This paper focuses on the concept of delaying laminar–turbulent transition in hypersonic boundary layers by stabilising fundamental resonance (FR), a key nonlinear mechanism in which finite-amplitude Mack modes support the rapid growth of oblique perturbations. As a pioneering demonstration of this control strategy, we introduce surface heating applied exclusively during the nonlinear phase. Unlike traditional control methods that target the linear phase, the suppressive effect of surface heating on secondary instability modes during FR is evident across various Reynolds numbers, wall temperatures and fundamental frequencies, as confirmed by direct numerical simulations (DNS) and secondary instability analyses (SIA). To gain deeper insights into this control concept, an asymptotic analysis is conducted, revealing an almost linear relationship between the suppression effect and the heating intensity. The asymptotic predictions align overall with the DNS and SIA calculations. The asymptotic theory reveals that the suppression effect of FR is primarily influenced by modifications to the fundamental-mode profile, while mean-flow distortion has a comparatively modest yet opposing impact on this process. This research presents a promising approach to controlling transition considering the nonlinear evolution of boundary-layer perturbations, demonstrating advantages over conventional methods that are sensitive to frequency variations.

In this paper, we study the receptivity of non-modal perturbations in hypersonic boundary layers over a blunt wedge subject to free stream vortical, entropy and acoustic perturbations. Due to the absence of the Mack-mode instability and the rather weak growth of the entropy-layer instability within the domain under consideration, the non-modal perturbation is considered as the dominant factor triggering laminar–turbulent transition. This is a highly intricate problem, given the complexities arising from the presence of the bow shock, the entropy layer and their interactions with oncoming disturbances. To tackle this challenge, we develop a highly efficient numerical tool, the shock-fitting harmonic linearised Navier–Stokes (SF-HLNS) approach, which offers a comprehensive investigation on the dependence of the receptivity efficiency on the nose bluntness and properties of the free stream forcing. The numerical findings suggest that the non-modal perturbations are more susceptible to free stream acoustic and entropy perturbations compared with the vortical perturbations, with the optimal spanwise length scale being comparable with the downstream boundary-layer thickness. Notably, as the nose bluntness increases, the receptivity to the acoustic and entropy perturbations intensifies, reflecting the transition reversal phenomenon observed experimentally in configurations with relatively large bluntness. In contrast, the receptivity to free stream vortical perturbations weakens with increasing bluntness. Additionally, through the SF-HLNS calculations, we examine the credibility of the optimal growth theory (OGT) on describing the evolution of non-modal perturbations. While the OGT is able to predict the overall streaky structure in the downstream region, its accuracy in predicting the early-stage evolution and the energy amplification proves to be unreliable. Given its high-efficiency and high-accuracy nature, the SF-HLNS approach shows great potential as a valuable tool for conducting future research on hypersonic blunt-body boundary-layer transition.

In this paper, we study the effect of lateral wall vibrations on the excitation and evolution of non-modal perturbations in hypersonic boundary layers subject to low-frequency freestream vortical disturbances (FSVDs). A novel, high-efficiency numerical approach, combining the harmonic weakly nonlinear Navier–Stokes and nonlinear parabolised stability equation approaches, is developed, which is sufficient to accommodate both the rapid distortion of the perturbation in the leading-edge vicinity and the nonlinear development of finite-amplitude high-order harmonics in the downstream region. The boundary-layer response to low-frequency FSVDs shows a longitudinal streaky structure, for which the temperature perturbation shows much greater magnitude than the streamwise velocity perturbation. The lateral vibration induces a Stokes layer solution for the spanwise velocity perturbation, which interacts with the FSVD-induced perturbations and leads to a suppression of the non-modal perturbation and an enhancement of the downstream modal perturbation. The new perturbations excited by the FSVD–vibration interaction strengthen as the vibration intensifies, and they could become comparable with the FSVD-induced perturbations in downstream locations at a high vibration intensity, indicating a remarkable modification of the streaky structure and its instability property. Secondary instability (SI) analyses based on the streaky base flow indicate that the vibration could enhance or suppress the SI modes, depending on their initial phases over the vibration period. Overall, the average effect is that the low-frequency and high-frequency SI modes are stabilised and destabilised by the vibration, respectively. Since the high-frequency SI modes undergo higher amplifications, the subsequent bypass transition is likely to be promoted by relatively strong vibrations.

The tension distribution problem of cable-driven parallel robots is inevitable in real-time control. Currently, iterative algorithms or geometric algorithms are commonly used to solve this problem. Iterative algorithms are difficult to improve in real-time performance, and the tension obtained by geometric algorithms may not be continuous. In this paper, a novel tension distribution method for four-cable, 3-DOF cable-driven parallel robots is proposed based on the wave equation. The tension calculated by this method is continuous and differentiable, without the need for iterative computation or geometric centroid calculations, thus exhibiting good real-time performance. Furthermore, the feasibility and rationality of this algorithm are theoretically proven. Finally, the real-time performance and continuity of cable tension are analyzed through a specific numerical example.

The discovery that blazars dominate the extra-galactic $\gamma$-ray sky is a triumph in the Fermi era. However, the exact location of $\gamma$-ray emission region still remains in debate. Low-synchrotron-peaked blazars (LSPs) are estimated to produce high-energy radiation through the external Compton process, thus their emission regions are closely related to the external photon fields. We employed the seed factor approach proposed by Georganopoulos et al. It directly matches the observed seed factor of each LSP with the characteristic seed factors of external photon fields to locate the $\gamma$-ray emission region. A sample of 1 138 LSPs with peak frequencies and peak luminosities was adopted to plot a histogram distribution of observed seed factors. We also collected some spectral energy distributions (SEDs) of historical flare states to investigate the variation of $\gamma$-ray emission region. Those SEDs were fitted by both quadratic and cubic functions using the Markov-chain Monte Carlo method. Furthermore, we derived some physical parameters of blazars and compared them with the constraint of internal $\gamma\gamma$-absorption. We find that dusty torus dominates the soft photon fields of LSPs and most $\gamma$-ray emission regions of LSPs are located at 1–10 pc. The soft photon fields could also transition from dusty torus to broad line region and cosmic microwave background in different flare states. Our results suggest that the cubic function is better than the quadratic function to fit the SEDs.

The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude and the low-amplitude oblique travelling modes with the same frequency as the dominant mode, together with the stationary streak modes, undergo the strongest amplification among all the Fourier components. This regime may be the most efficient means to trigger the natural transition in hypersonic boundary layers. In this paper, we aim to reveal the intrinsic mechanism of the FR in the weakly nonlinear framework based on the large-Reynolds-number asymptotic technique. It is found that the FR is, in principle, a triad resonance among a dominant planar fundamental mode, a streak mode and an oblique mode. In the major part of the boundary layer, the nonlinear interaction of the fundamental mode and the streak mode seeds the growth of the oblique mode, whereas the interaction of the oblique mode and the fundamental mode drives the roll components (transverse and lateral velocity) of the streak mode, which leads to a stronger amplification of the streamwise component of the streak mode due to the lift-up mechanism. This asymptotic analysis clearly shows that the dimensionless growth rates of the streak and oblique modes are the same order of magnitude as the dimensionless amplitude of the fundamental mode $(\bar {\epsilon }_{10})$, and the amplitude of the streak mode is $O(\bar {\epsilon }_{10}^{-1})$ greater than that of the oblique mode. The main-layer solution of the streamwise velocity, spanwise velocity and temperature of both the streak and the oblique modes become singular as the wall is approached, and so a viscous wall layer appears underneath. The wall layer produces an outflux velocity to the main-layer solution, inclusion of which leads to an improved asymptotic theory whose accuracy is confirmed by comparing with the calculations of the nonlinear parabolised stability equations (NPSEs) at moderate Reynolds numbers and the secondary instability analysis (SIA) at sufficiently high Reynolds numbers.

Energy loss of protons with 90 and 100 keV energies penetrating through a hydrogen plasma target has been measured, where the electron density of the plasma is about 1016 cm−3 and the electron temperature is about 1-2 eV. It is found that the energy loss of protons in the plasma is obviously larger than that in cold gas and the experimental results based on the Bethe model calculations can be demonstrated by the variation of effective charge of protons in the hydrogen plasma. The effective charge remains 1 for 100 keV protons, while the value for 90 keV protons decreases to be about 0.92. Moreover, two empirical formulae are employed to extract the effective charge.

This paper focuses on the linear evolution of Mack instability modes in a hypersonic boundary layer over a flat plate that is partially coated by a compliant section. The compliant section is a thin, flexible membrane covering on a porous wall consisting of micro holes. The instability pressure could induce a vibration of the membrane, leading to a feedback to the boundary-layer fluids through the transverse velocity fluctuation. Such a process is formulated by an admittance boundary condition for the boundary-layer perturbation, which is dependent on the thickness and tension of the membrane, the properties of the porous wall, and the frequency of the Mack-mode perturbation. Using this admittance condition, the impact of the compliant coating on the Mack growth rate is studied systematically by solving the compressible Orr–Sommerfeld equations. It is found that the compliant coating could suppress the Mack instability with a frequency band in the neighbourhood of the most unstable frequency, and the stabilising frequency band widens as the membrane thickness and tension decrease, indicating a more favourable effect of a softer membrane. For a Mack mode with a specified dimensional frequency – since its dimensionless frequency, normalised by the local boundary-layer thickness and oncoming velocity, increases as it propagates downstream – the second-mode frequency band usually appears in downstream locations, and so does the stabilising effect of the membrane. Thus it is favourable to apply a compliant panel at a downstream region. In this situation, the solid–compliant junction could produce an additional scattering effect on the evolution of the Mack mode due to the sudden change of its boundary condition. The scattering effect is quantified by a transmission coefficient defined by the equivalent amplitude of the compliant-wall perturbation to the solid-wall perturbation, which can be obtained by the harmonic linearised Navier–Stokes (HLNS) approach. If the admittance is weak, then the transmission coefficient can also be predicted by an analytical solution based on the residue theorem. It is found that most of the second modes are suppressed by the scattering effect as long as the argument of the admittance is in the interval $[150^\circ, 210^\circ ]$, agreeing with most of the physical situation. The analytical predictions agree well with the HLNS calculations when the modulus of the admittance is less than $O(0.1)$.

In this paper, we present a systematic study of the nonlinear evolution of the travelling Mack modes in a Mach 3 supersonic boundary layer over a rotating cone with a $7^{\circ }$ half-apex angle using the nonlinear parabolic stability equation (NPSE). To quantify the effect of cone rotation, six cases with different rotation rates are considered, and from the same streamwise position, a pair of oblique Mack modes with the same frequency but opposite circumferential wavenumbers are introduced as the initial perturbations for NPSE calculations. As the angular rotation rate $\varOmega$ increases such that $\bar \varOmega$ (defined as the ratio of the rotation speed of the cone to the streamwise velocity at the boundary-layer edge) varies from 0 to $O(1)$, three distinguished nonlinear regimes appear, namely the oblique-mode breakdown, the generalised fundamental resonance and the centrifugal-instability-induced transition. For each regime, the mechanisms for the amplifications of the streak mode and the harmonic travelling waves are explained in detail, and the dominant role of the streak mode in triggering the breakdown of the laminar flow is particularly highlighted. Additionally, from the linear stability theory, the dominant travelling mode undergoes the greatest amplification for a moderate $\varOmega$, which, according to the $e^N$ transition-prediction method, indicates premature transition to turbulence. However, this is in contrast to the NPSE results, in which a delay of the transition onset is observed for a moderate $\varOmega$. Such a disagreement is attributed to the different nonlinear regimes appearing for different rotation rates. Therefore, the traditional transition-prediction method based on the linear instability should be carefully employed if multiple nonlinear regimes may appear.

Breast cancer is a high-risk disease with a high mortality rate among women. Chemotherapy plays an important role in the treatment of breast cancer. However, chemotherapy eventually results in tumours that are resistant to drugs. In recent years, many studies have revealed that the activation of Wnt/β-catenin signalling is crucial for the emergence and growth of breast tumours as well as the development of drug resistance. Additionally, drugs that target this pathway can reverse drug resistance in breast cancer therapy. Traditional Chinese medicine has the properties of multi-target and tenderness. Therefore, integrating traditional Chinese medicine and modern medicine into chemotherapy provides a new strategy for reversing the drug resistance of breast tumours. This paper mainly reviews the possible mechanism of Wnt/β-catenin in promoting the process of breast tumour drug resistance, and the progress of alkaloids extracted from traditional Chinese medicine in the targeting of this pathway in order to reverse the drug resistance of breast cancer.

In this paper, we study the local receptivity of the inviscid Mack modes in hypersonic boundary layers induced by the interaction between a surface heating or cooling source (HCS) and a freestream acoustic wave. The asymptotic analysis reveals that among the three distinguished layers, i.e. the main, wall and Stokes layers, the leading-order receptivity is attributed to the interaction of the HCS-induced mean-flow distortion and the acoustic signature in the wall layer; the second-order contribution appears in the Stokes layer; the third-order contribution appears in both the main and wall layers. Interestingly, at a moderate Reynolds number, the third-order contribution to the receptivity efficiency may be quantitatively greater than the second-order one, but this does not lead to breakdown of this asymptotic theory. Assuming the HCS intensity to be sufficiently weak, the asymptotic predictions are made for four representative cases involving different Mach numbers and wall temperatures, which are compared with the results obtained by the finite-Reynolds-number theory based on either the extended compressible Orr–Sommerfeld equations or the harmonic linearised Navier–Stokes (HLNS) calculations. Taking into account the first three orders of the receptivity efficiency, the asymptotic predictions are confirmed to be sufficiently accurate even when the Reynolds number is a few thousands, and the agreement with the finite-Reynolds-number calculations is better when the wall temperature of the base flow approaches the adiabatic wall temperature. The HLNS calculations are also conducted for moderate HCS intensities. It is found that the nonlinearity does not affect the receptivity coefficient much even when the temperature distortion of the HCS reaches $80\,\%$ of the temperature at the wall.

Everyone faces uncertainty on a daily basis. Two kinds of probability expressions, verbal and numerical, have been used to characterize the uncertainty that we face. Because our cognitive concept of living things differs from that of non-living things, and distinguishing cognitive concepts might have linguistic markers, we designed four studies to test whether people use different probability expressions when faced with animate or inanimate uncertainty. We found that verbal probability is the preferred way to express animate uncertainty, whereas numerical probability is the preferred way to express inanimate uncertainty. The “verbal-animate” and “numerical-inanimate” associations were robust enough to persist when tested with forced-choice response patterns regardless of the information (e.g., equally likely outcomes, frequencies, or personal beliefs) used to construct probabilities of events. When the response pattern was changed to free-responses, the associations were evident unless the subjects were asked to write their own probability predictions for vague uncertainty. Given that the world around us consists of both animate (i.e., living) and inanimate (i.e., non-living) things, “verbal-animate” and “numerical-inanimate” associations may play a major role in risk communication and may otherwise be useful for practitioners and consultants.

According to the positive time-discounting assumption of intertemporal decision-making, people prefer to undergo negative events in the future rather than in the present. However, negative discounting has been identified in the intertemporal choice and loss domains, which refers to people’s preference to experience negative events earlier rather than later. Studies have validated and supported the "anticipated dread" as an explanation for negative discounting. This study again explored the effect of anticipated dread on intertemporal choice using content analysis; that is, having participants identify anticipated dread among reasons for negative discounting. This study also validated the effect of anticipated dread on negative discounting by manipulating anticipated dread. This study adds empirical and direct evidence for the role of anticipated dread in negative discounting.

Intertemporal choices involve tradeoffs between outcomes that occur at different times. Most of the research has used pure gains tasks and the discount rates yielding from those tasks to explain and predict real-world behaviors and consequences. However, real decisions are often more complex and involve mixed outcomes (e.g., sooner-gain and later-loss or sooner-loss and later-gain). No study has used mixed gain-loss intertemporal tradeoff tasks to explain and predict real-world behaviors and consequences, and studies involving such tasks are also scarce. Considering that tasks involving a combination of gains and losses may yield different discount rates and that existing pure gains tasks do not explain or predict real-world outcomes well, this study conducted two experiments to compare the discount rates of mixed gain-loss intertemporal tradeoffs with those of pure gains or pure losses (Experiment 1) and to examine whether these tasks predicted different real-world behaviors and consequences (Experiment 2). Experiment 1 suggests that the discount rate ordering of the four tasks was, from highest to lowest, pure gains, sooner-loss and later-gain, pure losses, and sooner-gain and later-loss. Experiment 2 indicates that the evidence supporting the claim that the discount rates of the four tasks were related to different real-world behaviors and consequences was insufficient.

Recently, Scholten and Read (2014) found new violations of dominance in intertemporal choice. Although adding a small receipt before a delayed payment or adding a small delayed receipt after an immediate receipt makes the prospect objectively better, it decreases the preference for that prospect (better is worse). Conversely, although adding a small payment before a delayed receipt or adding a small delayed payment after an immediate payment makes the prospect objectively worse, it increases the preference for that prospect (worse is better). Scholten and Read explained these violations in terms of a preference for improvement. However, to produce violations such as these, we find that the temporal sequences need not be constructed as Scholten and Read suggested. In this study, adding a small receipt before a dated receipt (thus constructed as improving) or adding a receipt after a dated payment (thus constructed as improving) decreases preferences for those prospects. Conversely, adding a small payment after a dated receipt (thus constructed as deteriorating) or adding a small payment before a delayed payment (thus constructed as deteriorating) increases preferences for those prospects.

We present an experimental study of Rayleigh–Bénard convection using liquid metal alloy gallium-indium-tin as the working fluid with a Prandtl number of $Pr=0.029$. The flow state and the heat transport were measured in a Rayleigh number range of $1.2\times 10^{4} \le Ra \le 1.3\times 10^{7}$. The temperature fluctuation at the cell centre is used as a proxy for the flow state. It is found that, as $Ra$ increases from the lower end of the parameter range, the flow evolves from a convection state to an oscillation state, a chaotic state and finally a turbulent state for $Ra>10^5$. The study suggests that the large-scale circulation in the turbulent state is a residual of the cell structure near the onset of convection, which is in contrast with the case of $Pr\sim 1$, where the cell structure is transiently replaced by high order flow modes before the emergence of the large-scale circulation in the turbulent state. The evolution of the flow state is also reflected by the heat transport characterised by the Nusselt number $Nu$ and the probability density function (p.d.f.) of the temperature fluctuation at the cell centre. It is found that the effective local heat transport scaling exponent $\gamma$, i.e. $Nu\sim Ra^{\gamma }$, changes continuously from $\gamma =0.49$ at $Ra\sim 10^4$ to $\gamma =0.25$ for $Ra>10^6$. Meanwhile, the p.d.f. at the cell centre gradually evolves from a Gaussian-like shape before the transition to turbulence to an exponential-like shape in the turbulent state. For $Ra>10^6$, the flow shows self-similar behaviour, which is revealed by the universal shape of the p.d.f. of the temperature fluctuation at the cell centre and a $Nu=0.19Ra^{0.25}$ scaling for the heat transport.