Solutions to and Validation of Matrix-Diffusion Models

A model transport system is considered in which a pulse of tracer molecules is advected along a flow channel with porous walls. The advected tracer thus undergoes diffusion, matrix-diffusion, inside the walls, which affects the breakthrough curve of the tracer. Analytical solutions in the form of series expansions are derived for a number of situations which include a finite depth of the porous matrix, varying aperture of the flow channel, and longitudinal diffusion and Taylor dispersion of the tracer in the flow channel. Novel expansions for the Laplace transforms of the concentration in the channel facilitated closed-form expressions for the solutions. A rigorous result is also derived for the asymptotic form of the breakthrough curve for a finite depth of the porous matrix, which is very different from that for an infinite matrix. A specific experimental system was created for validation of matrix-diffusion modeling for a matrix of finite depth. A previously reported fracture-column experiment was also modeled. In both cases model solutions gave excellent fits to the measured breakthrough curves with very consistent values for the diffusion coefficients used as the fitting parameters. The matrix-diffusion modeling performed could thereby be validated.     

Intra-elemental photoelectron line intensities and their significance to quantitative analysis

Intraelemental relative photoelectron line intensities for 20 pure elements obtained under ultrahigh vacuum (5·10^?9 torr) and high resolution with cleaned surfaces are presented. Theoretical and experimental aspects of relative photoelectron line intensities as well as other characteristics of significance to quantitative analysis are discussed. Experimental data are related to theoretical results and compared with other recent work.     

Transition moment directions of some important in-plane vibrations of uracil,thymine and cytosine. A fixed partial charge model calculation

Transition moment directions for the double-bond region vibrations of uracil, thymine and cytosine are calculated using the fixed partial charge model approximation. The coupling between the two carbonyl bonds and the carbon—carbon double bond in uracil and thymine is sensitive to the choice of the corresponding stretching force constants. The transition moment directions are correspondingly changed, thus, in principle, enabling the quantitative determination of coupling between the vibrations from linear dichroism measurements.     

Wavelet-based reconstruction for limited-angle X-ray tomography

The aim of X-ray tomography is to reconstruct an unknown physical body from a collection of projection images. When the projection images are only available from a limited angle of view, the reconstruction problem is a severely ill-posed inverse problem. Statistical inversion allows stable solution of the limited-angle tomography problem by complementing the measurement data by a priori information. In this work, the unknown attenuation distribution inside the body is represented as a wavelet expansion, and a Besov space prior distribution together with positivity constraint is used. The wavelet expansion is thresholded before reconstruction to reduce the dimension of the computational problem. Feasibility of the method is demonstrated by numerical examples using in vitro data from mammography and dental radiology.     

A reform in undergraduate mathematics curriculum : more emphasis on social and pedagogical skills

The paper describes the changes that are being made in the mathematics teachers' subject studies in the Department of Mathematics at the University of Joensuu, in order to provide our mathematics students both with a sufficiently deep knowledge of mathematics and science, and with present-day expertise in their profession as teachers. While the formal structure of the mathematics curriculum remains structured and taught as courses with mostly traditional names like algebra, analysis, and linear algebra, there are also totally new ‘professionally oriented’ courses. Some of the old courses—with rather traditional and rigorous contents—have been changed in a more student-driven direction. In these ‘pedagogically oriented’ courses students are encouraged, and even forced, to study co-operatively in social interaction, for example to negotiate how to solve a problem decently, or how to build a formal definition for a concept with certain wanted attributes. As an ultimate example of a pedagogical experiment we describe in more detail an abstract algebra course, where co-operative learning is combined with intensive programming in a mathematically oriented computer environment.     

Nonlinear optical and structural properties of langmuir-blodgett films of thiohelicenebisquinones

We provide a detailed investigation of the second-order nonlinear optical and structural properties of Langmuir-Blodgett (LB) films of nonracemic thiohelicenebisquinone (THBQ). We prepare both X- and Y-type films of different thicknesses and characterize them using optical second-harmonic generation and atomic-force microscopy (AFM). We find that the overall nonlinear properties of the samples are essentially independent of the film thickness and the deposition type and arise from susceptibility tensor components associated with chirality. Both X- and Y-type films can be described by D2 symmetry, which is a higher symmetry than the previously assumed C2 of LB films of THBQ and a similar helicenebisquinone (HBQ). However, the two types of films are shown to differ significantly with respect to the orientation of the in-plane axis. For Y type, the axis follows the direction of vertical sample deposition, but for X type, the direction of the axis varies randomly and significantly between different samples. The Y-type samples are therefore more ordered than the X-type samples. This was confirmed by AFM measurements in which the Y type exhibits uniform ordering into columnar structures. Similar structures in X type, on the other hand, are shorter and more randomly oriented, like those earlier observed for racemic samples of HBQ [Verbiest, T., et al. Science 1998, 282, 913]. The common nonlinear properties and different high-level ordering observed here for two different types of nonracemic samples reinforces that the nonlinearity of THBQ (and probably HBQ, as well) originates from the low-level columnar aggregation of the molecules with the higher-level structures playing a lesser role. In addition, within the columns, the molecules likely assume fairly random azimuthal orientations so that the columns themselves exhibit approximate Dinfinity symmetry.     

Photoabsorption spectra of small fullerenes and Si-heterofullerenes

We study the spectral properties of two kinds of derivatives of the carbon fullerene C(60), small fullerenes and Si-heterofullerenes, by ab initio calculations. The principal method of study is the time-dependent density-functional theory in its full time-propagation form. C(20), C(28), C(32), C(36), and C(50), the most stable small fullerenes in the range of C(20)-C(50), are found to have characteristic features in their optical absorption spectra, originating from the geometry of the molecules in question. The comparison of measured and calculated absorption spectra is found to be a useful tool in differentiating between different, almost isoenergetic ground state structure candidates of small fullerenes. Substitutionally doped fullerenes are of interest due to their enhanced chemical reactivity. It is suggested that the doping degree can be obtained by studying the absorption spectra. For example, it is observed that the spectra gradually change when doping C(60) up to C(48)Si(12) so that absorption in the visible and near infrared regions increases.     

Iron and Cobalt Complexes of a Series of Tridentate P,N, P Ligands — Synthesis,Characterization, and Application in Ethene Polymerization Reactions

A series of tridentate P, N, P ligands comprising a central pyridine unit and two pendent diarylphosphane moieties (2, 6‐bis(CH₂PAr₂)pyridine; Ar = phenyl ( 1 ), 2‐methylphenyl ( 2 ), 2, 4, 6‐trimethylphenyl ( 3 )) as well as the corresponding iron ( 1‐FeCl₂ , 2‐FeCl₂ , 3‐FeCl₂ ) and cobalt ( 1‐CoCl₂ , 2‐CoCl₂ , 3‐CoCl₂ ) complexes were synthesized and characterized. An X‐ray structure analysis of 2‐CoCl₂ and 3‐CoCl₂ exhibited a trigonal‐bipyramidal coordination geometry at the metal center, the two chlorine atoms and the nitrogen occupying the equatorial and the phosphane units the apical positions. IR analysis indicated, that in all complexes the pyridine unit is coordinated to the metal center. The cobalt compounds were applied as catalyst precursors for the polymerization of ethene after activation with MAO.     

Diffusion of Tracer in Altered Tonalite: Experiments and Simulations with Heterogeneous Distribution of Porosity

Numerical time-domain-diffusion simulations were used for studying the diffusion behavior of tracer molecules in rock matrix with homogeneous and heterogeneous porosity. As the heterogeneous sample in these simulations, a 3D tomographic image of altered tonalite was used, in which the mineral components and the pores resolved by X-ray microtomography were represented by their respective intragranular porosities determined previously by the ¹⁴C-PMMA method. The apparent diffusion coefficient of a tracer in altered tonalite was determined experimentally, and was then used in the simulations. In the altered tonalite analyzed, inclusion of heterogeneity in the porosity increased the diffusion coefficient by 16 %. Altered and pristine feldspar was the main mineral component in the sample (72 %), and it also provided the dominant contribution to tracer diffusion, explaining alone 52 % of the diffusion coefficient. The large pores resolved by microtomography (6 %) and altered and pristine mica (22 %) gave an equal contribution to the diffusion coefficient. The simulation method applied was also validated by comparing the results to both an analytical and a numerical solution to the diffusion equation in a homogenous medium. In addition, the method was compared to discrete-time random-walk simulations in the case of randomly placed overlapping spheres.