A spectral method for nonlinear elliptic equations

Let Ω be an open, simply connected, and bounded region in \(\mathbb {R}^{d}\), d ≥ 2, and assume its boundary ?Ω is smooth and homeomorphic to \(\mathbb {S}^{d-1}\). Consider solving an elliptic partial differential equation L u = f(?, u) over Ω with zero Dirichlet boundary value. The function f is a nonlinear function of the solution u. The problem is converted to an equivalent elliptic problem over the open unit ball \(\mathbb {B}^{d}\) in \(\mathbb {R}^{d}\), say \(\widetilde {L}\widetilde {u} =\widetilde {f}(\cdot ,\widetilde {u})\). Then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials \(\widetilde {u} _{n}\) of degree ≤ n that is convergent to \(\widetilde {u}\). The transformation from Ω to \(\mathbb {B}^{d}\) requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For \(u\in C^{\infty } \left (\overline {\Omega }\right ) \) and assuming ?Ω is a C ^∞ boundary, the convergence of \(\left \Vert \widetilde {u} -\widetilde {u}_{n}\right \Vert _{H^{1}}\) to zero is faster than any power of 1/n. The error analysis uses a reformulation of the boundary value problem as an integral equation, and then it uses tools from nonlinear integral equations to analyze the numerical method. Numerical examples illustrate experimentally an exponential rate of convergence. A generalization to ?Δu + γ u = f(u) with a zero Neumann boundary condition is also presented.     

Power‐to‐Gas

The power‐to‐gas concept is a promising technology to chemically store energy and therefore a feasible approach to mitigate the challenges of energy transition. Heterogeneous catalysis plays a crucial role in CO₂ conversion to methane using nickel based catalysts. A thorough catalyst characterization facilitates the synthesis of optimized catalyst systems. The determination of reaction kinetics is fundamental for industrial reactor design.     

Adaptive space-time boundary element methods for the wave equation

For the solution of the wave equation a space-time energetic boundary integral formulation is used. The resulting single layer boundary integral equation is discretised by a conforming ansatz space on the lateral boundary. To derive an adaptive scheme an a posteriori error estimator based on the representation formula is used. Finally, numerical examples for a one-dimensional spatial domain are presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid Structure Interaction of Blood Vessels in Circle of Willis

This work involves studying the role of the Brain Blood Barriers (BBB) on damping the stress applied on brain tissue through blood pressure that is the main cause of brain aneurysm. The numerical simulations are focused on the geometry of the Anterior Communicating Artery (ACoA) because there is a 30 % higher probability for a brain aneurysm in this location. A linear elastic model is used to model the structure part including BBB and brain tissue. Regarding the fluid properties, blood is assumed to behave as a Newtonian fluid. The stress and deformation of the brain tissue is analyzed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The coordination chemistry of the proton

It is well known that an acidic hydrogen atom can form hydrogen bonds to a hydrogen bond acceptor, a Lewis base. It is considerably less known that the proton can coordinate two or more atoms conveniently in bonding modes that cannot be described as hydrogen bonding. Agostic interactions, bridging hydrides, 3-centre-2-electron bonds in boranes, bifurcated hydrogen atoms, they are all elements of the coordination chemistry of the proton and, of course, the hydrogen bond comes in more than one facette as well.     

Azobenzene-containing triazatriangulenium adlayers on Au(111): structural and spectroscopic characterization

Adlayers of different azobenzene-functionalized derivatives of the triazatriangulenium (TATA) platform on Au(111) surfaces were studied by scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), gap-mode surface-enhanced Raman spectroscopy (gap-mode SERS), and cyclic voltammetry (CV). The chemical composition of the adlayers is in good agreement with the molecular structure, i.e., different chemical groups attached to the azobenzene functionality were identified. Furthermore, the presence of the azobenzene moieties in the adlayers was verified by the vibration spectra and electrochemical data. These results indicate that the molecules remain intact upon adsorption with the freestanding functional groups oriented perpendicularly to the TATA platform and thus also to the substrate surface.     

Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 2 – Development of an experimental procedure for the determination of the molar mass of silicon using MC-ICP-MS

The isotopic abundances and thus molar mass M(Si) of a silicon crystal material with natural isotopic abundances have been measured for the first time using multicollector-ICP-mass spectrometry (MC-ICP-MS) in combination with a novel concept of a modified isotope dilution mass spectrometry (IDMS)-method. This experimental work is the further development of part 1 of this series of papers. While part 1 describes the theoretical background and the mathematical derivation of the novel concept in detail, the measurements presented here serve to validate the novel concept and give experimental proof of its capability. Moreover, the also new method for the analytical calculation of calibration factors needed in the determination of absolute isotope amount ratios has been tested successfully. Silicon isotopic abundances have been measured directly from an aqueous alkaline matrix following a new sample preparation protocol developed within the framework of this study. A molar mass of M(Si) = 28.08548(13) g/mol with an associated relative uncertainty of u_rel = 4.6 × 10^?6 (k = 1) has been measured. This is in excellent agreement with the current IUPAC value for the molar mass of natural silicon M(Si_nat) = 28.08550(15) g/mol with u_rel = 5.3 × 10^?6 (k = 1). An uncertainty budget according to the Guide to the Expression of Uncertainty in Measurement (GUM) was calculated to assess the presented results and to validate the novel concept with the help of experimental data. The development of a new experimental procedure is presented in detail and the contributions to the uncertainty are discussed in comparison to part 1 of this work.     

Counting of Oxygen Defects versus Metal Surface Sites in Methanol Synthesis Catalysts by Different Probe Molecules

Different surface sites of solid catalysts are usually quantified by dedicated chemisorption techniques from the adsorption capacity of probe molecules, assuming they specifically react with unique sites. In case of methanol synthesis catalysts, the Cu surface area is one of the crucial parameters in catalyst design and was for over 25 years commonly determined using diluted N₂O. To disentangle the influence of the catalyst components, different model catalysts were prepared and characterized using N₂O, temperature programmed desorption of H₂, and kinetic experiments. The presence of ZnO dramatically influences the N₂O measurements. This effect can be explained by the presence of oxygen defect sites that are generated at the Cu‐ZnO interface and can be used to easily quantify the intensity of Cu‐Zn interaction. N₂O in fact probes the Cu surface plus the oxygen vacancies, whereas the exposed Cu surface area can be accurately determined by H₂.