Triangulations in CGAL

This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library .     

Simplified liquid chromatographic determination of glyphosate and metabolite residues in environmental water using post-column fluorogenic labelling

Glyphosate and its metabolite aminomethylphosphonic acid in environmental water can be preconcentrated with an anion-exchange column, eluted with potassium citrate solution and determined directly by liquid chromatography with a post-column reactor and a fluorescence detector. The limit of detection and average recovery are 1 μg 1^?1 and 89.3% for glyphosate and 0.4 μg l^?1 and 86.3% for the metabolite.     

Estimation of the parameters of Herschel-Bulkley fluid under wall slip using a combination of capillary and squeeze flow viscometers

The determination of the parameters of viscoplastic fluids subject to wall slip is a special challenge and accurate results are generally obtained only when a number of viscometers are utilized concomitantly. Here the characterization of the parameters of the Herschel-Bulkley fluid and its non-linear wall slip behavior is formulated as an inverse problem which utilizes the data emanating from capillary and squeeze flow rheometers. A finite element method of the squeeze flow problem is employed in conjunction with the analytical solution of the capillary data collected following Mooneys procedure, which uses dies with differing surface to volume ratios. The uniqueness of the solution is recognized as a major problem which limits the accuracy of the solution, suggesting that the search methodology should be carefully selected.     

Total Synthesis of Albicidin: A Lead Structure from Xanthomonas albilineans for Potent Antibacterial Gyrase Inhibitors

The peptide antibiotic albicidin, which is synthesized by the plant pathogenic bacterium Xanthomonas albilineans, displays remarkable antibacterial activity against various Gram‐positive and Gram‐negative microorganisms. The low amounts of albicidin obtainable from the producing organism or through heterologous expression are limiting factors in providing sufficient material for bioactivity profiling and structure–activity studies. Therefore, we developed a convergent total synthesis route toward albicidin. The unexpectedly difficult formation of amide bonds between the aromatic amino acids was achieved through a triphosgene‐mediated coupling strategy. The herein presented synthesis of albicidin confirms the previously determined chemical structure and underlines the extraordinary antibacterial activity of this compound. The synthetic protocol will provide multigram amounts of albicidin for further profiling of its drug properties.     

Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization

We consider the problem of minimizing a continuous function f over a compact set \({\mathbf {K}}\). We analyze a hierarchy of upper bounds proposed by Lasserre (SIAM J Optim 21(3):864–885, 2011), obtained by searching for an optimal probability density function h on \({\mathbf {K}}\) which is a sum of squares of polynomials, so that the expectation \(\int _{{\mathbf {K}}} f(x)h(x)dx\) is minimized. We show that the rate of convergence is no worse than \(O(1/\sqrt{r})\), where 2r is the degree bound on the density function. This analysis applies to the case when f is Lipschitz continuous and \({\mathbf {K}}\) is a full-dimensional compact set satisfying some boundary condition (which is satisfied, e.g., for convex bodies). The rth upper bound in the hierarchy may be computed using semidefinite programming if f is a polynomial of degree d, and if all moments of order up to \(2r+d\) of the Lebesgue measure on \({\mathbf {K}}\) are known, which holds, for example, if \({\mathbf {K}}\) is a simplex, hypercube, or a Euclidean ball.     

A Grobman–Hartman Theorem for Control Systems

We consider the problem of locally linearizing a control system via topological transformations. According to [2,3], there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of under-determined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman–Hartman theorem for control systems.     

Rheological behavior of concentrated suspensions as affected by the dynamics of the mixing process

The rheological characterizations of concentrated suspensions are generally carried out assuming “well-mixed” suspensions. However, the variation of the concentration distributions of the ingredients of the formulation, i.e., the “goodness of mixing”, the size and shape distributions of the particle clusters and the rheological behavior of the suspension all depend on the thermo-mechanical history that the suspension is exposed to during the mixing process. Here, various experimental tools are used for the characterization of the degree of mixedness (concentration distributions) of various ingredients along with the characterization of rheological material functions, wall slip behavior and the maximum packing fraction of a graphite/elastomer suspension. The degree of mixedness values of the ingredients of the suspensions processed using batch and continuous processes and under differing operating conditions were characterized quantitatively using wide-angle X-ray diffraction and thermo gravimetric analysis and were elucidated under the light of the electrical properties of the suspension as affected by the mixing process. Upon achieving better homogeneity of the graphite particles and the binder and decreases in the size and breadth of the size distributions of particle clusters (as inferred from electrical measurements and maximum packing fraction values), the elasticity (storage modulus) and the shear viscosity (magnitude of the complex viscosity from small-amplitude oscillatory shear and shear viscosity from steady torsional and capillary rheometry) of the suspension decreased significantly and the wall slip velocity values increased. These findings demonstrate the intimate relationships that exist between the rheological behavior of concentrated suspensions and the thermo-mechanical history that they are exposed to during the processing stage and suggest that the preparation conditions for suspensions should be carefully selected and well documented to achieve reproducible characterization of rheological material functions.     

Biomimetic membrane arrays on cast hydrogel supports

Lipid bilayers are intrinsically fragile and require mechanical support in technical applications based on biomimetic membranes. Tethering the lipid bilayer membranes to solid substrates, either directly through covalent or ionic substrate-lipid links or indirectly on substrate-supported cushions, provides mechanical support but at the cost of small molecule transport through the membrane-support sandwich. To stabilize biomimetic membranes while allowing transport through a membrane-support sandwich, we have investigated the feasibility of using an ethylene tetrafluoroethylene (ETFE)/hydrogel sandwich as the support. The sandwich is realized as a perforated surface-treated ETFE film onto which a hydrogel composite support structure is cast. We report a simple method to prepare arrays of lipid bilayer membranes with low intrinsic electrical conductance on the highly permeable, self-supporting ETFE/hydrogel sandwiches. We demonstrate how the ETFE/hydrogel sandwich support promotes rapid self-thinning of lipid bilayers suitable for hosting membrane-spanning proteins.