Three-dimensional cellular automaton simulation of tumour growth in inhomogeneous oxygen environment

Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.     

THE TRANSFORMATION BETWEEN THE AKNS HIERARCHY AND THE KN HIERARCHY WITH SELF-CONSISTENT SOURCES

It is shown that the AKNS hierarchy with self-consistent sources can transform to KN hierarchy with self-consistent sources through a transformation operator and gauge transformation. Besides, there exists transformation in their conservation laws and Hamiltonian structures.     

N‐glycosylation approach to glucose‐functionalized diamine and its use for protection‐free synthesis of polyurea bearing glucoside pendant

A glucose‐functionalized diamine was prepared and used as a new monomer for polyurea synthesis. The diamine was prepared by N‐glycosylation of 1,6‐hexamethylenediamine with D ‐glucose. Upon adding diisocyanates to the diamine, isocyanate reacted selectively with the amino groups, not with the hydroxyl groups of the glucose‐derived structure, to give the corresponding polyureas. The polyureas exhibited highly hydrophilic nature due to the presence of the glucose‐derived side chain. A ternary system consisting of the glucose‐functionalized diamine, piperazine, and diisocyanate gave the corresponding polyureas, where content of the glucose‐derived moiety was tunable by feed ratio between the diamine and piperazine. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Insider Trading in Convergent Markets

Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints.     

The convenient setting for quasianalytic Denjoy-Carleman differentiable mappings

For quasianalytic Denjoy-Carleman differentiable function classes CQ where the weight sequence Q=(Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of CQ-mappings is cartesian closed in the sense that CQ(E,CQ(F,G))≅CQ(E×F,G) for convenient vector spaces. Applications to manifolds of mappings are given: The group of CQ-diffeomorphisms is a regular CQ-Lie group but not better.     

A Free Boundary Problem for an Elliptic–Parabolic System: Application to a Model of Tumor Growth

Abstract

In this article, we study a free boundary problem for a system of two partial differential equations, one parabolic and other elliptic. The system models the growth of a tumor with arbitrary initial shape. We establish the existence and uniqueness of a solution for some time interval. In the special case where we only have the elliptic equation, the problem coincides with the Hele–Shaw problem.     

Heterogeneous polycondensation for composition control of poly(p‐mercaptobenzoyl‐co‐p‐benzamide) by shearing

Composition control of aromatic poly(thioester‐amide) was examined by the reaction‐induced phase separation during polymerization of S‐acetyl‐4‐mercaptobenzoic acid (AMBA) and p‐acetylaminobenzoic acid (AABA) in aromatic solvent. The poly(thioester‐amide)s were obtained as precipitates and their yields became lower at the middle range of the content of AMBA in feed (χ_f). The contents of p‐mercaptobenzoyl (MB) moiety (χ_p) in the precipitates prepared without shearing were in good agreement with the χ_f values. In contrast to this, the χ_p values of the precipitates prepared at χ_f of 50–70 mol % under shearing were much lower than the χ_f values. The reaction rate of AMBA increased with shearing, whereas that of AABA was unchanged by shearing. This shearing effect on the reaction rates accelerated to form the homo‐oligomers. The solubility of MB oligomers enhanced by shearing, whereas that of p‐benzamide oligomers did not enhance owing to the strong interaction through hydrogen bonding. The MB oligomers were inhibited to be precipitated, resulting in the lower χ_p values than the χ_f values. The composition could be controlled by the application of the shearing to the heterogeneous polymerization. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 4301–4308     

EAST快速极紫外光谱仪绝对强度的原位标定

磁约束等离子体中杂质(特别是高Z杂质)的存在将大大增强等离子体辐射功率损失，破坏等离子体的约束性能。杂质行为的定量研究首先要求对杂质测量的光谱诊断系统进行绝对强度标定，获得灵敏度响应曲线。介绍了EAST托卡马克上的快速极紫外光谱仪系统绝对强度的原位标定方法。在波长范围20～150Å内，通过对比极紫外(EUV)波段连续轫致辐射强度的计算值和测量值得到光谱仪的绝对强度标定。在此过程中，首先由(523±1) nm范围内可见连续轫致辐射强度的绝对测量值计算出有效电荷数Z_eff，进而结合电子温度和密度分布计算EUV波段连续轫致辐射强度；EUV波段连续轫致辐射强度的测量值即为不同波长处探测器的连续本底计数扣除背景噪声计数值。对于较长波段范围130～280Å，通过对比等离子体中类锂杂质离子(Fe23+，Cr21+，Ar15+)和类钠杂质离子(Mo31+，Fe15+)发出的共振谱线对(跃迁分别为1s22s 2S_1/2-1s22p 2P_{1/2, 3/2}及2p63s 2S_1/2-2p63p 2P_{1/2, 3/2})强度比的理论和实验值进行相对强度标定。其中共振谱线对强度比的理论值由辐射碰撞模型计算得到，模型中处在各个能级的离子数主要由电子碰撞激发，去激发以及辐射衰变三个过程决定。两种方法相结合，实现了光谱仪20～280Å范围的绝对强度标定。考虑轫致辐射、电子温度及电子密度的测量误差，绝对标定误差约为30%。在绝对标定的基础上，我们对杂质特征谱线强度进行绝对测量，并将测量结果与杂质输运程序结合ADAS(Atomic Data and Analysis Structure)原子数据库计算得到的模拟值进行比较，进而估算等离子体中的杂质浓度。