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José A. Iglesias Martin Rumpf Otmar Scherzer 《Foundations of Computational Mathematics》2018,18(4):891-927
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples. 相似文献
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Wolfgang G. Kreyling Pratim Biswas Maria E. Messing Neil Gibson Marianne Geiser Alexander Wenk Manoranjan Sahu Knut Deppert Izabela Cydzik Christoph Wigge Otmar Schmid Manuela Semmler-Behnke 《Journal of nanoparticle research》2011,13(2):511-524
The intensive use of nano-sized titanium dioxide (TiO2) particles in many different applications necessitates studies on their risk assessment as there are still open questions on their safe handling and utilization. For reliable risk assessment, the interaction of TiO2 nanoparticles (NP) with biological systems ideally needs to be investigated using physico-chemically uniform and well-characterized NP. In this article, we describe the reproducible production of TiO2 NP aerosols using spark ignition technology. Because currently no data are available on inhaled NP in the 10?C50 nm diameter range, the emphasis was to generate NP as small as 20 nm for inhalation studies in rodents. For anticipated in vivo dosimetry analyses, TiO2 NP were radiolabeled with 48V by proton irradiation of the titanium electrodes of the spark generator. The dissolution rate of the 48V label was about 1% within the first day. The highly concentrated, polydisperse TiO2 NP aerosol (3?C6 × 106 cm?3) proved to be constant over several hours in terms of its count median mobility diameter, its geometric standard deviation, and number concentration. Extensive characterization of NP chemical composition, physical structure, morphology, and specific surface area was performed. The originally generated amorphous TiO2 NP were converted into crystalline anatase TiO2 NP by thermal annealing at 950 °C. Both crystalline and amorphous 20-nm TiO2 NP were chain agglomerated/aggregated, consisting of primary particles in the range of 5 nm. Disintegration of the deposited TiO2 NP in lung tissue was not detectable within 24 h. 相似文献
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Piotr T. Czekala Haiping Lin Werner A. Hofer Andris Gulans 《Surface science》2011,605(15-16):1341-1346
The aim of this work is to revisit the problem of acetylene adsorption on silicon (100). Extending previous theoretical work and including van der Waals forces explicitly in the simulations we remove existing ambiguities about the adsorption sites. The simulated adsorption energies and scanning tunneling microscopy contours are in good agreement with experimental data, they support the interpretation of a two-dimer feature at the surface as resulting from the adsorption of two individual molecules. It is also found that the simulated apparent heights agree with experimental values, if the actual bandgap of silicon is taken into account. 相似文献
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Irina Krasnochtanova Andreas Rauh Marco Kletting Harald Aschemann Eberhard P. Hofer Karl-Michael Schoop 《Applied Mathematical Modelling》2010
This paper presents sophisticated interval algorithms for the simulation of discrete-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Since naive implementations of interval algorithms might lead to guaranteed enclosures of all system states which are too conservative to be practically useful, we present algorithmic extensions of classical approaches which are applicable to the simulation of non-cooperative systems with time-varying uncertain parameters. Overestimation arising in the interval evaluation of dynamical system models due to the wrapping effect is reduced by an exact pseudo-linear transformation of nonlinear state equations and by new heuristics for the subdivision of interval enclosures which especially prefer splitting of unstable intervals. To highlight the typical procedure for parameterization of interval-based simulation routines and to demonstrate their efficiency, a nonlinear model of biological wastewater treatment processes is discussed. For this application, we consider the maximum specific growth rate of substrate consuming bacteria as a time-varying uncertain parameter. Only worst-case bounds are assumed to be available for the range of this parameter while no information is provided about its actual variation rate. 相似文献