A flux-limiter method for dam-break flows over erodible sediment beds

Finite volume methods for dam-break flows over erodible sediment beds require a monotone numerical flux. In the present study we present a new flux-limiter scheme based on the Lax–Wendroff method coupled with a non-homogeneous Riemann solver and a flux limiter function. The non-homogeneous Riemann solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The proposed method satisfy the conservation property such that the discretization of the flux gradients and the source terms are well-balanced in the numerical solution of suspended sediment models. The flux-limiter method provides accurate results avoiding numerical oscillations and numerical dissipation in the approximated solutions. Several standard test examples are considered to verify the performance and the accuracy of the proposed method.     

Agler-Commutant Lifting on an Annulus

This note presents a commutant lifting theorem (CLT) of Agler type for the annulus \({\mathbb A}\) . Here the relevant set of test functions are the minimal inner functions on \({\mathbb A}\) —those analytic functions on \({\mathbb A}\) which are unimodular on the boundary and have exactly two zeros in \({\mathbb A}\) —and the model space is determined by a distinguished member of the Sarason family of kernels over \({\mathbb A}\) . The ideas and constructions borrow freely from the CLT of Ball et al. (Indiana Univ Math J 48(2):653–675, 1999) and Archer (Unitary dilations of commuting contractions. PhD thesis, University of Newcastle, 2004) for the polydisc, and Ambrozie and Eschmeier (A commutant lifting theorem on analytic polyhedra. Topological algebras, their applications, and related topics, 83108, Banach Center Publications, vol 67. Polish Academy of Sciences, Warsaw, 2005) for the ball in \({\mathbb C^n}\) , as well as generalizations of the de Branges–Rovnyak construction like found in Agler (On the representation of certain holomorphic functions defined on a polydisc. Topics in operator theory: Ernst D. Hellinger memorial volume, operator theory: advances and applications, vol 48. Birkhäuser, Basel, pp 47–66, 1990) and Ambrozie et al. (J Oper Theory 47(2):287–302, 2002). It offers a template for extending the result in McCullough and Sultanic (Complex Anal Oper Theory 1(4):581–620, 2007) to infinitely many test functions. Among the needed new ingredients is the formulation of the factorization implicit in the statement of the results in Ball et al. (Indiana Univ Math J 48(2):653–675, 1999) and Archer (Unitary dilations of commuting contractions. PhD thesis, University of Newcastle, 2004) and McCullough and Sultanic (Complex Anal Oper Theory 1(4):581–620, 2007) in terms of certain functional Hilbert spaces of Hilbert space valued functions.     

An unstructured finite‐volume method for coupled models of suspended sediment and bed load transport in shallow‐water flows

The aim of this work is to develop a well‐balanced finite‐volume method for the accurate numerical solution of the equations governing suspended sediment and bed load transport in two‐dimensional shallow‐water flows. The modelling system consists of three coupled model components: (i) the shallow‐water equations for the hydrodynamical model; (ii) a transport equation for the dispersion of suspended sediments; and (iii) an Exner equation for the morphodynamics. These coupled models form a hyperbolic system of conservation laws with source terms. The proposed finite‐volume method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe's scheme using the sign of the Jacobian matrix in the coupled system. A well‐balanced discretization is used for the treatment of source terms. In this paper, we also employ an adaptive procedure in the finite‐volume method by monitoring the concentration of suspended sediments in the computational domain during its transport process. The method uses unstructured meshes and incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep sediment concentrations and bed load gradients that may form in the approximate solutions. Details are given on the implementation of the method, and numerical results are presented for two idealized test cases, which demonstrate the accuracy and robustness of the method and its applicability in predicting dam‐break flows over erodible sediment beds. The method is also applied to a sediment transport problem in the Nador lagoon.Copyright © 2013 John Wiley & Sons, Ltd.     

Anion-directed formation and degradation of an interlocked metallohelicate

Although there are many examples of catenanes, those of more complex mechanically interlocked molecular architectures are rare. Additionally, little attention has been paid to the degradation of such interlocked systems into their starting complexes, although formation and degradation are complementary phenomena and are equally important. Interlocked metallohelicate, [(Pd(2)L(4))(2)](8+) (2(8+)), is a quadruply interlocked molecular architecture consisting of two mechanically interlocked monomers, [Pd(2)L(4)](4+) (1(4+)). 2(8+) has three internal cavities, each of which encapsulates one NO(3)(-) ion (1:3 host-guest complex, 2?(NO(3)|NO(3)|NO(3))(5+)) and is characterized by unusual thermodynamic stability. However, both the driving force for the dimerization and the origin of the thermodynamic stability remain unclear. To clarify these issues, BF(4)(-), PF(6)(-), and OTf(-) have been used to demonstrate that the dimerization is driven by the anion template effect. Interestingly, the stability of 2(8+) strongly depends on the encapsulated anions (2?(NO(3)|NO(3)|NO(3))(5+) ? 2?(BF(4)|BF(4)|BF(4))(5+)). The origins of this differing thermodynamic stability have been shown through detailed investigations to be due to the differences in the stabilization of the interlocked structure by the host-guest interaction and the size of the anion. We have found that 2-naphthalenesulfonate (ONs(-)) induces the monomerization of 2?(NO(3)|NO(3)|NO(3))(5+) via intermediate 2?(ONs|NO(3)|ONs)(5+), which is formed by anion exchange. On the basis of this finding, and using p-toluenesulfonate (OTs(-)), the physical separation of 2?(NO(3)|NO(3)|NO(3))(5+) and 1(4+) as OTs(-) salt was accomplished.     

Rapid and implicit effects of color category on visual search

Many studies suggest that the color category influences visual perception. It is also well known that oculomotor control and visual attention are closely linked. In order to clarify temporal characteristics of color categorization, we investigated eye movements during color visual search. Eight color disks were presented briefly for 20–320 ms, and the subject was instructed to gaze at a target shown prior to the trial. We found that the color category of the target modulated eye movements significantly when the stimulus was displayed for more than 40 ms and the categorization could be completed within 80 ms. With the 20 ms presentation, the search performance was at a chance level, however, the first saccadic latency suggested that the color category had an effect on visual attention. These results suggest that color categorization affects the guidance of visual attention rapidly and implicitly.     

Biological monitoring of solar UV radiation at 17 sites in Asia, Europe and South America from 1999 to 2004

A small and robust dosimeter for determining the biologically effective dose of ambient UV radiation has been developed using UV-sensitive mutant spores of Bacillus subtilis strain TKJ6312. A membrane filter with four spots of the spores was snapped to a slide mount. The slide was wrapped and covered with two or more layers of polyethylene sheet to protect the sample from rain and snow and to reduce monthly-cumulative doses within the measurable range. From 1999, monthly data were collected at 17 sites for more than 1 year, and data for 4 to 6 consecutive years were obtained from 12 sites. Yearly total values of the spore inactivation dose (SID) ranged from 3200 at subarctic Oulu to 96000 at tropical Denpasar, and the mean yearly values of SID exhibited an exponential dependence on latitude in both hemispheres with a doubling for about every 14 degrees of change. During the observation period, increasing trends of UV doses have been observed at all sites with more than 5 years of data available. Year-to-year variations at high and middle latitude sites are considered due mostly to climatic variation. At three tropical sites, negative correlations between the yearly doses and the column ozone amounts were observed. The results verified the applicability of spore dosimetry for global and long-time monitoring of solar UV radiation, in particular at tropical sites where no monitoring is taking place.     

Gradient-Based Blind Deconvolution with Phase Spectral Constraints

This paper proposes a new blind deconvolution method with additional phase spectral constraints for a blurred image. A degradation of an original image is mathematically modeled by a convolution of an original image and a point-spread function (PSF). The proposed method consists of the following three steps: (i) projection onto a complex set satisfying the phase spectral constraint in a frequency space; (ii) minimization of a cost function preserving the constrained phase spectra; and (iii) projection onto an image space satisfying nonnegative and support constraints. This method restores both the original image and the PSF with high accuracy. The effectiveness of the proposed method is verified by applying it to some blind deconvolution problems for digital images, and the experimental results show that the performance is superior to the conventional blind deconvolution methods.     

Monodromy at Infinity and the Weights of Cohomology

We show that for a polynomial map, the size of the Jordan blocks for the eigenvalue 1 of the monodromy at infinity is bounded by the multiplicity of the reduced divisor at infinity of a good compactification of a general fiber. The existence of such Jordan blocks is related to global invariant cycles of the graded pieces of the weight filtration. These imply some applications to period integrals. We also show that such a Jordan block of size greater than 1 for the graded pieces of the weight filtration is the restriction of a strictly larger Jordan block for the total cohomology group. If there are no singularities at infinity, we have a more precise statement on the monodromy.     

Effect of “topotactic” reduction product of molybdenum disulfide on catalytic activity of metallocene catalyst for olefin polymerization

N,N-Dimethylanilinium salt of molybdenum disulfide (MoS₂) was developed as a novel cocatalyst for metallocene catalysts. The cocatalyst is composed of N,N-dimethylanilinium ion as a cationic part and “topotactic” reduction product of MoS₂, obtained by acquisition of an electron by neutral host lattice of MoS₂ without structural alteration, as an anionic part. In ethylene polymerization, addition of the N,N-dimethylanilinium salt of MoS₂ to the bis(indenyl)zirconium dichloride (Ind₂ZrCl₂)/triethylaluminum (Et₃Al) catalyst improved the catalytic activity per mmol of Ind₂ZrCl₂. The catalytic activity of this system activated by addition of the cocatalyst depended significantly on the amount of the cocatalyst and the N,N-dimethylanilinium ion content in the cocatalyst. Poly(ethylene) and poly(ethylene-co-1-hexene) obtained with the metallocene catalyst activated by addition of the cocatalyst have typical features such as narrow molecular weight distribution and narrow composition distribution like polymers obtained with conventional metallocene catalysts.