A topological space has a domain model if it is homeomorphic to the maximal point space $\mbox{Max}(P)$ of a domain $P$. Lawson proved that every Polish space $X$ has an $\omega$-domain model $P$ and for such a model $P$, $\mbox{Max}(P)$ is a $G_{\delta }$-set of the Scott space of $P$. Martin (2003) then asked whether it is true that for every $\omega$-domain $Q$, $\mbox{Max}(Q)$ is $G_{\delta }$-set of the Scott space of $Q$. In this paper, we give a negative answer to Martin’s long-standing open problem by constructing a counterexample. The counterexample here actually shows that the answer is no even for $\omega$-algebraic domains. In addition, we also construct an $\omega$-ideal domain $\widetilde{Q}$ for the constructed $Q$ such that their maximal point spaces are homeomorphic. Therefore, $\textrm{Max}(Q)$ is a $G_\delta$-set of the Scott space of the new model $\widetilde{Q}$ .

This study investigates the spatial distribution of inertial particles in turbulent Taylor–Couette flow. Direct numerical simulations are performed using a one-way coupled Eulerian–Lagrangian approach, with a fixed inner-wall Reynolds number of 2500 for the carrier flow, while the particle Stokes number ($St$) varies from 0.034 to 1 for the dispersed phase. We first examine the issue of preferential concentration of particles near the outer-wall region. Employing two-dimensional Voronoï analysis, we observe a pronounced particle clustering with increasing $St$, particularly evident in regions of low fluid velocity. Additionally, we investigate the concentration balance equation, inspired by the work of Johnson et al. (J. Fluid Mech., vol. 883, 2020, A27), to examine the particle radial distribution. We discern the predominant sources of influence, namely biased sampling, turbophoresis and centrifugal effects. Across all cases, centrifugal force emerges as the primary driver, causing particle migration toward the outer wall. Biased sampling predominantly affects smaller inertial particles, driving them toward the inner wall due to sampling within Taylor rolls with inward radial velocity. Conversely, turbophoresis primarily impacts larger inertial particles, inducing migration towards both walls where turbulent intensity is weaker compared with the bulk. With the revealed physics, our work provides a basis for predicting and controlling particle movement and distribution in industrial applications.

This study employs direct numerical simulations to examine the effects of varying backpressure conditions on the turbulent atomisation of impinging liquid jets. Using the incompressible Navier–Stokes equations, and a volume-of-fluid approach enhanced by adaptive mesh refinement and an isoface-based interface reconstruction algorithm, we analyse spray characteristics in the environments with ambient gas densities ranging from 1 to 40 times the atmospheric pressure under five different backpressure scenarios. We investigate the behaviour of turbulent jets, incorporate realistic orifice geometries and identify significant variations in the atomisation patterns depending on backpressure. Two distinct atomisation types emerge, namely jet-sheet-ligament-droplet at lower backpressures and jet-sheet-fragment-droplet at higher ones, alongside a transition from dilute to dense spray patterns. This variation affects the droplet size distribution and spray dynamics, with increased backpressure reducing the spray's spreading angle and breakup length, while increasing the droplet size variation. Furthermore, these conditions promote distributions that induce rapid, nonlinear wavy motion in liquid sheets. Topological analysis of the atomisation field using velocity-gradient tensor invariants reveals significant variations in topology volume fractions across different regions. Downstream, the droplet Sauter mean diameter increases and then stabilises, reflecting the continuous breakup and coalescence processes, notably under higher backpressures. This research underscores the substantial impact of backpressure on impinging-jet atomisation and provides essential insights for nozzle design to optimise droplet distributions.

We study the melting process of a solid under microgravity, driven solely by lateral vibrations that are perpendicular to the applied temperature gradient due to the absence of gravity-induced convection. Using direct numerical simulations with the phase-field method, we examine two-dimensional vibration-induced melting in a square cavity over four orders of magnitude of vibrational Rayleigh numbers, $10^5\le Ra_{{vib}}\le 10^9$. Our results show that as melting progresses, the flow structure transitions from a periodic-circulation regime with diffusion-dominated heat transfer to a columnar regime with vibroconvection. The mean height of the liquid–solid interface follows a power-law dependency with time, $\bar {\xi } \sim \tilde t^{1/(2-2\alpha )}$, where $\alpha = 0$ in the periodic-circulation regime and $\alpha = 1/2$ in the columnar regime. We further observe that within the columnar regime, the morphological evolution of the liquid–solid interface is influenced by the interaction of columnar thermal plumes in the central regions and the peripheral flow near the sidewalls. Specifically, we offer a comprehensive analysis of the plume merging behaviour, which is governed by the aspect ratio ($\bar {\xi }$) of the liquid layer and the intensity of vibration, quantified by the effective vibrational Rayleigh number $Ra_{vib}^{eff}$. We identify the relationship between the number of columnar plumes $K_m$ and $Ra_{vib}^{eff}$, finding that $K_m \sim \bar {\xi }^{-1} (Ra_{vib}^{eff})^{\gamma }$ with the fitting scaling exponent $\gamma = 0.150 \pm 0.025$. We subsequently quantify the characteristics of the interface roughness amplitude evolution in microgravity vibroconvection. Our results indicate that the roughness amplitude exhibits a power-law dependence on the mean height of the liquid layer. Drawing from the Stefan boundary condition, we theoretically deduce this dependence under the assumption of a non-uniform heat flux distribution at the interface, where the theory is corroborated by our numerical simulations.

We report the unified constitutive law of vibroconvective turbulence in microgravity, i.e. $Nu \sim a^{-1} Re_{os}^\beta$ where the Nusselt number $Nu$ measures the global heat transport, $a$ is the dimensionless vibration amplitude, $Re_{os}$ is the oscillational Reynolds number and $\beta$ is the universal exponent. We find that the dynamics of boundary layers plays an essential role in vibroconvective heat transport and the $Nu$-scaling exponent $\beta$ is determined by the competition between the thermal boundary layer (TBL) and vibration-induced oscillating boundary layer (OBL). Then a physical model is proposed to explain the change of scaling exponent from $\beta =2$ in the TBL-dominant regime to $\beta = 4/3$ in the OBL-dominant regime. Our finding elucidates the emergence of universal constitutive laws in vibroconvective turbulence, and opens up a new avenue for generating a controllable effective heat transport under microgravity or even microfluidic environment in which the gravity effect is nearly absent.

Mesoporous materials have a wide range of applications in the fields of nanotechnology, biotechnology, information technology, and medicine, but historically, the resource materials used for their synthesis have been expensive. Natural silicate minerals are characterized by their abundance, low cost, and large SiO2 contents, making them an alternative silicon source for mesoporous silica. The objective of the present study was to determine the utility of natural chlorite as the source of Si for synthesizing hexagonal mesoporous silica materials (MCM-41). The natural chlorite was pretreated by acid leaching and calcination, followed by a hydrothermal reaction with cetyltrimethylammonium bromide (CTAB) as the template, and subsequent calcination to prepare MCM-41. The structures and the porosity of MCM-41 were characterized by powder X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), 29Si magic-angle spinning solid-state nuclear magnetic resonance spectroscopy (29Si MAS NMR), and N2 adsorption–desorption measurements. The mechanism of structural evolution from natural chlorite to MCM-41 was investigated using these techniques. Calcination of chlorite results in amorphization and partial structural breakdown, while subsequent acid leaching dissolves the Mg and Al in the octahedral sheets to leave the Si–O framework as a silicon source. 29Si MAS NMR results revealed that the ratio of Q4/Q3 increased from 0.91 to 1.21 after hydrothermal synthesis of MCM-41 from leached chlorite, demonstrating more polymerization of the Si–O structure in MCM-41. The final MCM-41 products were amorphous SiO2, with a large surface area of 630 m2/g, a pore volume of 0.46 mL/g, and a narrow pore-size distribution of 2.8 nm. MCM-41 showed favorable adsorption toward methylene blue (MB) with a monolayer adsorption capacity of up to 302 mg/g, indicating potential for application in adsorption.

This study investigates the effect of vibration on the flow structure transitions in thermal vibrational convection (TVC) systems, which occur when a fluid layer with a temperature gradient is excited by vibration. Direct numerical simulation (DNS) of TVC in a two-dimensional enclosed square box is performed over a range of dimensionless vibration amplitudes $0.001 \le a \le 0.3$ and angular frequencies $10^{2} \le \omega \le 10^{7}$, with a fixed Prandtl number of 4.38. The flow visualisation shows the transition behaviour of flow structure upon the varying frequency, characterising three distinct regimes, which are the periodic-circulation regime, columnar regime and columnar-broken regime. Different statistical properties are distinguished from the temperature and velocity fluctuations at the boundary layer and mid-height. Upon transition into the columnar regime, columnar thermal coherent structures are formed, in contrast to the periodic oscillating circulation. These columns are contributed by the merging of thermal plumes near the boundary layer, and the resultant thermal updrafts remain at almost fixed lateral position, leading to a decrease in fluctuations. We further find that the critical point of this transition can be described nicely by the vibrational Rayleigh number ${{Ra}}_{vib}$. As the frequency continues to increase, entering the so-called columnar-broken regime, the columnar structures are broken, and eventually the flow state becomes a large-scale circulation (LSC), characterised by a sudden increase in fluctuations. Finally, a phase diagram is constructed to summarise the flow structure transition over a wide range of vibration amplitude and frequency parameters.

This paper, based on the idea of redundancy angle discretisation, proposes an obstacle avoidance method for the fixed tip pose trajectory of a seven degrees-of-freedom (7-DOF) modular manipulator. First, for the case in which a specific redundancy angle is given, the analytical solutions of the redundant manipulator left 6-DOF subchain are found. Then, through the discretisation of the redundancy angle, the concept of the self-motion space of the tip pose is proposed and is extended to the concept of the self-motion space of the trajectory. Based on this discrete space, a path-planning algorithm is proposed to help select the appropriate redundancy angles to obtain the collision-free solution set of the fixed Cartesian trajectory. However, due to the large fluctuation of the obtained path, a path optimisation method based on the path cost is proposed to smooth the path, and the continuous and collision-free solution set of the manipulator tip’s trajectory is obtained. The method proposed in this paper provides a new thought for the problem of collision-free solution set planning for the Cartesian trajectory of a 7-DOF manipulator and it has great application potential in working environments with high accuracy requirements for the trajectory.

We report that vertical vibration with small amplitude and high frequency can tame convective heat transport in Rayleigh–Bénard convection in a turbulent regime. When vertical vibration is applied, a dynamically averaged ‘anti-gravity’ results that stabilizes the thermal boundary layer and inhibits the eruption of thermal plumes. This eventually leads to the attenuation of the intensity of large-scale mean flow and a significant suppression of turbulent heat transport. Accounting for both the thermally led buoyancy and the vibration-induced anti-gravitational effects, we propose an effective Rayleigh number that helps to extend the Grossmann–Lohse theory to thermal vibrational turbulence. The prediction of the reduction on both the Nusselt and Reynolds numbers obtained by the extended model is found to agree well with the numerical data. In addition, vibrational influences on the mean flow structure and the temporal evolution of Nusselt and Reynolds numbers are investigated. The non-uniform characteristic of vibration-induced ‘anti-gravity’ is discussed. The present findings provide a powerful basis for studying thermal vibrational turbulence and put forward a novel strategy for actively controlling thermal turbulence.

In this paper, we report that reversals of the large-scale circulation in two-dimensional Rayleigh–Bénard (RB) convection can be suppressed by imposing sinusoidally distributed heating to the bottom plate. We examine how the frequency of flow reversals depends on the dimensionless wavenumber $k$ of the spatial temperature modulation with various modulation amplitude $A$. For sufficiently large $k$, the flow reversal frequency is close to that in the standard RB convection under uniform heating. However, when $k$ decreases, the frequency of flow reversal gradually becomes lower and can even be largely reduced. Furthermore, we examine the growth of the corner roll and the global flow structure based on Fourier mode decomposition, and reveal that the size of the corner roll diminishes as the wavenumber decreases. The reason is that the regions occupied by the cold phase can absorb heat from the hot plumes and thus lower their temperature, which reduces the corner roll's kinetic energy input provided by the buoyancy force, and weakens the feeding process of the corner rolls. This results in the locking of the corner roll into a smaller region near the corner, making it harder for a reversal to occur. Using the concept of horizontal convection caused by non-uniform heating, we find a relevant parameter $k/A$ to describe briefly how the reversal frequency depends on wavenumber and modulation amplitude. The present work provides a new way to control the flow reversals in RB convection through modifying temperature boundary conditions.

“Context” has been increasingly featured and acknowledged in second language (L2) research because L2 teaching is recognised to be shaped by the environments in which it is situated. Numerous theoretical perspectives were introduced to L2 research that aim to capture the contextual forces at work in teaching and learning, including but not limited to Activity Theory, Complexity Theory, and Sociocultural Theory. Activity Theory holds that a learner's motives (human needs directed towards an object) are highly malleable, subject to the influence of such contextual variables as institutional rules, community, tools and artefacts available (see Leont'ev, 1978, 1981 who popularised Activity Theory from Sergei Rubenstein's founding and also Engeström's more current work in 1999). Complexity Theory, which has been widely adopted in both physical and social sciences, originates from physics (Martin et al., 2019). Complexity Theory was later introduced into L2 research by Diane Larsen-Freeman who posits that language learning is not only a process but a volatile and emerging system that is shaped by components of the system (e.g., learners, teachers, schools) engaging in constant and vibrant interactions (Larsen-Freeman, 2014). Sociocultural Theory highlights the sociocultural contexts where learning takes place (Lantolf, 2000; Vygotsky, 1978). Informed by a social constructivist view of learning, key concepts such as scaffolding (e.g., teachers’ support for learners) are put forward. In particular, Vygotsky argues that communication plays an indispensable role in language learning. Extrapolating Vygotsky's work to L2 research, Swain (2006) claims that languaging, dialogues among learners to discuss issues in L2 learning, is an important process of learning a L2.

We present a self-biased three-stage GaN-based monolithic microwave integrated circuit low-noise amplifier (LNA) operating between 26 and 29 GHz for 5G mobile communications. The self-biasing circuit, common-source topology with inductive source feedback, and RLC negative feedback loops between gate and drain of the third transistor were implemented to achieve low noise, good port match, high stability, high gain, and compact size. Measurement results show that the LNA has a high and flat gain of 30.5 ± 0.4 dB with noise figure (NF) of 1.65–1.8 dB across the band. The three-stage topology also achieves high linearity, providing the 1 dB compression point output power (P1dB) of 21 dBm in the band. To our knowledge, this combination of NF, gain, and linearity performance represents the state of art of self-biased LNA in this frequency band.

Physical representation of coherent motions in wall-bounded turbulence satisfying Townsend's attached-eddy hypothesis (AEH) is still an open question to be debated. Here, we apply proper orthogonal decomposition (POD) to instantaneous snapshots of $u$ component velocity fields in the streamwise–wall-normal plane of three turbulent boundary layers, which cover a frictional Reynolds number ($Re$) of $Re_\tau \approx 1000{\sim} 4000$ and were either measured by large-field-of-view planar particle image velocimetry or calculated by direct numerical simulation. The $u$ component POD modes characterized by streamwise recurring large-scale motions are decomposed into wall-attached and wall-detached parts depending on the wall-attachment condition. The former, i.e. wall-attached POD eddies, are believed to be the prime statistical representations of attached eddies. The reason lies in three aspects. Firstly, wall-attached POD eddies are geometrically self-similar and statistically independent. Secondly, the wall-normal variation of the variance of reduced-order streamwise velocity components $\tilde {u}_{AE}$, which is only contributed by wall-attached POD eddies, presents logarithmic decay in the inertial flow region. Thirdly, analysis on the scaling behaviour of the high-even-order moment, moment generating function, as well as longitudinal two-point structure function, all indicate a quasi-Gaussian behaviour of $\tilde {u}_{AE}$. None of these AEH-predicted behaviours are evident when the contribution of superstructure-like POD eddies are considered. Furthermore, wall-detached POD eddies are found to also present quasi-Gaussian behaviour. They might be treated as passive fragments of wall-attached ones.

The modulations of high/low-speed large-scale motions (H/L-SMs) on the turbulent/non-turbulent interface (TNTI) and turbulent entrainment are investigated in turbulent boundary layers via both experimental and numerical studies. The spanwise locations of large-scale motions can be locked by the spanwise heterogeneity, so the boundary layers over such a configuration are investigated first as an instructive case. In the engulfment process, it is found that irrotational ‘bubbles’ near the TNTI are more likely to originate from engulfment, while bubbles far from the TNTI could be produced by the local turbulence itself. Additionally, H-SMs are found to enhance the engulfment by the sweep flow. In the nibbling process, a competition relationship is observed: L-SMs induce stronger instantaneous ‘nibbling’ events by transporting more fluids towards the TNTI, while the H-SMs induced a more distorted TNTI. Consequently, the integral nibbling flux is greater above H-SMs. Furthermore, the explored mechanisms are verified to be insensitive to the wall shapes such as smooth and homogeneous roughness walls, which demonstrates that these modulations are universal for turbulent boundary layers. Finally, a conceptual modulation model is proposed to illustrate the entrainment process above the large-scale motions.

Celestial navigation is an important means of maritime navigation; it can automatically achieve inertially referenced positioning and orientation after a long period of development. However, the impact of different accuracy of observations and the influence of nonstationary states, such as ship speed change and steering, are not taken into account in existing algorithms. To solve this problem, this paper proposes an adaptively robust maritime celestial navigation algorithm, in which each observation value is given an equivalent weight according to the robust estimation theory, and the dynamic balance between astronomical observation and prediction values of vessel motion is adjusted by applying the adaptive factor. With this system, compared with the frequently used least square method and extended Kalman filter algorithm, not only are the real-time and high-precision navigation parameters, such as position, course, and speed for the vessel, calculated simultaneously, but also the influence of abnormal observation and vessel motion status change could be well suppressed.

The present study aimed to explore the association between dietary patterns in abdominal obesity obtained by reduced-rank regression (RRR) with visceral fat index (VFI) as a dependent variable and dyslipidemia in rural adults in Henan, China. A total of 29538 people aged 18–79 were selected from the Henan Rural Cohort Study. RRR analysis was used to identify dietary patterns; logistic regression analysis and restricted cubic spline regression models were applied to analyze the association between dietary patterns in abdominal obesity and dyslipidemia. VFI was used as a mediator to estimate the mediation effect. The dietary pattern in abdominal obesity was characterized by high carbohydrate and red meat intake and low consumption of fresh fruits, vegetables, milk, etc. After full adjustment, the highest quartile of dietary pattern scores was significantly associated with an increased risk of dyslipidemia (OR: 1·33, 95 % CI 1·23–1·44, P trend < 0·001), there was a non-linear dose–response relationship between them (P overall-association < 0·001, P non-lin-association = 0·022). The result was similar in dose-response between the dietary pattern scores and VFI. The indirect effect partially mediated by VFI was significant (OR: 1·07, 95 % CI 1·06–1·08). VIF explained approximately 53·3 % of odds of dyslipidemia related to the dietary pattern. Abdominal obesity dietary pattern scores positively affected VFI and dyslipidemia; there was a dose-response in both relationships. Dyslipidemia progression increased with higher abdominal obesity dietary pattern scores. In addition, VFI played a partial mediating role in relationship between abdominal obesity dietary pattern and dyslipidemia.

Epidemiological studies have shown that higher intake of flavonoid is inversely associated with CHD risk. However, which flavonoid subclass could reduce CHD risk has remained controversial. The present meta-analysis of prospective cohort studies aimed to quantitatively assess the associations between flavonoid subclasses and CHD risk. A systematic literature search was implemented from PubMed and Web of Science databases up to March 2021, and eligible studies were identified. Multivariate-adjust relative risks (RR) with corresponding 95 % CI were pooled by using a random-effects model. A restricted cubic spline regression model was performed for non-linear dose–response analysis. A total of 19 independent prospective cohort studies with 894 471 participants and 34 707 events were included. The results showed that dietary intakes of anthocyanins (RR = 0·90; 95 % CI: 0·83, 0·98), proanthocyanidins (RR = 0·78; 95 % CI: 0·65, 0·94), flavonols (RR = 0·88; 95 % CI: 0·79, 0·98), flavones (RR = 0·94; 95 % CI: 0·89, 0·99) and isoflavones (RR = 0·90; 95 % CI: 0·83, 0·98) were negatively associated with CHD risk. Dose–response analysis showed that increment of 50 mg/d anthocyanins, 100 mg/d proanthocyanidins, 25 mg/d flavonols, 5 mg/d flavones and 0·5 mg/d isoflavones were associated with 5 % reduction in CHD risk, respectively. Sensitivity and subgroup analyses were used to further support these associations. The present results indicate that dietary intakes of fruits and vegetables abundant five flavonoid subclasses, namely anthocyanins, proanthocyanidins, flavonols, flavones and isoflavones, are associated with a lower risk of CHD.