Port-Hamiltonian representation for pdes with second-order derivatives in the energy density

In this contribution we consider a port-Hamiltonian setting for partial differential equations. A crucial property of this system class is the property to be able to link a power balance relation to the structure of the equations. However, one has to take into account also the effects of energy flows via the boundary. This is straightforward when the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If second-order derivatives appear then integration by parts cannot be used without due care, thus we suggest an approach by using the so-called Cartan-form. We visualize the derivation of a power balance relation by using the Kirchhoff plate as an example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dicarboxylate-bridged (Mo2)n (n = 2, 3, 4) paddle-wheel complexes: potential intermediate building blocks for metal-organic frameworks

The treatment of the dimeric paddle-wheel (PW) compound [Mo(2)(NCCH(3))(10)][BF(4)](4)1 with oxalic acid (0.5 equiv.), 1,1-cyclobutanedicarboxylic acid (1 equiv.), 5-hydroxyisophthalic acid (1 equiv.) (m-bdc-OH) or 2,3,5,6-tetrafluoroterephthalic acid (0.5 or 1 equiv.) leads to the formation of macromolecular dicarboxylate-linked (Mo(2))(n) entities (n = 2, 3, 4). The structure of the compounds depends on the length and geometry of the organic linkers. In the case of oxalic acid, the dimeric compound [(CH(3)CN)(8)Mo(2)(OOC-COO)Mo(2)(NCCH(3))(8)][BF(4)](6)2 is formed selectively, whereas the use of 2,3,5,6-tetrafluoroterephthalic acid affords the square-shaped complex [(CH(3)CN)(6)Mo(2)(OOC-C(6)F(4)-COO)](4)[BF(4)](8)3. Bent linkers with a bridging angle of 109° and 120°, respectively, lead to the formation of the molecular loop [(CH(3)CN)(6)Mo(2)(OOC-C(4)H(6)-COO)](2)[BF(4)](4)4 and the bowl-shaped molecular triangle [(CH(3)CN)(6)Mo(2)(m-bdc-OH)](3)[BF(4)](6)5. All complexes are characterised by X-ray single crystal diffraction, NMR ((1)H, (11)B, (13)C and (19)F) and UV-Vis spectroscopy.     

Highly luminescent nanocrystal quantum dots fabricated by lattice-type mismatched epitaxy

Lattice-type mismatched heteroepitaxy is demonstrated as a novel concept for the fabrication of almost ideal, highly luminescent nanocrystal quantum dots that are coherently embedded in a single-crystalline matrix. In this approach, the formation of quantum dots is induced by transformation of a metastable epitaxial 2D quantum well into an array of isolated nanocrystals with-highly symmetric shape. This process is driven by the lattice-type mismatch between the constituent materials and the resulting miscibility gap. The investigated PbTe/CdTe heterosystem has a model character because it combines two compounds with different cubic lattice types but almost identical lattice constants. The obtained epitaxial nanocrystals exhibit outstanding properties such as a well-defined symmetric shape, the absence of strain, intermixing and a wetting layer, which is in contrast to the conventional Stranski–Krastanow quantum dots. The small-rhomboedric-cubo-octahedron PbTe/CdTe nanocrystals on GaAs substrates display intense room temperature mid-infrared luminescence as is crucial for device applications. Ab initio density functional theory is used to clarify the interface structure, indicating that the covalent and ionic bonding character of CdTe and PbTe is maintained across the interface.     

A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

Numerical schemes using piecewise polynomial approximation are very popular for high order discretization of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Difference scheme has often been found attractive as well, because of its simplicity of formulation and implementation. However, recently it has been shown that the scheme is not linearly stable on triangles. In this paper we present an alternate formulation of the scheme, featuring a new flux interpolation technique using Raviart–Thomas spaces, which proves stable under a similar linear analysis in which the standard scheme failed. We demonstrate viability of the concept by showing linear stability both in the semi-discrete sense and for time stepping schemes of the SSP Runge–Kutta type. Furthermore, we present convergence studies, as well as case studies in compressible flow simulation using the Euler equations.