An implicit approach to predict the dynamics of granular media

The objective of this study is to present an implicit method to predict the dynamics of granular particles. In the proposed methodology, the dynamics equation of colliding particles are solved implicitly which means the positions of particles at the next time step are also used to compute the next state of the particles. This is in contrast with the explicit approach where only known i.e. past information is used to calculate the new positions. The method is tested in a simple setting where a spherical particle is in continuous movement between two boundary walls. The results show that considerably larger time steps are enabled with the implicit method compared to the explicit method. Future work will compare the overall efficiency of the implicit and explicit methods in more detail. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Proving the existence of zeros using the topological degree and interval arithmetic

The invariance of the topological degree under certain homotopies is used to computationally prove the existence of zeros of nonlinear mappings in Rⁿ${\mathbb{R}}^n$. These existence tests use interval arithmetic to enclose the range of a function over a box. We show that our test is more general than a well-known test based on Miranda's theorem, and we show by a numerical example that the new test can be successful on substantially larger boxes.     

Patterned polyfluorene surfaces by functionalization of nanoimprinted polymeric features

A new procedure is described for surface grafting polymer brushes by step-growth polymerization from initiator-embedded polymeric thin films and micron- and nanometer-scale patterns. An imprint lithographic process, nanocontact molding, was used to prepare thin patterned cross-linked polyacrylate network films on silicon wafers that incorporated 4-bromostyrene in the networks. These networks present reactive 4-bromophenyl functionality at the surface that act as attachment sites for the subsequent Ni(0)- mediated step-growth condensation polymerization of 2,7-dibromo-9,9-dihexylfluorene The step-growth polymerization medium consisted of 2,7-dibromo-9,9-dihexylfluorene, Ni(0)-catalyst, and bipyridine in a toluene/dimethylformamide solvent mixture. The resulting growth of polydihexylfluorene brushes from the patterned surface was monitored by contact angle, optical spectrometry, surface profilometry and AFM. Brush growth was conducted from patterned features ranging from 100 microm to 100 nm in width and 50 nm in height. The optical and fluorescence behavior of the polyfluorene brushes was similar to that of thin polyfluorene films made by spin coating.     

Two acceleration mechanisms in verified global optimization

Acceleration devices are very important to speed up interval global optimization algorithms. We propose here two techniques which can be applied in addition to other known techniques. Firstly, we propose a test based on the one-dimensional Newton iteration to discard or split the current box. This test is usually cheap and it is likely to be successful when a good approximation of the minimum is known early. The other technique proposed deals with parallelization. We propose to share the task of the manager process among other non-idle processes in such a way that not only one process is responsible for the load balancing. Experimental results presented show that both techniques yield significant improvements in many cases.     

Réduction des tores déployés par une extension modérément ramifiée

We study the connected component of the special fiber of the Néron model of a torus split over a tamely ramified extension. It turns out to be a product of Witt vectors of finite length, explicitly calculable. We are thus able to correct a result presented in Kunyavskii and Sansuc (C. R. Acad. Sci. Paris, Ser. I 324 (1997) 307–312). To cite this article: C. Buchheim, H. Frommer, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Parallel nonlinear multisplitting methods

Summary Linear multisplitting methods are known as parallel iterative methods for solving a linear systemAx=b. We extend the idea of multisplittings to the problem of solving a nonlinear system of equationsF(x)=0. Our nonlinear multisplittings are based on several nonlinear splittings of the functionF. In a parallel computing environment, each processor would have to calculate the exact solution of an individual nonlinear system belonging to his nonlinear multisplitting and these solutions are combined to yield the next iterate. Although the individual systems are usually much less involved than the original system, the exact solutions will in general not be available. Therefore, we consider important variants where the exact solutions of the individual systems are approximated by some standard method such as Newton's method. Several methods proposed in literature may be regarded as special nonlinear multisplitting methods. As an application of our systematic approach we present a local convergence analysis of the nonlinear multisplitting methods and their variants. One result is that the local convergence of these methods is determined by an induced linear multisplitting of the Jacobian ofF.Dedicated to the memory of Peter Henrici     

Parallel interval multisplittings

Summary We introduce interval multisplittings to enclose the setS={A^–1b|A[A], b[b]}, where [A] denotes an interval matrix and [b] an interval vector. The resulting iterative multisplitting methods have a natural parallelism. We investigate these methods with respect to convergence, speed of convergence and quality of the resulting enclosure forS.Dedicated to the memory of Peter Henrici