Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table

Tune in to your emotions: a robust personalized affective music player

The emotional power of music is exploited in a personalized affective music player (AMP) that selects music for mood enhancement. A biosignal approach is used to measure listeners’ personal emotional reactions to their own music as input for affective user models. Regression and kernel density estimation are applied to model the physiological changes the music elicits. Using these models, personalized music selections based on an affective goal state can be made. The AMP was validated in real-world trials over the course of several weeks. Results show that our models can cope with noisy situations and handle large inter-individual differences in the music domain. The AMP augments music listening where its techniques enable automated affect guidance. Our approach provides valuable insights for affective computing and user modeling, for which the AMP is a suitable carrier application

Mechanical investigation of polyurethane elastomers in terms of fracture mechanics methods

Poliuretanowe elastomery zastępują w układach zawieszenia pojazdów mechanicznych materiały gumowe. W artykule przedstawiono wyniki badań eksperymentalnych elastomerów poliuretanowych. Główną uwagę poświęcono odporności na pękanie i rozdzieranie elastomerów poliuretanowych w dwóch różnych konfiguracjach twardości – 80ShA – zbliżonej do twardości seryjnie użytkowanych gumowych elastomerów i 90ShA dedykowanej dla pojazdów, gdzie wymagana jest większa sztywność zawieszenia. Zbadano wpływ twardości tworzywa na odporność na pękanie wyrażoną w krytycznej wartości energii Wf oraz odporności na rozdzieranie. Wykazano, że wśród powszechnie stosowanych materiałów o dwóch twardościach; 80ShA i 90ShA, występują znacząco różne mechanizmy dyssypatywne przed frontem szczeliny. Pomimo zbliżonych wartości wydłużenia całkowitego przy zerwaniu (statyczna próba rozciągania próbek gładkich) zaobserwowano istotnie różną skłonność materiału do pochłaniania energii, jak również odporności na rozdzieranie. Z perspektywy użytkowej parametry te są kluczowe w kontekście dynamicznego charakteru pracy tego typu materiałów.In the paper, the experimental results of the mechanical investigation have been presented. The main attention was paid to fracture toughness and tearing resistance of polyurethane elastomers in terms of two different hardness configurations; 80ShA and 90ShA. The impact of material hardness on the fracture resistance is reflected in experimental results. For fracture toughness characterization, the EWF (essential work of fracture) method was involved. It has been shown, that the 80ShA and 90ShA materials demonstrate completly different behavior under high stress concentration condition - see the results for the cracked DENT specimens. The higher values of the essential work of fracture for the 90ShA material confirm a higher ductility level of this material. From the perspective of usefulness of fracture mechanics, the energy approach seems to be crucial in the context of the real operating conditions of the bushing in suspension system of vehicles

Contribution to the study of the influence of the stress ratio on the high cycle fatigue behaviour of riveted joints

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