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.     

The Roper resonance in a finite volume

We calculate the energy levels corresponding to the Roper resonance based on a two-flavor chiral effective Lagrangian for pions, nucleons, deltas, and the Roper resonance at the leading one-loop order. We show that the Roper mass can be extracted from these levels for lattice volumes of moderate size.     

高雷诺数下非混相Rayleigh-Taylor不稳定性的格子Boltzmann方法模拟

本文采用相场格子Boltzmann方法研究了竖直微通道内中等Atwoods数流体的单模Rayleigh-Taylor不稳定性问题,系统分析了雷诺数对相界面动力学行为以及扰动在各发展阶段演化规律的影响.数值结果表明高雷诺数条件下,不稳定性界面扰动的增长经历了四个不同的发展阶段,包括线性增长阶段、饱和速度阶段、重加速阶段及混沌混合阶段.在线性增长阶段,我们计算获得的气泡与尖钉振幅符合线性稳定性理论,并且线性增长率随着雷诺数的增加而增大.在第二个阶段,我们观察到气泡与尖钉将以恒定的速度增长,获得的尖钉饱和速度略高于Goncharov经典势能模型的解析解[Phys.Rev.Lett.200288134502],这归因于系统中产生了多个尺度的旋涡,而涡之间的相互作用促进了尖钉的增长.随着横向速度和纵向速度的差异扩大,气泡和尖钉界面演化诱导产生的Kelvin–Helmholtz不稳定性逐渐增强,从而流体混合区域出现许多不同层次的涡结构,加速了气泡与尖钉振幅的演化速度,并在演化后期阶段,导致界面发生多层次卷起、剧烈变形、混沌破裂等行为,最终形成了非常复杂的拓扑结构.此外,我们还统计了演化后期气泡与尖钉的无量纲加速度,发现气泡和尖钉的振幅在后期呈现二次增长规律,其增长率系数分别为0.045与0.233.而在低雷诺条件下,重流体在不稳定性后期以尖钉的形式向下运动而轻流体以气泡的形式向上升起.在整个演化过程中,界面变得足够光滑,气泡与尖钉在后期的演化速度接近于常数,未观察到后期的重加速与混沌混合阶段.     

The application of the Lattice Boltzmann method to the one-dimensional modeling of pulse waves in elastic vessels

The one-dimensional nonlinear equations for the blood flow motion in distensible vessels are considered using the kinetic approach. It is shown that the Lattice Boltzmann (LB) model for non-ideal gas is asymptotically equivalent to the blood flow equations for compliant vessels at the limit of low Knudsen numbers. The equations of state for non-ideal gas are transformed to the pressure-luminal area response. This property allows to model arbitrary pressure-luminal area relations. Several test problems are considered: the propagation of a sole nonlinear wave in an elastic vessel, the propagation of a pulse wave in a vessel with varying mechanical properties (artery stiffening) and in an artery bifurcation, in the last problem Resistor–Capacitor–Resistor (RCR) boundary conditions are considered. The comparison with the previous results shows a good precision.     

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This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.     

Study on the design of ZnO/PANI composites and the mechanism of enhanced humidity sensing properties

ZnO/PANI composite humidity sensor was prepared by hydrothermal method. The first principles of density functional theory study the sensing mechanism. The calculation shows that the oxygen vacancy on ZnO surface is beneficial to the adsorption of water molecules. The {0 0 0‾1} crystal plane with the largest lattice oxygen number in ZnO has a strong adsorption capacity for water molecules, which is also conducive to improving the humidity sensitivity. PANI is easy to be combined on {0 1‾1 0} plane of ZnO, and it indirectly promotes the growth of {0 0 0‾1} plane, increasing the adsorption of water molecules and the proportion of H⁺ and H₃O⁺ ions. In addition, the N–H group in ZnO/PANI enhances the H⁺ conduction, which further improves the performance of the sensor. The results concluded that the proportion of lattice oxygen in humidity sensor is an important factor of humidity sensor sensitive detection.     

Lattice Compression Revealed at the ≈1 nm Scale

Lattice tuning at the ≈1 nm scale is fascinating and challenging; for instance, lattice compression at such a minuscule scale has not been observed. The lattice compression might also bring about some unusual properties, which waits to be verified. Through ligand induction, we herein achieve the lattice compression in a ≈1 nm gold nanocluster for the first time, as detected by the single-crystal X-ray crystallography. In a freshly synthesized Au₅₂(CHT)₂₈ (CHT=S-c−C₆H₁₁) nanocluster, the lattice distance of the (110) facet is found to be compressed from 4.51 to 3.58 Å at the near end. However, the lattice distances of the (111) and (100) facets show no change in different positions. The lattice-compressed nanocluster exhibits superior electrocatalytic activity for the CO₂ reduction reaction (CO₂RR) compared to that exhibited by the same-sized Au₅₂(TBBT)₃₂ (TBBT=4-tert-butyl-benzenethiolate) nanocluster and larger Au nanocrystals without lattice variation, indicating that lattice tuning is an efficient method for tailoring the properties of metal nanoclusters. Further theoretical calculations explain the high CO₂RR performance of the lattice-compressed Au₅₂(CHT)₂₈ and provide a correlation between its structure and catalytic activity.     

Lattice Distortion and H-passivation in Pure Carbon Electrocatalysts for Efficient and Stable Two-electron Oxygen Reduction to H2O2

The exploration of inexpensive and efficient catalysts for oxygen reduction reaction (ORR) is crucial for chemical and energy industries. Carbon materials have been proved promising with different catalysts enabling 2 and 4e⁻ ORR. Nevertheless, their ORR activity and selectivity is still complex and under debate in many cases. Many structures of these active carbon materials are also chemically unstable for practical implementations. Unlike the well-discussed structures, this work presents a strategy to promote efficient and stable 2e⁻ ORR of carbon materials through the synergistic effect of lattice distortion and H-passivation (on the distorted structure). We show how these structures can be formed on carbon cloth, and how the reproducible chemical adsorption can be realized on these structures for efficient and stable H₂O₂ production. The work here gives not only new understandings on the 2e⁻ ORR catalysis, but also the robust catalyst which can be directly used in industry.