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The flow past a cylinder in proximity to a plane wall is investigated numerically for small gap ratios. Three vortex dynamic processes associated with different hairpin vortex generation mechanisms are identified for the first time, and the wake-induced turbulent transition is analysed. The vortex shedding is suppressed at $G/D = 0.1$, while the spanwise vortex is generated via a Kelvin–Helmholtz instability and evolves into hairpin vortices. For $G/D= 0.3$, the upper and lower rollers alternatively shedding from the cylinder, interact with the secondary vortex. The split secondary vortex merges with the upper roller and results in a new vortex downstream, which develops into hairpin vortices. When $G/D = 0.9$, the secondary vortex interacts with the lower roller and then evolves into hairpin vortices. A tertiary vortex induced by the secondary vortex is observed, rotating in the opposite direction to the secondary vortex the wake-induced transitions share the same route. The velocity fluctuations deviate from the optimal growth theory in the pre-transitional region. In the transitional region low-frequency disturbances penetrate the sheltering edge to generate streaks where the disturbance energy declines. In the turbulent region the logarithmic layer is formed, indicating that the turbulent equilibrium is established.
Understanding the patterns of treatment response is critical for the treatment of patients with schizophrenia; one way to achieve this is through using a longitudinal dynamic process study design.
This study aims to explore the response trajectory of antipsychotics and compare the treatment responses of seven different antipsychotics over 6 weeks in patients with schizoprenia (trial registration: Chinese Clinical Trials Registry Identifier: ChiCTR-TRC-10000934).
Data were collected from a multicentre, randomised open-label clinical trial. Patients were evaluated with the Positive and Negative Syndrome Scale (PANSS) at baseline and follow-up at weeks 2, 4 and 6. Trajectory groups were classified by the method of k-means cluster modelling for longitudinal data. Trajectory analyses were also employed for the seven antipsychotic groups.
The early treatment response trajectories were classified into a high-trajectory group of better responders and a low-trajectory group of worse responders. The results of trajectory analysis showed differences compared with the classification method characterised by a 50% reduction in PANSS scores at week 6. A total of 349 patients were inconsistently grouped by the two methods, with a significant difference in the composition ratio of treatment response groups using these two methods (χ2 = 43.37, P < 0.001). There was no differential contribution of high- and low trajectories to different drugs (χ2 = 12.52, P = 0.051); olanzapine and risperidone, which had a larger proportion in the >50% reduction at week 6, performed better than aripiprazole, quetiapine, ziprasidone and perphenazine.
The trajectory analysis of treatment response to schizophrenia revealed two distinct trajectories. Comparing the treatment responses to different antipsychotics through longitudinal analysis may offer a new perspective for evaluating antipsychotics.
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