基于XFEM的混凝土纯弯曲梁的裂缝扩展模拟研究

选取纯弯曲梁进行裂缝扩展研究,在理论上符合Ⅰ型断裂模式．因此,本文利用扩展有限元法(XFEM)模拟了混凝土纯弯曲梁裂缝发展的全过程,结合线性叠加渐进假定,得到了不同初始缝高比的P-δ曲线、P-CMOD曲线以及临界有效裂缝扩展长度(a_c-a₀)/h与裂缝发展路经．对比试验数据和模拟结果表明：随着初始缝高比的增大,起裂荷载P_ini、最大荷载P_max、离散弗雷歇距离δ_dF与δ_{d F}^′,以及临界有效裂缝长度(a_c-a₀)/h均逐渐减小;试验与模拟的裂纹发展路径存在一定偏差,可知试验数据与模拟结果存在规律性差异．     

Flow evolution of a turbulent submerged two-dimensional rectangular free jet of air. Average Particle Image Velocimetry (PIV) visualizations and measurements

The paper presents average flow visualizations and measurements, obtained with the Particle Image Velocimetry (PIV) technique, of a submerged rectangular free jet of air in the range of Reynolds numbers from Re = 35,300 to Re = 2200, where the Reynolds number is defined according to the hydraulic diameter of a rectangular slot of height H. According to the literature, just after the exit of the jet there is a zone of flow, called zone of flow establishment, containing the region of mixing fluid, at the border with the stagnant fluid, and the potential core, where velocity on the centerline maintains a value almost equal to the exit one. After this zone is present the zone of established flow or fully developed region. The goal of the paper is to show, with average PIV visualizations and measurements, that, before the zone of flow establishment is present a region of flow, never mentioned by the literature and called undisturbed region of flow, with a length, L_U, which decreases with the increase of the Reynolds number. The main characteristics of the undisturbed region is the fact that the velocity profile maintains almost equal to the exit one, and can also be identified by a constant height of the average PIV visualizations, with length, L_CH, or by a constant turbulence on the centerline, with length L_CT. The average PIV velocity and turbulence measurements are compared to those performed with the Hot Film Anemometry (HFA) technique. The average PIV visualizations show that the region of constant height has a length L_CH which increases from L_CH = H at Re = 35,300 to L_CH = 4–5H at Re = 2200. The PIV measurements on the centerline of the jet show that turbulence remains constant at the level of the exit for a length, L_CT, which increases from L_CT = H at Re = 35,300 to L_CT = 4–5H at Re = 2200. The PIV measurements show that velocity remains constant at the exit level for a length, L_U, which increases from L_U = H at Re = 35,300 to L_U = 6H at Re = 2200 and is called undisturbed region of flow. In turbulent flow the length L_U is almost equal to the lengths of the regions of constant height, L_CH, and constant turbulence, L_CT. In laminar flow, Re = 2200, the length of the undisturbed region of flow, L_U, is greater than the lengths of the regions of constant height and turbulence, L_CT = L_CH = 4–5H. The average PIV and HFA velocity measurements confirm that the length of potential core, L_P, increases from L_P = 4–5H at Re = 35,300 to L_P = 7–8H at Re = 2200, and are compared to the previous experimental and theoretical results of the literature in the zone of mixing fluid and in the fully developed region with a good agreement.     

Points of Bounded Height on Equivariant Compactifications of Vector Groups, I

We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane.     

一类优美树

§1. Preliminary Lemma Using A to denote the cardinal number of a finite set A, we do not explain anymore what are similar to A in this paper. For a given tree T(V,E), if there is a labeling f of its vertices, which satisfiesf［V(T)］={f(u)u∈V(T)}={0,1,2,…,E(T)},lf［E(T)］={lf(uv)=f(u)-f(v), uv∈E(T)}={1,2,…,E(T)},then f is called a graceful labeling of T, and T is called a graceful tree. lf denotes the labeling of edges that is derived from f. In the 1960s, RingedKotzing and A. R…     

Efficient exponential-time algorithms for edit distance between unordered trees

The edit distance problem for rooted unordered trees is known to be NP-hard. Based on this fact, this paper studies exponential-time algorithms for the problem. For a general case, an $O(\min ({1.26}^{n_1+n_2},2^{b_1+b_2}\cdot \text{<mi mathvariant="italic" is="true">poly</mi>}(n_1,n_2)))$ time algorithm is presented, where $n_1$ and $n_2$ are the numbers of nodes and $b_1$ and $b_2$ are the numbers of branching nodes in two input trees. This algorithm is obtained by a combination of dynamic programming, exhaustive search, and maximum weighted bipartite matching. For bounded degree trees over a fixed alphabet, it is shown that the problem can be solved in $O({(1+ϵ)}^{n_1+n_2})$ time for any fixed $ϵ>0$. This result is achieved by avoiding duplicate calculations for identical subsets of small subtrees.     

On the spectral radius of weighted trees with given number of pendant vertices and a positive weight set

Let 𝒯(n,?r;?W _n?1) be the set of all n-vertex weighted trees with r vertices of degree 2 and fixed positive weight set W _n?1, 𝒫(n,?γ;?W _n?1) the set of all n-vertex weighted trees with q pendants and fixed positive weight set W _n?1, where W _n?1?=?{w ₁,?w ₂,?…?,?w _n?1} with w ₁???w ₂???···???w _n?1?>?0. In this article, we first identify the unique weighted tree in 𝒯(n,?r;?W _n?1) with the largest adjacency spectral radius. Then we characterize the unique weighted trees with the largest adjacency spectral radius in 𝒫(n,?γ;?W _n?1).     

Three-dimensional cellular automaton simulation of tumour growth in inhomogeneous oxygen environment

Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.     

The average norm of polynomials of fixed height

Let be any integer and let

be the set of all polynomials of height 1 and degree . Let

Here is the power of the norm on the boundary of the unit disc. So is the average of the power of the norm over

In this paper we give exact formulae for for various values of . We also give a variety of related results for different classes of polynomials including polynomials of fixed height H, polynomials with coefficients and reciprocal polynomials. The results are surprisingly precise. Typical of the results we get is the following.

Theorem 0.1. For , we have

and

     

Projective functors for algebraic groups

We investigate the regular subquotient category introduced by Soergel in [W. Soergel, On the relation between intersection cohomology and representation theory in positive characteristic, J. Pure Appl. Algebra 152 (1–3) (2000) 311–335]. A detailed study of projective functors enables one to relate those categories for semi-simple algebraic group G and its subgroup schemata G_rT. As an application we derive some information about the characters of tilting modules for G.