For a nondegenerate r-graph F, large n, and t in the regime $[0, c_{F} n]$, where $c_F>0$ is a constant depending only on F, we present a general approach for determining the maximum number of edges in an n-vertex r-graph that does not contain $t+1$ vertex-disjoint copies of F. In fact, our method results in a rainbow version of the above result and includes a characterization of the extremal constructions.

Our approach applies to many well-studied hypergraphs (including graphs) such as the edge-critical graphs, the Fano plane, the generalized triangles, hypergraph expansions, the expanded triangles, and hypergraph books. Our results extend old results of Erdős [13], Simonovits [76], and Moon [58] on complete graphs, and can be viewed as a step toward a general density version of the classical Corrádi–Hajnal [10] and Hajnal–Szemerédi [32] theorems.

Our method relies on a novel understanding of the general properties of nondegenerate Turán problems, which we refer to as smoothness and boundedness. These properties are satisfied by a broad class of nondegenerate hypergraphs and appear to be worthy of future exploration.

The three-dimensional flow over a low-aspect-ratio (low-$A\!R$) trapezoidal plate is investigated experimentally with a focus on how the tip effects impact the structure and dynamics of the separation bubble. The chord-based Reynolds number is $5800$, and the angle of attack varies from $4^\circ$ to $10^\circ$. Once the flow separates, the separation bubble emerges and features a swallow-tailed structure that shrinks near the midspan, which is first found for the flows over low-$A\!R$ plates. This structure develops into the conventional single-tailed structure as the angle of attack increases. Moreover, the vortex shedding within the swallow-tailed separation bubble is restored from multiple asynchronously measured local velocity fields. It is revealed that the leading-edge vortex undergoes the novel transformation from a C-shape vortex into an M-shape vortex. This vortex transformation stems from the mass transport of the near-wall spanwise flow, which affects the fluid motion on the windward side of the C-shape vortex head, strengthening and accelerating the vortex head. The strengthened vortex head facilitates the entrainment of high-momentum fluid from the outer flow. This is responsible for the formation of the swallow-tailed structure. These findings help to fill the gaps left by the downwash at low angles of attack for low-$A\!R$ wings, and are of value in improving the cruising and gliding performance of micro-air vehicles.

Straightplasma channels are widely used to guide relativistic intense laser pulses over several Rayleigh lengths for laser wakefield acceleration. Recently, a curved plasma channel with gradually varied curvature was suggested to guide a fresh intense laser pulse and merge it into a straight channel for staged wakefield acceleration [Phys. Rev. Lett. 120, 154801 (2018)]. In this work, we report the generation of such a curved plasma channel from a discharged capillary. Both longitudinal and transverse density distributions of the plasma inside the channel were diagnosed by analyzing the discharging spectroscopy. Effects of the gas-filling mode, back pressure and discharging voltage on the plasma density distribution inside the specially designed capillary are studied. Experiments show that a longitudinally uniform and transversely parabolic plasma channel with a maximum channel depth of 47.5 μm and length of 3 cm can be produced, which is temporally stable enough for laser guiding. Using such a plasma channel, a laser pulse with duration of 30 fs has been successfully guided along the channel with the propagation direction bent by 10.4°.

This paper presents systematic molecular dynamics modelling of Na-montmorillonite subjected to uniaxial compression and unidirectional shearing. An initial 3D model of a single-cell Na-montmorillonite structure is established using the Build Crystal module. The space group is C2/m, and COMPASS force fields are applied. Hydration analysis of Na-montmorillonite has been performed to validate the simulation procedures, where the number of absorbed water molecules varied with respect to the various lattice parameters. A series of uniaxial compression stress σzz and unidirectional shear stress τxy values are applied to the Na-montmorillonite structure. It is shown that the lattice parameter and hydration degree exhibit significant influence on the stress–strain relationship of Na-montmorillonite. The ultimate strain increases with increases in the lattice parameter but decreases in the number of water molecules. For saturated Na-montmorillonite, more water molecules result in a stiffer clay mineral under uniaxial compression and unidirectional shearing.

The subduction model of the Neo-Tethys during the Early Cretaceous has always been a controversial topic, and the scarcity of Early Cretaceous magmatic rocks in the southern part of the Gangdese batholith is the main cause of this debate. To address this issue, this article presents new zircon U–Pb chronology, zircon Hf isotope, whole-rock geochemistry and Sr–Nd isotope data for the Early Cretaceous quartz diorite dykes with adakite affinity in Liuqiong, Gongga. Zircon U–Pb dating of three samples yielded ages of c. 141–137 Ma, indicating that the Liuqiong quartz diorite was emplaced in the Early Cretaceous. The whole-rock geochemical analysis shows that the Liuqiong quartz diorite is enriched in large-ion lithophile elements (LILEs) and light rare-earth elements (LREEs) and is depleted in high-field-strength elements (HFSEs), which are related to slab subduction. Additionally, the Liuqiong quartz diorite has high SiO2, Al2O3 and Sr contents, high Sr/Y ratios and low heavy rare-earth element (HREE) and Y contents, which are compatible with typical adakite signatures. The initial 87Sr/86Sr values of the Liuqiong adakite range from 0.705617 to 0.705853, and the whole-rock ϵNd(t) values vary between +5.78 and +6.24. The zircon ϵHf(t) values vary from +11.5 to +16.4. Our results show that the Liuqiong adakite magma was derived from partial melting of the Neo-Tethyan oceanic plate (mid-ocean ridge basalt (MORB) + sediment + fluid), with some degree of subsequent peridotite interaction within the overlying mantle wedge. Combining regional data, we favour the interpretation that the Neo-Tethyan oceanic crust was subducted at a low angle beneath the Gangdese during the Early Cretaceous.