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.

In this paper, we introduce a new class of $T_0$ spaces called wb-sober spaces, which is strictly larger than the class of open well-filtered spaces. Unlike open well-filtered spaces, wb-sober spaces are defined more intuitively by requiring certain special subsets, termed wb-irreducible closed sets, to have singleton closures. We establish several key results about these spaces, including (1) every open well-filtered space is wb-sober, but not vice versa; (2) every strongly core-coherent wb-sober space is open well-filtered; (3) a space is core-compact iff its irreducible closed sets are wb-irreducible, providing a characterization of core-compactness; (4) every core-compact wb-sober space is sober, thereby generalizing the Jia-Jung problem. In addition, we investigate the core-coherence of the Xi-Zhao model. We prove that a $T_1$ space contains finite number of isolated points iff its Xi-Zhao model is core-coherent iff its Xi-Zhao model is strongly core-coherent. Based on this result, we then propose a general approach to constructing a non-routine open well-filtered but not well-filtered dcpo.

Rotational effects are commonly neglected when considering the dynamics of freely rising or settling isotropic particles. Here, we demonstrate that particle rotations play an important role for rising as well as for settling cylinders in situations when mass eccentricity, and thereby a new pendulum time scale, is introduced to the system. We employ two-dimensional simulations to study the motion of a single cylinder in a quiescent unbounded incompressible Newtonian fluid. This allows us to vary the Galileo number, density ratio, relative moment of inertia (MOI) and centre-of-mass (COM) offset systematically and beyond what is feasible experimentally. For certain buoyant density ratios, the particle dynamics exhibits a resonance mode, during which the coupling via the Magnus lift force causes a positive feedback between translational and rotational motions. This mode results in vastly different trajectories with significantly larger rotational and translational amplitudes and an increase of the drag coefficient easily exceeding a factor two. We propose a simple model that captures how the occurrence of the COM offset induced resonance regime varies, depending on the other input parameters, specifically the density ratio, the Galileo number and the relative MOI. Remarkably, depending on the input parameters, resonance can be observed for COM offsets as small as a few per cent of the particle diameter, showing that the particle dynamics can be highly sensitive to this parameter.

The global transition towards diets high in calories has contributed to 2.1 billion people becoming overweight, or obese, which damages male reproduction and harms offspring. Recently, more and more studies have shown that paternal exposure to stress closely affects the health of offspring in an intergenerational and transgenerational way. SET Domain Containing 2 (SETD2), a key epigenetic gene, is highly conserved among species, is a crucial methyltransferase for converting histone 3 lysine 36 dimethylation (H3K36me2) into histone 3 lysine 36 trimethylation (H3K36me3), and plays an important regulator in the response to stress. In this study, we compared patterns of SETD2 expression and the H3K36me3 pattern in pre-implantation embryos derived from normal or obese mice induced by high diet. The results showed that SETD2 mRNA was significantly higher in the high-fat diet (HFD) group than the control diet (CD) group at the 2-cell, 4-cell, 8-cell, and 16-cell stages, and at the morula and blastocyst stages. The relative levels of H3K36me3 in the HFD group at the 2-cell, 4-cell, 8-cell, 16-cell, morula stage, and blastocyst stage were significantly higher than in the CD group. These results indicated that dietary changes in parental generation (F0) male mice fed a HFD were traceable in SETD2/H3K36me3 in embryos, and that a paternal high-fat diet brings about adverse effects for offspring that might be related to SETD2/H3K36me3, which throws new light on the effect of paternal obesity on offspring from an epigenetic perspective.

Bubble–particle collisions in turbulence are central to a variety of processes such as froth flotation. Despite their importance, details of the collision process have not received much attention yet. This is compounded by the sometimes counter-intuitive behaviour of bubbles and particles in turbulence, as exemplified by the fact that they segregate in space. Although bubble–particle relative behaviour is fundamentally different from that of identical particles, the existing theoretical models are nearly all extensions of theories for particle–particle collisions in turbulence. The adequacy of these theories has yet to be assessed as appropriate data remain scarce to date. In this investigation, we study the geometric collision rate by means of direct numerical simulations of bubble–particle collisions in homogeneous isotropic turbulence using the point-particle approach over a range of the relevant parameters, including the Stokes and Reynolds numbers. We analyse the spatial distribution of bubble and particles, and quantify to what extent their segregation reduces the collision rate. This effect is countered by increased approach velocities for bubble–particle compared to monodisperse pairs, which we relate to the difference in how bubbles and particles respond to fluid accelerations. We found that in the investigated parameter range, these collision statistics are not altered significantly by the inclusion of a lift force or different drag parametrisations, or when assuming infinite particle density. Furthermore, we critically examine existing models and discuss inconsistencies therein that contribute to the discrepancy.

Immiscible and incompressible liquid–liquid flows are considered in a Taylor–Couette geometry and analysed by direct numerical simulations coupled with the volume-of-fluid method and a continuum surface force model. The system Reynolds number $Re \equiv r_i \omega _i d / \nu$ is fixed to $960$, where the single-phase flow is in the steady Taylor vortex regime, whereas the secondary-phase volume fraction $\varphi$ and the system Weber number $We \equiv \rho r_i^2 \omega _i^2 d / \sigma$ are varied to study the interactions between the interface and the Taylor vortices. We show that different Weber numbers lead to two distinctive flow regimes, namely an advection-dominated regime and an interface-dominated regime. When $We$ is high, the interface is easily deformed because of its low surface tension. The flow patterns are then similar to the single-phase flow, and the system is dominated mainly by advection (advection-dominated regime). However, when $We$ is low, the surface tension is so large that stable interfacial structures with sizes comparable to the cylinder gap can exist. The background velocity field is modulated largely by these persistent structures, thus the overall flow dynamics is governed by the interface (interface-dominated regime). The effect of the interface on the global system response is assessed by evaluating the Nusselt number $Nu_{\omega }$ based on the non-dimensional angular velocity transport. It shows non-monotonic trends as functions of the volume fraction $\varphi$ for both low and high $We$. We explain how these dependencies are closely linked to the velocity and interfacial structures.

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.

One of the most important results in domain theory is the Hofmann-Mislove Theorem, which reveals a very distinct characterization for the sober spaces via open filters. In this paper, we extend this result to the d-spaces and well-filtered spaces. We do this by introducing the notions of Hofmann-Mislove-system (HM-system for short) and $\Psi$ -well-filtered space, which provide a new unified approach to sober spaces, well-filtered spaces, and d-spaces. In addition, a characterization for $\Psi$ -well-filtered spaces is provided via $\Psi$ -sets. We also discuss the relationship between $\Psi$ -well-filtered spaces and H-sober spaces considered by Xu. We show that the category of complete $\Psi$ -well-filtered spaces is a full reflective subcategory of the category of $T_0$ spaces with continuous mappings. For each HM-system $\Psi$ that has a designated property, we show that a $T_0$ space X is $\Psi$ -well-filtered if and only if its Smyth power space $P_s(X)$ is $\Psi$ -well-filtered.

We report on the mobility and orientation of finite-size, neutrally buoyant, prolate ellipsoids (of aspect ratio $\varLambda =4$) in Taylor–Couette flow, using interface-resolved numerical simulations. The set-up consists of a particle-laden flow between a rotating inner and a stationary outer cylinder. The flow regimes explored are the well-known Taylor vortex, wavy vortex and turbulent Taylor vortex flow regimes. We simulate two particle sizes $\ell /d=0.1$ and $\ell /d=0.2$, $\ell$ denoting the particle major axis and $d$ the gap width between the cylinders. The volume fractions are $0.01\,\%$ and $0.07\,\%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes (i) to (iii) are observed in the Taylor vortex flow regime, while mode (iv) encompasses both the wavy vortex and turbulent Taylor vortex flow regimes. Mode (i) corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit {Ta}$ range, particles get trapped in the Taylor vortex cores (mode (ii)). Mode (iii) is the transition when both modes (i) and (ii) are observed. For mode (iv), particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. The focus of the present study is on mode (ii). We find the particle clustering for this mode to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell /d=0.2$ compared with $\ell /d=0.1$. Secondly, the $\textit {Ta}$ range for which clustering is observed depends on the particle size. For this mode (ii) we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell /d=0.2$ at around $\textit {Ta}=4.2\times 10^5$. This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ($\textit {Ta}=6\times 10^5$) and we explain why.

This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent wall-bounded multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh–Bénard set-up, filled with an oil–water mixture. For oleophilic walls, using only $10\,\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\,\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is only of about $20\,\%$ as compared to pure water. The physical explanation of the heat transport increment for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and carry the heat with them. In the bulk, the oil–water interface prevents the plumes from mixing with the turbulent water bulk and to diffuse their heat. To confirm this physical picture, we show that the minimum amount of oil necessary to achieve the maximum heat transport is set by the volume fraction of the thermal plumes. Our findings provide guidelines of how to optimize heat transport in wall-bounded thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one of the phases of a two-phase system has very general applicability for controlling transport properties in other turbulent wall-bounded multiphase flows.

Indoor ventilation is essential for a healthy and comfortable living environment. A key issue is to discharge anthropogenic air contamination such as CO$_2$ gas or, of potentially more direct consequence, airborne respiratory droplets. Here, by employing direct numerical simulations, we study mechanical displacement ventilation with a wide range of ventilation rates $Q$ from 0.01 to 0.1 m$^3$ s$^{-1}$ person$^{-1}$. For this ventilation scheme, a cool lower zone is established beneath a warm upper zone with interface height $h$, which depends on $Q$. For weak ventilation, we find the scaling relation $h\sim Q^{3/5}$, as suggested by Hunt & Linden (Build. Environ., vol. 34, 1999, pp. 707–720). Also, the CO$_{2}$ concentration decreases with $Q$ within this regime. However, for too strong ventilation, the interface height $h$ becomes insensitive to $Q$, and the ambient averaged CO$_2$ concentration decreases towards the ambient value. At these values of $Q$, the concentrations of pollutants are very low and so further dilution has little effect. We suggest that such scenarios arise when the vertical kinetic energy associated with the ventilation flow is significant compared with the potential energy of the thermal stratification.

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$. This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$. For the considered parameter range $1\leq {Pr} \leq 100$, $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$, we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$, the heat flux is found to scale linearly with the friction velocity $V_\ast$. Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also buoyancy can play an important role at breakup. In order to better understand this role, here we numerically study two-dimensional Rayleigh–Bénard convection for two immiscible fluid layers, in order to identify the effects of buoyancy on interface breakup. We explore the parameter space spanned by the Weber number $5\leqslant We \leqslant 5000$ (the ratio of inertia to surface tension) and the density ratio between the two fluids $0.001 \leqslant \varLambda \leqslant 1$, at fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=1$. At low $We$, the interface undulates due to plumes. When $We$ is larger than a critical value, the interface eventually breaks up. Depending on $\varLambda$, two breakup types are observed. The first type occurs at small $\varLambda \ll 1$ (e.g. air–water systems) when local filament thicknesses exceed the Hinze length scale. The second, strikingly different, type occurs at large $\varLambda$ with roughly $0.5 < \varLambda \leqslant 1$ (e.g. oil–water systems): the layers undergo a periodic overturning caused by buoyancy overwhelming surface tension. For both types, the breakup criteria can be derived from force balance arguments and show good agreement with the numerical results.

We present results on the effect of dispersed droplets in vertical natural convection (VC) using direct numerical simulations based on a two-way fully coupled Euler–Lagrange approach with a liquid phase and a dispersed droplets phase. For increasing thermal driving, characterised by the Rayleigh number, Ra, of the two analysed droplet volume fractions, $\alpha = 5\times 10^{-3}$ and $\alpha = 2\times 10^{-2}$, we find non-monotonic responses to the overall heat fluxes, characterised by the Nusselt number, Nu. The Nu number is larger when the droplets are thermally coupled to the liquid. However, Nu values remain close to the 1/4-laminar VC scaling, suggesting that the heat transport is still modulated by thermal boundary layers. Local analyses reveal the non-monotonic trends of local heat fluxes and wall-shear stresses: whilst regions of high heat fluxes are correlated to increased wall-shear stresses, the spatio-temporal distribution and magnitude of the increase are non-monotonic, implying that the overall heat transport is obscured by competing mechanisms. Most crucially, we find that the transport mechanisms inherently depend on the dominance of droplet driving to thermal driving that can quantified by (i) the bubblance parameter $b$, which measures the ratio of energy produced by the dispersed phase and the energy of the background turbulence, and (ii) ${\textit {Ra}}_d/{\textit {Ra}}$, where ${\textit {Ra}}_d$ is the droplet Rayleigh number, which we introduce in this paper. When $b \lesssim O(10^{-1})$ and ${\textit {Ra}}_d/{\textit {Ra}} \lesssim O(100)$, the Nu scaling is expected to recover to the VC scaling without droplets, and comparison with $b$ and ${\textit {Ra}}_d/{\textit {Ra}}$ from our data supports this notion.

We numerically investigate both single and multiple droplet dissolution with droplets consisting of less dense liquid dissolving in a denser host liquid. In this situation, buoyancy can lead to convection and thus plays an important role in the dissolution process. The significance of buoyancy is quantified by the Rayleigh number $Ra$, which is the buoyancy force over the viscous damping force. In this study, $Ra$ spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number $Sh$, and the flow morphologies depend on $Ra$. For single droplet dissolution, we first show the transition of the $Sh(Ra)$ scaling from a constant value to $Sh\sim Ra^{1/4}$, which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45–67). The two distinct regimes, namely the diffusively and the convectively dominated regimes, exhibit different flow morphologies: when $Ra\geqslant 10$, a buoyant plume is clearly visible, which contrasts sharply with the pure diffusion case at low $Ra$. For multiple droplet dissolution, the well-known shielding effect comes into play at low $Ra$, so that the dissolution rate is slower as compared to the single droplet case. However, at high $Ra$, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matt., vol. 12 (26), 2016, pp. 5787–5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal $Ra$ at which the enhancement is maximized, because the single plume is narrower at larger $Ra$, which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, which leads to non-trivial phenomena, contrasting the shielding effect.

Rabbits play an important role in people’s lives due to their high nutritional value and high-quality hair that can be used as raw material for textiles. Furthermore, rabbits are an important animal model for human disease, as genome-edited animals are particularly valuable for studying gene functions and pathogenesis. Somatic cell nuclear transfer (SCNT) is an important technique for producing genome-edited animals and it has great value in saving endangered species and in clone stem cell therapy. However, the low efficiency of SCNT limits its application, with the selection of suitable rabbit oocytes being crucial to its success. In the present study, we collected oocytes from ovarian follicles and stained them with 26 μM brilliant cresyl blue (BCB). We then matured the oocytes in vitro and used them for SCNT. Comparison of the BCB-positive oocytes with BCB-negative oocytes and the control group showed that the BCB-positive group had a significantly higher maturation rate (81.4% vs. 48.9% and 65.3% for the negative and control groups, respectively), cleavage rate (86.6% vs. 67.9% and 77.9%), blastocyst rate (30.5% vs. 12.8% and 19.6%), total number of blastocysts (90±7.5 vs. 65.3±6.3 and 67.5±5.7), and inner cell mass (ICM)/ trophectoderm (TE) index (42.3±4.2 vs. 30.2±2.1 and 33.9±5.1) (P<0.05). The BCB-positive group had a significantly lower apoptosis index (2.1±0.6 vs. 8.2±0.9 and 6.7±1.1 for the negative and control groups, respectively) (P<0.05). These findings demonstrate that BCB-positive oocytes have a higher maturation ability and developmental competence in vitro, indicating that BCB staining is a reliable method for selecting oocytes to enhance the efficiency of SCNT.

Previous numerical studies on homogeneous Rayleigh–Bénard convection, which is Rayleigh–Bénard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($\mathit{Nu}$) and the Reynolds number ($\mathit{Re}$) vary with the Rayleigh number ($\mathit{Ra}$) according to $\mathit{Nu}\sim \mathit{Ra}^{1/2}$ and $\mathit{Re}\sim \mathit{Ra}^{1/2}$ at small Prandtl numbers ($\mathit{Pr}$). In this study, we consider a flow that is similar to RBC but with the direction of temperature gradient perpendicular to gravity instead of parallel to it; we refer to this configuration as vertical natural convection (VC). Since the direction of the temperature gradient is different in VC, there is no exact relation for the average kinetic dissipation rate, which makes it necessary to explore alternative definitions for $\mathit{Nu}$, $\mathit{Re}$ and $\mathit{Ra}$ and to find physical arguments for closure, rather than making use of the exact relation between $\mathit{Nu}$ and the dissipation rates as in RBC. Once we remove the walls from VC to obtain the homogeneous set-up, we find that the aforementioned $1/2$-power-law scaling is present, similar to the case of homogeneous RBC. When focusing on the bulk, we find that the Nusselt and Reynolds numbers in the bulk of VC too exhibit the $1/2$-power-law scaling. These results suggest that the $1/2$-power-law scaling may even be found at lower Rayleigh numbers if the appropriate quantities in the turbulent bulk flow are employed for the definitions of $\mathit{Ra}$, $\mathit{Re}$ and $\mathit{Nu}$. From a stability perspective, at low- to moderate-$\mathit{Ra}$, we find that the time evolution of the Nusselt number for homogenous vertical natural convection is unsteady, which is consistent with the nature of the elevator modes reported in previous studies on homogeneous RBC.

In thermal convection for very large Rayleigh numbers ($Ra$), the thermal and viscous boundary layers are expected to undergo a transition from a classical state to an ultimate state. In the former state, the boundary-layer thicknesses follow a laminar-like Prandtl–Blasius–Polhausen scaling, whereas in the latter, the boundary layers are turbulent with logarithmic corrections in the sense of Prandtl and von Kármán. Here, we report evidence of this transition via changes in the boundary-layer structure of vertical natural convection (VC), which is a buoyancy-driven flow between differentially heated vertical walls. The numerical dataset spans $Ra$ values from $10^{5}$ to $10^{9}$ and a constant Prandtl number value of $0.709$. For this $Ra$ range, the VC flow has been previously found to exhibit classical state behaviour in a global sense. Yet, with increasing $Ra$, we observe that near-wall higher-shear patches occupy increasingly larger fractions of the wall areas, which suggest that the boundary layers are undergoing a transition from the classical state to the ultimate shear-dominated state. The presence of streaky structures – reminiscent of the near-wall streaks in canonical wall-bounded turbulence – further supports the notion of this transition. Within the higher-shear patches, conditionally averaged statistics yield a logarithmic variation in the local mean temperature profiles, in agreement with the log law of the wall for mean temperature, and an $Ra^{0.37}$ effective power-law scaling of the local Nusselt number. The scaling of the latter is consistent with the logarithmically corrected $1/2$ power-law scaling predicted for ultimate thermal convection for very large $Ra$. Collectively, the results from this study indicate that turbulent and laminar-like boundary layer coexist in VC at moderate to high $Ra$ and this transition from the classical state to the ultimate state manifests as increasingly larger shear-dominated patches, consistent with the findings reported for Rayleigh–Bénard convection and Taylor–Couette flows.

We study the convergence of an Ulm-like Cayley transform method for solving inverse eigenvalue problems which avoids solving approximate Jacobian equations. Under the nonsingularity assumption of the relative generalized Jacobian matrices at the solution, a convergence analysis covering both the distinct and multiple eigenvalues cases is provided and the quadratical convergence is proved. Moreover, numerical experiments are given in the last section to illustrate our results.