On the difficulty of triangulating three-dimensional Nonconvex Polyhedra

A number of different polyhedraldecomposition problems have previously been studied, most notably the problem of triangulating a simple polygon. We are concerned with thepolyhedron triangulation problem: decomposing a three-dimensional polyhedron into a set of nonoverlapping tetrahedra whose vertices must be vertices of the polyhedron. It has previously been shown that some polyhedra cannot be triangulated in this fashion. We show that the problem of deciding whether a given polyhedron can be triangulated is NP-complete, and hence likely to be computationally intractable. The problem remains NP-complete when restricted to the case of star-shaped polyhedra. Various versions of the question of how many Steiner points are needed to triangulate a polyhedron also turn out to be NP-hard.This work was supported by National Science Foundation Grant CCR-8809040.     

On second-order antidiffusive Lagrangian-remap schemes for multispecies kinematic flow models

This paper focuses on the numerical approximation of the solutions of multi-species kinematic flow models. These models are strongly coupled nonlinear first-order conservation laws with various applications like sedimentation of a polydisperse suspension in a viscous fluid, or traffic flow modeling. Since the eigenvalues and eigenvectors of the corresponding flux Jacobian matrix have no closed algebraic form, this is a challenging issue. A new class of simple schemes based on a Lagrangian- Eulerian decomposition (the so-called Lagrangian-remap (LR) schemes) was recently advanced in [4] for traffic flow models with nonnegative velocities, and extended to models of polydisperse sedimentation in [5]. These schemes are supported by a partial numerical analysis when one species is considered only, and turned out to be competitive in both accuracy and efficiency with several existing schemes. Since they are only first-order accurate, it is the purpose of this contribution to propose an extension to second-order accuracy using quite standard MUSCL and Runge-Kutta techniques. Numerical illustrations are proposed for both applications and involving eleven species (sedimentation) and nine species (traffic) respectively.     

N-K electron energy-loss near-edge structures for TiN/VN layers: an ab initio and experimental study

We study N-K-edge electron energy-loss near-edge structures for well-defined TiN/VN bilayers grown on a MgO(100) substrate by both calculations and experiments. The structural relaxations and the electronic structure of TiN/VN multilayers are calculated using the Vienna Ab Initio Simulation Package computer code, which uses density functional theory to describe the electronic interaction. The effects of the core hole created in the excitation process are included in the calculations. For VN, off-stoichiometric effects due to nitrogen vacancies are modelled. The partial density of states (PDOS) for the N-K edge of atoms in the vicinity of the TiN/MgO interface revealed that two new peaks appear between 7 and 9 eV instead of a broad shoulder typical for the bulk. For the VN/TiN interface, the PDOS is modified only slightly, owing to similar bonding on both sides of the interface, and is thus very similar to the respective bulk spectra. An experimental spectrum taken at the VN/TiN interface is, however, well described by an average of the simulated spectra for VN and TiN bulk (interface). Such a finding is characteristic of an intermixed interface.      

Antidiffusive Lagrangian‐remap schemes for models of polydisperse sedimentation

One‐dimensional models of gravity‐driven sedimentation of polydisperse suspensions with particles that belong to N size classes give rise to systems of N strongly coupled, nonlinear first‐order conservation laws for the local solids volume fractions. As the eigenvalues and eigenvectors of the flux Jacobian have no closed algebraic form, characteristic‐wise numerical schemes for these models become involved. Alternative simple schemes for this model directly utilize the velocity functions and are based on splitting the system of conservation laws into two different first‐order quasi‐linear systems, which are solved successively for each time iteration, namely, the Lagrangian and remap steps (so‐called Lagrangian‐remap [LR] schemes). This approach was advanced in (Bürger, Chalons, and Villada, SIAM J Sci Comput 35 (2013), B1341–B1368) for a multiclass Lighthill–Whitham‐Richards traffic model with nonnegative velocities. By incorporating recent antidiffusive techniques for transport equations a new version of these Lagrangian‐antidiffusive remap (L‐AR) schemes for the polydisperse sedimentation model is constructed. These L‐AR schemes are supported by a partial analysis for N = 1. They are total variation diminishing under a suitable CFL condition and therefore converge to a weak solution. Numerical examples illustrate that these schemes, including a more accurate version based on MUSCL extrapolation, are competitive in accuracy and efficiency with several existing schemes. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1109–1136, 2016     

DAE-index monitoring for semi-discretized viscous Cosserat rod models

The dynamics of viscous jets due to external forces like gravity and aerodynamics can be described by Cosserat rod models consisting of a system of partial and ordinary differential equations. Depending on the formulation of the equations, in particular the compatibility conditions, the semi-discretization in space yields systems of differential-algebraic equations (DAE) in time of different indices. We present a DAE-index monitoring and discuss the numerical results for the application in a rotational 2d fiber spinning scenario. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the modeling of slender heat sources

Studying the heat exchange of small, slender objects in a surrounding flow, we approximate the impact of extended heat sources by Dirac-distributions (point sources) with appropriate amplitudes in the context of slender-body theory. The proposed model for the source strength functions is deduced from analytical considerations (Green's functions) of the stationary two-dimensional heat equation. Numerical simulations show the L2-approximation quality of the strategy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On an asymptotic upper-convected Maxwell model for a viscoelastic jet

In this work we present a strict systematic derivation of a one-dimensional upper convected Maxwell model (UCM) for the dynamics of a curved viscoelastic jet using asymptotic analysis in the slenderness ratio of the jet. The model does not pose any restrictions on shape and motion of the center-line or the velocity profile. Numerical results are shown for stationary gravitational fiber spinning. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radical detection in harsh environments by means of laser-induced fluorescence using a single bidirectional optical fiber

A new experimental method is described enabling detection of hydroxyl radicals (OH) by laser-induced fluorescence in high-temperature gas-phase reactions. This is accomplished by means of a bidirectional optical fiber probe, which is of interest for applications where optical access is limited. An optical setup that allows simultaneous excitation and detection of fluorescence using one and the same fiber has been developed. Complications resulting from coupling as well as laser-induced scattering are addressed, and different fibers are compared with regard to core material composition and geometric collection efficiency. On this basis, a suitable fiber is identified, and OH detection and profile measurements are demonstrated in a premixed laminar flame as reference experiment.     

On the hyperbolicity of certain models of polydisperse sedimentation

The sedimentation of a polydisperse suspension of small spherical particles dispersed in a viscous fluid, where particles belong to N species differing in size, can be described by a strongly coupled system of N scalar, nonlinear first‐order conservation laws for the evolution of the volume fractions. The hyperbolicity of this system is a property of theoretical importance because it limits the range of validity of the model and is of practical interest for the implementation of numerical methods. The present work, which extends the results of R. Bürger, R. Donat, P. Mulet, and C.A. Vega (SIAM Journal on Applied Mathematics 2010; 70:2186–2213), is focused on the fluxes corresponding to the models by Batchelor and Wen, Höfler and Schwarzer, and Davis and Gecol, for which the Jacobian of the flux is a rank‐3 or rank‐4 perturbation of a diagonal matrix. Explicit estimates of the regions of hyperbolicity of these models are derived via the approach of the so‐called secular equation (J. Anderson. Linear Algebra and Applications 1996; 246:49–70), which identifies the eigenvalues of the Jacobian with the poles of a particular rational function. Hyperbolicity of the system is guaranteed if the coefficients of this function have the same sign. Sufficient conditions for this condition to be satisfied are established for each of the models considered. Some numerical examples are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive multiresolution schemes for reaction-diffusion systems

This note outlines a fully adaptive multiresolution scheme with local time stepping for the efficient numerical solution of (possibly degenerate) reaction–diffusion systems. A new numerical example showing Turing–type pattern formation is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)