Determination of unknown functions in a mathematical model of ductal carcinoma in situ

This study deals with the numerical investigation of a mathematical model of breast cancer at the initial growth stage known as ductal carcinoma in situ. This model considered as an inverse problem and the uniqueness of solution of this inverse problem is proved. To solve this problem, a computational approach is developed based on an iterative procedure and space marching and mollification methods. The stability and convergence results are given to support the method theoretically. Two test problems are considered to demonstrate the efficiency and ability of the proposed numerical approach.     

A point implicit unstructured grid solver for the euler and Navier–Stokes equations

An upwind finite element technique that uses cell-centred quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive triangular grids. The approach is an extension to unstructured grids of the LAURA algorithm due to Gnoffo. A structured grid of quadrilaterals is laid out near a solid surface. For inviscid flows the method is stable at Courant numbers of over 100000. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view to simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are distinctly captured with a sequence of adaptively generated grids.     

A stochastic theory for clustering of quenched-in vacancies—2. A solvable model

The model introduced for clustering of quenched-in vacancies in the first part of this series of papers is considered. Using a generating function, the rate equations are converted into a first order partial differential equation for the generating function coupled to a differential equation for the rate of change of the concentration of single vacancy units. A decoupling scheme is effected which gives an exponentially decaying solution with a very short time constant for the concentration of single vacancy units. The differential equation for the generating function is solved for times larger than the time required for the concentration of single vacancy units to reach its asymptotic value. The distribution for the size of the clusters is obtained by inverting the solution thus obtained. Several results that follow are shown to be in reasonably good agreement with the experimental results.     

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part I: interactions with screw dislocations

We present a comprehensive dislocation dynamics (DD) study of the strength of stacking fault tetrahedra (SFT) to screw dislocation glide in fcc Cu. Our methodology explicitly accounts for partial dislocation reactions in fcc crystals, which allows us to provide more detailed insights into the dislocation–SFT processes than previous DD studies. The resistance due to stacking fault surfaces to dislocation cutting has been computed using atomistic simulations and added in the form of a point stress to our DD methodology. We obtain a value of 1658.9 MPa, which translates into an extra force resolved on the glide plane that dislocations must overcome before they can penetrate SFTs. In fact, we see they do not, leading to two well differentiated regimes: (i) partial dislocation reactions, resulting in partial SFT damage, and (ii) impenetrable SFT resulting in the creation of Orowan loops. We obtain SFT strength maps as a function of dislocation glide plane-SFT intersection height, interaction orientation, and dislocation line length. In general SFTs are weaker obstacles the smaller the encountered triangular area is, which has allowed us to derive simple scaling laws with the slipped area as the only variable. These laws suffice to explain all strength curves and are used to derive a simple model of dislocation–SFT strength. The stresses required to break through obstacles in the 2.5–4.8-nm size range have been computed to be 100–300 MPa, in good agreement with some experimental estimations and molecular dynamics calculations.     

强流脉冲电子束辐照诱发多晶纯铝中的空位缺陷簇结构

利用强流脉冲电子束（HCPEB）技术对多晶纯铝样品进行辐照,采用透射电子显微镜详细分析了辐照诱发的空位簇缺陷.HCPEP辐照后,在辐照表层内形成了大量的四方形空位胞,其间包含位错圈和堆垛层错四面体（SFT）等类型的空位簇缺陷.1次辐照后,空位胞内产生空位型位错圈,5次辐照则主要产生SFT;10次辐照后,空位胞内产生的空位簇缺陷主要是位错圈,局部区域也观察到了SFT缺陷,在产生SFT的附近区域具有很低的位错密度或者几乎无位错出现.HCPEB辐照产生的瞬间加热和冷却诱发了幅值极大且应变速率极高的应力,这一因素 关键词： 强流脉冲电子束 多晶纯铝 空位簇缺陷 堆垛层错四面体     

Hamilton–Jacobi equation,reaction action surface and the emergence of the force concept in chemical reaction dynamics

A combination of Hamilton–Jacobi equation and fast marching algorithm can be used to study reaction dynamics by converting the potential energy surface to a reaction action surface. The reaction action surface has been found to be an important tool in theoretical chemistry, allowing us to provide a different force-based perspective of chemical reactions. Several properties such as reaction force, reaction force surface, reaction path force and reaction path force constant have been defined and calculated by using the reaction action surface. This paper investigates these newly defined properties in order to understand the role they play in chemical reaction with reference to a model 4-well potential energy surface.     

金纳米四面体增强有机太阳电池光吸收及光伏性能研究

为增强有机太阳能电池的光利用率,提高能量转换效率,本文合成了金四面体形状的纳米粒子,并用聚苯乙烯磺酸钠(PSS)包裹形成了核壳结构的金纳米四面体(Au@PSS tetrahedra NPs).将其掺杂到有机太阳能电池空穴提取层与活性层的界面处,利用表面等离子体共振效应来增强活性层对光的吸收,从而提高有机太阳能电池的能量转换效率.研究了掺杂浓度和PSS包裹厚度对电池性能的影响.结果表明:掺杂浓度为6%时,器件性能最佳,能量转换效率达到3.08%; PSS壳层厚度优化为2.5 nm时,转换效率达到3.65%,较标准电池提升了22.9%.电池性能的改善主要源于金四面体纳米粒子的共振吸收峰位于给体材料吸收谱范围内,纳米粒子的共振促进了给体的吸收,同时PSS壳层的引入促进了激子的解离和电荷的转移,上述因素的改善提升了电池的短路电流、填充因子和转换效率.     

Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement

A family of quadrature rules for integration over tetrahedral volumes is developed. The underlying structure of the rules is based on the cubic close-packed (CCP) lattice arrangement using 1, 4, 10, 20, 35, and 56 quadrature points. The rules are characterized by rapid convergence, positive weights, and symmetry. Each rule is an optimal approximation in the sense that lower-order terms have zero contribution to the truncation error and the leading-order error term is minimized. Quadrature formulas up to order 9 are presented with relevant numerical examples.     

New Models for the Solution of Intermediate Regimes in Transport Theory and Radiative Transfer: Existence Theory, Positivity, Asymptotic Analysis, and Approximations

In this paper we propose, derive, and establish the mathematical foundations of new models for the solution of intermediate regimes in transport theory and radiative transfer. These new models consist of coupling the transport equations with their diffusion approximations. Our mathematical theory includes the existence theory, the positivity of the solutions, and the asymptotic analysis. We also give the rate of the asymptotic decay. In order to solve the new coupled problem we propose to use the transmission time marching algorithm introduced and studied in refs. 10, 13–15. We then study the convergence of the resulting algorithm. These studies are based in an essential way on the methods we introduced in refs. 14, 15.