In gas evolving electrolysis, bubbles grow at electrodes due to a diffusive influx from oversaturation generated locally in the electrolyte by the electrode reaction. When considering electrodes of micrometre size resembling catalytic islands, direct numerical simulations show that bubbles may approach dynamic equilibrium states at which they neither grow nor shrink. These are found in undersaturated and saturated bulk electrolytes during both pinning and expanding wetting regimes of the bubbles. The equilibrium is based on the balance of local influx near the bubble foot and global outflux. To identify the parameter regions of bubble growth, dissolution and dynamic equilibrium by analytical means, we extend the solution of Zhang & Lohse (2023 J. Fluid Mech. vol. 975, R3) by taking into account modified gas fluxes across the bubble interface, which result from a non-uniform distribution of dissolved gas. The Damköhler numbers at equilibrium are found to range from small to intermediate values. Unlike pinned nanobubbles studied earlier, for micrometre-sized bubbles the Laplace pressure plays only a minor role. With respect to the stability of the dynamic equilibrium states, we extend the methodology of Lohse & Zhang (2015a Phys. Rev. E vol. 91, 031003(R)) by additionally taking into account the electrode reaction. Under contact line pinning, the equilibrium states are found to be stable for flat nanobubbles and for microbubbles in general. For unpinned bubbles, the equilibrium states are always stable. Finally, we draw conclusions on how to possibly enhance the efficiency of electrolysis.

Emission line galaxies (ELGs) are crucial for cosmological studies, particularly in understanding the large-scale structure of the Universe and the role of dark energy. ELGs form an essential component of the target catalogue for the Dark Energy Spectroscopic Instrument (DESI), a major astronomical survey. However, the accurate selection of ELGs for such surveys is challenging due to the inherent uncertainties in determining their redshifts with photometric data. In order to improve the accuracy of photometric redshift estimation for ELGs, we propose a novel approach CNN–MLP that combines convolutional neural networks (CNNs) with multilayer perceptrons (MLPs). This approach integrates both images and photometric data derived from the DESI Legacy Imaging Surveys Data Release 10. By leveraging the complementary strengths of CNNs (for image data processing) and MLPs (for photometric feature integration), the CNN–MLP model achieves a $\sigma_{\mathrm{NMAD}}$ (normalised median absolute deviation) of 0.0140 and an outlier fraction of 2.57%. Compared to other models, CNN–MLP demonstrates a significant improvement in the accuracy of ELG photometric redshift estimation, which directly benefits the target selection process for DESI. In addition, we explore the photometric redshifts of different galaxy types (Starforming, Starburst, AGN, and Broadline). Furthermore, this approach will contribute to more reliable photometric redshift estimation in ongoing and future large-scale sky surveys (e.g. LSST, CSST, and Euclid), enhancing the overall efficiency of cosmological research and galaxy surveys.

In gas evolving electrolysis, bubbles grow at electrodes due to a diffusive influx from oversaturation generated locally in the electrolyte by the electrode reaction. When considering electrodes of micrometre size resembling catalytic islands, direct numerical simulations show that bubbles may approach dynamic equilibrium states at which they neither grow nor shrink. These are found in under- and saturated bulk electrolytes during both pinning and expanding wetting regimes of the bubbles. The equilibrium is based on the balance of local influx near the bubble foot and global outflux. To identify the parameter regions of bubble growth, dissolution and dynamic equilibrium by analytical means, we extend the solution of Zhang & Lohse (2023) J. Fluid Mech. 975, R3, by taking into account modified gas fluxes across the bubble interface, that result from a non-uniform distribution of dissolved gas. The Damköhler numbers at equilibrium are found to range from small to intermediate values. Unlike pinned nano-bubbles studied earlier, for micrometre-sized bubbles the Laplace pressure plays only a minor role. With respect to the stability of the dynamic equilibrium states, we extend the methodology of Lohse & Zhang (2015a) Phys. Rev. E 91 (3), 031003(R), by additionally taking into account the electrode reaction. Under contact line pinning, the equilibrium states are found to be stable for flat nano-bubbles and for micro-bubbles in general. For unpinned bubbles, the equilibrium states are always stable. Finally, we draw conclusions on how to possibly enhance the efficiency of electrolysis.

Turbulent emulsions are ubiquitous in chemical engineering, food processing, pharmaceuticals and other fields. However, our experimental understanding of this area remains limited due to the multiscale nature of turbulent flow and the presence of extensive interfaces, which pose significant challenges to optical measurements. In this study, we address these challenges by precisely matching the refractive indices of the continuous and dispersed phases, enabling us to measure local velocity information at high volume fractions. The emulsion is generated in a turbulent Taylor–Couette flow, with velocity measured at two radial locations: near the inner cylinder (boundary layer) and in the middle gap (bulk region). Near the inner cylinder, the presence of droplets suppresses the emission of angular velocity plumes, which reduces the mean azimuthal velocity and its root mean squared fluctuation. The former effect leads to a higher angular velocity gradient in the boundary layer, resulting in greater global drag on the system. In the bulk region, although droplets suppress turbulence fluctuations, they enhance the cross-correlation between azimuthal and radial velocities, leaving the angular velocity flux contributed by the turbulent flow nearly unchanged. In both locations, droplets suppress turbulence at scales larger than the average droplet diameter and increase the intermittency of velocity increments. However, the effects of the droplets are more pronounced near the inner cylinder than in the bulk, likely because droplets fragment in the boundary layer but are less prone to break up in the bulk. Our study provides experimental insights into how dispersed droplets modulate global drag, coherent structures and the multiscale characteristics of turbulent flow.

This paper investigates the behaviour of turbulence production in adverse pressure gradient (APG) turbulent boundary layers (TBLs), including the range of pressure gradients from zero-pressure-gradient (ZPG) to separation, moderate and high Reynolds numbers, and equilibrium and non-equilibrium flows. The main focus is on predicting the values and positions of turbulence production peaks. Based on the unique ability of turbulence production to describe energy exchange, the idea that the ratios of the mean flow length scales to the turbulence length scales are locally smallest near peaks is proposed. Thereby, the ratios of length scales are defined for the inner and outer regions, respectively, as well as the ratios of time scales for further consideration of local information. The ratios in the inner region are found to reach the same constant value in different APG TBLs. Like turbulence production in the ZPG TBL, turbulence production in APG TBLs is shown to have a certain invariance of the inner peak. The value and position of the inner peak can also be predicted quantitatively. In contrast, the ratios in the outer region cannot be determined with unique coefficients, which accounts for the different self-similarity properties of the inner and outer regions. The outer time scale ratios establish a link between mean flow and turbulence, thus participating in the discussion on half-power laws. The present results support the existence of a half-power-law region that is not immediately adjacent to the overlapping region.

When a droplet impacts onto a superheated liquid pool, vapour generation and drainage within the gas cushion play a crucial role in postponing or even preventing contact between the droplet and the pool surface. Through direct numerical simulations, we closely examine the transient dynamics of vapour flow confined within the thin film, with a particular focus on the minimum thickness of this film under a range of impact conditions. Our numerical findings manifest the significant influence of evaporation on the vertical motion of the liquid–vapour interface, revealing how the minimum film thickness evolves in response to variations in impact velocity and degree of superheat. In our numerical simulations, we have identified two distinct evolution laws for the minimum film thickness, corresponding to moderate and high superheat regimes, respectively. These regimes are differentiated by the dominance of evaporation effects within the vapour film during the early falling stage. Subsequently, we establish scaling relations to characterize these regimes by carefully balancing inertial, pressure and evaporation effects within the thin vapour film. Furthermore, we observe that the vapour pressure eventually reaches equilibrium with the rapid increase in capillary pressure at the spreading front, thereby controlling the minimum thickness of the vapour layer in both moderate and high superheat regimes. We derive self-similar solutions based on this equilibrium, and the predicted minimum film thickness aligns remarkably well with our numerical results. This provides compelling evidence that evaporation alone is insufficient to prevent droplet–pool coalescence.

We present an experimental study on the drag reduction by polymers in Taylor–Couette turbulence at Reynolds numbers ($Re$) ranging from $4\times 10^3$ to $2.5\times 10^4$. In this $Re$ regime, the Taylor vortex is present and accounts for more than 50 % of the total angular velocity flux. Polyacrylamide polymers with two different average molecular weights are used. It is found that the drag reduction rate increases with polymer concentration and approaches the maximum drag reduction (MDR) limit. At MDR, the friction factor follows the $-0.58$ scaling, i.e. $C_f \sim Re^{-0.58}$, similar to channel/pipe flows. However, the drag reduction rate is about $20\,\%$ at MDR, which is much lower than that in channel/pipe flows at comparable $Re$. We also find that the Reynolds shear stress does not vanish and the slope of the mean azimuthal velocity profile in the logarithmic layer remains unchanged at MDR. These behaviours are reminiscent of the low drag reduction regime reported in channel flow (Warholic et al., Exp. Fluids, vol. 27, no. 5, 1999, pp. 461–472). We reveal that the lower drag reduction rate originates from the fact that polymers strongly suppress the turbulent flow while only slightly weaken the mean Taylor vortex. We further show that polymers steady the velocity boundary layer and suppress the small-scale Görtler vortices in the near-wall region. The former effect reduces the emission rate of both intense fast and slow plumes detached from the boundary layer, resulting in less flux transport from the inner cylinder to the outer one and reduces energy input into the bulk turbulent flow. Our results suggest that in turbulent flows, where secondary flow structures are statistically persistent and dominate the global transport properties of the system, the drag reduction efficiency of polymer additives is significantly diminished.

The presence of dispersed-phase droplets can result in a notable increase in a system's drag. However, our understanding of the mechanism underlying this phenomenon remains limited. In this study, we use three-dimensional direct numerical simulations with a modified multi-marker volume-of-fluid method to investigate liquid–liquid two-phase turbulence in a Taylor–Couette geometry. The dispersed phase has the same density and viscosity as the continuous phase. The Reynolds number $Re\equiv r_i\omega _i d/\nu$ is fixed at 5200, the volume fraction of the dispersed phase is up to $40\,\%$, and the Weber number $We\equiv \rho u^2_\tau d/\sigma$ is approximately 8. It is found that the increase in the system's drag originates from the contribution of interfacial tension. Specifically, droplets experience significant deformation and stretching in the streamwise direction due to shear near the inner cylinder. Consequently, the rear end of the droplets lags behind the fore head. This causes opposing interfacial tension effects on the fore head and rear end of the droplets. For the fore head of the droplets, the effect of interfacial tension appears to act against the flow direction. For the rear end, the effect appears to act in the flow direction. The increase in the system's drag is attributed primarily to the effect of interfacial tension on the fore head of the droplets which leads to the hindering effect of the droplets on the surrounding continuous phase. This hindering effect disrupts the formation of high-speed streaks, favouring the formation of low-speed ones, which are generally associated with higher viscous stress and drag of the system. This study provides new insights into the mechanism of drag enhancement reported in our previous experiments.

We present a practical verification method for safety analysis of the autonomous driving system (ADS). The main idea is to build a surrogate model that quantitatively depicts the behavior of an ADS in the specified traffic scenario. The safety properties proved in the resulting surrogate model apply to the original ADS with a probabilistic guarantee. Given the complexity of a traffic scenario in autonomous driving, our approach further partitions the parameter space of a traffic scenario for the ADS into safe sub-spaces with varying levels of guarantees and unsafe sub-spaces with confirmed counter-examples. Innovatively, the partitioning is based on a branching algorithm that features explainable AI methods. We demonstrate the utility of the proposed approach by evaluating safety properties on the state-of-the-art ADS Interfuser, with a variety of simulated traffic scenarios, and we show that our approach and existing ADS testing work complement each other. We certify five safe scenarios from the verification results and find out three sneaky behavior discrepancies in Interfuser which can hardly be detected by safety testing approaches.

An ultra-wideband current-reused low-noise amplifier (LNA) monolithic microwave integrated circuit design is presented in this letter. Negative feedback networks are employed at both stages of the proposed LNA to expand bandwidth. Furthermore, source adaptive bias networks is designed in the first stage and combined with a current-reused construction to acquire a compact chip size and maintain low power consumption. Then, the validation of design theory is implemented by employing a 0.15-µm gallium arsenide pseudomorphic high-electron-mobility transistor process. The measured results show that the proposed LNA achieves a small signal gain of 15.5–17.8 dB, a noise figure of 3–3.65 dB, and an output 1 dB compression point (OP1 dB) of 14.5–15.5 dBm from the target bandwidth of 2–18 GHz. In addition, the fabricated LNA consumes 220 mW from a 5 V supply and occupies a chip area of 1.2 × 1.5 mm2.

We investigate the coupling effects of the two-phase interface, viscosity ratio and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor–Couette turbulence at a system Reynolds number of $6\times 10^3$ and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, whereas light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. In addition, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the physics of turbulence modulation by the dispersed phase in two-phase turbulence systems.

We prove interior boundedness and Hölder continuity for the weak solutions of nonlocal double phase equations in the Heisenberg group $\mathbb{H}^n$. This solves a problem raised by Palatucci and Piccinini et al. in 2022 and 2023 for the nonlinear integro-differential problems in Heisenberg setting. Our proof of the a priori estimates bases on De Giorgi–Nash–Moser theory, where the important ingredients are Caccioppoli-type inequality and Logarithmic estimate. To achieve this goal, we establish a new and crucial Sobolev–Poincaré type inequality in local domain, which may be of independent interest and potential applications.

We report on an experimental study of turbulent Rayleigh–Bénard convection with asymmetric top and bottom plates. The plates are covered with pyramid-shaped roughness elements whose aspect ratios are $\lambda =1$ or $\lambda =4$. In the low-Rayleigh-number regime ($Ra<1.9\times 10^9$), the heat transport efficiencies in the asymmetric cells, characterized by the Nusselt number, are smaller than those measured in a symmetric $\lambda = 1$ cell and are greater than those for a symmetric $\lambda = 4$ cell, whereas in the high-Rayleigh-number regime ($Ra>1.9\times 10^9$), the Nusselt numbers of the asymmetric cells are, in turn, greater than those for the symmetric cell with $\lambda = 1$ and smaller than those for the symmetric cell with $\lambda = 4$. In addition, the heat transports of individual plates are studied based on the temperature drops across both halves of the cell. In the low-$Ra$ regime, the $\lambda =1$ plate shows higher heat transfer than the $\lambda =4$ plate, while for the high-$Ra$ regime, the $\lambda =4$ plate shows a higher heat transport ability. In both regimes, the individual Nusselt number of the plate with lower heat transfer is insensitive to the topology of the other plate. Besides, it is found that the symmetry of the centre temperature distribution is robust to the symmetry breaking of boundary topographies. For the $Ra$ range explored, a weak temperature inversion is observed in the bulk of asymmetric rough cells. Finally, we remark that the temperature fluctuation at the cell centre and the Reynolds number associated with the large-scale circulation show universal power laws in terms of the flux Rayleigh number as $\sigma _{T_{c}}\sim Ra_F^{0.68}$ and $Re_{LSC}\sim Ra_F^{0.36}$, respectively.

We present a systematic study on the effects of small aspect ratios $\varGamma$ on heat transport in liquid metal convection with a Prandtl number of $Pr=0.029$. The study covers $1/20\le \varGamma \le 1$ experimentally and $1/50\le \varGamma \le 1$ numerically, and a Rayleigh number $Ra$ range of $4\times 10^3 \le Ra \le 7\times 10^{9}$. It is found experimentally that the local effective heat transport scaling exponent $\gamma$ changes with both $Ra$ and $\varGamma$, attaining a $\varGamma$-dependent maximum value before transition-to-turbulence and approaches $\gamma =0.25$ in the turbulence state as $Ra$ increases. Just above the onset of convection, Shishkina (Phys. Rev. Fluids, vol 6, 2021, 090502) derived a length scale $\ell =H/(1+1.49\varGamma ^{-2})^{1/3}$. Our numerical study shows $Ra_{\ell }$, i.e. $Ra$ based on $\ell$, serves as a proper control parameter for heat transport above the onset with $Nu-1=0.018(1+0.34/\varGamma ^2)(Ra/Ra_{c,\varGamma }-1)$. Here $Ra_{c,\varGamma }$ represents the $\varGamma$-dependent critical $Ra$ for the onset of convection and $Nu$ is the Nusselt number. In the turbulent state, for a general scaling law of $Nu-1\sim Ra^\alpha$, we propose a length scale $\ell = H/(1+1.49\varGamma ^{-2})^{1/[3(1-\alpha )]}$. In the case of turbulent liquid metal convection with $\alpha =1/4$, our measurement shows that the heat transport will become weakly dependent on $\varGamma$ with $Ra_{\ell }\equiv Ra/(1+1.49\varGamma ^{-2})^{4/3} \ge 7\times 10^5$. Finally, once the flow becomes time-dependent, the growth rate of $Nu$ with $Ra$ declines compared with the linear growth rate in the convection state. A hysteresis is observed in a $\varGamma =1/3$ cell when the flow becomes time-dependent. Measurements of the large-scale circulation suggest the hysteresis is caused by the system switching from a single-roll-mode to a double-roll-mode in an oscillation state.

This paper presents a design methodology for a broadband high-efficiency power amplifier (PA). The large available impedance space of the extended continuous Class-GF mode is employed. A novel output matching network of the PA consisting of a rectangular double transmission line structure is proposed to meet impedance requirements. To validate the effectiveness of this structure, a high-efficiency PA operating in 0.8–3.0 GHz is designed using a CGH40010F GaN transistor. The measured results demonstrate that the drain efficiency falls within the range of 63.2%–71.9%, the output power varies from 40.2 to 42.2 dBm, and the gain ranges from 9.4 to 11.3 dB within the frequency band of 0.8–3 GHz. The realized PA exhibits an extremely competitive relative bandwidth of 115.8%.