Analysis of hybrid discontinuous Galerkin methods for linearized Navier–Stokes equations

In this article, we introduce and analyze arbitrary-order, locally conservative hybrid discontinuous Galkerin methods for linearized Navier–Stokes equations. The unknowns of the global system are reduced to trace variables on the skeleton of a triangulation and the average of pressure on each cell via embedded static condensation. We prove that the lifting operator associated with trace variables is injective for any polynomial degree. This generalizes the result in (Y. Jeon and E.-J. Park, Numerische Mathematik 123 [2013], no. 1, pp. 97–119), where quadratic and cubic rectangular elements are analyzed. Moreover, optimal error estimates in the energy norm are obtained by introducing nonstandard projection operators for the hybrid DG method. Several numerical results are presented to show the performance of the algorithm and to validate the theory developed in the article.     

Time of acquisition and high spatial resolution mass spectrometry imaging

The field of mass spectrometry imaging (MSI) is constantly evolving to analyze a diverse array of biological systems. A common goal is the need to resolve cellular and subcellular heterogeneity with high spatial resolution. As the field continues to progress towards high spatial resolution, other parameters must be considered when developing a practical method. Here, we discuss the impacts of high spatial resolution on the time of acquisition and the associated implications they have on an MSI analysis (e.g., area of the region of interest). This work presents a brief tutorial serving to evaluate high spatial resolution MSI relative to time of acquisition and data file size.     

Polymer-modification of an anti-cancer drug: effects on hydrodynamic properties

Coupling of a hydrophobic pharmaceutical agents with the hydrophilic poly(ethylene oxide) chain can make the drug water soluble which is necessary for some applications. The modification of the polymer chain results in a different solution behaviour of the macromolecules compared with the unmodified polymer. There are strong indications that shape and rigidity of the modified molecule differ significantly from the simple chain. Some results from measurements of the self-diffusion coefficient and solution viscosity are discussed. The results are important for further engineering on active drug systems.