Periodic solution and its stability of a delayed Beddington‐DeAngelis type predator‐prey system with discontinuous control strategy

This paper investigates the periodic solution of a delayed Beddington‐DeAngelis (BD) type predator‐prey model with discontinuous control strategy. Firstly, the regularity and visibility analysis of the delayed predator‐prey model is carried out by using the principle of differential inclusion. Secondly, the positiveness and boundeness of the solution is discussed by employing the comparison theorem. Based on the boundary conditions of the model and the Mawhin‐like coincidence theorem, it is shown that the solution of the delayed BD system is asymptotically stable in finite time. Furthermore, it is found that there exists at least one periodic solution of the nonautonomous delayed predator‐prey model by using the principle of topological degree and set value mapping. Specially, when the nonautonomous delayed BD system degenerates into an autonomous system, some criteria are obtained to guarantee the convergence behavior of the harvesting solutions for the corresponding autonomous delayed BD system. Finally, numerical examples are given to demonstrate the applicability and effectiveness of main results. It is worthy to point out that the discontinuous control strategy is superior to the continuous harvesting policies adopted in existing literature.     

Fundamental groupoids for simplicial objects in Mal'tsev categories

We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with Kan complexes. By comparing the reflections of simplicial objects and reflexive graphs into groupoids, we exhibit a connection with weighted commutators (as defined by Gran, Janelidze and Ursini).     

Discontinuous Galerkin method for the coupled Stokes‐Biot model

In this paper, a semi‐discrete scheme and a fully discrete scheme of the Stokes‐Biot model are proposed, and we analyze the semi‐discrete scheme in detail. First of all, we prove the existence and uniqueness of the semi‐discrete scheme, and a‐priori error estimates are derived. Then, we present the same conclusions for the fully discrete scheme. Finally, under both matching and non‐matching meshes some numerical tests are given to validate the analysis of convergence, which well support the theoretical results.     

简化形式的积分中值定理另一种表述

阐述了简化形式的积分中值定理中f(x)不要求连续的情况下成立的条件.即"设函数f(x)在闭区间[a,b]上可积,同时f(x)在[a,b]上有原函数,则存在ξ∈(a,b),使∫ from x=a to b f(x)dx=f(ξ)(b-a)成立",并且给出了简洁的证明.     

DDA与FEM耦合法在分缝重力坝非线性分析中的应用

混凝土重力坝一般设有数条纵缝。纵缝使坝体的连续性遭到破坏,一般的有限单元法很难处理这样的不连续变形问题。本文首先阐述了DDA(Discontinuous Deformation Analysis)与FEM(Finite Element Method)耦合算法的原理,然后采用作者自行研制的DDA与FEM耦合法程序对一实际重力坝进行了详细的计算分析。重点讨论了纵缝的不同设置形式和缝宽大小对坝体变形和应力分布、坝底面接触应力分布以及坝基面应力分布的影响,为工程设计提供依据。     

双曲守恒律的几种新数值方法的比较研究

本文就一维线性双曲方程的光滑和间断两种初值问题的求解,对双曲守恒律的三种新数值方法,即,WENO方法、间断Galerkin方法和全局复合方法,进行了数值比较实验,在精度、计算速度等方面的比较上,对这三个方法有了一个较详细的了解,得到了一些有用的结论。     

球几何中子输运保正线性间断有限元格式

针对球几何中子输运方程线性间断有限元方法计算的负中子通量问题,构造了保正线性间断有限元格式,该格式保持中子角通量0阶矩和1阶矩。现有方法计算中子角通量非负时,采用传统的线性间断有限元方法,求解线性方程组;原方法计算出现负通量,则采用构造的保正格式,求解非线性方程组。编制了球几何中子输运问题保正格式程序模块,并集成到应用程序。数值算例表明构造的保正格式计算的中子通量非负,有效降低数值误差,提高数值计算的精度。     

RKDG有限元方法计算流体与刚体耦合

用Level set方法配合Runge-Kutta discontinuous Galerkin (RKDG)有限元方法求解流体与刚体耦合问题。用RKDG有限元方法求解欧拉方程,通过求解Level set方程对界面进行追踪,并用推广的Ghost fluid方法对流刚界面进行处理。数值实验表明,该方法具有较高的分辨率。由于该方法不需要对移动网格进行处理,因此可以处理任意形状的拓扑问题,并且很容易推广到三维。     

环形激波聚焦流场特性的数值研究

针对环形激波聚焦过程产生的高温、高压特性,采用间断有限元方法模拟了环形激波在同轴圆柱形激波管内的聚焦流场特性。计算结果表明,采用间断有限元方法能够有效地捕捉激波聚焦过程形成的二次激波、涡环、三波交点和球面双马赫反射等主要流动特征。此外,通过改变环形管道内外半径对聚焦流场进行模拟发现,环形管道外径对中心轴线上聚焦峰值压力的大小和位置影响较小,环形管道内径对中心轴线上聚焦峰值压力的大小和位置影响较大。计算结果可以为工程应用提供一定的理论指导。     

基于目标三角面元模型生成FDTD共形网格的方法

提出了一种基于目标三角面元数据的FDTD共形网格生成方法,该方法通过投影求交计算得到目标表面各三角面元与网格线的交点,将每条网格线与三角面元的交点按坐标进行排序,根据交点的坐标及其编号的奇偶性确定FDTD共形网格的位置,并生成相应的共形FDTD计算所需的元段长度。结合处理理想导体曲面的CFDTD方法修正共形网格上的磁场递推式。数值结果证实了共形网格生成方法的正确性和在提高FDTD方法计算精度方面的有效性。