Interaction among multiple vortices is of particular importance to biological locomotion. It plays an essential role in the force and energy capture. This study examines the motion and dynamics of multiple co-axial co-rotating vortex rings. The vortex rings, which have the same formation time, are successively generated in a piston-cylinder apparatus by accurately controlling the interval time. The flow fields are visualized by the finite-time Lyapunov exponent and then repelling Lagrangian coherent structures (r-LCSs) are determined. Two types of vortex interactions (“strong” and “weak”) are defined by investigating the r-LCSs: a strong interaction is indicated by connected r-LCSs showing a channel for fluid transport (termed as a “flux window”); a weak interaction is indicated by disconnected r-LCSs between the vortex rings. For strong interaction, leapfrogging and merger of vortex rings can happen in the later stage of the evolution process; however, the rings are separated for weak interaction. Two distinct formation modes, the formation enhancement mode (FEM) and formation restraint mode (FRM), refer to the effect of one or multiple vortex ring(s) on the initial circulation of the subsequently formed vortex ring. In the FEM, the circulation of a vortex ring is larger than that of an isolated (without interaction) vortex ring. On the other hand, the situation is opposite in the FRM. A dimensionless number reflecting the interaction mechanism, “structure stretching number” S*, is proposed, which evaluates the induced effect of the wake vortices on the formation of a vortex ring. A limiting S* (SL*=(2±0.4)×10−4) is the bifurcation point of the two formation modes. The augmentation of circulation reaches up to 10% for the FEM when S*<SL*, while in the FRM (S*>SL*), the circulation decreases for at most 20%. The newly defined formation modes and number could shed light on the understanding of the dynamics of multiple vortex ring flows.

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The dynamics of dual vortex ring flows is studied experimentally and numerically in a model system that consists of a piston-cylinder apparatus. The flows are generated by double identical strokes which have the velocity profile characterized by the sinusoidal function of half the period. By calculating the total wake impulse in two strokes in the experiments, it is found that the average propulsive force increases by 50% in the second stroke for the sufficiently small stroke length, compared with the first stroke. In the numerical simulations, two types of transient force augmentation are revealed, there being the transient force augmentation for the small stroke lengths and the absolute transient force augmentation for the large stroke lengths. The relative transient force augmentation increases to 78% for L/D = 1, while the absolute transient force augmentation for L/D = 4 is twice as much as that for L/D = 1. Further investigation demonstrates that the force augmentation is attributed to the interaction between vortex rings, which induces transport of vortex impulse and more evident fluid entrainment. The critical situation of vortex ring separation is defined and indicated, with vortex spacing falling in a narrow gap when the stroke lengths vary. A new model is proposed concerning the limiting process of impulse, further suggesting that apart from vortex formation timescale, vortex spacing should be interpreted as an independent timescale to reflect the dynamics of vortex interaction.

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BackgroundThis Bayesian network meta-regression analysis provides a head-to-head comparison of first-line therapeutic immune checkpoint inhibitors (ICI) and tyrosine kinase inhibitors (TKI) combinations for metastatic renal cell carcinoma (mRCC) using median follow-up time as covariate.MethodsWe searched Six databases for a comprehensive analysis of randomised clinical trials (RCTs). Comparing progression free survival (PFS) and overall survival (OS) of different interventions at the same time node by Bayesian network meta-analysis. Bayesian network meta-regression analysis was performed on objective response rate (ORR), adverse events (AEs) (grade ≥ 3) and the hazard ratios (HR) associated with PFS and OS, with the median follow-up time as the covariate.ResultsEventually a total of 22 RCTs reporting 11,090 patients with 19 interventions. Lenvatinib plus Pembrolizumab (LenPem) shows dominance of PFS, and Pembrolizumab plus Axitinib (PemAxi) shows superiority in OS at each time point. After meta-regression analysis, for HRs of PFS, LenPem shows advantages; for HRs of OS, PemAxi shows superiority; For ORR, LenPem provides better results. For AEs (grade ≥ 3), Atezolizumab plus Bevacizumab (AtezoBev) is better.ConclusionConsidering the lower toxicity and the higher quality of life, PemAxi should be recommended as the optimal therapy in treating mRCC.Systematic review registrationhttps://www.crd.york.ac.uk/prospero/, identifier CRD4202236775.

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Owing to the limiting effect of energy, vortex rings cannot grow indefinitely and thus pinch off. In this paper, experiments on the vortex rings generated using a piston-cylinder apparatus are conducted so as to investigate the pinch-off mechanisms and identify the limiting effect of energy. Both theoretical and experimental results show that the generated vortex rings share a unified energy feature, regardless of whether they are pinched-off or not. Moreover, the unified energy feature is quantitatively described by a dimensionless energy number γ, defined as γ=(E/I2Γωmax) and exhibiting a critical value γring = 0.14 ± 0.01 for the generated vortex rings. This unified energy feature reflects the limiting effect of energy and specifies the target of vortex ring formation. Furthermore, based on the tendency of γ during vortex ring formation, criteria for determining the two timescales, i.e., pinch-off time and separation time, which correspond to the onset and end of pinch-off process, respectively, are suggested.