Minimal loading conditions for higher-order numerical homogenisation schemes

The present study deals with the formulation of minimal loading conditions for microscale applications in numerical two-scale modelling (FE²) approaches. From the homogenisation concept, a set of volume average rules constrains the microscale PDE to be solved. They are considered to be the minimal set of loading conditions and can be specified by additional polynomial or periodic assumptions, for example, on the microscale displacement field. Whereas the resulting volume integrals can be transformed into surface integrals for so-called first-order homogenisation schemes, this is not possible for a second-order homogenisation of second gradient or micromorphic effective media substituting a heterogeneous microcontinuum represented by a volume element on the microscale. Several numerical examples compare the minimal loading condition concept with standard techniques discussed in literature.     

Inhomogeneous quantum groups and their quantized universal enveloping algebras

The quantum group IGL _q (N), the inhomogenization of GL _q (N), is formulated with -matrices. Theq-deformed universal enveloping algebra is constructed as the algebra of regular functionals in this formulation and contains the partial derivatives of the covariant differential calculus on the quantum space.     

Self-propelled droplets

Self-propelled droplets are a special kind of self-propelled matter that are easily fabricated by standard microfluidic tools and locomote for a certain time without external sources of energy. The typical driving mechanism is a Marangoni flow due to gradients in the interfacial energy on the droplet interface. In this article we review the hydrodynamic prerequisites for self-sustained locomotion and present two examples to realize those conditions for emulsion droplets, i.e. droplets stabilized by a surfactant layer in a surrounding immiscible liquid. One possibility to achieve self-propelled motion relies on chemical reactions affecting the surface active properties of the surfactant molecules. The other relies on micellar solubilization of the droplet phase into the surrounding liquid phase. Remarkable cruising ranges can be achieved in both cases and the relative insensitivity to their own ‘exhausts’ allows to additionally study collective phenomena.     

Quasiregular concentric waves in heterogeneous lattices of coupled oscillators

We study the pattern formation in a lattice of locally coupled phase oscillators with quenched disorder. In the synchronized regime quasiregular concentric waves can arise which are induced by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one-dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.     

Unusual nucleation and growth of γ′ iron nitride upon nitriding Fe–4.75 at.% Al alloy

The influence of substitutionally dissolved Al in ferritic Fe–4.75 at.% Al alloy on the nucleation and growth of γ′ iron nitride (Fe₄N_{1? x} ) was investigated upon nitriding in NH₃/H₂ gas mixtures. The nitrided specimens were characterised employing optical microscopy, scanning electron microscopy, transmission electron microscopy, electron probe microanalysis and X-ray diffraction. As compared to the nitriding of pure ferrite (α-Fe), where a layer of γ′ develops at the surface, upon nitriding ferritic Fe–4.75 at.% Al an unusual morphology of γ′ plates develops at the surface, which plates deeply penetrate the substrate. In the diffusion zone, nano-sized precipitates of γ′ and of metastable, cubic (NaCl-type) AlN occur, having, with the ferrite matrix, a Nishiyama–Wassermann orientation relationship and a Bain orientation relationship, respectively. The γ′ plates contain a high density of stacking faults and fine ε iron nitride (Fe₂N_{1? z} ) precipitates, although the formation of ε iron nitride is not expected for the employed nitriding parameters. On the basis of dedicated nitriding experiments it is shown that the unusual microstructural development is a consequence of the negligible solubility of Al in γ′ and the obstructed precipitation of the thermodynamically stable, hexagonal (wurtzite-type) AlN in ferrite.     

Large coherence area thin-film photonic stop-band lasers

We demonstrate that the shift of the stop-band position with increasing oblique angle in periodic structures results in a wide transverse exponential field distribution corresponding to strong angular confinement of the radiation. The beam expansion follows an effective diffusive equation depending only upon the spectral mode width. In the presence of gain, the beam cross section is limited only by the size of the gain area. As an example of an active periodic photonic medium, we calculate and measure laser emission from a dye-doped cholesteric liquid crystal film.     

Microstructural characterization of Li insertion in individual silicon nanowires

The lithiation and delithiation process of silicon nanowire arrays (SiNWs) on silicon substrates has been studied with high-resolution electron microscopy. The composition of lithiated SiNWs was revealed, consisting of the unreacted crystalline silicon core and the reacted amorphous Li–Si shell. In particular, the Li–Si shell was comprised of a mixture of amorphous silicon oxide and crystalline silicon, leading to hindrance during Li–Si alloying/dealloying upon cycling.     

Zero-temperature magnetic transition in an easy-axis Kondo lattice model

We address the quantum transition of a spin-1/2 antiferromagnetic Kondo lattice model with an easy-axis anisotropy using the extended dynamical mean field theory. We derive results in real frequency by using the bosonic numerical renormalization group (BNRG) method and compare them with quantum Monte Carlo results in Matsubara frequency. The BNRG results show a logarithmic divergence in the critical local spin susceptibility, signaling a destruction of Kondo screening. The T=0 transition is consistent with being second order. The BNRG results also display some subtle features; we identify their origin and suggest means for further microscopic studies.     

Shellwise Mackay transformation in iron nanoclusters

Structure and magnetism of iron clusters with up to 641 atoms have been investigated by means of density functional theory calculations including full geometric optimizations. Body-centered cubic (bcc) isomers are found to be lowest in energy when the clusters contain more than about 100 atoms. In addition, another stable conformation has been identified for magic-number clusters, which lies well within the range of thermal energies as compared to the bcc isomers. Its structure is characterized by a close-packed particle core and an icosahedral surface, while intermediate shells are partially transformed along the Mackay path between icosahedral and cuboctahedral geometry. The gradual transformation results in a favorable bcc environment for the subsurface atoms. For Fe55, the shellwise Mackay-transformed morphology is a promising candidate for the ground state.