Kinetic energy preserving DG schemes based on summation-by-parts operators on interior node distributions

In this work, a kinetic energy preserving DG scheme in one space dimension using Gauss-Legendre nodes is presented. Stability problems will be demonstrated when using interface terms that are derived from the Lobatto nodes within the Gauss-Legendre skew-symmetric DG formulation. However, combined with correct interface terms, the skew-symmetric DG scheme constructed on Gauss-Legendre nodes is expected to yield higher accuracy compared to its Gauss-Lobatto counterpart. This advantage is demonstrated in the case of viscous compressible flow computation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On asymptotic equivalence of perturbed linear systems of differential and difference equations

Standard results on asymptotic integration of systems of linear differential equations give sufficient conditions which imply that a system is strongly asymptotically equivalent to its principal diagonal part. These involve certain dichotomy conditions on the diagonal part as well as growth conditions on the off-diagonal perturbation terms. Here, we study perturbations with a triangularly-induced structure and see that growth conditions can be substantially weakened. In addition, we give results for not necessarily triangular perturbations which in some sense “interpolate” between the classical theorems of Levinson and Hartman-Wintner. Some analogous results for systems of linear difference equations are also given.     

Hospital management games: a taxonomy and extensive review

Hospital management games have gained importance in better planning for scarce resources in times of growing health care demand and increasing technology costs. We classify and investigate the main characteristics of these games from an Operations Research (OR) perspective. Hospital management games model the complex decision making process of internal resource, process, and financial management all influenced by the external hospital environment (e.g., purchasing markets, job markets, legal/political conditions, competition) and simulate situations of the real world. We also highlight the potential of these games for teaching OR in the classroom. Experiencing the advantages of OR may reduce the reservations policy makers have and could make them increasingly open to promoting OR applications in practice. We also disclose potential for new applications.     

Electric cell-substrate impedance sensing with screen printed electrode structures

Impedance sensors in thick film technology have been tested as a tool for electric cell-substrate impedance sensing. The screen printed Pt electrodes have a width of 250-400 microm. Electrodes and the surrounding ceramic chip substrate could be homogeneously grown with L-929 and Hela cells. The performance of a screen printed interdigitated electrode structure (IDES) was compared with that of thin film structures with the same layout geometry. The thick film impedance sensors allowed to correctly record the morphological response of confluent Hela cell layers to stimulation with histamine. A thick film conductivity sensor also revealed impedance values which were dependent on cell growth on the electrode surface, even at a very low frequency range of approximately 1 Hz.     

A comparative Fourier analysis of discontinuous Galerkin schemes for advection–diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization

This work compares the wave propagation properties of discontinuous Galerkin (DG) schemes for advection–diffusion problems with respect to the behavior of classical discretizations of the diffusion terms, that is, two versions of the local discontinuous Galerkin (LDG) scheme as well as the BR1 and the BR2 scheme. The analysis highlights a significant difference between the two possible ways to choose the alternating LDG fluxes showing that the variant that is inconsistent with the upwind advective flux is more accurate in case of advection–diffusion discretizations. Furthermore, whereas for the BR1 scheme used within a third order DG scheme on Gauss-Legendre nodes, a higher accuracy for well-resolved problems has previously been observed in the literature, this work shows that higher accuracy of the BR1 discretization only holds for odd orders of the DG scheme. In addition, this higher accuracy is generally lost on Gauss–Legendre–Lobatto nodes.     

A kinetic energy preserving DG scheme applied to mechanical FSI

In the context of mechanical fluid-structure interaction (FSI) comprising moving or deforming structures, fluid discretizations need to cope with time-dependent fluid domains and resulting grid deformations in addition to the general challenges regarding e.g. boundary layers and turbulent phenomena. Recent approaches in the simulation of compressible turbulent flow are based on so-called split forms of conservation laws to guarantee the preservation of secondary physical quantities such as kinetic energy. For the simulation of turbulent flows, this often leads to a better representation of the kinetic energy spectrum. Initially, kinetic energy preserving(KEP) DG schemes have been constructed on Gauss-Legendre-Lobatto(GLL) nodes containing the interval end points, however, KEP DG schemes based on the classical Gauss-Legendre(GL) nodes are potentially more accurate and may be also more efficient than its GLL variant for certain applications. In this work, the KEP-DG schemes both on GL and GLL nodes are applied to the classical moving piston test case via an ALE formulation on moving fluid grids showing a more accurate frequency representation of the structure displacement in case of GLL nodes. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Approach to Asymptotic Diagonalization of Linear Differential Systems

We study the asymptotic diagonalization of a system consisting of an -matrix plus a finite number of -perturbations on an interval I ₀=[t ₀, ), where p, m _i[1, ). Using linear skew-product flows and spectral theory, we show that if the unperturbed system has full spectrum over its omega-limit set, then the entire system is asymptotically diagonalizable almost everywhere.     

Asymptotic solutions and error estimates for linear systems of difference and differential equations

Classical results concerning the asymptotic behavior solutions of systems of linear differential or difference equations lead to formulas containing factors that are asymptotically constant, i.e., k+o(1) as t tends to infinity. Here we are interested in more precise information about the o(1) terms, specifically how they depend precisely on certain perturbation terms in the equation. Results along these lines were given by Gel'fond and Kubenskaya for scalar difference equations and we will both extend and generalize one of them as well as provide some corresponding results for differential equations.