The Bray–Liebhafsky reaction is one of many intricate chemical systems that is known to exhibit periodic behaviour. Although the underlying chemistry is somewhat complicated and involves at least ten chemical species, in a recent work we suggested a reduced two-component model of the reaction involving the concentrations of iodine and iodous acid. Although it is drastically simplified, this reduced system retains enough structure so as to exhibit many of the oscillatory characteristics seen in experimental analyses. Here, we consider the possibility of spatial patterning in a nonuniformly mixed solution. Since many practical demonstrations of chemical oscillations are undertaken using circular containers such as beakers or Petri dishes, we develop both linearized and nonlinear pattern solutions in terms of cylindrical coordinates. These results are complemented by an analysis of the patterning that might be possible within a rectangular domain. The simulations give compelling evidence that spatial patterning may well be feasible in the Bray–Liebhafsky process.

We consider planar flow involving two viscous fluids in a porous medium. One fluid is injected through a line source at the origin and moves radially outwards, pushing the second, ambient fluid outwards. There is an interface between the two fluids and if the inner injected fluid is of lower viscosity, the interface is unstable to small disturbances and radially directed unstable Saffman–Taylor fingers are produced. A linearized theory is presented and is compared with nonlinear results obtained using a numerical spectral method. An additional theory is also discussed, in which the sharp interface is replaced with a narrow diffuse interfacial region. We show that the nonlinear results are in close agreement with the linearized theory for small-amplitude disturbances at early times, but that large-amplitude fingers develop at later times and can even detach completely from the initial injection region.

A viscous fluid is confined between two smooth horizontal walls, in a vertical channel. The upper wall may move with constant speed, but the lower wall is stationary and a portion of it is heated. A plume of heated fluid develops, and may also be swept downstream by the motion of the upper wall. When the heating effect is small and the upper plate does not move, a closed-form solution for the temperature profile is presented. A numerical spectral method is then presented, and allows highly accurate nonlinear solutions to be obtained, for the temperature and the fluid motion. These are compared against the closed-form solution in the linearized case, and the effects of nonlinearity on temperature and velocity are revealed. The results also show that periodic plume shedding from the heated region can occur in the nonlinear case.

The present study examined high-risk personality traits and associations with psychopathology across multiple levels of a hierarchical-dimensional model of psychopathology in a large adolescent, general population sample. Confirmatory factor analyses were run using data from two randomized controlled trials of Australian adolescents (N = 8,654, mean age = 13.01 years, 52% female). A higher-order model – comprised of general psychopathology, fear, distress, alcohol use/harms, and conduct/inattention dimensions – was selected based on model fit, reliability, and replicability. Indirect-effects models were estimated to examine the unique associations between high-risk personality traits (anxiety sensitivity, negative thinking, impulsivity, and sensation seeking) and general and specific dimensions and symptoms of psychopathology. All personality traits were positively associated with general psychopathology. After accounting for general psychopathology, anxiety sensitivity was positively associated with fear; negative thinking was positively associated with distress; impulsivity was positively associated with conduct/inattention; and sensation seeking was positively associated with alcohol use/harms and conduct/inattention, and negatively associated with fear. Several significant associations between personality traits and individual symptoms remained after accounting for general and specific psychopathology. These findings contribute to our understanding of the underlying structure of psychopathology among adolescents and have implications for the development of personality-based prevention and early intervention programs.

Recent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two or three bodies and total angular momentum for a simplified Solar System model, over moderate astronomical timescales (tens of millions of years). For a nonconservative system, we investigate a relativistic two-body problem with gravitational wave emission. We find that methods of tenth and twelfth order consistently outperform lower-order methods for the systems considered here.

We consider fully three-dimensional time-dependent outflow from a source into a surrounding fluid of different density. The source is distributed over a sphere of finite radius. The nonlinear problem is formulated using a spectral approach in which two streamfunctions and the density are represented as a Fourier-type series with time-dependent coefficients that must be calculated. Linearized theories are also discussed and an approximate stability condition for early stages in the outflow is derived. Nonlinear solutions are presented and different outflow shapes adopted by the fluid interface are investigated.

Long-duration gamma-ray burst (GRB) afterglow observations offer cutting-edge opportunities to characterise the star formation history of the Universe back to the epoch of reionisation, and to measure the chemical composition of interstellar and intergalactic gas through absorption spectroscopy. The main barrier to progress is the low efficiency in rapidly and confidently identifying which bursts are high redshift ($z > 5$) candidates before they fade, as this requires low-latency follow-up observations at near-infrared wavelengths (or longer) to determine a reliable photometric redshift estimate. Since no current or planned gamma-ray observatories carry near-infrared telescopes on-board, complementary facilities are needed. So far this task has been performed by instruments on the ground, but sky visibility and weather constraints limit the number of GRB targets that can be observed and the speed at which follow-up is possible. In this work we develop a Monte Carlo simulation framework to investigate an alternative approach based on the use of a rapid-response near-infrared nano-satellite, capable of simultaneous imaging in four bands from $0.8$ to $1.7\,\unicode{x03BC}$m (a mission concept called SkyHopper). Using as reference a sample of 88 afterglows observed with the GROND instrument on the MPG/ESO telescope, we find that such a nano-satellite is capable of detecting in the H-band (1.6 $\unicode{x03BC}$m) $72.5\% \pm 3.1\%$ of GRBs concurrently observable with the Swift satellite via its UVOT instrument (and $44.1\% \pm 12.3\%$ of high redshift ($z>5$) GRBs) within 60 min of the GRB prompt emission. This corresponds to detecting ${\sim}55$ GRB afterglows per year, of which 1–3 have $z > 5$. These rates represent a substantial contribution to the field of high-z GRB science, as only 23 $z > 5$ GRBs have been collectively discovered by the entire astronomical community over the last ${\sim}24$ yr. Future discoveries are critically needed to take advantage of next generation follow-up spectroscopic facilities such as 30m-class ground telescopes and the James Webb Space Telescope. Furthermore, a systematic space-based follow-up of afterglows in the near-infrared will offer new insight on the population of dusty (‘dark’) GRBs which are primarily found at cosmic noon ($z\sim 1-3$). Additionally, we find that launching a mini-constellation of 3 near-infrared nano-satellites would increase the detection fraction of afterglows to ${\sim}83\%$ and substantially reduce the latency in the photometric redshift determination.

The Hierarchical Taxonomy of Psychopathology (HiTOP) has emerged out of the quantitative approach to psychiatric nosology. This approach identifies psychopathology constructs based on patterns of co-variation among signs and symptoms. The initial HiTOP model, which was published in 2017, is based on a large literature that spans decades of research. HiTOP is a living model that undergoes revision as new data become available. Here we discuss advantages and practical considerations of using this system in psychiatric practice and research. We especially highlight limitations of HiTOP and ongoing efforts to address them. We describe differences and similarities between HiTOP and existing diagnostic systems. Next, we review the types of evidence that informed development of HiTOP, including populations in which it has been studied and data on its validity. The paper also describes how HiTOP can facilitate research on genetic and environmental causes of psychopathology as well as the search for neurobiologic mechanisms and novel treatments. Furthermore, we consider implications for public health programs and prevention of mental disorders. We also review data on clinical utility and illustrate clinical application of HiTOP. Importantly, the model is based on measures and practices that are already used widely in clinical settings. HiTOP offers a way to organize and formalize these techniques. This model already can contribute to progress in psychiatry and complement traditional nosologies. Moreover, HiTOP seeks to facilitate research on linkages between phenotypes and biological processes, which may enable construction of a system that encompasses both biomarkers and precise clinical description.

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour.

There is a growing body of evidence highlighting the presence of a single general dimension of psychopathology that can account for multiple associations across mental and substance use disorders. However, relatively little evidence has emerged regarding the validity of this model with respect to a range of factors that have been previously implicated across multiple disorders. The current study utilized a cross-sectional population survey of adolescents (n = 2,003) to examine the extent to which broad psychopathology factors account for specific associations between psychopathology and key validators: poor sleep, self-harm, suicidality, risky sexual behavior, and low self-esteem. Confirmatory factor models, latent class models, and factor mixture models were estimated to identify the best structure of psychopathology. Structural equation models were then estimated to examine the broad and specific associations between each psychopathology indicator and the validators. A confirmatory factor model with three lower-order factors, representing internalizing, externalizing, and psychotic-like experiences, and a single higher-order factor evidenced the best fit. The associations between manifest indicators of psychopathology and validators were largely nonspecific. However, significant and large direct effects were found between several pairwise associations. These findings have implications for the identification of potential targets for intervention and/or tailoring of prevention programs.

When open-cut mines are eventually abandoned, they leave a large hole with sloping sides. The hole fills with rain water, and there is also contaminated run-off from surrounding land, that moves through the rock and eventually through the sloping sides of the abandoned mine. This paper considers a two-dimensional unsteady model motivated by this leaching flow through the rock and into the rain-water reservoir. The stability of the interface between the two fluids is analysed in the inviscid limit. A viscous Boussinesq model is also presented, and a closed-form solution is presented to this problem, after it has been linearized in a manner consistent with Boussinesq theory. That solution suggests that the interfacial zone is effectively neutrally stable as it evolves in time. However, an asymptotic theory in the interfacial region shows the interface to be unstable. In addition, the nonlinear Boussinesq model is solved using a spectral method. Interfacial travelling waves and roll-up are observed and discussed, and compared against the predictions of asymptotic Boussinesq theory.

Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory.

We consider fluid in a channel of finite height. There is a circular hole in the channel bottom, through which fluid of a lower density is injected and rises to form a plume. Viscous boundary layers close to the top and bottom of the channel are assumed to be so thin that the viscous fluid effectively slips along each of these boundaries. The problem is solved using a novel spectral method, in which Hankel transforms are first used to create a steady-state axisymmetric (inviscid) background flow that exactly satisfies the boundary conditions. A viscous correction is then added, so as to satisfy the time-dependent Boussinesq Navier–Stokes equations within the fluid, leaving the boundary conditions intact. Results are presented for the “lazy” plume, in which the fluid rises due only to its own buoyancy, and we study in detail its evolution with time to form an overturning structure. Some results for momentum-driven plumes are also presented, and the effect of the upper wall of the channel on the evolution of the axisymmetric plume is discussed.

In this brief communication, a new method is outlined for modelling magnification patterns on an observer’s plane using a first-order approximation to the null geodesic path equations for a point mass lens. For each ray emitted from a source, an explicit calculation is made for the change in position on the observer’s plane due to each lens mass. By counting the number of points in each small area of the observer’s plane, the magnification at that point can be determined. This allows for a very simple and transparent algorithm. A short Matlab code sample for creating simple magnification maps due to multiple point lenses is included in an appendix.

The total magnification due to a point lens has been of particular interest as the theorem that gravitational lensing results in light amplification for all observers appears to contradict the conservation of photon number. This has been discussed several times, and various resolutions have been offered. In this note, we use a kinematic approach to provide a formula for the magnification factor for the primary image accurate to first order and valid for rays leaving the source at any trajectory. We thus determine the magnification over a sphere surrounding the system. A new result found is that while the magnification dips below unity far from the optical axis as noted by others, it returns to unity directly behind the source.

The Kelvin–Helmholtz flow is a shearing instability that occurs at the interface between two fluids moving with different speeds. Here, the two fluids are each of finite depth, but are highly viscous. Consequently, their motion is caused by the horizontal speeds of the two walls above and below each fluid layer. The motion of the fluids is assumed to be governed by the Stokes approximation for slow viscous flow, and the fluid motion is thus responsible for movement of the interface between them. A linearized solution is presented, from which the decay rate and the group speed of the wave system may be obtained. The nonlinear equations are solved using a novel spectral representation for the streamfunctions in each of the two fluid layers, and the exact boundary conditions are applied at the unknown interface location. Results are presented for the wave profiles, and the behaviour of the curvature of the interface is discussed. These results are compared to the Boussinesq–Stokes approximation which is also solved by a novel spectral technique, and agreement between the results supports the numerical calculations.