Boundary rigidity and stability for generic simple metrics

We study the boundary rigidity problem for compact Riemannian manifolds with boundary : is the Riemannian metric uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function known for all boundary points and ? We prove in this paper local and global uniqueness and stability for the boundary rigidity problem for generic simple metrics. More specifically, we show that there exists a generic set of simple Riemannian metrics such that for any , any two Riemannian metrics in some neighborhood of having the same distance function, must be isometric. Similarly, there is a generic set of pairs of simple metrics with the same property. We also prove Hölder type stability estimates for this problem for metrics which are close to a given one in .     

The glucosinolate-myrosinase system. New insights into enzyme-substrate interactions by use of simplified inhibitors

Myrosinase, a thioglucoside glucohydrolase, is the only enzyme able to hydrolyse glucosinolates, a unique family of molecules bearing an anomeric O-sulfated thiohydroximate function. Non-hydrolysable myrosinase inhibitors have been devised and studied for their biological interaction. Diverse modifications of the O-sulfate moiety did not result in a significant inhibitory effect, whereas replacing the D-glucopyrano residue by its carba-analogue allowed inhibition to take place. X-Ray experiments carried out after soaking allowed for the first time inclusion of a non-hydrolysable inhibitor inside the enzymatic pocket. Structural tuning of the aglycon part in its pocket is being used as a guide for the development of simplified and more potent inhibitors.     

Eine wahrscheinlichkeitstheoretische Begründung der Integrationsformeln von Newton-Cotes

Summary A definite integral is approximated by a linear combination of values of the integrand at equidistant points. As a measure for the goodness of fit we use the mean square deviation; for this we take a wide sense stationary stochastic process as basis. We prove that there exist always a best integration formula in this sense. The Taylor expansion of its coefficients begins with the coefficients ofNewton-Cotes. It is shown that the error of the best integration formula is of the same order of magnitude as in the well-known formula ofNewton-Cotes. Therefore we get a justification for the formulae ofNewton-Cotes also if the integrand is not differentiable. Besides we obtain estimates of the error, which use higher differences instead of higher differential quotients of the integrand.     

On the structure of glassy polymers. III. Small-angle x-ray scattering from amorphous polyethylene terephthalate

The small-angle x-ray scattering (SAXS) from glassy polyethylene terephthalate has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 15 min, decreases more gradually in the range between 15 min and 45 min, and reaches a nearly constant asymptotic value over the range between 45 min and 2 deg. The magnitude of the scattering in the constant range, about 0.4 (electrons)² Å^?3, is very close to the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass-transition temperature [0.34 (electrons)² Å^?3]. The increase in intensity at angles smaller than about 45 min cannot be described by structures on the scale and volume fraction of the nodules reported in amorphous PET (50–100 Å), but can be well represented by small concentrations of heterogeneities, ranging in size from 100 to 2000 Angstroms, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material seems well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration (<1 vol-%) of heterogeneities covering a range of sizes. The heterogeneities in the small end of the range may well be crystallites which formed on cooling.     

On the structure of glassy polymers. II. Small-angle x-ray scattering from poly(methyl methacrylate)

The small-angle x-ray scattering (SAXS) from glassy poly(methyl methacrylate) has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 30 min, and is nearly constant between 30 min and 2 deg. The magnitude of the scattering in the constant range, 0.6 (electrons)² Å^?3, is within a factor of 1.5 of the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at smaller angles cannot be described by structures on the scale of the nodules reported in highly isotactic PMMA (150–200 Å), but can be well represented by small concentrations of heterogeneities, several thousand angstrom units in size, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material is well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration of relatively large heterogeneities.     

Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in ${\mathbb{R}^n}$ , ${n \geq 3}$ , for the magnetic Schrödinger operator with L ^∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrödinger operator with a gain of two derivatives.     

Macroscopic and mesoscopic modeling based on the concept of generalized stresses for cutting simulation

Based on the concept of generalized stresses proposed by GURTIN [2] and FOREST et al. [1] macro- and meso-scopic modelling are presented. For the macroscopic modelling we develop a multi-mechanism model for strain rate and temperature dependent asymmetric plastic material behavior accompanied by phase transformation with consideration of the trip-strain. Furthermore, we extend the multi-mechanism model with the gradient of phase fraction, which is considered as an extra degree of freedom. For mesoscopic modelling a phase field model is implemented for describing phase transformations. For the scenario of a cutting process we have a martensite-austenite-martensite transformation. A generalized principle of virtual power is postulated involving generalized stresses and used to derive the constitutive equations for both approaches. Furthermore, parameters of the multi-mechanism model related to visco-plasticity with SD-effect and the trip-strain are identified for the material DIN 100Cr6. In the examples a cutting simulation for testing the multi-mechanism model and a phase-transformation simulation are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular Transport within Polymer Brushes: A FRET View at Aqueous Interfaces

Molecular permeability through polymer brush chains is implicated in surface lubrication, wettability, and solute capture and release. Probing molecular transport through polymer brushes can reveal information on the polymer nanostructure, with a permeability that is dependent on chain conformation and grafting density. Herein, we introduce a brush system to study the molecular transport of fluorophores from an aqueous droplet into the external “dry” polymer brush with the vapour phase above. The brushes consist of a random copolymer of N-isopropylacrylamide and a Förster resonance energy transfer (FRET) donor-labelled monomer, forming ultrathin brush architectures of about 35 nm in solvated height. Aqueous droplets containing a separate FRET acceptor are placed onto the surfaces, with FRET monitored spatially around the 3-phase contact line. FRET is used to monitor the transport from the droplet to the outside brush, and the changing internal distributions with time as the droplets prepare to recede. This reveals information on the dynamics and distances involved in the molecular transport of the FRET acceptor towards and away from the droplet contact line, which are strongly dependent on the relative humidity of the system. We anticipate our system to be extremely useful for studying lubrication dynamics and surface droplet wettability processes.