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.     

A single theory for some quasi-static,supersonic, atomic,and tectonic scale applications of dislocations

We describe a model based on continuum mechanics that reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. As applications, we explore the questions of the existence of a Peierls stress in a continuum theory, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-a-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics.     

Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order −1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.     

光电探测器组件光纤耦合移位特性分析

光电探测器组件响应度下降会造成光纤陀螺输出异常,响应度下降的主要原因为光纤耦合移位,分析光纤耦合移位的原因并采取有效措施可提高探测器组件的使用可靠性。通过对探测器尾纤出射高斯光斑在探测器管芯端面数学积分,计算出光纤耦合效率系数与光纤耦合间距及光纤偏转角度的关系,计算结果与实际封装探测器组件指标一致。根据计算结果,从光纤移位、探测器管芯移位和管壳形变三个方面分析了耦合移位的影响因素,提出避免探测器使用中发生耦合移位的措施,并通过试验验证了耦合焊接缺陷会造成探测器试验后响应度下降,采取耦合对准控制措施后封装的探测器试验后响应度保持稳定。     

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 $m$.