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61.
62.
Simone Göttlich Simon Hoher Patrick Schindler Veronika Schleper Alexander Verl 《Applied Mathematical Modelling》2014
In this paper a model comparison approach based on material flow systems is investigated that is divided into a microscopic and a macroscopic model scale. On the microscopic model scale particles are simulated using a model based on Newton dynamics borrowed from the engineering literature. Phenomenological observations lead to a hyperbolic partial differential equation on the macroscopic model scale. Suitable numerical algorithms are presented and both models are compared numerically and validated against real-data test settings. 相似文献
63.
A convergence analysis of time-splitting pseudo-spectral methods adapted for time-dependent Gross–Pitaevskii equations with additional rotation term is given. For the time integration high-order exponential operator splitting methods are studied, and the space discretization relies on the generalized-Laguerre–Fourier spectral method with respect to the $(x,y)$ -variables as well as the Hermite spectral method in the $z$ -direction. Essential ingredients in the stability and error analysis are a general functional analytic framework of abstract nonlinear evolution equations, fractional power spaces defined by the principal linear part, a Sobolev-type inequality in a curved rectangle, and results on the asymptotical distribution of the nodes and weights associated with Gauß–Laguerre quadrature. The obtained global error estimate ensures that the nonstiff convergence order of the time integrator and the spectral accuracy of the spatial discretization are retained, provided that the problem data satisfy suitable regularity requirements. A numerical example confirms the theoretical convergence estimate. 相似文献
64.
Ulrich Meier Christoph Van Wüllen Michael Schindler 《Journal of computational chemistry》1992,13(5):551-559
A direct method for the ab initio calculation of the magnetic susceptibility and chemical shielding tensors based on the individual gauge for localized molecular orbitals (IGLO) formalism is introduced. “Direct” in this context means we avoid storing the two-electron repulsion integrals in favor of recalculating them whenever necessary. In conjunction with the Direct-SCF package TURBOMOLE Direct IGLO (DIGLO) permits calculation of magnetic second-order properties for large molecules by minimizing peripheral disc storage requirements. The size of the molecules to be treated is limited only by the amount of CPU time available. The performance of DIGLO is demonstrated for some selected examples. 相似文献
65.
We present a MATLAB package for boundary value problems in ordinary differential equations. Our aim is the efficient numerical solution of systems of ODEs with a singularity of the first kind, but the solver can also be used for regular problems. The basic solution is computed using collocation methods and a new, efficient estimate of the global error is used for adaptive mesh selection. Here, we analyze some of the numerical aspects relevant for the implementation, describe measures to increase the efficiency of the code and compare its performance with the performance of established standard codes for boundary value problems. 相似文献
66.
67.
Ralf - Dieter Schindler 《Mathematical Logic Quarterly》1997,43(1):22-28
We show that weakly compact cardinals are the smallest large cardinals k where k+ < k+ is impossible provided 0# does not exist. We also show that if k+Kc < k+ for some k being weakly compact (where Kc is the countably complete core model below one strong cardinal), then there is a transitive set M with M ? ZFC + “there is a strong cardinal”. 相似文献
68.
This paper describes experiments where the bending of beams results in two or more fractures being formed, apparently simultaneously. This is explained in terms of the stress waves emitted by the initial fracture process. It is shown that three separate types of secondary fracture may occur as a result of the interaction between the stress pulses produced by the initial fracture and the loading stresses already present in the beam. In treating these problems it has been found helpful to use an analytical solution for the bending wave propagated when a semi-infinite beam, which is subjected to a constant bending moment, is suddenly unloaded at the free end. In modelling the longitudinal stress pulse produced by the fracture we have used a simplified model which assumes that the forcing function on the fracture plane is a force field equal to the resultant force acting on the unbroken portion of the fracture surface prior to the onset of fracture. 相似文献
69.
Photophysics of a Ruthenium 4H‐Imidazole Panchromatic Dye in Interaction with Titanium Dioxide
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Julian Schindler Dr. Stephan Kupfer Dr. Maria Wächtler Dr. Julien Guthmuller Prof. Dr. Sven Rau Prof. Dr. Benjamin Dietzek 《Chemphyschem》2015,16(5):1061-1070
The photophysics of bis(4,4′‐di‐tert‐butyl‐2,2′‐bipyridine‐κ2N,N′)[2‐(4‐carboxyphenyl)‐4,5‐bis(p‐tolylimino‐κN)imidazolato]ruthenium(II) hexafluorophosphate is investigated, both in solution and attached to a nanocrystalline TiO2 film. The studied substitution pattern of the 4H‐imidazole ligand is observed to block a photoinduced structural reorganization pathway within the 4H‐imidazole ligand that has been previously investigated. Protonation at the 4H‐imidazole ring decreases the excited‐state lifetime in solution. When the unprotonated dye is anchored to TiO2, photoinduced electron injection occurs from thermally nonrelaxed triplet metal‐to‐ligand charge transfer (3MLCT) states with a characteristic time constant of 0.5 ps and an injection efficiency of roughly 25 %. Electron injection from the subsequently populated thermalized 3MLCT state of the dye does not take place. The energy of this state seems to be lower than the conduction band edge of TiO2. 相似文献
70.
P. Biggs C. E. Canosa-Mas P. S. Monks R. P. Wayne Th. Benter R. N. Schindler 《国际化学动力学杂志》1993,25(10):805-817
This article describes the first direct determination of the rate coefficient for the self-reaction between two NO3 radicals. A laser photolysis technique was used to generate NO3, and time-resolved decays of NO3 were followed after stopping the photolysis. The products of the reaction are inferred to be NO2 and O2. The derived rate coefficient at room temperature for the self-reaction of (2.3 ± 0.8) ×10?16 cm3 molecule?1s?1 is in excellent agreement with the only other data, which were obtained in an indirect study. Consideration is given to the magnitude and influence of secondary chemistry and to the participation of FO in the chemistry of the NO3 buildup phase. The studies were conducted over a pressure range of 8 to 100 torr in helium. No clear pressure dependence was observed, and some tentative inferences are drawn both from this result and from the absolute magnitude of the rate coefficient about the mechanism of the reaction. There is apparently no role for the reaction in the chemistry of the atmosphere. © 1993 John Wiley & Sons, Inc. 相似文献