Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

Some preliminary observations on a defect Navier–Stokes system

Some implications of the simplest accounting of defects of compatibility in the velocity field on the structure of the classical Navier–Stokes equations are explored, leading to connections between classical elasticity, the elastic theory of defects, plasticity theory, and classical fluid mechanics.     

Powers of edge ideals with linear resolutions

We show that if G is a gap-free and diamond-free graph, then I(G)^s has a linear minimal free resolution for every s≥2.     

A novel rigid wheel for agricultural machinery applicable to paddy field with muddy soil

The working performance of agricultural machinery is largely determined by the walking performance of the wheel when driving in complex unstructured soil. However, the driving performance of existing wheels is not satisfactory for paddy field with muddy soil. The purpose of the current study is therefore to propose a novel rigid wheel for agricultural machinery which is applicable to paddy field with muddy soil. Firstly, a novel arc edge shaped wheel was designed based on the principles of mechanics on the ground. Then the driving performance of this arc edge shaped wheel was evaluated using FE modeling of interaction between rigid wheel and soil. Finally, the structure originally designed arc edge shaped wheel was improved according to FE modeling results, and this improved design was further evaluated by both FE simulation and prototype experiments. Both FE modeling and experimental results indicate that the improved arc edge shaped wheel proposed in this study has a good driving performance with regarding to wheel sinkage and soil reaction force. The proposed arc edge shaped wheel could be used as an effective component of rice harvester for paddy field with muddy soil.     

表面效应对铁<100>间隙型位错环的影响

在材料辐照损伤过程中,间隙型位错环的形成及动力学行为严重影响材料在辐照条件下的服役行为.在常用的以体心立方铁为基的合金材料中,1/2<111>和<100>是两种主要的位错环,其对辐照损伤的影响一直都是核材料领域研究的热点之一.在之前的研究中,人们对{111}面与单个1/2<111>位错环的相互作用进行了深入研究,发现表面对位错环性质确实有重要的影响.采用分子动力学方法,在原子尺度详细研究了另一个重要的表面铁{100}面对<100>间隙型位错环动力学过程的影响.模拟发现位错环伯格斯矢量与表面法线方向的关系、距表面的深度、位错环之间的相互作用以及温度等,都对位错环与表面的相互作用产生重要影响,其中,表面作用下的伯格斯矢量的演化以及<100>位错环在此过程中的一维运动首次被发现.基于这些模拟结果,就<100>位错环对表面辐照损伤结构的影响进行详细地研究,给出<100>位错环对表面凹凸结构的贡献,这些结果为理解辐照过程中材料表面的演化提供一种可能的解释.     

Edge proximity and matching extension in projective planar graphs

A graph $G$ with at least $2m+2$ vertices is said to be distance $d$ $m$-extendable if, for any matching $M$ of $G$ with $m$ edges in which the edges lie at distance at least $d$ pairwise, there exists a perfect matching of $G$ containing $M$. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 4 $m$-extendable for any $m$.     

磁电弹性体中多条位错与Griffith裂纹

根据本征方程，研究磁电弹性体中若干平行螺型位错与Griffith裂纹的相互作用.结合Muskhelishvili方法和算子理论，得到磁电弹性体中由位错和裂纹所诱导的应力场、电场和磁场的解析解.数值算例表明：在裂纹的端点及位错点上仍然存在应力的奇异性，离位错点越远处广义力越小，结论与已有的结果相符，证明了结论的正确性.当位错点与裂纹端点距离越近时，裂纹与位错间的应力场越小，并逐渐趋近于零.     

Implementation of a separate fluid-neutral energy equation in SOLPS-ITER and its impact on the validity range of advanced fluid-neutral models

In plasma edge transport codes for nuclear fusion devices, fluid-neutral models offer an interesting alternative to the currently used kinetic Monte Carlo simulations, especially for cases of high ion-neutral collisionality. In this paper, we elaborate a separate neutral energy equation in the state-of-the-art SOLPS-ITER code suite, which previously assumed perfect ion-neutral temperature equilibration. Furthermore, we study the coupled plasma-neutral solutions for a range of divertor operating regimes, proving the validity of these fluid-neutral models for high-recycling and detached regimes.