Our findings potentially provide a feasible GDM prevention strategy via individualised folate supplementation according to the MTHFR genotypes.

The carbonate-hosted Pb–Zn deposits in the Sichuan–Yunnan–Guizhou (SYG) triangle region are important Indosinian deposits in South China. The Tianbaoshan deposit is a typical large Pb–Zn deposit in the SYG area and occurs as pipe-like type, hosted by Sinian dolostone. It contains ∼26 Mt Zn–Pb ore (7.76–10.09 % Zn, 1.28–1.50 % Pb and 93.6 g t−1 Ag) and >0.1 Mt Cu ore (2.55 % Cu). In this study, the detailed mineral textures, mineral chemical and sulphur isotopic compositions of the various sulphides have been analysed to constrain the abnormal enrichment mechanism and mineralization relationship. Four mineralization stages have been recognized: Stage 1, minor early pyrite (Py1) with relics and infill of intergranular dolomite or quartz grains; Stage 2, Cu mineralization with coarse-grained, elliptical crystal chalcopyrite (Cp1); (3) Stage 3, Zn mineralization with dark fine-grained sphalerite (Sph1) and light coarse-grained sphalerite (Sph2); and (4) Stage 4, as represented by a quartz–calcite assemblage with galena, minor pyrite (Py2) and chalcopyrite (Cp2). The petrography of the sulphide minerals (Py1, Cp1, Sph1 and Sph2) demonstrates a mutual inclusion relationship. The nature of this relationship from core to rim and their similar sulphur isotope values (5.5–8.3 ‰) indicates a single sulphur source, suggesting that the different mineralization types are the result of different stages of a continuous hydrothermal system. Sphalerite geothermometer study suggests that sphalerite in the Tianbaoshan deposit formed in a low-temperature (<200 °C) hydrothermal system. The low concentrations of Mn and In, low In/Ge ratios and high Fe/Cd ratios in the sphalerite are consistent with those of Mississippi Valley-type (MVT) deposits, but different from those of magmatism-related deposits (e.g. epithermal, skarn and VMS deposits). The positive δ34S values for Py1 (5.1–7.9 ‰), Cp1 (5.1–7.2 ‰), Sph1 (4.7–7.4 ‰), Sph2 (3.9–8.7 ‰), Py2 (4.4–9.3 ‰) and Cp2 (5.0–6.8 ‰) indicate a sulphur source from thermochemical reduction of coeval seawater sulphate. Widely developed dissolved textures (caverns and breccias) with massive sulphide infillings and deformed host rock remnants suggest that replacement of host dolostones by ore fluids was volumetrically significant and the ore formed nearly simultaneously with the cavities. The Tianbaoshan deposit is a typical MVT deposit, which resulted from mixing of a H2S-rich fluid and a metal-rich fluid, with thermochemical sulphate reduction occurring before ore precipitation rather than during ore precipitation.

Gripper is one of the most important parts of robot because of contacting with workpieces directly and has attracted lots of research interests. However, the existing grippers are either simple in function or complex in structure. In this paper, we will propose a one-DOF gripper based on a compliant mechanism with four identical twofold-symmetric Bricard linkages. A mobile network with four identical twofold-symmetric Bricard linkages with particular design parameters is constructed at first. Kinematics, such as mobility, singularity, and folding performance, is then analyzed to show the potential of realizing the function of grasping. The result is demonstrated with a physical prototype. To simplify the fabricating process, a compliant mechanism of the network is designed and fabricated with a single polypropylene board, and the grasping function is realized by a cable-driven scheme. Some grasping experiments are carried out on different types of objects which shows that the proposed and fabricated four-figure gripper is simple in structure and has a great grasping function. The work provides a new idea for the design of grippers with low cost, simple structure, and rich functions.

In this study, a toroidal quartz ( $20\overline{2}3$ ) crystal is designed for monochromatic X-ray imaging at 72.3°. The designed crystal produces excellent images of a laser-produced plasma emitting He-like Ti X-rays at 4.75 keV. Based on the simulations, the imaging resolutions of the spherical and toroidal crystals in the sagittal direction are found to be 15 and 5 μm, respectively. Moreover, the simulation results show that a higher resolution image of the source can be obtained by using a toroidal crystal. An X-ray backlight imaging experiment is conducted using 4.75 keV He-like Ti X-rays, a 3 × 3 metal grid, an imaging plate and a toroidal quartz crystal with a lattice constant of 2d = 0.2749 nm. The meridional and sagittal radii of the toroidal α-quartz crystal are 295.6 and 268.5 mm, respectively. A highly resolved image of the microgrid, with a spatial resolution of 10 μm, is obtained in the experiment. By using similar toroidal crystal designs, the application of a spatially resolved spectrometer with high-resolution X-ray imaging ability is capable of providing imaging data with the same magnification ratio in the sagittal and meridional planes.

Determining an effective approach to replacing chemical fertilizer with organic fertilizer is a difficult challenge for the Chinese government. This paper constructs a dynamic analysis framework with broader application than previous statistical and case studies by theoretically deriving the impact of farmers' participation in contract farming on their organic fertilizer application behavior. The framework analyzes farmers' intertemporal organic fertilizer application behavior under the two scenarios of participation and nonparticipation in contract farming. Participation in contract farming positively impacts organic fertilizer application behavior in both the short and long terms. Survey data from 473 vegetable farmers in Shandong province of China were used to conduct an empirical analysis, and the endogenous switching probit model was used to solve the endogeneity problem of farmers' participation in contract farming. The empirical analysis supports the above results: farmers' participation in contract farming increases their probability of applying organic fertilizer by 50.7%. Robustness tests conducted using the recursive bivariate probit model and replacing the dependent variable (the intensity with which farmers replace chemical fertilizer with organic fertilizer) confirm the research results. Further heterogeneity analysis shows that farmers' participation in contract farming has a more obvious promoting effect on organic fertilizer application behavior in the older group, the group with an education level of primary school or below and the small-scale farming group. Therefore, the government should promote participation in contract farming, especially among elderly, low-education and small-scale farmers, to improve the adoption level of organic fertilizer in China.

The dynamics of two slender Hopf-linked vortex rings at vortex Reynolds numbers ($Re \equiv \varGamma /\nu, \mathrm {circulation/viscosity}$) $2000$, $3000$ and $4000$ is studied using direct numerical simulations of the incompressible Navier–Stokes equations. Under self-induction, the initially perpendicularly placed vortex rings approach each other and reconnect to form two separate vortex rings. The leading ring is closely cuddled and further undergoes secondary reconnection to form two even smaller rings. At high $Re$, the leading ring and the subsequent smaller rings are unstable and break up into turbulent clouds consisting of numerous even smaller-scale structures. Although the global helicity $H$ remains constant before reconnection, it increases and then rapidly decays during reconnection – both the growth and decay rates increase with $Re$. In the two higher $Re$ (i.e. 3000 and 4000) cases, $H$ further rises after the first reconnection and reaches a quasi-plateau with the asymptotic value continuously increasing with $Re$ – suggesting that $H$ for viscous flows is not conserved at very high $Re$. Further flow analysis demonstrates that significant numbers of positive and negative helical structures are simultaneously generated before and during reconnection, and their different decay rates is the main reason for the complex evolution of $H$. By examining the topological aspects of the helicity dynamics, we find that, different from $H$, the sum of link and writhe ($L_k+W_r$) continuously drop during reconnection. Our results also clearly demonstrate that the twist, which increases with $Re$, plays a significant role in the helicity dynamics, particularly at high $Re$.

Topological transition and helicity conversion of vortex torus knots and links are studied using direct numerical simulations of the incompressible Navier–Stokes equations. We find three topological transitional routes (viz. merging, reconnection and transition to turbulence) in the evolution of vortex knots and links over a range of torus aspect ratios and winding numbers. The topological transition depends not only on the initial topology but also on the initial geometry of knots/links. For small torus aspect ratios, the initially knotted or linked vortex tube rapidly merges into a vortex ring with a complete helicity conversion from the writhe and link components to the twist. For large torus aspect ratios, the vortex knot or link is untied into upper and lower coiled loops via the first vortex reconnection, with a helicity fluctuation including loss of writhe and link, and generation of twist. Then, the relatively unstable lower loop can undergo a secondary reconnection to split into multiple small vortices with a similar helicity fluctuation. Surprisingly, for moderate torus aspect ratios, the incomplete reconnection of tangled vortex loops together with strong vortex interactions triggers transition to turbulence, in which the topological helicity decomposition fails due to the breakdown of vortex core lines.

The subduction model of the Neo-Tethys during the Early Cretaceous has always been a controversial topic, and the scarcity of Early Cretaceous magmatic rocks in the southern part of the Gangdese batholith is the main cause of this debate. To address this issue, this article presents new zircon U–Pb chronology, zircon Hf isotope, whole-rock geochemistry and Sr–Nd isotope data for the Early Cretaceous quartz diorite dykes with adakite affinity in Liuqiong, Gongga. Zircon U–Pb dating of three samples yielded ages of c. 141–137 Ma, indicating that the Liuqiong quartz diorite was emplaced in the Early Cretaceous. The whole-rock geochemical analysis shows that the Liuqiong quartz diorite is enriched in large-ion lithophile elements (LILEs) and light rare-earth elements (LREEs) and is depleted in high-field-strength elements (HFSEs), which are related to slab subduction. Additionally, the Liuqiong quartz diorite has high SiO2, Al2O3 and Sr contents, high Sr/Y ratios and low heavy rare-earth element (HREE) and Y contents, which are compatible with typical adakite signatures. The initial 87Sr/86Sr values of the Liuqiong adakite range from 0.705617 to 0.705853, and the whole-rock ϵNd(t) values vary between +5.78 and +6.24. The zircon ϵHf(t) values vary from +11.5 to +16.4. Our results show that the Liuqiong adakite magma was derived from partial melting of the Neo-Tethyan oceanic plate (mid-ocean ridge basalt (MORB) + sediment + fluid), with some degree of subsequent peridotite interaction within the overlying mantle wedge. Combining regional data, we favour the interpretation that the Neo-Tethyan oceanic crust was subducted at a low angle beneath the Gangdese during the Early Cretaceous.

Pneumatic muscle actuator (PMA) similar to biological muscle is a new type of pneumatic actuator. The flexible manipulator based on PMAs was constructed to simulate the actual movement of the human upper arm. Considering the model errors and external disturbances, the fuzzing sliding mode control based on the saturation function was proposed. Compared with other fuzzy control methods, fuzzy control and saturation function are used to adjust the robust terms to improve the tracking accuracy and reduce the high-frequency chattering.

Embryo quality determines the success of in vitro fertilization and embryo transfer (IVF-ET) treatment. Biomarkers for the evaluation of embryo quality have some limitations. Apoptosis in cumulus cells (CCs) is important for ovarian function. PTEN (phosphatase and tensin homolog) is a well known tumour suppressor gene that functions as a mediator of apoptosis and is crucial for mammalian reproduction. In the present study, we analyzed the expression level of PTEN in human CCs and aimed to investigate its association with embryo developmental competence in IVF treatment cycles. The PTEN mRNA level in CCs was measured using real-time fluorescence quantitative PCR. The association of the differential expression of PTEN with embryo quality was analyzed. Our data showed that PTEN mRNA levels were significantly decreased in CCs surrounding mature oocytes compared with immature oocytes. Similar changes were found in the analysis of fertilization and blastocyst formation. The speculation that the measurement of PTEN mRNA levels in human CCs would provide a useful tool for selecting oocytes with greater chances to implant into the uterus needs to be further verified through single-embryo transfer in the future. The proapoptotic mechanism of PTEN in human reproduction needs to be further studied.