Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

HgCdTe薄膜的输运特性及其应力调控

窄禁带直接带隙半导体材料碲镉汞(Hg1–xCdxTe)是一种在红外探测与自旋轨道耦合效应基础研究方面都具有重要应用意义的材料.本文对单晶生长的体材料Hg0.851Cd0.149Te进行阳极氧化以形成表面反型层,将样品粘贴在压电陶瓷上减薄后进行磁输运测试,在压电陶瓷未加电压时观察到了明显的SdH振荡效应.对填充因子与磁场倒数进行线性拟合,获得样品反型层二维电子气的载流子浓度为ns=1.25×10^16m^-2.在不同磁场下,利用压电陶瓷对样品进行应力调控,观测到具有不同特征的现象,分析应是样品中存在二维电子气与体材料两个导电通道.零磁场下体材料主导的电阻的变化应来源于应力导致的带隙的改变;而高场下产生类振荡现象的原因应为应力导致的二维电子气能级的分裂.     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.     

A Closed‐Loop Control Strategy for Producing Nitrile Rubber of Uniform Chemical Composition in a Semibatch Reactor: A Simulation Study

To improve the quality of industrial nitrile rubbers, the copolymer chemical composition, p_A(t), should ideally be kept constant along the reaction. This work proposes a closed‐loop control strategy for the semibatch operation of the reactor with the aim of regulating p_A(t) within a reduced range of variability. The proposed strategy is evaluated by simulating a mathematical model of the process. To this effect, a simplified mathematical model of the reaction is first derived and then utilized to obtain a suboptimal control law and a soft‐sensor that estimates the polymerization rates. The suboptimal control law is compensated by adding a term proportional to errors in p_A(t). The simulated example considers the production of the low‐composition AJLT grade, with the copolymerization reaction represented by a detailed mathematical model adjusted to an industrial plant. Due to the high performance of the soft‐sensor, the simulation results suggest that the proposed closed‐loop strategy is efficient to adequately regulate p_A(t) in spite of structural and parametric uncertainties, while other quality variables remained practically unaffected.     

Measurement of Residual Dipolar Couplings of Organic Molecules in Multiple Solvent Systems Using a Liquid-Crystalline-Based Medium

Residual dipolar coupling (RDC), a robust anisotropic NMR parameter for structural elucidation of organic molecules, is only accessible in an anisotropic environment. Herein, we introduce a novel alignment medium based on the molecular self-assembly of oligopeptide amphiphile (OPA). This medium is compatible with different intermediate and polar solvent systems, such as CD₃OD, [D₆]DMSO, and D₂O. The preparation of the OPA-based medium is simple and rapid, while only very weak background signals were observed from OPAs. Furthermore, we show that the purity of OPA has only a minor influence on the quality of the RDC data. These advantages allow RDC measurements of organic molecules with different polarities and solubilities with high efficiency and accuracy.     

Suppressing Strong Exciton–Phonon Coupling in Blue Perovskite Nanoplatelet Solids by Binary Systems

Quasi-two-dimensional (2D) perovskites are promising candidates for light generation owing to their high radiative rates. However, strong exciton–phonon interactions caused by mechanical softening of the surface act as a bottleneck in improving their suitability for a wide range of lighting and display applications. Moreover, it is not easily available to tune the phonon interactions in bulk films. Here, we adopt bottom-up fabricated blue emissive perovskite nanoplatelets (NPLs) as model systems to elucidate and as well as tune the phonon interactions via engineering of binary NPL solids. By optimizing component domains, the phonon coupling strength can be reduced by a factor of 2 driven by the delocalization of 2D excitons in out-of-plane orientations. It shows the picosecond energy transfer originated from the Förster resonance energy transfer (FRET) efficiently competes with the exciton–phonon interactions in the binary system.     

Synthesis and characterization of VO–vanillin complex immobilized on MCM-41 and its facile catalytic application in the sulfoxidation reaction,and synthesis of 2,3-dihydroquinazolin-4(1H)-ones and disulfides in green media

In this work, a vanillin complex is immobilized onto MCM-41 and characterized by FT-IR, X-ray diffraction, scanning electron microscopy, energy dispersive spectroscopy, thermogravimetric analysis, and BET techniques. This supported Schiff base complex was found to be an efficient and recoverable catalyst for the chemoselective oxidation of sulfides into sulfoxides and thiols into their corresponding disulfides (using hydrogen peroxide as a green oxidant) and also a suitable catalyst for the preparation of 2,3-dihydroquinazolin-4(1H)-one derivatives in water at 90°C. Using this protocol, we show that a variety of disulfides, sulfoxides, and 2,3-dihydroquinazolin-4(1H)-one derivatives can be synthesized in green conditions. The catalyst can be recovered and recycled for further reactions without appreciable loss of catalytic performance.     

Phenazine Radical Cations as Efficient Homogeneous and Heterogeneous Catalysts for the Cross-Dehydrogenative Aza-Henry Reaction

The redox activity of molecular phenazine catalysts has been previously exploited for aerobic oxidative amine homo- and cross-coupling reactions. In this contribution, we have extended the reaction scope of this novel type of organocatalyst and used them in the cross-dehydrogenative aza-Henry coupling of isoquinolines with nitromethane under aerobic conditions. Additionally, we have designed and prepared a novel porous organic polymer by cross-linking of tetrakis(4-bromophenyl)silane and dihydrophenazine through Pd-catalyzed Buchwald-Hartwig cross-coupling. This new type of heterogeneous catalyst, apart from being robust and easily reusable, also showed outstanding catalytic activities and improved selectivity compared to its molecular counterpart. A plausible reaction mechanism was proposed based on spectroscopic and kinetic measurements.     

A new database and benchmark of the bond energies of noble-gas-containing molecules

We have developed a new database of structures and bond energies of 59 noble-gas-containing molecules. The structures were calculated by CCSD(T)/aug-cc-pVTZ methods and the bond energies were obtained using the CCSD(T)/complete basis set method. Many wavefunction-based and density functional theory methods have been benchmarked against the 59 accurate bond energies. Our results show that the MPW1B95, B2GP-PLYP, and DSD-BLYP functionals with the aug-cc-pVTZ basis set excel in predicting the bond energies of noble-gas molecules with mean unsigned errors (MUEs) of 2.0 to 2.1 kcal/mol. When combinations of Dunning's basis sets are used, the MPW1B95, B2GP-PLYP, DSD-BLYP, and BMK functionals give significantly lower MUEs of 1.6 to 1.9 kcal/mol. Doubly hybrid methods using B2GP-PLYP and DSD-BLYP functionals and MP2 calculation also provide satisfactory accuracy with MUEs of 1.4 to 1.5 kcal/mol. If the Ng bond energies and the total atomization energies of a group of 109 main-group molecules are considered at the same time, the MPW1B95/aug-cc-pVTZ single-level method (MUE = 2.7 kcal/mol) and the B2GP-PLYP and DSD-PLYP functionals with combinations of basis sets or using the doubly hybrid method (MUEs = 1.9-2.2 kcal/mol) give the overall best result.