Shape sensitivity for the Laplace-Beltrami operator with singularities

This paper considers shape sensitivity analysis for the Laplace-Beltrami operator formulated on a two-dimensional manifold with a fracture. We characterize the shape gradient of a functional as a bounded measure on the manifold and decompose it into a “distributed gradient” supported on the manifold, plus a singular part that we derive as the limit of a “jump” through the crack and Dirac measures at the crack extremities. The important point is that we introduce a technique that is not dimension dependent, and makes no use of classical arguments such as the maximum principle or continuation uniqueness. The technique makes use of a family of envelopes surrounding the fracture which enable us to relax certain terms and to overcome the lack of regularity resulting from the presence of the fracture. We use the min-max differentiation in order to avoid taking the derivative of the state equation and to manage the crack's singularities. Therefore, we write the functional in a min-max formulation on a space which takes into account the hidden boundary regularity established by the tangential extractor method.     

Direction-direction correlations of oriented polymers

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). LetJ (x) andJ ^v (0) be components of unit-length tangent vectors of an oriented SAW, at the spatial pointsx and 0, respectively. Then for distances |x| much less than the average distance between the endpoints of the walk, the correlation function ofJ (x) withJ ^v (0) has, ind dimensions, the form . The dimensionless amplitudek(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to bek(2)=12/25 ². In three dimensions, the -expansion to second order in together with the exact value ofk(2)in two dimensions allows the estimatek(3)=0.0178±0.0005. In dimensionsd4, the universal amplitudek(d) of the direction-direction correlation functions of an oriented SAW is the same as the universal amplitude of the direction-direction correlation functions of an oriented random walk, and is given byk(d)= ²(d/2)/(d–2) ^d .     

Crashing a maximum-weight complementary basis

We consider the problem of finding a maximum-weight complementary basis of anm × 2m matrix. The problem arises naturally, for example, when a complementary set of columns is proposed as an initial basis for a warm start of Lemke's algorithm, but the set of columns is rank-deficient. We show that the problem is a special case of the problem of finding a maximum-weight common base of two matroids. Furthermore, we show how to efficiently implement an algorithm for the general problem in the present context. Finally, we give computational results demonstrating the practicality of our algorithm in a typical application.Supported by the Canadian Natural Science and Engineering Research Council.     

Cell alignment guided by nano/micro oriented collagen fibers and the synergistic vascularization for nervous cell functional expression

The majority of tissues within human body are constituted of designated structures to enable specific functions. Much effort has been done to engineer artificial fabric cell-laden scaffolds which are widely used for a great diversity of linear tissue constructs. For this purpose, collagen microfibers are of great concern among diverse materials while the control of cell-laden fiber formation and orientated structure is still unsolvable. Here, we developed a novel microfluidic-based strategy for continuous fabrication and assembly of three-dimensional (3D) cell-laden oriented collagen hydrogel microfibers. Inspired by the flow-introduced shear force in a microfluidic chip, collagen hydrogel microfibers obtained the oriented fabric structure which could guide rat pheochromocytoma cells (PC12) oriented spreading and enhance relative cellular functional expression. Rat aortic endothelial cells (RAOECs) were introduced to construct a co-cultured microfiber model, which further facilitated the functional expression of neural cells due to the synergistic effect of both vascularized-like cells and neural-like cells. Moreover, the ability of assembling collagen microfibers into larger constructs will benefit a variety of applications in tissue engineering and biomedical research.     

Solving the linear matroid parity problem as a sequence of matroid intersection problems

In this paper, we present an O(r ⁴ n) algorithm for the linear matroid parity problem. Our solution technique is to introduce a modest generalization, the non-simple parity problem, and identify an important subclass of non-simple parity problems called easy parity problems which can be solved as matroid intersection problems. We then show how to solve any linear matroid parity problem parametrically as a sequence of easy parity problems.In contrast to other algorithmic work on this problem, we focus on general structural properties of dual solutions rather than on local primal structures. In a companion paper, we develop these ideas into a duality theory for the parity problem.     

On the geometric structure of independence systems

A bouquet of matroids is a combinatorial structure that generalizes the properties of matroids. Given an independence system, there exist several bouquets of matroids having the same family of independent sets. We show that the collection of these geometries forms in general a meet semi-lattice and, in some cases, a lattice (for instance, when is the family of the stable sets in a graph). Moreover, one of the bouquets that correspond to the highest elements in the meet semi-lattice provides the smallest decomposition of into matroidal families, such that the rank functions of the different matroids have the same values for common sets. In the last section, we give sharp bounds on the performance of the greedy algorithm, using parameters of some special bouquets in the semi-lattice.     

用对称透射二维WAXS强度研究PET取向非晶态结构

用对称透射法，测试聚酯（ＰＥＴ）取向非晶试样的二维广角Ｘ射线散射相干强度Ｉ（Ｋ，α），将不同方位角α上的Ｉ（Ｋ，α）非晶重叠峰曲线进行计算分解，获得分子链间原子散射引起的二个峰为Ａ（Ｋ＝０．１２６），Ｂ（Ｋ＝０．１６９），分子链内原子散射引起五个峰分别为Ｃ（Ｋ＝０．３０４），Ｄ（Ｋ＝０．５５３），Ｅ（Ｋ＝０．３７４），Ｆ（Ｋ＝０．４６５），Ｇ（Ｋ＝０．６０６），Ｋ单位为ｎｍ＾－１，分析了它们的结构     

基于认识视角与认识思路的化学课堂教学*——物质的分类及转化

以解决“保存NaOH溶液的试剂瓶为什么不用玻璃塞”这一真实问题为情境,设计3个教学板块:运用分类方法认识物质、对物质进行分类、合成物质,从物质组成和物质变化的认识视角,对物质进行分类,建构分类观。依据物质分类研究同一类别物质的性质及应用,在完成知识结构化的同时,重在凝练基于物质分类及转化的认识视角和认识思路,寻找并体验陌生情境下解决复杂化学问题的突破口和思维框架,发展学生的化学学科核心素养。     

Numerical simulations of sonochemical production and oriented aggregation of BaTiO3 nanocrystals

Numerical simulations of sonochemical production and oriented attachment of BaTiO₃ nanocrystals are performed in aqueous solution with pH 14. It is suggested that most significant effect of ultrasound is the dissolution of Ti-based gel in aqueous solution. It results in the dissolution-precipitation mechanism in the production of BaTiO₃ nanoparticles, while with mechanical stirring without ultrasound it is the in situ mechanism that BaTiO₃ is gradually formed on Ti-based gel. The oriented attachment of spherical BaTiO₃ nanocrystals occurs by van der Waals torque (Casimir torque). Large aggregates of nanocrystals do not attach with each other as the repulsive double layer interaction is stronger for larger aggregates. For smaller spherical nanocrystals, the alignment of the crystal axes is less accurate due to more significant rotational Brownian motion of the nanocrystals.     

ON THE PHYSICAL PROCESS OF POLYMER CRYSTALLIZATION

Polymer crystallization is a process that connects the initial amorphous state and the final semicrystalline state. It is important to take due consideration of the initial state before crystallization, which determines the path of the crystallization process. New physical ideas are presented in regard to the processes of polymer crystallization from a dilute solution, from a melt or rubbery state, and from an oriented state, all based on experimental facts available with detailed discussions.