Simulation model for shapiro time delay and light deflection experiments

The time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.     

Geometrical characteristics of polyelectrolyte nanogel particles and their polyelectrolyte complexes studied by dynamic and static light scattering

The geometric characteristics of nanogel particles in aqueous solutions were studied by determining their ratios of radius of gyration (mean-square radius; Rg) to hydrodynamic radius (Rh), Rg/Rh, derived from static light scattering and dynamic light scattering experiments, respectively. The various nanogel samples studied included ones composed of lightly cross-linked N-isopropylacrylamide (NIPA) polymer, NIPA-based anionic or cationic copolymers, and amphoteric terpolymers. Polyelectrolyte complexes between anionic or cationic nanogels and oppositely charged polyions or nanogels having opposite charges were also studied. Most NIPA and NIPA-based polyelectrolyte nanogels in a swollen state had Rg/Rh values >0.775, which is the theoretically predicted value for a solid sphere. In a collapsed state, one may expect nanogel particles to be spherical in shape; however, this was not the case for a variety of nanogel samples, either with or without charges. These data were consistent with the idea that the surfaces of these nanogel particles were decorated with attached dangling chains. The Rg/Rh data from polyelectrolyte-nanogel complexes, however, indicated different structures from this. It was found that most of the polyelectrolyte-nanogel complex particles had Rg/Rh approximately 0.775. This suggested that the complexed nanogel particles were spherical in shape and that there were no dangling surface chains.     

Schur complement preconditioners for anisotropic problems

We present two new variants of Schur complement domain decompositionpreconditioners suitable for 2D anisotropic problems. Thesevariants are based on adaptations of the probing idea, describedby Chan et al (1992 Fifth Int. Symp. on Domain DecompositionMethods for Partial Differential Equations, Philadelphia: SIAM,pp 236-249), used in conjunction with a coarse grid approximationas introduced by Bramble et al (1986 Math. Comput. 47, 103-134).The new methods are specifically designed for situations wherethe coupling between neighbouring interfaces is stronger thanthe coupling within an interface. Taking into account this strongcoupling, one variant uses a multicolour probing technique toavoid distortion in the probe approximations that appear whenusing the method proposed by Chan et al. The second techniqueuses additional probe matrices to approximate not only the couplingwithin the interfaces but also the coupling between interfacepoints across the subdomains. This latter procedure looks somewhatlike an alternating line relaxation method for anisotropic problems,see Brandt (1977 Math. Comput.. 31, 333-390). To assess therelevance of the new preconditioners, we compare their numericalbehaviour with well known robust preconditioners such as thebalanced Neumann-Neumann method proposed by Mandel (1993 Commun.Numer. Methods Eng.. 9, 233-241).     

评《马氏决策过程》

（《马氏决策过程》,侯振挺、郭先平著,长沙,湖南科技出版社,1997,中文版,386页,定价：28元）马尔可夫决策过程是概率论的运筹学的理论研究和实际应用中极其重要的领域之一．随着中国和国际上对马尔可夫决策过程（MarkovDecisionProcesses,简记为MDP）研究的新进展,许     

Simulation model for anomalous precession of the perihelion of mercury's orbit

The ‘anomalous perihelion precession’ of Mercury, announced by Le Verrier in 1859, was a highly controversial topic for more than half a century and invoked many alternative theories until 1916, when Einstein presented his theory of general relativity as an alternative theory of gravitation and showed perihelion precession to be one of its potential manifestations. As perihelion precession was a directly derived result of the full General Theory and not just the Equivalence Principle, Einstein viewed it as the most critical test of his theory. This paper presents the computed value of the anomalous perihelion precession of Mercury's orbit using a new relativistic simulation model that employs a simple transformation factor for mass and time, proposed in an earlier paper. This computed value compares well with the prediction of general relativity and is, also, in complete agreement with the observed value within its range of uncertainty. No general relativistic equations have been used for computing the results presented in this paper.     

MAD: practical implementation of MCAO concepts

The European Southern Observatory (ESO) together with external research institutes have built a Multi-Conjugate Adaptive Optics (MCAO) Demonstrator (MAD) to perform wide field-of-view adaptive optics correction (2′ in K band). The aim of MAD is to demonstrate the on-sky feasibility of the MCAO technique and to evaluate its critical aspects in the framework of both the 2nd generation instrumentation for the Very Large Telescope (VLT) and the Overwhelmingly Large Telescope (OWL). The MAD module will be installed on the VLT to perform on-sky observations. MAD comprises two deformable mirrors and two different multi-reference wavefront sensors with natural guide stars. In this article we present the MAD design, some aspects of the MAD calibration and the first closed-loop results in the laboratory in Single Conjugated Adaptive Optics (SCAO) and Ground Layer Adaptive Optics (GLAO) configurations. To cite this article: E. Marchetti et al., C. R. Physique 6 (2005).     

LINC-NIRVANA: MCAO toward Extremely Large Telescopes

LINC-NIRVANA is a Fizeau (imaging) interferometer exploiting the full spatial resolution of a 23 m class telescope in the combined beam of the Large Binocular Telescope supported through Multi-Conjugated Adaptive Optics (MCAO). By means of science cases, we show how LINC-NIRVANA takes advantage of the MCAO, increasing the sky coverage of the instrument and the field of view for the Fringe and Flexure tracker. We introduce the MCAO system of LINC-NIRVANA in detail, which in a first step will be installed with two deformable mirrors per arm and has the provision to be upgraded with a third mirror. The MCAO system implements several novel concepts proposed for extremely large telescopes, such as layer oriented MCAO, optical co-adding of guide stars, or Multiple Field of View sensing. LINC-NIRVANA will demonstrate some of the concepts for the first time on sky. To cite this article: W. Gaessler et. al., C. R. Physique 6 (2005).     

Surface tension of polymers with long unbranched side chains

The surface tension of polymers having long unbranched side chains was measured by a contact-angle technique. It ranges between 20–29 dynes/cm and is almost entirely due to dispersion forces. At the lower end of this range the side chains are attached to every other carbon atom of the main chain and the structure is characterized by extended alkyl side chains at right angles to the main chain with methyl groups forming the interface. As the spacing frequency of the side chains increases and the main chain becomes the site of other bulky groups, this structure becomes less ordered and the surface tension increases to the high twenties. The same effect, to a lesser extent, is observed when the length of the side chains is gradually diminished to 12 carbon atoms from 21. A sudden increase of the polar force contribution of the surface tension at 10–12 carbon atoms indicates collapse of the ordered side-chain structure.     

Potentiometric titration behavior of poly(acrylic acid) within a cross-linked polymer network having amide groups

This study aimed to investigate the effect of COOH group distribution within a polymer network having amide groups, with which the COOH could form hydrogen bonds. We employed here two polyelectrolyte gels composed of N-isopropylacrylamide (NIPA) networks, either copolymerized with acrylic acid (AA) or within which poly(acrylic acid) (PAA) was entrapped. Both gels (AA–NIPA ∼ 1:4 mol/mol) were prepared by aqueous red-ox polymerization with N,N’-methylenebisacrylamide as the cross-linker. Finely divided gels in NaCl solutions (0.025 and 0.1 M) were titrated with NaOH and back-titrated with HCl at 25 °C. The results of the copolymer gel (CG) agreed well with those of a linear copolymer and a nanoscale gel which had a similar AA content to CG. However, marked differences were observed in the titration behaviors of the AA-copolymerized and PAA-entrapped gels, mainly due to the hydrogen bonding between the entrapped PAA chain and its surrounding NIPA network.