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The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The distinct combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce an unusual and tunable sequence of FQH states. Here, we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors ν = 2p + 2/3, with hints of additional states appearing at ν = 2p + 3/5, where p = –2, –1, 0, and 1. This sequence breaks particle-hole symmetry and obeys a ν → ν + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.

Energetic benefit and enhanced performance are considered among the most fascinating achievements of collective behaviours, e.g. fish schools and flying formations. The collective locomotion of two self-propelled flapping plates initially in a side-by-side arrangement is investigated numerically. Both in-phase and antiphase oscillations for the two plates are considered. It is found that the plates will spontaneously form some stable configurations as a result of the flow-mediated interaction, specifically, the staggered-following (SF) mode and the alternate-leading (AL) mode for the in-phase scenario and the moving abreast (MA) mode and the AL mode for the antiphase scenario. In the SF mode, the rear plate follows the front one with a staggered configuration. In the AL mode, the plates chase each other side-by-side alternately. In terms of propulsive speed and efficiency, the performance of the plates in the SF mode with small lateral spacing $H$ is found to be better than those in the tandem following case ( $H=0$ ) and the side-by-side case (i.e. the AL mode). To achieve higher propulsive efficiency, no matter in-phase or antiphase oscillations, the two plates with moderate bending stiffness, e.g. $K\\approx O(1)$ , are preferred and they should be close enough in the lateral direction. For the side-by-side configuration, the performance of each plate in the antiphase and in-phase scenarios is enhanced and weakened in comparison with that of the isolated plate, respectively. Besides the pressure and vorticity contours, the normal force and thrust acting on the plates are also analysed. It is revealed that the thrust is mainly contributed by the normal force at moderate bending stiffness. The normal force and thrust are critical to the propulsive speed and efficiency. For two self-propelled plates, in view of hydrodynamics, to achieve higher performance the in-phase SF mode and antiphase flappings in the side-by-side configuration are preferred.

Symmetry-breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field, electron interactions can cause spontaneous symmetry-breaking within the spin and valley degrees of freedom, resulting in quantum Hall effect (QHE) states with complex order. Here, we report fractional QHE states in BLG that show phase transitions that can be tuned by a transverse electric field. This result provides a model platform with which to study the role of symmetry-breaking in emergent states with topological order.

One-dimensional (1D) interacting electrons are often described as a Luttinger liquid 1 – 4 having properties that are intrinsically different from those of Fermi liquids in higher dimensions 5 , 6 . In materials systems, 1D electrons exhibit exotic quantum phenomena that can be tuned by both intra- and inter-1D-chain electronic interactions, but their experimental characterization can be challenging. Here we demonstrate that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays. We have imaged the evolution of DW Luttinger liquids under different interaction regimes tuned by electron density using scanning tunnelling microscopy. Single DWs at low carrier density are highly susceptible to Wigner crystallization consistent with a spin-incoherent Luttinger liquid, whereas at intermediate densities dimerized Wigner crystals form because of an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions that gives rise to new quantum phases. At low electron densities, inter-chain interactions are dominant and induce a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase in which electrons are ordered with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures provides opportunities to explore Luttinger liquid physics. Layer-stacking domain walls in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays.

The combined effects of channel curvature and rotor configuration on the performance of two-stage viscous micropumps were studied numerically. The Navier-Stokes equations were simulated to investigate the performance of two-stage micropumps. The performance of two-stage micropumps was studied in terms of the dimensionless mass flow rate and dimensionless driving power. Four different rotor configurations were designed by changing placement of two rotors inside a microchannel: Two aligned and two staggered configurations. The aligned rotor configuration of type 1 is to place the two rotors along the convex wall, while type 2 is to place them along the concave wall. Numerical results show that the rotor configuration plays a significant role in the performance of two-stage micropumps. The channel curvature acts in a different way according to the rotor configuration. The mass flow rate of aligned rotor configuration of type 1 is greatly improved by the channel curvature, while it diminishes the mass flow rate of type 2. The maximum mass flow rate for the aligned rotor configuration of type 1 is obtained when the two rotors are placed at the junction of the circular and straight sections of the channel. The performance of staggered configurations is negligibly affected by the channel curvature. This characteristics is found due to rotation direction of the rotors. As the two rotors rotate in the opposite direction for the staggered configurations, the flow characteristics in the circular section is little affected by the channel curvature. The circumferential distance between the two rotors can be optimized in terms of the mass flow rate. The optimal value of the circumferential distance is about L = 1.4 for the staggered rotor configurations, and it is almost independent of the channel curvature. As the channel height increases, the circumferential distance becomes less significant for the staggered rotor configurations while it becomes significant for the aligned rotor configurations.

Bilayer graphene has a distinctive electronic structure influenced by a complex interplay between various degrees of freedom. We probed its chemical potential using double bilayer graphene heterostructures, separated by a hexagonal boron nitride dielectric. The chemical potential has a nonlinear carrier density dependence and bears signatures of electron-electron interactions. The data allowed a direct measurement of the electric field–induced bandgap at zero magnetic field, the orbital Landau level (LL) energies, and the broken-symmetry quantum Hall state gaps at high magnetic fields. We observe spin-to-valley polarized transitions for all half-filled LLs, as well as emerging phases at filling factors ν = 0 and ν = ±2. Furthermore, the data reveal interaction-driven negative compressibility and electron-hole asymmetry in N = 0, 1 LLs.

The flow that crosses the arrangement of four circular cylinders will form a certain flow pattern according to the geometry of the body contour, the distance between the cylinders, and the flow orientation (α), and generated aerodynamic forces, such as lift force, drag force, as well as induced vibration on the body. The force coefficients on four circular cylinders in an equispaced arrangement with a staggered configuration located near a plane wall were calculated through the pressure distributions measurement. The pressure distributions on each cylinder surface and the plane wall were measured for various gap ratio values of G/D= 0.0 and 0.2 (G, the gap between cylinder to the plane wall; D, diameter) and L/D= 2.7 (L, gap spacing between cylinders) in a uniform flow at a Reynolds Number of 1.743 x 10 4 . The results show that the drag and lift coefficients on the cylinders depend on the gap ratio value of G/D. The drag coefficient decreases, when the amount of G/D increases, especially on the upstream cylinders. The lift coefficient on the upper-downstream cylinders has a significant value more than other cylinders at a small spacing ratio.

In comparison to a plain fin, the addition of dimples or protrusions to the fins of a finned tube heat exchanger significantly affects the promotion of heat transfer. The impact of the number of dimples or protrusions and the arrangement of inline and staggered configurations on pressure drop and heat transfer is examined numerically in this research. The outcomes demonstrate that increasing the number of dimples and protrusions significantly affects heat transfer magnitude and pressure drop. Increasing the number of dimples and protrusions within the Reynolds number range of 150-1200 enhances the friction coefficient and heat transfer by 108%-163% and 16%-112%, respectively, in contrast to the plain fin. In evaluating the result of the arrangement of inline and staggered configurations, the heat transfer amounts of these two models are almost the same, and the friction coefficient is higher in the model that uses the arrangement of inline. In the inline arrangement model utilizing dimples-protrusions, the resultant heat transfer and friction coefficient increase 11%-92% and 64%-113% within the Reynolds number range of 150-1200, respectively, compared to the plain fin.

In this study, the flow dynamics and heat transfer in partially filled pin-based microchannel heat sinks (MCHS) are examined. The lattice Boltzmann method is used to analyse the physics of these systems and examine the effects of the flow, pin configuration, size and porous medium height. The results of the study reveal that, unlike the fully filled pin-based MCHS, there is no unique behaviour for the pin configuration effects and the performance of partially filled pin-based MCHS depends on the porous medium size and structure as well as the inertial forces in the flow. In particular, it is found that there are hydrodynamic and thermal-based critical porous medium heights at which the best performance in terms of heat removal switches from the inline to the staggered configuration. The dependence of these critical heights on the Reynolds number and the porous medium properties are analysed and the effects of the flow dynamics are further unravelled through a particle tracing technique. Furthermore, a simple flow model is developed, and is shown to capture well the main trends obtained from the simulations and to bring to light more of the system physics that help explain the interplay between the different parameters.

Dynamic remodeling of the extracellular matrix affects many cellular processes, either directly or indirectly, through the regulation of soluble ligands; however, the mechanistic details of this process remain largely unknown. Here we propose that type I collagen remodeling regulates the receptor-binding activity of pigment epithelium-derived factor (PEDF), a widely expressed secreted glycoprotein that has multiple important biological functions in tissue and organ homeostasis. We determined the crystal structure of PEDF in complex with a disulfide cross-linked heterotrimeric collagen peptide, in which the α(I) chain segments—each containing the respective PEDF-binding region (residues 930 to 938)—are assembled with an α2α1α1 staggered configuration. The complex structure revealed that PEDF specifically interacts with a unique amphiphilic sequence, KGHRGFSGL, of the type I collagen α1 chain, with its proposed receptor-binding sites buried extensively. Molecular docking demonstrated that the PEDF-binding surface of type I collagen contains the cross-link–susceptible Lys930 residue of the α1 chain and provides a good foothold for stable dockingwith the α1(I) N-telopeptide of an adjacent triple helix in the fibril. Therefore, the binding surface is completely inaccessible if intermolecular crosslinking between two crosslink-susceptible lysyl residues, Lys9 in the N-telopeptide and Lys930, is present. These structural analyses demonstrate that PEDF molecules, once sequestered around newly synthesized pericellular collagen fibrils, are gradually liberated as collagen crosslinking increases, making them accessible for interaction with their target cell surface receptors in a spatiotemporally regulated manner.