The research on elasto-inertial turbulence (EIT), a new type of turbulent flow, has reached the stage of identifying the minimal flow unit (MFU). On this issue, direct numerical simulations of FENE-P fluid flow in two-dimensional channels with variable sizes are conducted in this study. We demonstrate with the increase of channel length that the simulated flow experiences several different flow patterns, and there exists an MFU for EIT to be self-sustained. At Weissenberg number ($Wi$) higher than the one required to excite EIT, when the channel length is relatively small, a steady arrowhead regime (SAR) flow structure and a laminar-like friction coefficient is achieved. However, as the channel length increases, the flow can fully develop into EIT characterized with high flow drag. Close to the size of the MFU, the simulated flow behaves intermittently between the SAR state with low drag and EIT state with high drag. The flow falling back to ‘laminar flow’ is caused by the insufficient channel size below the MFU. Furthermore, we give the relationship between the value of the MFU and the effective $Wi$, and explain its physical reasons. Moreover, the intermittent flow regime obtained based on the MFU gives us an opportunity to look into the origin and exciting process of EIT. Through capturing the onset process of EIT, we observed that EIT originates from the sheet-like extension structure located near the wall, which is maybe related to the wall mode rather than the centre mode. The fracture and regeneration of this sheet-like structure is the key mechanism for the self-sustaining of EIT.

Previous studies have indicated an association between vitamin D and thyroid- and parathyroid-related diseases. However, it remains unclear whether it is a cause of the disease, a side effect of treatment or a consequence of the disease. The Mendelian randomisation (MR) study strengthens the causal inference by controlling for non-heritable environmental confounders and reverse causation. In this study, a two-sample bidirectional MR analysis was conducted to investigate the causal relationship between serum vitamin D levels and thyroid- and parathyroid-related diseases. Inverse variance weighted, weighted median and MR-Egger methods were performed, the Cochran Q test was used to evaluate the heterogeneity and the MR-PRESSO and MR-Egger intercepts were utilised to assess the possibility of pleiotropy. The Bonferroni-corrected significance threshold was 0·0038. At the Bonferroni-corrected significance level, we found that vitamin D levels suggestively decreased the risk of benign parathyroid adenoma (OR = 0·244; 95 % CI 0·074, 0·802; P = 0·0202) in the MR analyses. In the reverse MR study, a genetically predicted risk of thyroid cancer suggestively increased the risk of elevated vitamin D (OR = 1·007; 95 % CI 1·010, 1·013; P = 0·0284), chronic thyroiditis significantly increased the risk of elevated vitamin D (OR = 1·007; 95 % CI 1·002, 1·011; P = 0·0030) and thyroid nodules was significantly decreased the vitamin D levels (OR = 0·991; 95 % CI 0·985, 0·997; P = 0·0034). The findings might be less susceptible to horizontal pleiotropy and heterogeneity (P > 0·05). This study from a gene perspective indicated that chronic thyroiditis and thyroid nodules may impact vitamin D levels, but the underlying mechanisms require further investigation.

Radio frequency (RF) breakdown can result in pulse shortening and seriously degrade the stability and reliability of relativistic backward wave oscillators (RBWOs). This paper discusses the energy range of electrons causing breakdown traces in slow-wave structures (SWSs) through particle-in-cell (PIC) simulation, numerical calculation, and experimental verification. The PIC simulation and numerical calculation results reveal that the energy of the majority of the field-induced electrons bombarding the SWS surfaces after being accelerated is less than 120 keV. Furthermore, the micro appearances of the breakdown traces in SWSs and the witness targets bombarded directly by electrons of various energy levels have been analyzed. Scanning electron microscope (SEM) shows that the breakdown traces are featured with corrugated morphologies with a wide range and a shallow depth. A mass of craters emerge in the vicinity of the corrugated morphologies. These appearances are quite similar to destructive traces impacted directly by low-energy electrons (around 160 keV). Thus, it is confirmed that the breakdown traces result from the bombardment of low-energy electrons. Therefore, the breakdown mechanism of field-emitted electrons impacting on the structure surfaces in RBWOs has been further improved.

The essence of the maximum drag reduction (MDR) state of viscoelastic drag-reducing turbulence (DRT) is still under debate, which mainly holds two different types of views: the marginal state of inertial turbulence (IT) and elasto-inertial turbulence (EIT). To further promote its understanding, this paper conducts a large number of direct numerical simulations of DRT at a modest Reynolds number Re with $Re = 6000$ for the FENE-P model that covers a wide range of flow states and focuses on the problem of how nonlinear extension affects the nature of MDR by varying the maximum extension length $L$ of polymers. It demonstrates that the essence of the MDR state can be both IT and EIT, where $L$ is somehow an important parameter in determining the dominant dynamics. Moreover, there exists a critical $L_c$ under which the minimum flow drag can be achieved in the MDR state even exceeding the suggested MDR limit. Systematic analyses on the statistical properties, energy spectrum, characteristic structures and underly dynamics show that the dominant dynamics of the MDR state gradually shift from IT-related to EIT-related dynamics with an increase of $L$. The above effects can be explained by the effective elasticity introduced by different $L$ at a fixed Weissenberg number (Wi) as well as the excitation of pure EIT. It indicates that larger $L$ introduces more effective elasticity and is favourable to EIT excitation. Therefore, we argue that the MDR state is still dominated by IT-related dynamics for the case of small $L$, but replaced by EIT-related dynamics at high $L$. The obtained results can harmonize the seemingly controversial viewpoints on the dominant dynamics of the MDR state and also provide some ideas for breaking through the MDR limit, such as searching for a polymer solution with a proper molecular length and concentration.