A model for crack formation during active solid pyrolysis of a char-forming solid: crack patterns; surface area generation; volatile mass efflux

A model is developed for the formation and propagation of cracks in a material sample that is heated at its top surface, pyrolyses, and then thermally degrades to form char. In this work the sample is heated uniformly over its entire top surface by a hypothetical flame (a heat source). The pyrolysis mechanism is described by a one-step overall reaction that is dependent nonlinearly on the temperature (Arrhenius form). Stresses develop in response to the thermal degradation of the material by means of a shrinkage strain caused by local mass loss during pyrolysis. When the principal stress exceeds a prescribed threshold value, the material forms a local crack. Cracks are found to generally originate at the surface in response to heating, but occasionally they form in the bulk, away from ever-changing material boundaries. The resulting cracks evolve and form patterns whose characteristics are described. Quantities examined in detail are: the crack spacing in the pyrolysis zone; the crack length evolution; the formation and nature of crack loops which are defined as individual cracks that have joined to form loops that are disconnected from the remaining material; the formation of enhanced pyrolysis area; and the impact of all of the former quantities on mass flux. It is determined that the mass flux from the sample can be greatly enhanced over its nominal (non-cracking) counterpart. The mass efflux profile qualitatively resembles those observed in Cone Calorimeter tests.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.     

CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).     

碳纳米管阵列、捆束的三步升温工艺制备及其形貌与结构

使用结构简单的单温炉设备，通过三步升温热解二茂铁、三聚氰氨混合物方法，在二氧化硅、多晶陶瓷基底上分别合成了碳纳米管阵列、碳纳米管捆束.使用扫描电子显微镜、透射电子显微镜、电子能量损失谱和x射线光电子能谱对合成样品进行了结构和成分分析.结果显示：两种基底上合成的纳米管均为多壁纯碳管；生长于光滑二氧化硅表面的碳纳米管具有高度取向性和一致的外径，长度为10—40μm.碳纳米管采取催化剂顶端生长模式并展示出类杯状形貌；生长于粗糙多晶陶瓷表面的碳纳米管捆束随机取向，碳纳米管直径为15—80nm，长度在几百微米，展示 关键词： 碳纳米管 热解法 三步升温工艺     

Boundedness of Multilinear Operators on Herz Type Spaces： Extreme Cases

In this paper, two classes of closely related multilinear singular and fractional integrals,which include the commutators as special cases, are studied and their boundedness on Herz type spaces is discussed. In fact, it is proved that these operators are actually not bounded in certain extreme cases.     

Several parameters of generalized Mycielskians

The generalized Mycielskians (also known as cones over graphs) are the natural generalization of the Mycielski graphs (which were first introduced by Mycielski in 1955). Given a graph G and any integer m?0, one can transform G into a new graph μ_m(G), the generalized Mycielskian of G. This paper investigates circular clique number, total domination number, open packing number, fractional open packing number, vertex cover number, determinant, spectrum, and biclique partition number of μ_m(G).     

β分式α稳定过程的1/H变差

本文主要讨论了β分式α稳定过程的1/H变差,这对关于β分式α稳定过程的随机分析是非常重要的.     

用多焦点全息透镜实现多重谱分数傅里叶变换

提出用多焦点全息透镜实现多重谱分数傅里叶变换.利用全息方法通过一次曝光制作出多焦点的全息透镜,分析了用此全息元件实现这种变换的条件,并在实验上实现了多重谱分数傅里叶变换. 实验结果表明这种变换方法简便可行,可广泛应用于多通道光学信息处理系统及多目标图像识别系统中.