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Numerical solution of the heat equation with non-linear, time derivative-dependent source term
(2010)
The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non-linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non-linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi-implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley & Sons, Ltd.
Oxorhenium(V) complexes [ReOX3(PPh3)2] (X = Cl, Br) react with phenylacetylene under formation of complexes with ylide-type ligands. Compounds of the compositions [ReOCl3(PPh3){C(Ph)C(H)(PPh3)}] (1), [ReOBr3(OPPh3){C(Ph)C(H)(PPh3)}] (2), and [ReOBr3(OPPh3){C(H)C(Ph)(PPh3)}] (3) were isolated and characterized by X-ray diffraction. They contain a ligand, which was formed by a nucleophilic attack of released PPh3 at coordinated phenylacetylene. The structures of the products show that there is no preferable position for this attack. Cleavage of the Re–C bond in 3 and dimerization of the organic ligand resulted in the formation of the [{(PPh3)(H)CC(Ph)}2]2+ cation, which crystallized as its [(ReOBr4)(OReO3)]2– salt.
AgTcO4 reacts with R3ECl compounds (E = C, Si, Ge, Sn, Pb; R = Me, iPr, tBu, Ph), tBu2SnCl2, or PhMgCl under formation of novel trioxotechnetium(VII) derivatives. The carbon and silicon derivatives readily undergo decomposition, which was proven by 99Tc NMR spectroscopy and the isolation of decomposition products such as [TcOCl3(THF)(OH2)]. Compounds [Ph3GeOTcO3], [(THF)Ph3SnOTcO3], [(O3TcO)SntBu2(OH)]2, and [(THF)4Mg(OTcO3)2] are more stable and were isolated in crystalline form and characterized by X-ray diffraction.
As the field strength and, therefore, the operational frequency in MRI is increased, the wavelength approaches the size of the human head/body, resulting in wave effects, which cause signal decreases and dropouts. Several multichannel approaches have been proposed to try to tackle these problems, including RF shimming, where each element in an array is driven by its own amplifier and modulated with a certain (constant) amplitude and phase relative to the other elements, and Transmit SENSE, where spatially tailored RF pulses are used. In this article, a relatively inexpensive and easy to use imaging scheme for 7 Tesla imaging is proposed to mitigate signal voids due to B1 field inhomogeneity. Two time-interleaved images are acquired using a different excitation mode for each. By forming virtual receive elements, both images are reconstructed together using GRAPPA to achieve a more homogeneous image, with only small SNR and SAR penalty in head and body imaging at 7 Tesla.
Leon Battista Alberti, probably the most innovative architect of early Renaissance Italy, has always fascinated scholars by virtue of the striking interpenetration of theory and practice manifest in his work. As an architect, Alberti was an autodidact. Without the benefit of the formative influence of a master or design education, the roots of his conception of architecture lie in his intellectual formation through humanistic rhetoric. The present study demonstrates with reference to a specific project — the Tempietto of the Holy Sepulchre in Florence — how Alberti’s humanist approach conditioned his method of architectural design.