Nonstandard methods for the convective transport equation with nonlinear reactions

A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467–485, 1998     

Redox Hyperactive MOF for Li+, Na+ and Mg2+ Storage

To create both greener and high-power metal-ion batteries, it is of prime importance to invent an unprecedented electrode material that will be able to store a colossal amount of charge carriers by a redox mechanism. Employing periodic DFT calculations, we modeled a new metal-organic framework, which displays energy density exceeding that of conventional inorganic and organic electrodes, such as Li- and Na-rich oxides and anthraquinones. The designed MOF has a rhombohedral unit cell in which an Ni(II) node is coordinated by 2,5-dicyano-p-benzoquinone linkers in such a way that all components participate in the redox reaction upon lithiation, sodiation and magnesiation. The spatial and electronic changes occurring in the MOF after the interaction with Li, Na and Mg are discussed on the basis of calculated electrode potentials versus Li⁰/Li⁺, Na⁰/Na⁺ and Mg⁰/Mg²⁺, respectively. In addition, the specific capacities and energy densities are calculated and used as a measure for the electrode applicability of the designed material. Although the highest capacity and energy density are predicted for Li storage, the greater structural robustness toward Na and Mg uptake suggests a higher cycling stability in addition to lower cost. The theoretical results indicate that the MOF is a promising choice for a green electrode material (with <10% heavy metal content) and is well worth experimental testing.     

Dependence of the lidar signal depolarization on the receiver’s field of view in the sounding of fog and clouds

We report an experimental study of the lidar signal depolarization as a function of the relative contribution of the multiple scattering in case of optically dense objects in the atmospheric planetary boundary layer. Results of the observation of fog and stratus clouds are presented, as well as those obtained by sounding of stratocumulus clouds during a snowfall. The lidar data point to a rise of the depolarization coefficient as the influence of the multiple scattering increases in consequence of both viewing angle enlargement and penetration into the object sounded. The variations of the depolarization coefficient are studied as a function of the field of view. In the case of fog, this dependence is approximated by a three-parameter exponential law; it is found that the depolarization increases steeply when the viewing angle is increased from 9 mrad to 12.5 mrad. The relationships between the approximation parameters and the microphysical characteristics of the scattering medium are considered. The experimentally determined size of the area where multiple scattering occurs is in good agreement with that calculated according to the diffusion model. The results obtained on the multiple scattering effect on the depolarization can also be employed in determining the extinction coefficient profiles in optically dense objects, as well as in evaluating the characteristic size of the scattering particles. Received: 6 September 1999 / Revised version: 7 February 2000 / Published online: 6 September 2000     

Experimental determination of the multiple-scattering effect on the lidar-signal polarization characteristics during liquid- and solid-phase precipitation

We present results of experimental investigations of the signal-polarization characteristics in the case of lidar sounding during precipitation. We show and discuss the lidar signals and the depolarization profiles along the sounding path for liquid- and solid-phase precipitation. In the former case we compare the signal characteristics at different degrees of precipitation rate. In the latter situation, we consider snowfall with particle shape close to that of Chebyshev particles. We also follow the lidar-signal changes depending on the field-of-view of the receiving optics. The experimental data are compared with results of theoretical estimates and models concerning the optical and microphysical characteristics of the rain and snow particles. In the case of liquid-phase precipitation – rain – the observed dependence of the lidar’s signal-polarization structure on the precipitation intensity has two aspects: on the one hand, the change of the raindrops’ shape, and, on the other, the multiple-scattering effects. The lidar data demonstrate that the signal depolarization, and, more specifically, its behavior along the sounding path, can be used as a criterion for the presence of multiple scattering. In the case of a snowfall consisting of Chebyshev particles, the simultaneous role is evident of two factors influencing the lidar-signal depolarization, namely, the non-spherical shape of the particles and the multiple-scattering effects. When the scattering takes place off particles with a large size and a shape strongly differing from spherical, we observed the predominant role of the non-sphericity of the scattering centers in the signal depolarization. Received: 6 December 2000 / Revised version: 11 July 2001 / Published online: 19 September 2001     

Surface homeomorphisms with zero-dimensional singular set

We prove that if ƒ is an orientation-preserving homeomorphism of a closed orientable surface M² whose singular set Σ(ƒ) is totally disconnected, then ƒ is topologically conjugate to a conformal transformation.     

Effects of Neutral and Anionic Substituents on the Carbonyl Stretching Band of Substituted Benzophenones

Satisfactory correlations were found of the frequencies of the title band (ν_CO) with 6⁺ and other substituent constants. The correlations proved valid for benzophenones with both neutral and anionic substituents (more than 100 compounds). The integrated intensities of the ν_CO bands (A^1/2 _CO) did not correlate with any type of substituent constants; the decrease in A_CO in the cases of benzophenones with strong electron-releasing substituents was ascribed to a resonance-induced intensity borrowing from ν_CO BY THE aromatic skeletal bands (8-type). This statement wa confirmed by IR data few deuterated benzophenones.     

AnO(n logn) algorithm for computing the link center of a simple polygon

We present an algorithm that determines the link center of a simplen-vertex polygonP inO(n logn) time. The link center of a simple polygon is the set of pointsx insideP at which the maximal link-distance fromx to any other point inP is minimized. The link distance between two pointsx andy insideP is defined to be the smallest number of straight edges in a polygonal path insideP connectingx andy. Using our algorithm we also obtain anO(n logn)-time solution to the problem of determining the link radius ofP. The link radius ofP is the maximum link distance from a point in the link center to any vertex ofP. Both results are improvements over theO(n ²) bounds previously established for these problems. The research of J.-R. Sack was supported by the Natural Sciences and Engineering Research Council of Canada.