A Smooth 3D Model for Fiber Lay-Down Processes

We present an improved three-dimensional stochastic model concerning the fiber lay-down in the production process of nonwoven materials. The model describes the position of the deposited fibers on a conveyor belt, which is determined by a system of stochastic differential equations. Here we remove a drawback of a previous 3D model, that is the non-smoothness of the fiber paths. Besides the derivation of the smooth 3D model we show its connection to the non-smooth model in a white noise limit. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotics and numerics for non-Newtonian jet dynamics

This work deals with the modeling and simulation of non-Newtonian jet dynamics. Proceeding from a 3d boundary value problem of upper-convected Maxwell equations, a 1d viscoelastic string model can be derived asymptotically. The resulting system of PDEs has a hyperbolic-elliptic character with an additional differential constraint. Its applicability regime is limited depending on physical parameters and boundary conditions. Numerical results are shown for gravitational in-/outflow set-ups. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A discontinuous method for oil-water flow in heterogeneous porous media

An oil-water flow-transport problem in a heterogeneous porous medium (HPM), given by the Brinkman model coupled with a fractional flow formulation, is solved numerically by a discontinuous finite volume element (DFVE) method coupled with a Runge-Kutta Discontinuous Galerkin (RKDG) scheme. A new (original) numerical example is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the class of attainable multidimensional NMR spectra

It is shown that a large class of two‐dimensional NMR spectra is characterized by a matrix algebra and an invariant subspace. Both the matrix algebra and the invariant subspace are determined by the system matrices of the bilinear system which describes the NMR experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bulk single crystals of β-Ga2O3 and Ga-based spinels as ultra-wide bandgap transparent semiconducting oxides

In the course of development of transparent semiconducting oxides (TSOs) we compare the growth and basic physical properties bulk single crystals of ultra-wide bandgap (UWBG) TSOs, namely β-Ga₂O₃ and Ga-based spinels MgGa₂O₄, ZnGa₂O₄, and Zn_1-xMg_xGa₂O₄. High melting points of the materials of about 1800 -1930 °C and their thermal instability, including incongruent decomposition of Ga-based spinels, require additional tools to obtain large crystal volume of high structural quality that can be used for electronic and optoelectronic devices. Bulk β-Ga₂O₃ single crystals were grown by the Czochralski method with a diameter up to 2 inch, while the Ga-based spinel single crystals either by the Czochralski, Kyropoulos-like, or vertical gradient freeze / Bridgman methods with a volume of several to over a dozen cm³. The UWBG TSOs discussed here have optical bandgaps of about 4.6 - 5 eV and great transparency in the UV / visible spectrum. The materials can be obtained as electrical insulators, n-type semiconductors, or n-type degenerate semiconductors. The free electron concentration (n_e) of bulk β-Ga₂O₃ crystals can be tuned within three orders of magnitude 10¹⁶ - 10¹⁹ cm^?3 with a maximum Hall electron mobility (μ) of 160 cm²V^?1s^?1, that gradually decreases with n_e. In the case of the bulk Ga-based spinel crystals with no intentional doping, the maximum of n_e and μ increase with decreasing the Mg content in the compound and reach values of about 10²⁰ cm^?3 and about 100 cm²V^?1s^?1 (at n_e > 10¹⁹ cm^?3), respectively, for pure ZnGa₂O₄.     

A Diffusively Corrected Multiclass Lighthill-Whitham-Richards Traffic Model with Anticipation Lengths and Reaction Times

Multiclass Lighthill-Whitham-Richards traffic models [Benzoni-Gavage and Colombo, Euro. J. Appl. Math., 14 (2003), pp. 587–612; Wong and Wong, Transp. Res. A, 36 (2002), pp. 827–841] give rise to first-order systems of conservation laws that are hyperbolic under usual conditions, so that their associated Cauchy problems are well-posed. Anticipation lengths and reaction times can be incorporated into these models by adding certain conservative second-order terms to these first-order conservation laws. These terms can be diffusive under certain circumstances, thus, in principle, ensuring the stability of the solutions. The purpose of this paper is to analyze the stability of these diffusively corrected models under varying reaction times and anticipation lengths. It is demonstrated that instabilities may develop for high reaction times and short anticipation lengths, and that these instabilities may have controlled frequencies and amplitudes due to their nonlinear nature.     

Note – On the Number of Triangulations of Planar Point Sets

n points in the plane is at most . Received: November 1, 1995     

Cation distribution of the cochlea wall (Stria vascularis)

Summary It was possible to maintain the differentiated structure of inner ear tissues by freezing in supercooled propane, freeze-drying under special conditions and embedding the tissue in a low viscosity resin. Using LAMMA we were able to measure intracellular ion concentration and concentration gradients in the soft tissues such as muscle and stria vascularis specimens. The preliminary results demonstrate that the distribution of cations in the lateral wall of the cochlear duct is not uniform. The K/Na ratio in the basal cells was significantly higher (121) than in the spiral ligament and middle part of the stria vascularis (71). Changes of such concentration ratios recorded after anoxia suggest that an energy dependent active transport mechanism must exist in the stria vascularis.

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Kationenverteilung in der Schneckengangwand des Ohres (Stria vascularis)