A uniformly well-conditioned, unfitted Nitsche method for interface problems

A finite element method for elliptic partial differential equations that allows for discontinuities along an interface not aligned with the mesh is presented. The solution on each side of the interface is separately expanded in standard continuous, piecewise-linear functions, and jump conditions at the interface are weakly enforced using a variant of Nitsche’s method. In our method, the solutions on each side of the interface are extended to the entire domain which results in a fixed number of unknowns independent of the location of the interface. A stabilization procedure is included to ensure well-defined extensions. We prove that the method provides optimal convergence order in the energy and the L ² norms and a condition number of the system matrix that is independent of the position of the interface relative to the mesh. Numerical experiments confirm the theoretical results and demonstrate optimal convergence order also for the pointwise errors.     

A simple homemade spectrophotometer

A simple portable spectrophotometer was constructed and used to perform analytical experiments. The developed model uses available tools and materials such as light emitting diode lamps, compact discs, plastic and cardboard boxes and a cell phone camera to build a design that illustrates the major components of spectrophotometers. The spectra of serial concentrations of KMnO₄ (50?600 μM) were recorded and the values of absorbance were extracted at λ_max to build the calibration curve. A linear relationship between the concentration and absorbance was obtained with the coefficient of determination 0.994. The model was also utilized to study the spectra of KMnO₄, phenolphthalein and bromothymol blue in comparison with a Shimadzu UV-1800 spectrophotometer as a reference instrument. In spite of the differences in the observed spectra, the recorded λ_max were almost identical to those measured by the developed model. The model was successfully used to determine the concentration of sodium alendronate through ligand-exchange complexation with ferric salicylate.     

Unravelling the Time Scale of Conformational Plasticity and Allostery in Glycan Recognition by Human Galectin-1

The interaction of human galectin-1 with a variety of oligosaccharides, from di-(N-acetyllactosamine) to tetra-saccharides (blood B type-II antigen) has been scrutinized by using a combined approach of different NMR experiments, molecular dynamics (MD) simulations, and isothermal titration calorimetry. Ligand- and receptor-based NMR experiments assisted by computational methods allowed proposing three-dimensional structures for the different complexes, which explained the lack of enthalpy gain when increasing the chemical complexity of the glycan. Interestingly, and independently of the glycan ligand, the entropy term does not oppose the binding event, a rather unusual feature for protein-sugar interactions. CLEANEX-PM and relaxation dispersion experiments revealed that sugar binding affected residues far from the binding site and described significant changes in the dynamics of the protein. In particular, motions in the microsecond-millisecond timescale in residues at the protein dimer interface were identified in the presence of high affinity ligands. The dynamic process was further explored by extensive MD simulations, which provided additional support for the existence of allostery in glycan recognition by human galectin-1.     

Density lower bound estimate for local minimizer of free interface problem with volume constraint

We prove a density lower bound for some functionals involving bulk and interfacial energies. The bulk energies are convex functions with p-power growth not subjected to any further structure conditions. The interface \(\partial E\) is the boundary of a set \(E\subset \Omega \) such that \(|E|=d\) is prescribed. Then we get \(\mathcal {H}^{n-1}((\partial E{\setminus }\partial E^*)\cup \Omega )=0\).

     

Some trends in the theory of groups with finitely many normalizers

Ricerche di Matematica - This paper provides an account of results and methods from the theory of infinite groups admitting only finitely many normalizers of subgroups with a given property. Some...     

CoII Cryptates Convert CO2 into CO and CH4 under Visible Light

Three Co^II octaazacryptates, with different substituents on the aromatic rings (Br, NO₂, CCH), were synthesised and characterised. These and the already published non-substituted cryptate catalysed CO₂ photoreduction to CO and CH₄ under blue visible light at room temperature. Although CO was observed after short irradiation times and a large range of catalyst concentrations, CH₄ was only observed after longer irradiation periods, such as 30 h, but with a small catalyst concentration (25 nm ). Experiments with ¹³C labelled CO₂ showed that CO is formed and reacts further when the reaction time is long. The CCH catalyst is deactivated faster than the others and the more efficient catalyst for CH₄ production is the one with Br. This reactivity trend was explained by an energy decomposition analysis based on DFT calculations.     

Multifunctional mesoporous silica nanoparticles in poly(ethylene‐co‐vinyl acetate) for transparent heat retention films

Transparent inorganic‐polymer nanocomposite films are of tremendous current interest inemerging solar coverings including photovoltaic encapsulants and commercial greenhouse plastics, but suffer from significant radiative heat loss. This work provides a new and simple approach for controlling this heat loss by using mesoporous silica/quantum dot nanoparticles in poly(ethylene‐co‐vinyl acetate) (EVA) films. Mesoporous silica shells were grown on CdS‐ZnS quantum dot (QDs) cores using a reverse microemulsion technique, controlling the shell thickness. These mesoporous silica nanoparticles (MSNs) were then melt‐mixed with EVA pellets using a mini twin‐screw extruder and pressed into thin films of concentration variable controlled thickness. The results demonstrate that the experimental MSNs showed improved infrared and thermal wavebands retention in the EVA transparent films compared to commercial silica additives, even at lower concentrations. It was also found MSNs enhanced the quantum yield and photostability of the QDs, providing high visible light transmission and blocking of UV transmission of interest for next generation solar coatings. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 851–859