Semiclassical Asymptotics of the Aharonov‐Bohm Interference Process

We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov‐Bohm interference of two half‐waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling‐wave representation of the exact propagator, and to previous approaches on the system's asymptotics.     

Random Bit Quadrature and Approximation of Distributions on Hilbert Spaces

Foundations of Computational Mathematics - We study the approximation of expectations $${\text {E}}(f(X))$$ for Gaussian random elements X with values in a separable Hilbert space H and Lipschitz...     

Synthesis of a Novel Glycopeptide by Polymeranalogous Reaction of Gelatin with Mono‐6‐para‐toluenesulfonyl‐β‐cyclodextrin and its Supramolecular Properties

A synthetic model glycoprotein was successfully synthesized using gelatin and mono‐6‐para‐toluenesulfonyl‐β‐cyclodextrin which were reacted under microwave conditions in basic media. The resulting glycoprotein is observed to form intermolecular inclusion complexes through complexation of the aromatic moieties along the polymer chain by the attached cyclodextrins. This phenomenon was analyzed and proven by 2D NMR spectroscopy (ROESY) and dynamic light scattering (DLS). Above the denaturation temperature, a strong increase of the hydrodynamic diameter was found due to enhanced supramolecular agglomeration. Such a novel glycoprotein with supramolecular self‐recognition would be promising in biomedical applications serving as a drug‐delivery basis polymer.

     

One Decade of Microwave‐Assisted Polymerizations: Quo vadis?

The application of microwave irradiation in polymer syntheses and modifications is of continuously growing interest and has received significant international interest since the beginning of the millennium. Preceded by a review that was published 6 years ago, the present paper summarizes the most recent trends in this research area. Radical as well as step‐growth and ring‐opening polymerizations will be addressed; furthermore, the evolution from microwave‐assisted polymerizations to microwave‐assisted material fabrication will be described on the examples of polymeranalogous reactions, polymer/metal composites and bio‐based materials.

     

A new incorporation mechanism for trivalent actinides into bioapatite: a TRLFS and EXAFS study

One of the most toxic byproducts of nuclear power and weapons production is the transuranics, which have a high radiotoxicity and long biological half-life due to their tendency to accumulate in the skeletal system. This accumulation is inhomogeneous and has been associated with the chemical properties and structure of the bone material rather than its location or function. This suggests a chemical driving force to incorporation and requires an atomic scale mechanistic understanding of the incorporation process. Here we propose a new incorporation mechanism for trivalent actinides and lanthanides into synthetic and biologically produced hydroxyapatite. Time-resolved laser fluorescence spectroscopy and extended X-ray absorption fine structure have been used to demonstrate that trivalent actinides and lanthanides incorporate into the amorphous grain boundaries of apatite. This incorporation site can be used to explain patterns in uptake and distribution of radionuclides in the mammalian skeletal system.     

A Local Refinement Strategy for Constructive Quantization of Scalar SDEs

We present a fully constructive method for quantization of the solution X of a scalar SDE in the path space L _p [0,1] or C[0,1]. The construction relies on a refinement strategy which takes into account the local regularity of X and uses Brownian motion (bridge) quantization as a building block. Our algorithm is easy to implement, its computational cost is close to the size of the quantization, and it achieves strong asymptotic optimality provided this property holds for the Brownian motion (bridge) quantization.     

Simulation of Electrolytes in the Modeling of Batteries

Calculating the cell voltage of a lead-acid battery requires the solution of a complex multiphysical problem including electrochemical reactions on the electrode surfaces and diffusive transport in the enclosed electrolyte. Recently, the authors proposed a new electrolyte model with a thermodynamically correct coupling of mechanics to the diffusive transport. In the analysis of that model, formal asymptotic expansions were applied to handle sharp interface layers. Here, we use this analysis to formulate a simplified model for a lead-acid battery such that it is not necessary to resolve the layers numerically, but instead there are jump conditions at double layers imposed. The cell voltage is then derived using Butler-Volmer Formula. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanical examination of PZT microfibre defects structure

The major problem in the production process of efficient ultrasonic transducer is the preparation of defect-free PZT fibres. A considerable amount of empirical work is presently in progress to achieve this goal of special importance for high-sensitive transducers. However, there is a lack of basic research on the detection of residual stress and defects areas in these fibres due to difficulties in mechanical examination of such flexible elements. This work presents use of the nanoindenter for material characterisation of PZT fibres of 140 µm radius obtained by extrusion method. The sudden depth-excursions during indentation on the edge of fibres have been clarified using Piezoresponse Mode Atomic Force Microscopy method and XRD measurements. The nanoindentation method proves to be the efficient tool capable to detect contribution of defects along the radius, properly estimate hardness as well as corresponding Young's modulus and concluding on structural properties of the micrometre-range ceramics fibres.