Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Enhancing the Water Stability of Al‐MIL‐101‐NH2 via Postsynthetic Modification

The resistance of metal–organic frameworks towards water is a very critical issue concerning their practical use. Recently, it was shown for microporous MOFs that the water stability could be increased by introducing hydrophobic pendant groups. Here, we demonstrate a remarkable stabilisation of the mesoporous MOF Al‐MIL‐101‐NH₂ by postsynthetic modification with phenyl isocyanate. In this process 86 % of the amino groups were converted into phenylurea units. As a consequence, the long‐term stability of Al‐MIL‐101‐URPh in liquid water could be extended beyond a week. In water saturated atmospheres Al‐MIL‐101‐URPh decomposed at least 12‐times slower than the unfunctionalised analogue. To study the underlying processes both materials were characterised by Ar, N₂ and H₂O sorption measurements, powder X‐ray diffraction, thermogravimetric and chemical analysis as well as solid‐state NMR and IR spectroscopy. Postsynthetic modification decreased the BET equivalent surface area from 3363 to 1555 m² g^?1 for Al‐MIL‐101‐URPh and reduced the mean diameters of the mesopores by 0.6 nm without degrading the structure significantly and reducing thermal stability. In spite of similar water uptake capacities, the relative humidity‐dependent uptake of Al‐MIL‐101‐URPh is slowed and occurs at higher relative humidity values. In combination with ¹H‐²⁷Al D ‐HMQC NMR spectroscopy experiments this favours a shielding mechanism of the Al clusters by the pendant phenyl groups and rules out pore blocking.     

Existence of stationary,collisionless plasmas in bounded domains

We consider a collisionless plasma, which consists of electrons and positively charged ions and is confined to a bounded domain in ?³. The distribution functions of the particles are assumed to satisfy specular reflections on the boundary of the domain and the boundary is assumed to be perfectly conducting. We establish the existence of stationary plasmas in the non-relativistic, electrostatic case described by the Vlasov–Poisson system as well as in the relativistic, electrodynamic case described by the relativistic Vlasov–Maxwell system.     

Subgroup separable free products with cyclic amalgamation

Using topological methods we give a proof that the free product of two strict subgroup separable groups with infinite cyclic amalgamation is subgroup separable.