Strong Convergence in Stabilised Degenerate Convex Problems

Solutions to non–convex variational problems typically exhibit enforced finer and finer oscillations called microstructures such that the infimal energy is not attained. Those oscillations are physically meaningful, but finite element approximations typically experience dramatic difficulty in their reproduction. The relaxation of the non–convex minimisation problem by (semi–)convexification leads to a macroscopic model for the effective energy. The resulting discrete macroscopic problem is degenerate in the sense that it is convex but not strictly convex. This paper discusses a modified discretisation by adding a stabilisation term to the discrete energy. It will be announced that, for a wide class of problems, this stabilisation technique leads to strong H¹–convergence of the macroscipic variables even on unstructured triangulations. This is in contrast to the work [2] for quasi–uniform triangulations and enables the use of adaptive algorithms for the stabilised formulations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bifurcation analysis of a stochastic non-smooth friction model

Non-smooth friction systems such as systems with dry friction show several bifurcation phenomena. The discontinuity of these so called slip-stick vibrations makes these systems interesting and there has been a lot of research in this field, see for example Hinrichs [1]. Due to the non-smooth friction force even the deterministic system shows a rich bifurcation behavior. Measurements indicate that the friction coefficient which plays a large role in the system behavior is not deterministic but can be described as a friction characteristic with added white noise. Therefore, the stochastic characteristic is introduced into the non-smooth system and the change of the bifurcation behavior is studied. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment

We realize an absolute position control of drifting dissipative optical solitons by injecting an incoherent amplitude parameter gradient onto the nonlinear optical system. This allows for two-dimensional, arbitrary control patterns. The control of the soliton drift velocity is studied applying a periodic, hexagonally shaped modulation. The guiding of dissipative solitons by one- and two-dimensional parameter modulations is demonstrated. Furthermore, one-dimensional, line-shaped parameter modulations are designed to act as barriers for dissipative solitons, allowing implementations of position selectors for solitons. The interaction of dissipative optical solitons with barriers is studied for different barrier parameters.     

Density waves and cooper pairing on the honeycomb lattice

Motivated by the surge in research activities on graphene, we investigate instabilities of electrons on the honeycomb lattice, interacting by onsite and nearest-neighbor terms, using a renormalization group scheme. Near half band filling, critical minimal interaction strengths are required for instabilities toward antiferromagnetic or charge-density-wave order. Away from half-filling, f-wave triplet-pairing and d + id singlet-pairing instabilities are found to emerge out of density-wave regimes.     

Mixed analytical–numerical relaxation in finite single-slip crystal plasticity

The modeling of the finite elastoplastic behaviour of single crystals with one active slip system leads to a nonconvex variational problem, whose minimization produces fine structures. The computation of the quasiconvex envelope of the energy density involves the solution of a nonconvex optimization problem and faces severe numerical difficulties from the presence of many local minima. In this paper, we consider a standard model problem in two dimensions and, by exploiting analytical relaxation results for limiting cases and the special structure of the problem at hand, we obtain a fast and efficient numerical relaxation algorithm. The effectiveness of our algorithm is demonstrated with numerical examples. The precision of the results is assessed by lower bounds from polyconvexity.      

Near-infrared chemical imaging used for in-line analysis of inside adhesive layers in textile laminates

This paper demonstrates for the first time that near-infrared (NIR) chemical imaging can be used for in-line analysis of textile lamination processes. In particular, it was applied for the quantitative determination of the applied coating weight and for monitoring of the spatial distribution of hot melt adhesive layers using chemometric approaches for spectra evaluation. Layers with coating weights between about 25 and 130 g m⁻² were used for the lamination of polyester fabrics and nonwovens as well as for polyurethane foam. It was shown that quantitative data with adequate precision can be actually obtained for layers applied to materials with significantly heterogeneous surface structure such as foam or for hidden layers inside fabric laminates. Even the coating weight and the homogeneity of adhesive layers in composites consisting of black textiles only could be quantitatively analyzed. The prediction errors (RMSEP) determined in an external validation of each calibration model were found to range from about 2 g m⁻² to 6 g m⁻² depending on the specific system under investigation. All calibration models were applied for chemical imaging in order to prove their performance for monitoring the thickness and the homogeneity of adhesive layers in the various textile systems. Moreover, they were used for the detection of irregularities and coating defects. Investigations were carried out with a large hyperspectral camera mounted above a conveyor. Therefore, this method allows large-area monitoring of the properties of laminar materials. Consequently, it is potentially suited for process and quality control during the lamination of fabrics, foams and other materials in field-scale.     

A Variational Approach to Particles in Lipid Membranes

A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a variational framework, relate apparently different modelling approaches in terms of successive approximation, and investigate existence and uniqueness. Numerical computations illustrate that the new variational formulations are directly accessible to effective numerical methods.     

1,2‐Thiazines: One‐Pot Syntheses Utilizing Mono and Diaza Analogs of Sulfones

A one‐pot Michael addition/cyclization/condensation reaction sequence for the regioselective synthesis of 1,2‐thiazines, starting from propargyl ketones and NH‐sulfoximines or NH‐sulfondiimines, has been developed. Under mild and operationally simple reaction conditions previously unprecedented 1,2‐thiazine 1‐imide and 1‐oxide derivatives are formed in good to excellent yields. The products represent heterocyclic building blocks, readily modifiable by a regioselective C?H bond functionalization, classical cross‐coupling reactions, and deprotection.     

Covalent Photosensitizer–Polyoxometalate‐Catalyst Dyads for Visible‐Light‐Driven Hydrogen Evolution

A general concept for the covalent linkage of coordination compounds to bipyridine‐functionalized polyoxometalates is presented. The new route is used to link an iridium photosensitizer to an Anderson‐type hydrogen‐evolution catalyst. This covalent dyad catalyzes the visible‐light‐driven hydrogen evolution reaction (HER) and shows superior HER activity compared with the non‐covalent reference. Hydrogen evolution is observed over periods >1 week. Spectroscopic, photophysical, and electrochemical analyses give initial insight into the stability, electronic structure, and reactivity of the dyad. The results demonstrate that the proposed linkage concept allows synergistic covalent interactions between functional coordination compounds and reactive molecular metal oxides.