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This paper investigates the linear and nonlinear dynamics of two-dimensional penetrative convection subjected to radiative volumetric thermal forcing, focusing on ice-covered freshwater systems. Linear stability analysis reveals how critical wavenumbers $k_c$ and Rayleigh numbers $Ra_c$ are influenced by the attenuation lengths and incoming heat flux. In this configuration, the system easily becomes unstable with a small $Ra_c$, which is two decades smaller than that of the classical Rayleigh–Bénard convection problem, with typically $O(10)$. Weakly nonlinear analysis figures out that this configuration is supercritical, contrasting with the subcritical case by Veronis (Astrophys. J., vol. 137, 1963, 641–663). Numerical bifurcation solutions are performed from the critical points and over several decades, up to $Ra \sim O(10^6)$. This paper found that the system exhibits multiple steady solutions, and under certain specific conditions, a staircase temperature profile emerges. Meanwhile, we further discuss the influence of incoming heat flux and the Prandtl number $Pr$ on the primary bifurcation. Direct numerical simulations are also carried out, showing that heat is transported more efficiently via unsteady convection.
Given a number field K, we show that certain K-integral representations of closed surface groups can be deformed to being Zariski dense while preserving many useful properties of the original representation. This generalises a method due to Long and Thistlethwaite who used it to show that thin surface groups in $\textrm{SL}(2k+1,\mathbf{Z})$ exist for all k.
In this article, we discuss the introduction and reception of the theology of natural and divine laws in late Ming China. Natural law and the twofold divine laws appear collectively as an object of discussion and exposition in a number of writings by Jesuit missionaries and Chinese Catholic converts of this time. We focus primarily on Michele Ruggieri’s Tianzhu shilu 天主實錄 (The True Record of the Lord of Heaven) and then consider additional texts by Yang Tingyun and Giulio Aleni, referring to other works in passing. While laying out in more detail than previous scholarship the scholastic basis of these discussions, we nonetheless emphasize that these texts do not reflect a fixed version of scholastic teaching but accommodate their discussions to Chinese cultural sensibilities and/or philosophical concepts. Our historical analysis serves as the basis for a comparative philosophical consideration of the relationship between the doctrine of natural law and the Chinese concept of liangzhi 良知 “innate moral knowledge”.
In the past decade, no meta-analytical estimates of the prevalence of post-traumatic stress disorder (PTSD) among children and adolescents have been published, despite a host of new prevalence studies and updated DSM-5 criteria.
Aims
We set out to estimate the prevalence rates of PTSD in trauma-exposed children and adolescents on the basis of DSM-IV and DSM-5 criteria, and investigate differences in prevalence across trauma type, gender, time since exposure, type of informant and diagnostic measures.
Method
Studies identified in a previous meta-analysis were combined with more recent studies retrieved in a new systematic literature search, resulting in a total of 95 studies describing 64 independent samples (n = 6745 for DSM-IV, n = 12 644 for DSM-5) over a 30-year period. Three-level random-effects models were used to estimate prevalence for DSM-IV and DSM-5 criteria separately, and for testing coded variables as moderators.
Results
The DSM-IV meta-analysis estimated a PTSD prevalence of 20.3% (95% CI 14.9–26.2%) using 56 samples with age range 0–18 years, and revealed moderating effects of gender, trauma type and diagnostic interview type. The DSM-5 meta-analysis found an overall prevalence of 12.0% (95% CI 3.7–24.2%) using eight samples with age range 1–18 years. There was insufficient data for moderation analyses.
Conclusions
Although most trauma-exposed children and adolescents do not develop PTSD, a significant proportion (20% under DSM-IV criteria and 12% under DSM-5 criteria) do, particularly girls and individuals exposed to interpersonal trauma. These findings highlight the urgent need of continuous efforts in prevention, early trauma-related screening, and effective diagnostics and treatment to address the substantial burden of PTSD.
In inviscid, incompressible flows, the evolution of vorticity is exactly equivalent to that of an infinitesimal material line-element and, hence, vorticity can be traced forward or backward in time in a Lagrangian fashion. This elegant and powerful description is not possible in viscous flows due to the action of diffusion. Instead, a stochastic Lagrangian interpretation is required and was recently introduced, where the origin of vorticity at a point is traced back in time as an expectation over the contribution from stochastic trajectories. We herein introduce for the first time an Eulerian, adjoint-based approach to quantify the back-in-time origin of vorticity in viscous, incompressible flows. The adjoint variable encodes the advection, tilting and stretching of the earlier-in-time vorticity that ultimately leads to the target value. Precisely, the adjoint vorticity is the volume-density of the mean Lagrangian deformation of the earlier vorticity. The formulation can also account for the injection of vorticity into the domain at solid boundaries. We demonstrate the mathematical equivalence of the adjoint approach and the stochastic Lagrangian approach. We then provide an example from turbulent channel flow, where we analyse the origin of high streamwise wall-shear-stress events and relate them to Lighthill’s mechanism of stretching of near-wall vorticity.
At constant pressure, a mixture of water parcels with equal density but differing salinity and temperature will be denser than the parent water parcels. This is known as cabbeling and is a consequence of the nonlinear equation of state for seawater density. With a source of turbulent vertical mixing, cabbeling has the potential to trigger and drive convection in gravitationally stable water columns and there is observational evidence that this process shapes the thermohaline structure of high-latitude oceans. However, the evolution and maintenance of turbulent mixing due to cabbeling has not been fully explored. Here, we use turbulence-resolving direct numerical simulations to investigate cabbeling’s impact on vertical mixing and pathways of energy in closed systems. We find that cabbeling can sustain convection in an initially gravitationally stable two-layer configuration where relatively cold/fresh water sits atop warm/salty water. We show the mixture of the cold/fresh and warm/salty water is constrained by a density maximum and that cabbeling enhances mixing rates by four orders of magnitude. Cabbeling’s effect is amplified as the static stability limit is approached, leading to convection being sustained for longer. We find that available potential energy, which is classically thought to only decrease with mixing, can increase with mixing due to cabbeling’s densification of the mixed water. Our direct numerical dimulations support the notion that cabbeling could be a source of enhanced ocean mixing and that conventional definitions of energetic pathways may need to be reconsidered to take into account densification under mixing.
A new fossil of Lycidae, Domipteron gaoi n. gen. n. sp., is described from Miocene Dominican amber. The fossil exhibits a combination of characteristics found in both Calopterini and Eurrhacini. To determine its systematic placement, we conducted phylogenetic analyses based on adult morphological features. Our analyses indicate that the new fossil belongs to Calopterini.
The development of parenting behaviors is influenced by the coparenting relationship – how parents coordinate and manage their shared parenting responsibilities. However, mothers and fathers may exhibit varying degrees of susceptibility to the coparenting relationship, and different factors may further shape their susceptibility. Longitudinal data from 182 different-sex dual-earner parent families were used (86% White, mostly middle- and upper-class families). Observations of coparenting and parenting behaviors were obtained at 3 and 9 months postpartum. Mothers and fathers reported their beliefs about parental roles and parenting at the third trimester of pregnancy and reported their parenting self-efficacy and infant temperament at 3 months. The results of cross-lagged panel models showed that the associations between coparenting and parenting were not significantly different for mothers and fathers. However, the moderators that shaped the associations between coparenting and parenting were distinct for mothers and fathers. Fathers’ less progressive parental role beliefs strengthened the association between supportive coparenting and positive parenting, and mothers’ lower parenting self-efficacy and children’s lower regulatory capacity enhanced the link between undermining coparenting and negative parenting. Implications for research and practice are discussed.
Using quantitative analysis and qualitative in-depth interviews conducted in China in 2022–2024, this study explores a new form of grievance expression and dispute resolution adopted by the Chinese Communist Party (CCP): the online petition. While digital technology can receive and handle public complaints more efficiently, local officials under intense top-down pressure and increased accountability often only address citizens’ demands performatively to satisfy the political needs of their superiors. The study of “mechanical responsiveness” reveals that the CCP’s reinforced scrutiny of petitioners as well as local officials not only fails to prevent and resolve disputes at the source but also may lead to increased social discontent and pent-up resentments in the long run when the government fails to live up to its promises. Citizens will also lose faith in the institution and become politically disengaged if grassroots officials are always trying to curry favour with their superiors and avoid punishment rather than address public demands.
This study examines the effect of nozzle flexibility on vortex ring formation at a Reynolds Number of Re = 1000. The flexible nozzles impart elastic energy to the flow, increasing the hydrodynamic impulse of the vortex ring dependent on the input fluid acceleration and the initial nozzle tip deflection (predicted by the measured nozzle damped natural frequency). When these time scales are synchronised, the output velocity and hydrodynamic impulse of the vortex ring are maximised. Vortex ring pinch-off is predicted using the output velocity for each nozzle and is confirmed with closed finite time Lypunov exponent contours. The lowest tested input formation length, L/D = 1, where L is the piston stroke length and D is the nozzle diameter, generates a greater increase in impulse than L/D = 2 and L/D = 4, due to a higher relative increase in total ejected volume and by remaining in the single vortex formation regime. At L/D = 2 and L/D = 4, multiple vortex structures are observed due to the interplay of the counter-flow generated by the nozzles re-expanding and the steady input flow. At the end of the pumping cycle, during fluid deceleration, the flexible nozzles collapse. This helps in suppressing unfavourable negative pressure regions from forming within the nozzle, instead expelling additional fluid from the nozzle. Upon reopening, beneficial stopping vortices form within the nozzles, with circulation correlated to nozzle stiffness. This highlights a secondary optimal stiffness criterion that must be considered in a full-cycle analysis: the nozzle must be compliant enough to collapse during deceleration, yet remain as stiff as possible to reopen quickly to maximise efficiency in refilling.
For multi-scale differential equations (or fast–slow equations), one often encounters problems in which a key system parameter slowly passes through a bifurcation. In this article, we show that a pair of prototypical reaction–diffusion equations in two space dimensions can exhibit delayed Hopf bifurcations. Solutions that approach attracting/stable states before the instantaneous Hopf point stay near these states for long, spatially dependent times after these states have become repelling/unstable. We use the complex Ginzburg–Landau equation and the Brusselator models as prototypes. We show that there exist two-dimensional spatio-temporal buffer surfaces and memory surfaces in the three-dimensional space-time. We derive asymptotic formulas for them for the complex Ginzburg–Landau equation and show numerically that they exist also for the Brusselator model. At each point in the domain, these surfaces determine how long the delay in the loss of stability lasts, that is, to leading order when the spatially dependent onset of the post-Hopf oscillations occurs. Also, the onset of the oscillations in these partial differential equations is a hard onset.
This paper develops a theoretical framework to examine the technology adoption decisions of insurers and their impact on market share, considering heterogeneous customers and two representative insurers. Intuitively, when technology accessibility is observable, an insurer’s access to a new technology increases its market share, no matter whether it adopts the technology or not. However, when technology accessibility is unobservable, the insurer’s access to the new technology has additional side effects on its market share. First, the insurer may apply the available technology even if it increases costs and premiums, thereby decreasing market share. Second, the unobservable technology accessibility leads customers to expect that all insurers might have access to the new technology and underestimate the premium of those without access. This also decreases the market share of an insurer with access to the new technology. Our findings help explain the unclear relationship between technology adoption and the market share of insurance companies in practice.
Severe Ebstein’s disease often necessitates early neonatal surgical intervention, although, in some patients, surgery may be delayed until infancy or later, and medical management may be undertaken instead. Various indicators, such as tricuspid regurgitation flow velocity, have been studied to predict single or biventricular circulation; however, indicators predicting the need for neonatal surgery have not been addressed. We aimed to identify predictive indices for neonatal surgical necessity by analysing the clinical characteristics of those requiring and not requiring neonatal surgery. We enrolled eight patients with severe Ebstein’s disease who were born at our hospital from 2018 to 2023. Four patients underwent neonatal surgery (Group S), whereas four did not (Group F). We compared pregnancy, delivery, and postnatal clinical courses and laboratory indices before and after birth between the groups. The systolic/diastolic time ratio, an index of ventricular function calculated from the TR waveform of echocardiography at birth, was significantly prolonged in Group S [2.18 ± 0.31 vs. 1.72 ± 0.20 in Group F (p = 0.043)]. The area under the receiver operating characteristic curve was 0.94, with a threshold systolic/diastolic time ratio value of 1.99 using Youden’s method. This ratio predicted neonatal surgery necessity with 100% sensitivity and 75% specificity. Despite the small sample size, we demonstrated that the systolic/diastolic time ratio is a valuable predictive index of ventricular function and prognosis in severe Ebstein’s disease patients. A systolic/diastolic time ratio <2, determined from the tricuspid regurgitation waveform on echocardiography at birth, supports patient monitoring without surgical intervention through the newborn period and beyond.
The impinging–freezing of supercooled water droplets (SLDs) is the root cause of aircraft icing. This work presented an experimental investigation of a millimeter-sized supercooled droplet (−10 $^\circ {\rm{C}}$) impact onto cold surfaces. For the majority of the current research on freezing behaviour, the quantitative analysis of impingement contributions was neglected. The present study established prediction models for the frozen area ratio, initial freezing height and solidification time by changing Weber number and Stefan number. The results showed that with the decrease in surface temperatures, the maximum spreading factor and the peak height factor were unchanged; however, the receding velocity of the liquid film reduced. Besides, regardless of the three freezing modes (quasi-static, instantaneous and delayed), the frozen area ratio consistently increased with decreasing Weber number. For the Stefan number exceeded 0.12, the frozen area ratio increased with decreasing surface temperature; otherwise, it was independent of the surface temperature. In addition, the initial height of asymmetrical frozen droplets was characterised using the ‘two-ellipse’ method, revealing an inverse proportionality to the square root of the frozen area ratio. Furthermore, the solidification time of the hemisphere and pancake frozen droplets shortened with the decrease in the initial height and surface temperature. This fundamental study provides valuable insights for understanding aircraft icing and optimising anti-icing systems.
In recent years, various unique properties of microswimmer suspensions have been revealed. Some microswimmers are deformable; however, the influence of the swimmer’s deformability has been overlooked. The present study examined the impact of soft microswimmers’ membrane deformations in a mono-dispersed dense suspension on microstructure formation. Due to the small size of the microswimmers, the flow field is described by the Stokes equation. The soft microswimmer was modelled as a capsule with a two-dimensional hyperelastic membrane enclosing a Newtonian fluid that is driven by propulsion torques distributed slightly above the membrane surface. Changes to the torque distribution caused the soft swimmer to exhibit different swimming modes as a pusher or puller. Similar to rigid squirmers, soft swimmers displayed self-organised local clusters in the suspension. Membrane deformation changed the mutual interference among swimmers in the cluster, bringing the interactions closer together than those of rigid squirmers. Especially among soft pushers, rotational diffusion due to hydrodynamic interference was reduced and the swimming trajectory became relatively straight. As a result, polar order was less likely to form, especially in regions of high $Ca$. On the other hand, pullers showed strong interactions due to retraction flow and an increase in mean membrane tension. For pushers (pullers), the rear (side) interaction produced the greatest change in tension. These findings are expected to be useful for effort to understand the propulsion mechanisms of medical and industrial soft microrobots, as well as the biological responses of microorganisms induced by mechanical stimuli.
The system composed of a circular cylinder free to move along a transverse rectilinear path within a cross-current has often served as a canonical problem to study the vortex-induced vibrations (VIV) developing in the absence of structural restoring force, thus without structural natural frequency. The object of the present work is to extend the exploration of the behaviour of this system when the path is set to an arbitrary orientation, varying from the transverse to the streamwise direction, and the cylinder is forced to rotate about its axis. The investigation is conducted numerically at a Reynolds number equal to $100$, based on the body diameter and oncoming flow velocity, for structure to displaced fluid mass ratios down to $0.01$ and values of the rotation rate (ratio between body surface and oncoming flow velocities) ranging from $0$ to $1$. When the transverse symmetry is broken by the orientation of the trajectory or the forced rotation, the cylinder drifts along the rectilinear path, at a velocity that can be predicted by a quasi-steady approach. Three distinct regimes are encountered: a pure drift regime, where the body translates at a constant velocity, and two oscillatory regimes, characterised by contrasted forms of displacement fluctuation about the drifting motion, but both closely connected to flow unsteadiness. VIV, nearly sinusoidal, persist over a wide range of path orientations, for all rotation rates. On the other hand, irregular jumps of the body, triggered by the rotation and named saccades, emerge when the trajectory is aligned, or almost aligned, with the current. The two forms of response differ by their regularity, but also by their amplitudes and frequencies, which deviate by one or more orders of magnitude. The rotation attenuates both VIV and saccades. Yet, an increase of the rotation rate enhances the erratic nature of the saccade regime.