基于箭形累积损伤的裂纹尖端力学:奇异性分级和多尺度分段

在适度的空间和时间尺度组合下,裂纹既可在几个月中蠕变几个纳米,也能在几秒钟内扩展10km.虽然裂纹的尖端没有实际的质量,但是它能通过激活周围的物质而处于高能量状态.依赖于材料的损伤方向,激活质量的减少和增加可发生在尺度转变之前或之后.每个尺度区的分段阈值被假定为与裂纹尖端速度的平方a~2和激活质量密度M的乘积有关:W=M_(↓↑)a_(↑↓)~2和D=M~(↓↑)a_(↑↓)~2.W和D分别被称为直接吸收和自耗散能量密度.正如下标/上标符号所示,激活的质量密度M_(↓↑)和M~(↓↑)与裂纹尖端速度a变化趋势相反,既可增加也可减少.a~2和M的互补效应隐含着常用于宇宙物理学建模的膨胀和/或收缩的物理过程.在用于尺度敏感的裂纹尖端的行为时,激活的质量密度有相同的解释.分段时的多尺度可以由…皮观、纳观、微观和宏观…组成.因此,形象地说,材料损伤过程可以通过裂纹扩展过程中非均匀的总体和局部能量的传递来模拟.疲劳裂纹扩展引起的材料损伤被用来阐释由大到小和由慢到快的尺度/时间序,热力学中的冷→热和有序→无序转换.这一过程正巧与宇宙演化的箭形方向相反,宇宙演化遵循小→大和快→慢,而热力学相反,遵循热→冷和无序→有序.为了表示由损伤萌生所造成的类裂缝型缺陷的不均匀性,提出了一个被称为裂纹尖端力学(crack tip mechanics,CTM)的新模式.涉及的范围是模拟原子列之间的界面裂纹或连续体中分叉的切口.假如需要的话,尺寸和时间的范围可以复盖从皮观到宏观甚至更大.虽然采用疲劳裂纹来说明CTM的基本原理,在宇宙物理学背景中与直接吸收和自耗散相关的膨胀和收缩的情况可以描述裂纹周围激活质量的行为,它们可看为能量的汇或源.奇异性被用来捕获能量的源或汇的特性,物理上,两者作为界面的一部分,从数学上看则是不连续的线的一部分.能量从一种形式变为另一种形式取决于能量吸收或耗散的箭形损伤时间,这之中牵涉到尺度分段和奇异性强度的联合应用.材料组分随时间的劣化是根据指定的设计寿命导出的,从而使材料的响应与加载率的时间历史匹配.2024-T3铝板的皮观/纳观/微观/宏观开裂模型用来说明什么地方可以增加结构的寿命部分.皮观/纳观/微观/宏观/结构系统的性能随时间劣化可以用9个尺度转变物理参数来描述:纳观/微观区有3个(μ_(na/mi)~*,σ_(na/mi)~*,d_(na/mi)~*),微观/宏观区有3个(μ_(mi/ma)~*,σ_(mi/ma)~*,d_(mi/ma)~*),皮观/纳观区有3个(μ_(pi/na)~*,σ_(pi/na)~*,d_(pi/na)~*).下标pi,na,mi,ma和struc分别表示皮观、纳观、微观、宏观和结构.只要知道两个相连的尺度敏感参数,在较低尺度的时间相关的局部物理参数就完成了分析连续体的形式论,虽然它们并不需要用实验来知道.更具体地说,根据皮观→纳观→微观→宏观分别有1.25/1.00/0.75/0.50的λ奇异性强度,皮观裂纹、纳观裂纹、微观裂纹和宏观裂纹的转变特征是从时间箭形的指定的寿命预期来确定的.附加的0.25强度的奇异性可用于结构元件.回想起来,λ=0.5相应于断裂力学中的应力分量与r~(0.5)成反比,r是与宏观裂纹尖端的距离.微观裂纹、纳观裂纹和皮观裂纹分别赋予r~(-0.75),r~(-1.0),r~(-1.25)的奇异性.箭形时间(以年为单位)取决于问题的定义.设备的关键部件可用1.5~±/2.5~±/3.5~±/5.5~±寿命分布和总寿命为13~±年(a)的皮观/纳观/微观/宏观尺度来设计运行.上标±表示多于或少于实际运行的时间.累进损伤被假定为发生在皮观→纳观→微观→宏观方向.同样的方案用于20年总寿命的2024-T3铝板的疲劳损伤,按照1.5~±/2.5~±/3.5~±/5.5~±/7.0~±的方式将它的寿命分布在皮观、纳观、微观、宏观和结构的尺度上,这样的指定只是满足在每个尺度范围内损伤内部材料结构所用的能量匹配,因此可以强制执行在总寿命的跨度内精确的时间相关的材料性能劣化过程.     

Synthesis of Novel Chiral Diol Ligands for the Enantioselective Reactions

The chiral diols ((,(,((,((-Tetraaryl-1,3-dioxolane-4,5-dimethanols) have been used for the formation of cyclic titanates and similar derivatives of Mg, Al and Zr. These complexes of oxophilic metal centers were employed in catalytic and stiochiometric enantioselective reactions such as enantioselective addition reactions of carbon-centered nucleophiles to aldehydes1, [2+2] cycloadditions2, and Diels-Alder reactions3. So far, the two hydrogen atoms of all this type of diols are in trans form…     

Exact and heuristic approaches for the index tracking problem with UCITS constraints

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.     

Alpha-methylene-beta-amino ketone derivatives from beta-ketoallylsilanes

Beta-Ketoallylsilanes are synthesized by the Horner-Emmons reaction starting from novel silylated ketophosphonates and various aldehydes. The reactions of beta-ketoallylsilanes with NsONHCO2Et and CaO produce alpha-methylene-N-(ethoxycarbonyl)-beta-amino ketones through the ring opening of the intermediate aziridine, which is favored by the presence of the trimethylsilyl group. With chiral beta-ketoallylsilanes we obtained a stereoselective amination reaction with a 90% diastereomeric excess. alpha-Methylene-N-(ethoxycarbonyl)-beta-amino ketones are isolated in 39-60% yields and characterized.     

Structural and algorithmic properties for parametric minimum cuts

We consider the minimum s, t-cut problem in a network with parametrized arc capacities. Following the seminal work of Gallo et?al. (SIAM J. Comput. 18(1):30–55, 1989), classes of this parametric problem have been shown to enjoy the nice Structural Property that minimum cuts are nested, and the nice Algorithmic Property that all minimum cuts can be computed in the same asymptotic time as a single minimum cut by using a clever Flow Update step to move from one value of the parameter to the next. We present a general framework for parametric minimum cuts that extends and unifies such results. We define two conditions on parametrized arc capacities that are necessary and sufficient for (strictly) decreasing differences of the parametric cut function. Known results in parametric submodular optimization then imply the Structural Property. We show how to construct appropriate Flow Updates in linear time under the above conditions, implying that the Algorithmic Property also holds under these conditions. We then consider other classes of parametric minimum cut problems, without decreasing differences, for which we establish the Structural and/or the Algorithmic Property, as well as other cases where nested minimum cuts arise.     

Addition reactions of ethoxycarbonylnitrene and ethoxycarbonylnitrenium ion to allylic ethers

Ethoxycarbonylnitrene (EtOCON) generated by α-elimination adds cleanly to allylic ethers giving substituted aziridines. Similar addition via nitrenium ion (EtOCONH⁺) gives derivatives of β-amino alcohols.     

New and old bounds for standard quadratic optimization: dominance,equivalence and incomparability

A standard quadratic optimization problem (StQP) consists in minimizing a quadratic form over a simplex. Among the problems which can be transformed into a StQP are the general quadratic problem over a polytope, and the maximum clique problem in a graph. In this paper we present several new polynomial-time bounds for StQP ranging from very simple and cheap ones to more complex and tight constructions. The main tools employed in the conception and analysis of most bounds are Semidefinite Programming and decomposition of the objective function into a sum of two quadratic functions, each of which is easy to minimize. We provide a complete diagram of the dominance, incomparability, or equivalence relations among the bounds proposed in this and in previous works. In particular, we show that one of our new bounds dominates all the others. Furthermore, a specialization of such bound dominates Schrijver’s improvement of Lovász’s θ function bound for the maximum size of a clique in a graph.      

On the electric current from electrodes in a magnetized semiconductor film

The problem on the electric current from electrodes in a magnetizedsemiconductor film is reduced to the skew derivative problemfor the Laplace equation outside cuts in a plane. The problemfor the Laplace equation is studied under different conditionsat infinity, which have a certain physical meaning. With thehelp of potential theory, the skew derivative problem is reducedto a Fredholm integral equation of the second kind, which isuniquely solvable. The Neumann problem for the Laplace equationin the exterior of cuts in a plane is a particular case of ourproblem.     

One-pot synthesis of chiral multifunctionalized aziridines

A direct synthetic procedure to obtain chiral aziridines is reported, involving a diastereoselective aza-MIRC (Michael Initiated Ring Closure) reaction. Multifunctionalized aziridines are obtained in high overall yields (82-92%) and with a diastereomeric ratio up to 99:1. Further synthetic elaboration can lead to the formation of interesting biochemical molecules, such as amino glycosides. The diastereomeric induction seems to be strongly controlled both by the choice of chiral moiety and by the electron withdrawing groups (EWG) present on the starting alkenes.     

Amination of CF3-enones with nosyloxycarbamates

CF3-enones showed a different reactivity in amination reactions with nosyloxycarbamates. 4-Oxazolines or vinyl carbamates were obtained as unique products depending on the nature of double-bond substituents and on the choice of carbamates and bases. Starting from trans-trifluoroacetyl olefins carrying a heterocyclic residue or the p-methoxyphenyl group on the double bond, a rare loss of CF3CO was observed when the aminations were performed under heterogeneous conditions using CaO as the base.