This study presents a novel investigation into the vortex dynamics of flow around a near-wall rectangular cylinder based on direct numerical simulation at $Re=1000$, marking the first in-depth exploration of these phenomena. By varying aspect ratios ($L/D = 5$, $10$, $15$) and gap ratios ($G/D = 0.1$, $0.3$, $0.9$), the study reveals the vortex dynamics influenced by the near-wall effect, considering the incoming laminar boundary layer flow. Both $L/D$ and $G/D$ significantly influence vortex dynamics, leading to behaviours not observed in previous bluff body flows. As $G/D$ increases, the streamwise scale of the upper leading edge (ULE) recirculation grows, delaying flow reattachment. At smaller $G/D$, lower leading edge (LLE) recirculation is suppressed, with upper Kelvin–Helmholtz vortices merging to form the ULE vortex, followed by instability, differing from conventional flow dynamics. Larger $G/D$ promotes the formation of an LLE shear layer. An intriguing finding at $L/D = 5$ and $G/D = 0.1$ is the backward flow of fluid from the downstream region to the upper side of the cylinder. At $G/D = 0.3$, double-trailing-edge vortices emerge for larger $L/D$, with two distinct flow behaviours associated with two interactions between gap flow and wall recirculation. These interactions lead to different multiple flow separations. For $G/D = 0.9$, the secondary vortex (SV) from the plate wall induces the formation of a tertiary vortex from the lower side of the cylinder. Double-SVs are observed at $L/D = 5$. Frequency locking is observed in most cases, but is suppressed at $L/D = 10$ and $G/D = 0.9$, where competing shedding modes lead to two distinct evolutions of the SV.

Toroidal bubbles (TBs) represent cases of vortex rings with a gas–liquid interface where a gas vortex ring is encased within a liquid vortex ring, and can serve as effective media for mass conveyance, process mixing, noise reduction and reaction regulation. In this study, we carry out a systematic study on the interaction between a TB and a free surface. According to the high-speed photographic images from the experiments, we identify strong and weak interactions in terms of the normalized maximum free surface deformation $h_{max}^*$. Then, we perform numerical simulations based on the volume of fluid (VOF) method in the OpenFOAM platform. Based on both the experimental and the numerical results, we conclude that the Froude number, $Fr$, determines the main characteristics during the interaction process. The TB–free surface interaction is essentially the interaction between the liquid vortex ring enveloping the TB and the free surface, supplemented by the TB's complex behaviour. Next, we establish the scaling law of $h_{max}^*$ based on the energy balance condition. Based on this, we provide the critical $Fr$ and the slenderness of the TB, $\eta$, for identifying the strong and weak interactions, and a parametric plot of the interactions in terms of $Fr$ and $\eta$.

Motivated by the work initiated by Chapman [‘Determinants of Legendre symbol matrices’, Acta Arith. 115 (2004), 231–244], we investigate some arithmetical properties of generalised Legendre matrices over finite fields. For example, letting $a_1,\ldots ,a_{(q-1)/2}$ be all the nonzero squares in the finite field $\mathbb {F}_q$ containing q elements with $2\nmid q$, we give the explicit value of the determinant $D_{(q-1)/2}=\det [(a_i+a_j)^{(q-3)/2}]_{1\le i,j\le (q-1)/2}$. In particular, if $q=p$ is a prime greater than $3$, then

$$ \begin{align*}\bigg(\frac{\det D_{(p-1)/2}}{p}\bigg)= \begin{cases} 1 & \mbox{if}\ p\equiv1\pmod4,\\ (-1)^{(h(-p)+1)/2} & \mbox{if}\ p\equiv 3\pmod4\ \text{and}\ p>3, \end{cases}\end{align*} $$

where $(\frac {\cdot }{p})$ is the Legendre symbol and $h(-p)$ is the class number of $\mathbb {Q}(\sqrt {-p})$.

We explore the transition to chaos in a prototypical hydrodynamic oscillator, namely a globally unstable low-density jet subjected to external time-periodic forcing. As the forcing strengthens at an off-resonant frequency, we find that the jet exhibits a sequence of nonlinear states: period-1 limit cycle $\rightarrow $ quasiperiodicity $\rightarrow$ intermittency $\rightarrow$ low-dimensional chaos. We show that the intermittency obeys type-II Pomeau–Manneville dynamics by analysing the first return map and the scaling properties of the quasiperiodic lifetimes between successive chaotic epochs. By providing experimental evidence of the type-II intermittency route to chaos in a globally unstable jet, this study reinforces the idea that strange attractors emerge via universal mechanisms in open self-excited flows, facilitating the development of instability control strategies based on chaos theory.

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, $f_1$ and $f_2$. On increasing the forcing amplitude, $\epsilon _f$, at a fixed forcing frequency, $f_f$, we find two different types of synchronization: (i) $f_f/f_1 = 1:1$ or $2:1$ chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to $1:1$ CDS, the system transitions from an unforced chaotic state (${\rm {CH}}_{1,2}$) to a forced chaotic state (${\rm {CH}}_{1,2,f}$), then to a two-frequency quasiperiodic state where chaos is destroyed ($\mathbb {T}^2_{2,f}$), and finally to a phase-locked period-1 state (${\rm {P1}}_f$). The route to $2:1$ CDS is similar, but the quasiperiodic state hosts a doubled torus $(2\mathbb {T}^2_{2,f})$ that transforms into a phase-locked period-2 orbit $({\rm {P2}}_f)$ when CDS occurs. En route to PSC, the system transitions to a forced chaotic state (${\rm {CH}}_{1,2,f}$) followed by a phase-locked chaotic state, where $f_1$, $f_2$ and $f_f$ still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical $\epsilon _f$ required for the onset of CDS does not vary significantly with $f_f$. We then use two unidirectionally coupled Anishchenko–Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to $1:1$ CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the $f_f/f_1$–$\epsilon _f$ plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control.

The numerical investigation focuses on the flow patterns around a rectangular cylinder with three aspect ratios ($L/D=5$, $10$, $15$) at a Reynolds number of $1000$. The study delves into the dynamics of vortices, their associated frequencies, the evolution of the boundary layer and the decay of the wake. Kelvin–Helmholtz (KH) vortices originate from the leading edge (LE) shear layer and transform into hairpin vortices. Specifically, at $L/D=5$, three KH vortices merge into a single LE vortex. However, at $L/D=10$ and $15$, two KH vortices combine to form a LE vortex, with the rapid formation of hairpin vortex packets. A fractional harmonic arises due to feedback from the split LE shear layer moving upstream, triggering interaction with the reverse flow. Trailing edge (TE) vortices shed, creating a Kármán-like street in the wake. The intensity of wake oscillation at $L/D=5$ surpasses that in the other two cases. Boundary layer transition occurs after the saturation of disturbance energy for $L/D=10$ and $15$, but not for $L/D=5$. The low-frequency disturbances are selected to generate streaks inside the boundary layer. The TE vortex shedding induces the formation of a favourable pressure gradient, accelerating the flow and fostering boundary layer relaminarization. The self-similarity of the velocity defect is observed in all three wakes, accompanied by the decay of disturbance energy. Importantly, the decrease in the shedding frequency of LE (TE) vortices significantly contributes to the overall decay of disturbance energy. This comprehensive exploration provides insights into complex flow phenomena and their underlying dynamics.

Let H be a complex separable Hilbert space with $\dim H \geq 2$. Let $\mathcal {N}$ be a nest on H such that $E_+ \neq E$ for any $E \neq H, E \in \mathcal {N}$. We prove that every 2-local isometry of $\operatorname {Alg}\mathcal {N}$ is a surjective linear isometry.

We present experimental evidence of multifractality and scale-free network topology in a noise-perturbed laminar jet operated in a globally stable regime, prior to the critical point of a supercritical Hopf bifurcation and prior to the saddle-node point of a subcritical Hopf bifurcation. For both types of bifurcation, we find that (i) the degree of multifractality peaks at intermediate noise intensities, (ii) the conditions for peak multifractality produce a complex network whose node degree distribution obeys an inverse power-law scaling with an exponent of $2 < \gamma < 3$, indicating scale-free topology and (iii) the Hurst exponent and the global clustering coefficient can serve as early warning indicators of global instability under specific operating and forcing conditions. By characterising the noise-induced dynamics of a canonical shear flow, we demonstrate that the multifractal and scale-free network dynamics commonly observed in turbulent flows can also be observed in laminar flows under certain stochastic forcing conditions.

Recently, the nature of viscoelastic drag-reducing turbulence (DRT), especially the maximum drag reduction (MDR) state, has become a focus of controversy. It has long been regarded as polymer-modulated inertial turbulence (IT), but is challenged by the newly proposed concept of elasto-inertial turbulence (EIT). This study is to repicture DRT in parallel plane channels by introducing dynamics of EIT through statistical, structural and budget analysis for a series of flow regimes from the onset of drag reduction to EIT. Some underlying mechanistic links between DRT and EIT are revealed. Energy conversion between velocity fluctuations and polymers as well as pressure redistribution effects are of particular concern, based on which a new energy self-sustaining process (SSP) of DRT is repictured. The numerical results indicate that at low Reynolds number ($Re$), weak IT flow is replaced by a laminar regime before the barrier of EIT dynamics is established with the increase of elasticity, whereas, at moderate $Re$, EIT-related SSP can get involved and survive from being relaminarized. This further explains the reason why relaminarization phenomenon is observed for low $Re$ while the flow directly enters MDR and EIT at moderate $Re$. Moreover, with the proposed energy picture, the newly discovered phenomenon that streamwise velocity fluctuations lag behind those in the wall-normal direction can be well explained. The repictured SSP certainly justifies the conjecture that IT nature is gradually replaced by that of EIT in DRT with the increase of elasticity.

Hyperinsulinaemia and insulin resistance have been proposed to be associated with mortality risk, and diet can modulate insulin response. However, whether dietary patterns with high insulinaemic potential are associated with mortality remains unknown. We prospectively examined the associations between hyperinsulinaemic diets and the risk of total and cause-specific mortality in a large nationally representative population. Dietary factors were assessed by 24-h recalls. Two empirical dietary indices for hyperinsulinaemia (EDIH) and insulin resistance (EDIR) were developed to identify food groups most predictive of biomarkers for hyperinsulinaemia (C-peptide and insulin) and insulin resistance (homoeostatic model assessment for insulin resistance), respectively. Deaths from date of the first dietary interview until 31 December 2015 were identified by the National Death Index. Multivariable hazard ratios (HR) and 95 % CI were calculated using Cox regression models. During a median follow-up of 7·8 years, 4904 deaths were documented among 40 074 participants. For EDIH, the multivariable-adjusted HR (comparing extreme quintiles) were 1·20 (95 % CI 1·09, 1·32, P-trend<0·001) for overall mortality and 1·41 (95 % CI 1·15, 1·74, P-trend = 0·002) for CVD mortality. Similar associations were observed for EDIR with HR of 1·18 (95 % CI 1·07, 1·29, P-trend < 0·001) for total and 1·35 (95 % CI 1·09, 1·67, P-trend = 0·005) for CVD mortality. After further adjustments for BMI and diabetes, these positive associations were somewhat attenuated. Our findings suggested that diets with higher insulinaemic potential are associated with increased risk of overall and CVD-specific mortality.

High-Mg andesites (HMAs) are crucial for the reconstruction of plate tectonics, continental margin formation and lithospheric evolution. In this study, we present new fossil age, whole-rock geochemical and Sr–Nd isotope data on the newly discovered Dundunshan Group HMAs in the Dundunshan area of the Beishan orogen (central-southern Central Asian Orogenic Belt). The Dundunshan HMA samples are characterized by high MgO (6.47–7.02 wt%) contents and high Mg# values (67.27–68.77), with SiO2 (58.57–62.13 wt%), Al2O3 (14.49–16.07 wt%) and CaO (5.05–6.24 wt%) resembling typical HMAs. The Dundunshan HMA samples are calc-alkaline and strongly enriched in light rare earth elements (LREEs) and large-ion lithophile elements (LILEs), with slightly negative Eu anomaly and high-field-strength element (HFSE) depletions. Their (87Sr/86Sr)i ratios (0.7041–0.7057) and ϵNd(t) (3.73–5.59) indicate that the Dundunshan HMAs were mainly formed by the interactions between subducted oceanic sediment-derived melts and mantle peridotites. Fossil evidence and published radiometric age data constrain the formation of the Dundunshan HMAs to early Late Devonian time. Sedimentological features of the Middle Devonian Sangejing Formation and regional tectonic correlation suggest that the Hongliuhe–Niujuanzi–Xichangjing Ocean in the Dundunshan area was likely closed during late Middle Devonian time, and that the Dundunshan HMAs were formed in a post-collision extensional setting.

EPA and DHA are essential for maternal and fetal health, but epidemiological data are sparse in China. We examined the trends of EPA alone and a combination of EPA plus DHA in pregnant and lactating women in three distinct geographic regions in China and explored their potential influencing factors. A total of 1015 healthy women during mid-pregnancy, late pregnancy or lactation were recruited from Weihai (coastland), Yueyang (lakeland) and Baotou (inland) cities of China between May and July of 2014. Maternal EPA and DHA concentrations (percentage of total fatty acids) in plasma and erythrocytes were measured by capillary GC. Adjusted EPA plus DHA concentrations in both plasma and erythrocytes significantly declined from mid-pregnancy (2·92 %, 6·95 %) to late pregnancy (2·20 %, 6·42 %) and lactation (2·40 %, 6·29 %) (P trend < 0·001); and both concentrations were highest in coastland, followed by lakeland, and lowest in inland (P < 0·001). Regarding EPA alone, the concentrations were higher in women during lactation or late pregnancy and in women in coastland and inland areas. Moreover, concentrations of EPA or EPA plus DHA were higher in women with older age, higher education, higher annual family income per capita and higher dietary intake of marine aquatic product and mutton. In lactating women, erythrocyte EPA concentration was higher in those having breast-feeding partially v. exclusively. In conclusion, maternal plasma and erythrocyte concentrations of EPA plus DHA or EPA alone differed with geographic regions, physiological periods and maternal characteristics, indicating a need of population-specific health strategies to improve fatty acids status in pregnant and lactating women.

Inflammation is a central mechanism in metabolic disorders associated with morbidity and mortality and dietary factors can modulate inflammation. We aimed to prospectively investigate the association between an empirically developed, food-based dietary inflammatory pattern (EDIP) score and the risk of overall and cause-specific mortality, using data from the US National Health and Nutrition Examination Survey from 1999 to 2014. EDIP score was derived by entering thirty-nine predefined commonly consumed food groups into the reduced rank regression models followed by stepwise linear regression, which was most predictive of two plasma inflammation biomarkers including C-reactive protein and leucocyte count among 25 500 US adults. This score was further validated in a testing set of 9466 adults. Deaths from baseline until 31 December 2015 were identified through record linkage to the National Death Index. During a median follow-up of 7·8 years among 40 074 participants, we documented 4904 deaths. Compared with participants in the lowest quintile of EDIP score, those in the highest quintile had a higher risk of overall death (hazard ratio (HR) = 1·19, 95 % CI 1·08, 1·32, Ptrend = 0·002), and deaths from cancer (HR = 1·41, 95 % CI 1·14, 1·74, Ptrend = 0·017) and CVD (HR = 1·22, 95 % CI 0·98, 1·53, Ptrend = 0·211). When stratified by age, the association of EDIP with overall mortality was stronger among individuals under 65 years of age (Pinteraction = 0·001). Diets with a higher inflammatory potential were associated with increased risk of overall and cancer-specific mortality. Interventions to reduce the adverse effect of pro-inflammatory diets may potentially promote health and longevity.

In this paper, the generation of relativistic electron mirrors (REMs) and the reflection of an ultra-short laser off this mirrors are discussed, applying two-dimensional particle-in-cell (2D-PIC) simulations. REMs with ultra-high acceleration and expanding velocity can be produced from a solid nanofoil illuminated normally by an ultra-intense femtosecond laser pulse with a sharp rising edge. Chirped attosecond pulse can be produced through the reflection of a counter-propagating probe laser off the accelerating REM. In the electron moving frame, the plasma frequency of the REM keeps decreasing due to its rapidly expanding. The laser frequency, on the contrary, keeps increasing due to the acceleration of REM and the relativistic Doppler shift from the lab frame to the electron moving frame. Within an ultra-short time interval, the two frequencies will be equal in the electron moving frame, which leads the resonance between laser and REM. The reflected radiation near this interval and the corresponding spectra will be amplified due to the resonance. Through adjusting the arriving time of the probe laser, certain part of the reflected field could be selectively amplified or depressed, leading to the selectively adjusting of the corresponding spectra.

Folate status for women during early pregnancy has been investigated, but data for women during mid-pregnancy, late pregnancy or lactation are sparse or lacking. Between May and July 2014, we conducted a cross-sectional study in 1211 pregnant and lactating women from three representative regions in China. Approximately 135 women were enrolled in each stratum by physiological periods (mid-pregnancy, late pregnancy or lactation) and regions (south, central or north). Plasma folate concentrations were measured by microbiological assay. The adjusted medians of folate concentration decreased from 28·8 (interquartile range (IQR) 19·9, 38·2) nmol/l in mid-pregnancy to 18·6 (IQR 13·2, 26·4) nmol/l in late pregnancy, and to 17·0 (IQR 12·3, 22·5) nmol/l in lactation (Pfor trend < 0·001). Overall, lower folate concentrations were more likely to be observed in women residing in the northern region, with younger age, higher pre-pregnancy BMI, lower education or multiparity, and in lactating women who had undergone a Caesarean delivery or who were breastfeeding exclusively. In total, 380 (31·4 %) women had a suboptimal folate status (folate concentration <13·5 nmol/l). Women in late pregnancy and lactating, residing in the northern region, having multiparity and low education level had a higher risk of suboptimal folate status, while those with older age had a lower risk. In conclusion, maternal plasma folate concentrations decreased as pregnancy progressed, and were influenced by geographic region and maternal socio-demographic characteristics. Future studies are warranted to assess the necessity of folic acid supplementation during later pregnancy and lactation especially for women at a higher risk of folate depletion.

Mutation in CFAP43 leads to severe asthenozoospermia and multiple morphological abnormalities of the sperm flagellum (MMAF) in both human and mouse. Previous studies have shown that disruption of intra-manchette transport (IMT) caused failure of flagellum assembly and sperm head shaping. In a previous study, therefore, we postulated that disruption of IMT may contribute to the failure of sperm flagellum formation and result in MMAF, however the mechanisms underlying these defects are still poorly understood. Cfap43-deficient mice were studied here to reveal the cellular mechanisms of abnormal sperm head morphology and MMAF. Depletion of Cfap43 led to abnormal spermiogenesis and caused MMAF, sperm head abnormality and oligozoospermia. Furthermore, both abnormal manchette and disorganized ectoplasmic specialization (ES) could be observed at the elongated spermatids in Cfap43-deficient mice. Therefore, our findings demonstrated that, in mice, CFAP43-mediated IMT is essential for sperm head shaping and sperm flagellum formation.

A high-carbohydrate diet could achieve a protein-sparing effect, but it may cause negative impacts on the growth condition of fish due to their poor utilisation ability of carbohydrate. How to reduce the adverse effects caused by a high-carbohydrate diet is important for the development of aquaculture. In the present study, we aimed to identify whether inulin could attenuate the metabolic syndrome caused by a high-carbohydrate diet in fish. Nile tilapia (Oreochromis niloticus) (1·19 (sd 0·01) g) were supplied with 35 % carbohydrate (CON), 45 % carbohydrate (HC) and 45 % carbohydrate + 5 g/kg inulin (HCI) diets for 10 weeks. The results showed that addition of inulin improved the survival rate when fish were challenged with Aeromonas hydrophila, indicating that inulin had an immunostimulatory effect. Compared with the HC group, the HCI group had lower lipid accumulation in liver and the gene expression analyses indicated that addition of inulin down-regulated genes related to lipogenesis and up-regulated genes relevant to β-oxidation significantly (P < 0·05). Higher liver glycogen and glucose tolerance were found in the HCI group compared with the HC group (P < 0·05). These results indicated that inulin could alleviate the metabolic syndrome induced by a high-carbohydrate diet. Furthermore, addition of inulin to a high-carbohydrate diet changed the intestinal bacterial composition and significantly increased the concentration of acetic acid and propionic acid in fish gut which have the potential to increase pathogen resistance and regulate metabolic characteristics in fish. Collectively, our results demonstrated a possible causal role for the gut microbiome in metabolic improvements induced by inulin in fish.

The extent of intertidal flats in the Yellow Sea region has declined significantly in the past few decades, resulting in severe population declines in several waterbird species. The Yellow Sea region holds the primary stopover sites for many shorebirds during their migration to and from northern breeding grounds. However, the functional roles of these sites in shorebirds’ stopover ecology remain poorly understood. Through field surveys between July and November 2015, we investigated the stopover and moult schedules of migratory shorebirds along the southern Jiangsu coast, eastern China during their southbound migration, with a focus on the ‘Critically Endangered’ Spoon-billed Sandpiper Calidris pygmaea and ‘Endangered’ Nordmann’s Greenshank Tringa guttifer. Long-term count data indicate that both species regularly occur in globally important number in southern Jiangsu coast, constituting 16.67–49.34% and 64.0–80.67% of their global population estimates respectively, and it is highly likely that most adults undergo their primary moult during this southbound migration stopover. Our results show that Spoon-billed Sandpiper and Nordmann’s Greenshank staged for an extended period of time (66 and 84 days, respectively) to complete their primary moult. On average, Spoon-billed Sandpipers and Nordmann’s Greenshanks started moulting primary feathers on 8 August ± 4.52 and 27 July ± 1.56 days respectively, and their moult durations were 72.58 ± 9.08 and 65.09 ± 2.40 days. In addition, some individuals of several other shorebird species including the ‘Endangered’ Great Knot Calidris tenuirostris, ‘Near Threatened’ Bar-tailed Godwit Limosa lapponica, ‘Near Threatened’ Eurasian Curlew Numenius arquata and Greater Sand Plover Charadrius leschenaultii also underwent primary moult. Our work highlights the importance of the southern Jiangsu region as the primary moulting ground for these species, reinforcing that conservation of shorebird habitat including both intertidal flats and supratidal roosting sites in this region is critical to safeguard the future of some highly threatened shorebird species.