Pseudo global energy released locally by crack extension involving multiscale reliability

The energy release rate criterion, being mono scale by definition, is incompatible with the failure behavior of solids that are inherently dual, if not, multiscale. Time span of reliability is scale sensitive and can be addressed with consistency only by use of transitional functions that are designed to transform a function from one scale to another. A pseudo transitional energy release rate G^∗ is defined to address the cross-scaling properties of energy release rate. The reliability of such a function is found to fall quickly when the scale range deviates from that of micro-macro. In general, the time span of reliability based on G^* shortens considerably within the nano-micro and pico-nano scale ranges, resulting in fast turnover of system usability. Prediction accuracy tends to be scale range specific. Stress or strain based criteria are also mono scale. They may be adequate for some situations at the macroscopic scale, but can be ambiguous for multiscale problems. These situations are analyzed by application of the principle of least variance in conjunction with the R-integrals.Accelerated test data for the equivalent of 20 years’ fatigue crack growth in 2024-T3 aluminum panels were analyzed using the mutliscale reliability model. A time span plateau within the micro-macro range is from 8 to 17 years. This corresponds to the reliable portion of prediction, while the terminal 3 years are regarded as unreliable. A similar time span plateau were also found from 4 to 6 years within the nano-micro scale range. And an even smaller plateau hovering around 1.2 years were found for the pico-nano scale range. Time span of reliable prediction narrows with down sized scale range. The overlapping ends of the scale ranges are rendered unreliable as anticipated. These regions can be suppressed by the addition of meso scale ranges. Reference can be made to past discussions related to multiscaling and mesomechanics.     

Nonvanishing at spatial extremity solutions of the defocusing nonlinear Schrödinger equation

We show local existence of certain type of solutions for the Cauchy problem of the defocusing nonlinear Schrödinger equation with pure power nonlinearity, in various cases of open sets, unbounded or bounded. These solutions do not vanish at the boundary or at infinity. We also show, in certain cases, that these solutions are unique and global.     

Isometric Extension Problem Between Strictly Convex Two-dimensional Normed Spaces

In this paper, based on the smooth point of the unit ball and its support linear functional,we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case.     

Automorphisms of Extensions of ℚ by a Direct Sum of Finitely Many Copies of ℚ

Let G be an extension of ℚ by a direct sum of r copies of ℚ. (1) If G is abelian, then G is a direct sum of r + 1 copies of ℚ and AutG ≅ GL(r + 1, Q); (2) If G is non-abelian, then G is a direct product of an extraspecial ℚ-group E and m copies of ℚ, where E/ζE is a linear space over Q with dimension 2n and m + 2n = r. Furthermore, let AutG′G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G′ of G, and AutG/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then (i) The extension 1 → AutG′G → AutG → AutG′ → 1 is split; (ii) AutG′G/AutG/ζG,ζGG ≅ Sp(2n,Q) × (GL(m, Q) ⋉ ℚ(m)); (iii) AutG/ζG,ζGG/InnG ≅ ℚ(2nm).     

A ruled residue theorem for function fields of conics

The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from 2 this theorem is extended here to function fields of conics. The main result is that there is at most one extension of a valuation on the base field to the function field of a conic for which the residue field extension is transcendental but not ruled. Furthermore the situation when this valuation is present is characterised.     

浅海非均匀水平阵宽带声场信号无源孔径扩展

大孔径水平阵对于浅海低频水声物理实验研究和应用至关重要,然而受实际情况制约,通常使用的水平基阵孔径十分有限,通过孔径扩展处理来扩展基阵孔径是一条重要途径。传统的无源孔径扩展方法是建立在均匀线阵、匀速相对运动和相干窄带连续信号的基础上的,难以适用于非均匀阵以及非连续宽带声源的情况。针对这些问题,提出了非均匀阵宽带声场信号的无源孔径扩展方法。使用静止布设在海底的非均匀水平短阵接收运动声源重复发射的宽带声信号,先开展均匀空间插值,然后在阵元域和波束域进行宽带扩展孔径处理。仿真和实验结果表明,在水深约70 m的浅海波导环境中,纵向间隔27.5 m的2个阵元接收20~200 Hz宽带声场,其空间插值结果与真值的相关系数大于0.99,说明宽带声场插值方法的合理性。在水平非均匀、纵向孔径250 m的短阵接收声场无法分析简正波频散特征的情况下,仿真和实验数据经过宽带无源孔径扩展处理得到孔径大于1 km的均匀线阵的声场,能高分辨区分各阶简正波,证明所提方法是有效的。     

城市基层党建与社区社会资本生成—基层社区党建的延展效应

与强调纵向协调有损社区社会资本的观点不同,基层社区党建的延展效应和居民有分寸的自律协调概念,可用以解释中国城市居民住宅小区、尤其是新建商品房住宅小区中社会资本得以生成的现象。居民社区党组织在发挥纵向协调职能时,具有一种作为潜在社会过程的延展效应,导致了居民住宅小区里“有分寸的自律协调机制”的出现,进而生成了居民间的横向社会网络和社区社会资本。对2016年“上海社区研究”（SCS）资料的分析发现,建有活跃党组织的居民住宅小区,会拥有相对较多的居民社团,包括自发型居民社团;在商品房住宅小区里,拥有活跃党组织,同样更有可能形成自发型居民社团。这些发现支持了基于上述论辩的研究假设,表明所提出的中国城市基层党建的延展效应和有分寸的自律协调机制,是能够解释在纵向协调起主导作用的制度环境下社区社会资得以生成的现象的。     

反射型云纹法在岩石爆破机理研究中的应用

利用反射型动态云纹实验方法,对爆炸载荷作用下岩石平板试件中应力波传播及裂纹动态扩展进行研究,给出了高速转镜相机记录到的岩石平板爆炸加载实验时的动态云纹图。根据动态云纹图分析了炸药爆炸产生的应变场,并对裂纹的形成及其扩展速度的变化趋势进行了讨论。     

任意阶标度分形格分抗与非正则格型标度方程

Carlson分形格电路是分抗的理想逼近情形,但仅具有负半阶运算性能,逼近效益随着电路节次数的增加逐渐降低.虽然可嵌套得到-1/2~n阶(n为大于或等于2的整数)分抗逼近电路,但结构复杂,无法实现任意分数阶运算.通过类比拓展Carlson分形格电路,获得具有高逼近效益的任意实数阶微积算子的分抗逼近电路——标度分形格分抗,并用非正则格型标度方程进行数学描述.分别探讨非正则格型标度方程的近似求解和真实解.通过调节电阻递进比α与电容递进比β的取值,可构造出具有任意运算阶的标度分形格分抗逼近电路.标度拓展极大地提高了标度分形格分抗电路的逼近效益.随着标度因子的增加,负半阶标度分形格分抗的逼近效益逐渐增大并明显高于Carlson分形格分抗.设计了基于五节Carlson分形格分抗与负半阶标度分形格分抗的半阶微分运算电路,并对周期三角波和周期方波信号进行半阶微分运算,实验测试结果与理论分析一致.     

基于扩展孔径波达方向矩阵法的高精度二维DOA估计

该文针对扩展孔径会产生估计模糊的现象,提出一种高精度扩展孔径波达方向矩阵算法。算法由个阵列单元组成双平行阵列几何结构,利用阵列传感器沿轴和沿轴的不同间距,分别构造波达方向矩阵,由此计算出高精度模糊的方向余弦估计和低精度无模糊的方向余弦估计,然后利用低精度无模糊的方向余弦估计值对高精度模糊的方向余弦估计值进行解模糊处理,得到高精度无模糊的方向余弦的估计值。该算法无需配对运算和2维搜索,是一种低运算量高精度的算法,计算机仿真实验验证了该算法的性能。