Atomic step motion during the dewetting of ultra-thin films

We report on three key processes involving atomic step motion during the dewetting of thin solid films: (i) the growth of an isolated island nucleated far from a hole; (ii) the spreading of a monolayer rim; and (iii) the zipping of a monolayer island along a straight dewetting front. Kinetic Monte Carlo results are in good agreement with simple analytical models assuming diffusion-limited dynamics.     

Virtual and effective control for distributed systems and decomposition of everything

For the numerical approximation of the solution of boundary value problems (BVP), decomposition techniques are very important, in particular in view of parallel computations. The same is true, in principle, for optimal control of distributed systems, i.e., systems governed (modelled) by partial differential equations (PDE). Very many techniques have been studied for the approximation of BVP, such as DDM (domain decomposition method), decomposition of operators (splitting up, for instance). In contrast, not so many techniques of decomposition have been used in control problems for distributed systems, as pointed out in the contributions of Benamou [1], Benamou and Després [2], and Lagnese and Leugering [11]. However, it has been observed by Pironneau and Lions [24], [26] that by using so-calledvirtual controls, systematic DDM can be obtained, and that problems of optimal control and analysis of BVP can be considered in the same framework. We then deal with virtual control problems for BVP, virtual and effective control problems for the control of PDE (cf. Pironneau and Lions [25]). Using the idea of virtual control in other guises, Glowinski, Lions and Pironneau [9] have shown how to obtain new decomposition methods for the energy spaces (cf. Section 3), and Pironneau and Lions [27] have shown how to obtain systematically operator decomposition in BVP. In the present paper, we show (without assuming prior knowledge) how to apply the virtual control ideas in several different guises to the “decomposition of everything” for PDE of evolution and for their control. In this way, one can decompose the geometrical domain, the energy space and the operator. This is briefly presented in Sections 2, 3 and 4. We show in Section 5 how one can simultaneously apply two of the decomposition techniques and also indicate briefly how virtual control ideas can be used in case of bilinear control. The content of this paper is presented here for the first time. It is part of a systematic program which is in progress, developed with several colleagues. I wish to thank particularly F. Hecht, R. Glowinski, J. Periaux, O. Pironneau, H. Q. Chen and T. W. Pan. Of course we do not claim by any means that the methods based on “virtual control” are “better” than the many decomposition techniques already available (no attempt has been made to compile a Bibliography on these topics). Numerical works in progress show that the methods are “not bad”, but no serious benchmarking has been made yet. Possible interest lies in the fact thatone technique, with some variants, seems to lead to all possible Decompositions of Everything.     

第22卷B辑第三者期(2001)目次和提要

该文研究形如-div(a(x,x/ε,x/ε2,Duε))非线性单调算子的重迭代齐性化 J. L. Lions D. Lukassen L. E. Persson P. Wall该文研究形如-div(a(x,x/,x/2, Du))=f的非线性方程的重迭代齐性化,这里a关于前两个变量是周期的, 关于第3个变量是单调的. 证明了当 0时,u在W1,p()中(甚至在某种多尺度意义上)弱收敛于一个极限问题的解.此外, 还给出了这个极限问题的显式表达和主要结果的完整证明. 线性弹性壳动力学问题的渐近分析---动力学弯曲壳方程的验证 肖黎明 从三维弹性壳动力学方程出发, 在某些条件下用渐近分析方法给出了动力学弯曲壳方程的验证. 等变上同调和对称群的表示 M. Atiyah 作者在最近一篇论文中, 构造了一个从3维空间中, n个不同的有序点的构形空间到酉群U(n)的旗流形的连续映射, 该映射与对称群的作用相容, 它也与旋转群SO(3)适当的作用相容. 该文研究了在SO(3)-等变上同调中的诱导同态, 并证明了这个同态包含了许多涉及对称群的表示的有趣信息. 超线性可逆系统解的有界性     

A remark on regularization in Hilbert spaces

Every graph with uncountable chromatic number contains for every finiten ann-connected subgraph with infinite degrees which has uncountable chromatic number.     

Du discret au continu pour des modèles de réseaux aléatoires d'atomes

We study in this Note the continuum (macroscopic) limit for some atomistic models for crystals. The purpose is to derive densities of mechanical energies from microscopic models. In contrast to the setting of a previous study, where the microscopic structure was assumed to be periodic, it is modelled here by a stochastic lattice, which enjoys some stationarity and ergodicity properties, following notions previously introduced elsewhere. To cite this article: X. Blanc et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).