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The linear stability of plane Couette flow is investigated when the plates are horizontal, and the fluid is stably stratified with a cubic basic density profile. The disturbances are treated as inviscid and diffusion of the density field is neglected. Previous studies have shown that this density profile can develop multiple neutral curves, despite the stable stratification, and the fact that plane Couette flow of homogeneous fluid is stable. It is shown that when the neutral curves are plotted with wave angle on one axis, and location of the density inflexion point on the other axis, they produce a self-similar fractal pattern. The repetition on smaller and smaller scales occurs in the limit when the waves are highly oblique, i.e. longitudinal vortices almost aligned with the flow; the corresponding limit for two-dimensional waves is that of strong buoyancy/weak flow. The fractal set of neutral curves also represents a fractal of bifurcation points at which nonlinear solutions can be continued from the trivial state, and these may be helpful for understanding turbulent states. This may be the first example of a fractal generated by a linear ordinary differential equation.
The Reinforcement Sensitivity Theory of Personality has as its main foundation a Behavioural Inhibition System (BIS), defined by anxiolytic drugs, in which high trait sensitivity should lead to internalising, anxiety, disorders. Conversely, it has been suggested that low BIS sensitivity would be a characteristic of externalising disorders. BIS output should lead to increased arousal and attention as well as behavioural inhibition. Here, therefore, we tested whether an externalising disorder, Attention Deficit Hyperactivity Disorder (ADHD), involves low BIS sensitivity. Goal-Conflict-Specific Rhythmicity (GCSR) in an auditory Stop Signal Task is a right frontal EEG biomarker of BIS function. We assessed children diagnosed with ADHD-I (inattentive) or ADHD-C (combined) and healthy control groups for GCSR in: a) an initial smaller study in Dunedin, New Zealand (population ~120,000: 15 control, 10 ADHD-I, 10 ADHD-C); and b) a main larger one in Tehran, Iran (population ~9 [city]-16 [metropolis] million: 27 control, 18 ADHD-I, 21 ADHD-C). GCSR was clear in controls (particularly at 6–7 Hz) and in ADHD-C (particularly at 8–9 Hz) but was reduced in ADHD-I. Reduced attention and arousal in ADHD-I could be due, in part, to BIS dysfunction. However, hyperactivity and impulsivity in ADHD-C are unlikely to reflect reduced BIS activity. Increased GCSR frequency in ADHD-C may be due to increased input to the BIS. BIS dysfunction may contribute to some aspects of ADHD (and potentially other externalising disorders) and to some differences between the ADHD subtypes but other prefrontal systems (and, e.g. dopamine) are also important.
Introduction: Atrial fibrillation (AF) is the most common sustained arrhythmia affecting 1-2% of the population. Oral anticoagulation (OAC) reduces stroke risk by 60-80% in AF patients, but only 50% of indicated patients receive OAC. Many patients present to the ED with AF due to arrhythmia symptoms, however; lack of OAC prescription in the ED has been identified as a significant gap in the care of AF patients. Methods: This was a multi-center, pragmatic, three-phase before-after study, in three Canadian sites. Patients who presented to the ED with electrocardiographically (ECG) documented, nonvalvular AF and were discharged home were included. Phase 1 was a retrospective chart review to determine OAC prescription of AF patients in each ED; Phase 2 was a low-intensity knowledge translation intervention where a simple OAC-prescription tool for ED physicians with subsequent short-term OAC prescription was used, as well as an AF patient education package and a letter to family physicians; phase 3 incorporated Phase 2 interventions, but added immediate follow-up in a community AF clinic. The primary outcome of the study was the rate of new OAC prescriptions at ED discharge in AF patients who were OAC eligible and were not on OAC at presentation. Results: A total of 632 patients were included from June, 2015-November, 2016. ED census ranged from 30000-68000 annual visits. Mean age was 71±15, 67±12, 67±13 years, respectively. 47.5% were women, most responsible ED diagnosis was AF in 75.8%. The mean CHA2DS2-VASc score was 2.6±1.8, with no difference amongst groups. There were 266 patients eligible for OAC and were not on this at presentation. In this group, the prescription of new OAC was 15.8% in Phase 1 as compared to 54% and 47%, in Phases 2 and 3, respectively. After adjustment for center, components of the CHA2DS2-VASc score, prior risk of bleeding and most responsible ED diagnosis, the odds ratio for new OAC prescription was 8.0 (95%CI (3.5,18.3) p<0.001) for Phase 3 vs 1, and 10.0 (95%CI (4.4,22.9) p<0.001), for Phase 2 vs 1). No difference in OAC prescription was seen between Phases 2 and 3. Conclusion: Use of a simple OAC-prescription tool was associated with an increase in new OAC prescription in the ED for eligible patients with AF. Further testing in a rigorous study design to assess the effect of this practice on stroke prevention in the AF patients who present to the ED is indicated.
This article examines the likely role of competition in the regulatory analysis of bank mergers in China. Despite financial reforms, the banking sector remains subject to a complex web of financial regulation, with industrial policy favouring stability to facilitate national economic development. While there are currently no Ministry of Commerce (MOFCOM) bank merger determinations under the Anti-Monopoly Law (AML), examples of MOFCOM’s merger analysis in other sensitive industries diverge from a pure competition-based analysis, favouring grounds linked to national economic development broadly within the terms of the AML. Given the importance of banking to the Chinese economy, this article argues that competition is unlikely to play a large part in any assessment of bank mergers by MOFCOM, particularly where a foreign bank is involved. Instead, issues linked to ‘national economic development’ and stability are likely to play the most important role, leading to less predictable merger approval outcomes.
Introduction: The recently published ProMISe, ARISE and ProCESS trials demonstrated that protocol-based resuscitation (EGDT) of ER patients in whom septic shock was diagnosed did not improve outcome when compared to usual care. The objective of this project was to survey McMaster emergency physicians in areas including sepsis definition, clinical recognition in adults, self-rated skills assessment, attitudes towards skills augmentation and compare results to the cohort surveyed 11 years ago, close to the introduction of EGDT. Methods: Full time faculty at McMaster’s Department of Emergency Medicine and ER residents were surveyed anonymously using an electronic survey. The questions covered demographics and training data, identification of septic patients, sepsis intervention and attitudes towards skills augmentation. Results: A total of 18 physicians responded to the electronic survey to date. All respondents were able to correctly input definitions for SIRS, sepsis, severe sepsis and septic shock. The majority of respondents felt the best strategy to identify potentially septic adults involved monitoring abnormal vital signs (67%) with some stating serum lactate assessment (33%). Of the 11 possible interventions options provided to care for septic patients, respondents appeared more comfortable with placement of lines, giving vasopressors and appropriate use of fluids for resuscitation. This was compared to more specialized interventions like initiating IV steroids in vasopressor dependant shock despite adequate fluid loading. 22% of respondents believed that patients without respiratory compromise with clinically severe sepsis should be intubated which was found to be 48% in the previous cohort surveyed 11 years ago. 78% believed patients in septic shock without respiratory comprise should be intubated, reassuringly similar to the previous survey result of 87%. Conclusion: Emergency physicians at our Canadian institution are comfortable with the skill set required to care for patients with sepsis. Respondents surveyed to date were all comfortable with important resuscitative measures including accurate identification, placement of lines and appropriate fluid administration and were receptive to additional training. Our study emphasizes that our physicians have the skill set to identify and provide care for sepsis using their clinical judgment in cases that may not require protocolized based care.
Hydrodynamic stability of round viscous fluid jets is considered within the framework of the non-modal approach. Both the jet fluid and surrounding gas are assumed to be incompressible and Newtonian; the effect of surface capillary pressure is taken into account. The linearized Navier–Stokes equations coupled with boundary conditions at the jet axis, interface and infinity are reduced to a system of four ordinary differential equations for the amplitudes of disturbances in the form of spatial normal modes. The eigenvalue problem is solved by using the orthonormalization method with Newton iterations and the system of least stable normal modes is found. Linear combinations of modes (optimal disturbances) leading to the maximum kinetic energy at a specified set of governing parameters are found. Parametric study of optimal disturbances is carried out for both an air jet and a liquid jet in air. For the velocity profiles under consideration, it is found that the non-modal instability mechanism is significant for non-axisymmetric disturbances. The maximum energy of the optimal disturbances to the jets at the Reynolds number of 1000 is found to be two orders of magnitude larger than that of the single mode. The largest growth is gained by the streamwise velocity component.
China and Australia are extremely significant trade partners and investors. Australia has a very well established competition law, now called the Competition and Consumer Law 2010, with a well-established merger regime. China has a relatively new competition law, the Anti-Monopoly Law 2007. This article compares merger control in the two jurisdictions. The Ministry of Commerce (MOFCOM) has already referred to an Australian decision in rejecting a merger, the only reference to a foreign decision to date, which confirms the utility of the comparison. This article critically evaluates the determinations of MOFCOM and compares the approach of the Australian Competition and Consumer Commission (ACCC), the Australian regulator. It assesses the transparency and predictability of procedures and decision-making in the two jurisdictions.
Several single nucleotide polymorphisms (SNPs) in candidate genes of DNA repair and hormone pathways have been reported to be associated with endometrial cancer risk. We sought to confirm these associations in two endometrial cancer case-control sample sets and used additional data from an existing genome-wide association study to prioritize an additional SNP for further study. Five SNPs from the CHEK2, MGMT, SULT1E1 and SULT1A1 genes, genotyped in a total of 1597 cases and 1507 controls from two case-control studies, the Australian National Endometrial Cancer Study and the Polish Endometrial Cancer Study, were assessed for association with endometrial cancer risk using logistic regression analysis. Imputed data was drawn for CHEK2 rs8135424 for 666 cases from the Study of Epidemiology and Risk factors in Cancer Heredity study and 5190 controls from the Wellcome Trust Case Control Consortium. We observed no association between SNPs in the MGMT, SULT1E1 and SULT1A1 genes and endometrial cancer risk. The A allele of the rs8135424 CHEK2 SNP was associated with decreased risk of endometrial cancer (adjusted per-allele OR 0.83; 95%CI 0.70-0.98; p = .03) however this finding was opposite to that previously published. Imputed data for CHEK2 rs8135424 supported the direction of effect reported in this study (OR 0.85; 95% CI 0.65–1.10). Previously reported endometrial cancer risk associations with SNPs from in genes involved in estrogen metabolism and DNA repair were not replicated in our larger study population. This study highlights the need for replication of candidate gene SNP studies using large sample groups, to confirm risk associations and better prioritize downstream studies to assess the causal relationship between genetic variants and cancer risk. Our findings suggest that the CHEK2 SNP rs8135424 be prioritized for further study as a genetic factor associated with risk of endometrial cancer.
Cognition and emotion, traditionally thought of as largely distinct, have recently begun to be conceptualized as dynamically linked processes that interact to influence functioning. This study investigated the moderating effects of cognitive functioning on the relationship between negative emotionality and attention deficit/hyperactivity disorder (ADHD) symptom severity. A total of 216 (140 hyperactive/inattentive; 76 typically developing) preschoolers aged 3–4 years were administered a neuropsychological test battery (i.e., NEPSY). To avoid method bias, child negative emotionality was rated by teachers (Temperament Assessment Battery for Children-Revised), and parents rated symptom severity on the ADHD Rating Scale (ADHD-RS-IV). Hierarchical Linear Regression analyses revealed that both negative emotionality and Perceptual-Motor & Executive Functions accounted for significant unique variance in ADHD symptom severity. Significant interactions indicated that when negative emotionality is low, but not high, neuropsychological functioning accounts for significant variability in ADHD symptoms, with lower functioning predicting more symptoms. Emotional and neuropsychological functioning, both individually and in combination, play a significant role in the expression of ADHD symptom severity. (JINS, 2011, 17, 502–510)
This study uses spatio-temporal stability analysis to investigate the convective and absolute instability properties of a steady unconfined planar liquid jet. The approach uses a piecewise linear velocity profile with a finite-thickness shear layer at the edge of the jet. This study investigates how properties such as the thickness of the shear layer and the value of the fluid velocity at the interface within the shear layer affect the stability properties of the jet. It is found that the presence of a finite-thickness shear layer can lead to an absolute instability for a range of density ratios, not seen when a simpler plug flow velocity profile is considered. It is also found that the inclusion of surface tension has a stabilizing effect on the convective instability but a destabilizing effect on the absolute instability. The stability results are used to obtain estimates for the breakup length of a planar liquid jet as the jet velocity varies. It is found that reducing the shear layer thickness within the jet causes the breakup length to decrease, while increasing the fluid velocity at the fluid interface within the shear layer causes the breakup length to increase. Combining these two effects into a profile, which evolves realistically with velocity, gives results in which the breakup length increases for small velocities and decreases for larger velocities. This behaviour agrees qualitatively with existing experiments on the breakup length of axisymmetric jets.
Recent simulations and experiments appear to show that the rotating-disk boundary layer is linearly globally stable despite the existence of local absolute instability. However, we argue that linear global instability can be created by local absolute instability at the edge of the disk. This argument is based on investigations of the linearized complex Ginzburg–Landau equation with weakly spatially varying coefficients to model the propagation of a wavepacket through a weakly inhomogeneous unstable medium. Therefore, this mechanism could operate in a variety of locally absolutely unstable flows. The corresponding nonlinear global mode has a front at the radius of onset of absolute instability when the disk edge is far from the front. This front moves radially outwards when the Reynolds number at the disk edge is reduced. It is shown that the laminar–turbulent transition front also behaves in this manner, possibly explaining the scatter in observed transitional Reynolds numbers.
The absolute and convective instability properties of plane mixing layers are investigated for linearized inviscid disturbances. It is shown that confinement by plates parallel to the flow can enhance the absolute instability so much that even a co-flow plane mixing layer becomes absolutely unstable when the ratio of distances of the plates from the mixing layer lies in a certain range. Even when the plates are placed equidistantly from the mixing layer, a co-flow mixing layer can become absolutely unstable if the velocity profile has an asymmetry about its mid-plane. ‘Semiconfinement’, where a plate is only added to one side of the mixing layer, is also investigated. A substantial destabilization is possible when the plate is added on the side of the faster stream. Previous investigations seem only to have found absolute instability when the streams flow in opposite directions.
The propagation characteristics of inviscid axisymmetric linearized disturbances to swirling jets are investigated for two families of model velocity profiles. Briggs' method is applied to dispersion relations to determine when the basic swirling jets are absolutely or convectively unstable. The method is also applied to the neutral inertial waves used by Benjamin to characterize the subcritical or supercritical nature of the flow. Although these waves are neutral, Briggs' method nonetheless indicates a qualitative change in behaviour at Benjamin's criticality condition. The first model jet has uniform axial velocity, rigid-body rotation and issues into still fluid. A known difficulty in the application of Briggs' method to the analytical dispersion relation for inviscid waves in this flow is resolved. The difficulty is that the pinch point can cross into the left half of the complex-wavenumber plane, where waves grow exponentially with radius and fail to satisfy homogeneous boundary conditions. In this paper the physical consequences of this behaviour are explained. It is shown that if the still fluid is of infinite extent in the radial direction, then the jet is convectively unstable to axisymmetric waves, but if the jet is confined by an outer cylinder concentric with the jet axis, then it becomes absolutely unstable to axisymmetric waves provided that the swirl (ratio of azimuthal to axial velocity) is large enough. This destabilizing effect of confinement occurs however large the radius of the outer cylinder. A second family of model swirling jets with smooth profiles and a finite thickness shear layer at the jet edge is also studied. The inviscid stability equations are solved numerically in this case. The results from the analytical dispersion relations are reproduced as the shear layer thickness tends to zero. However, increasing this thickness acts to destabilize the absolute instability of axisymmetric waves, apparently due to the centrifugal instability present in the shear layer. It is suggested that the transition from convective to absolute instability could be associated with the onset of an unsteady vortex breakdown. The swirl required to produce this transition can be either greater, or less, than the swirl required to produce the transition from supercritical to subcritical flow, depending on the details of the basic velocity profiles. A codimension-two point in parameter space can exist where the unsteady bifurcation associated with the convective–absolute transition coincides with the steady bifurcation associated with the supercritical–subcritical transition. Such codimension-two points can control a rich variety of nonlinear dynamical behaviour.
We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question here.
In particular, we demonstrate that the determinant of the gradient of any admissible deformation with finite energy is strictly positive on the closure of the domain. With this in hand,
Gâteaux differentiability of the potential energy at a minimizer is automatic, yielding the existence of a weak solution. We indicate how our results hold for a general class of boundary value problems, including “mixed” boundary conditions. For each of the two possible pure displacement formulations (in second-gradient problems), we show that the resulting deformation is an injective mapping, whenever the imposed placement on the boundary is itself the trace of an injective map.
When a solid plate, with a boundary condition of no normal flow through it, is introduced parallel to a shear layer it is normally expected to exert a stabilizing influence on any inviscid linearly unstable waves. In this paper we present an example of an absolutely unstable boundary-layer flow that can be made more absolutely unstable by the addition of a plate parallel to the original flow and far from the boundary layer itself. In particular, the addition of the plate is found to increase the growth rate of the absolute instability of the original boundary-layer flow by an order of magnitude for long waves. This phenomenon is illustrated using piecewise-linear inviscid basic-flow profiles, for which analytical dispersion relations have been derived. Long-wave stability theories have been developed in several limits clarifying the mechanisms underlying the behaviour and establishing its generic nature. The class of flows expected to exhibit this phenomenon includes a class found recently to have an exponential growth of disturbances in the wall-normal direction, owing to the approach of certain saddle-points to certain branch-cuts in the complex-wavenumber plane. The theory also suggests that a convectively unstable flow in an infinite domain can be converted, in some circumstances, into an absolutely unstable flow when the domain is made finite by the addition of a plate, however far away the plate is.
In this paper we extend the familiar concept of spatial instability and growth of disturbances in the downstream direction to include spatial instability and growth in the wall-normal direction. The stability theory of boundary layers has generally been concerned with determining the evolution of disturbances inside a boundary layer (this is where disturbances have their largest amplitudes and can cause a laminar boundary layer to become turbulent). Outside a boundary layer, where the basic flow is uniform, normal-mode disturbances decay exponentially with distance from the wall to satisfy homogeneous boundary conditions. In this paper we present a surprising scenario where an impulsive disturbance, made up of a superposition of these normal modes, nonetheless grows exponentially with distance from the wall. While the usual convective instability with exponential growth in the downstream direction can be efficiently characterized by spatial modes with complex wavenumbers, the new convective instability can be efficiently characterized by modes with exponentially diverging ‘eigenfunctions’ obtained by moving certain branch-cuts in the complex wavenumber plane. The new instability is therefore associated with an interaction between the discrete spectrum and the continuous spectrum. We emphasize, however, that the homogeneous boundary conditions are always satisfied, and that at any finite time exponential growth only occurs over a finite distance from the wall, but this distance increases linearly with time. Interactions between poles and branch-cuts have been found before, but the results presented here provide a physical interpretation for this spectral behaviour. A further curiosity is that some of these divergent modes have been found to violate Howard's semi-circle theorem.