The C Chemical Shift Tensor Principal Values and Orientations in Dialkyl Carbonates and Trithiocarbonates

The ¹³C chemical shift tensor principal values for the trigonal carbonate and thiocarbonate carbon atoms in the dialkyl carbonates, dimethyl carbonate, ethylene carbonate, and diphenyl carbonate, and in the trithiocarbonates, ethylene trithiocarbonate and dimethyl trithiocarbonate, respectively, were measured in various solid-state one-dimensional and two-dimensional nuclear magnetic resonance experiments. Furthermore, the chemical shift tensor principal values and orientations were calculated for the corresponding isolated molecules with quantum mechanically fully optimized geometries. Proton-optimized X-ray geometries of ethylene carbonate, ethylene trithiocarbonate, and diphenyl carbonate were used in embedded ion method (EIM) calculations and in calculations on the isolated molecules to obtain the theoretical principal values and to assign the chemical shift tensor orientations in these three compounds. Considerable improvement in the correlation between the experimental and calculated principal values is obtained when the electrostatic crystal potentials are included in EIM calculations. The chemical shift tensor orientations and principal values obtained for the dialkyl compounds in this study complement the previous data on a series of ionic potassium carbonates and thiocarbonates.     

Numerical computation of nonsimple turning points and cusps

Summary A method is developed for the numerical computation of a double turning point corresponding to a cusp catastrophe of a nonlinear operator equation depending on two parameters. An augmented system containing the original equation is introduced, for which the cusp point is an isolated solution. An efficient implementation of Newton's method in the finite-dimensional case is presented. Results are given for some chemical engineering problems and this direct method is compared with some other techniques to locate cusp points.     

Cycles Avoiding a Color in Colorful Graphs

The Ramsey numbers of cycles imply that every 2‐edge‐colored complete graph on n vertices contains monochromatic cycles of all lengths between 4 and at least . We generalize this result to colors by showing that every k‐edge‐colored complete graph on vertices contains ‐edge‐colored cycles of all lengths between 3 and at least .     

On Korn's first inequality for tangential or normal boundary conditions with explicit constants

We will prove that for piecewise C²‐concave domains in Korn's first inequality holds for vector fields satisfying homogeneous normal or tangential boundary conditions with explicit Korn constant . Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic control and information processing in chemical reaction systems by tuning self-organization behavior

Specific external control of chemical reaction systems and both dynamic control and signal processing as central functions in biochemical reaction systems are important issues of modern nonlinear science. For example nonlinear input-output behavior and its regulation are crucial for the maintainance of the life process that requires extensive communication between cells and their environment. An important question is how the dynamical behavior of biochemical systems is controlled and how they process information transmitted by incoming signals. But also from a general point of view external forcing of complex chemical reaction processes is important in many application areas ranging from chemical engineering to biomedicine. In order to study such control issues numerically, here, we choose a well characterized chemical system, the CO oxidation on Pt(110), which is interesting per se as an externally forced chemical oscillator model. We show numerically that tuning of temporal self-organization by input signals in this simple nonlinear chemical reaction exhibiting oscillatory behavior can in principle be exploited for both specific external control of dynamical system behavior and processing of complex information.     

Compact efficient broadband grating coupler for silicon-on-insulator waveguides

We have designed a high-efficiency broadband grating coupler for coupling between silicon-on-insulator (SOI) waveguides and optical fibers. The grating is only 13 microm long and 12 microm wide, and the size of the grooves is optimized numerically. For TE polarization the coupling loss to single-mode fiber is below 1 dB over a 35-nm wavelength range when using SOI with a two-pair bottom reflector. The tolerances to fabrication errors are also calculated.     

Exponentiation for unitary structures

Motivated by the observation that both pretopologies and preapproach limits can be characterized as those convergence relations which have a unit for a suitable composition, we introduce the category Algu(T;V) of reflexive and unitary lax algebras, for a symmetric monoidal closed lattice V and a Set-monad T=(T,e,m). For T=U the ultrafilter monad, we characterize exponentiable morphisms in Algu(U;V). Further, we give a sufficient condition for an object to be exponentiable in the category Alg(U;V) of reflexive and transitive lax algebras. This specializes to known and new results for pretopological, preapproach and approach spaces.     

Local Existence and Uniqueness for a Two-Dimensional Surface Growth Equation with Space-Time White Noise

We study local existence and uniqueness for a surface growth model with space-time white noise in 2D. Unfortunately, the direct fixed-point argument for mild solutions fails here, as we do not have sufficient regularity for the stochastic forcing. Nevertheless, one can give a rigorous meaning to the stochastic PDE and show uniqueness of solutions in that setting. Using spectral Galerkin method and any other types of regularization of the noise, we obtain always the same solution.     

Baryon formation and dissociation in dense hadronic and quark matter

We study the formation of baryons as composed of quarks and diquarks in hot and dense hadronic matter in a Nambu-Jona-Lasinio (NJL)-type model. We first solve the Dyson-Schwinger equation for the diquark propagator and then use this to solve the Dyson-Schwinger equation for the baryon propagator. We find that stable baryon resonances exist only in the phase of broken chiral symmetry. In the chirally symmetric phase, we do not find a pole in the baryon propagator. In the color-superconducting phase, there is a pole, but it has a large decay width. The diquark does not need to be stable in order to form a stable baryon, a feature typical for so-called Borromean states. Varying the strength of the diquark coupling constant, we also find similarities to the properties of an Efimov state.     

Microscopic coexistence of superconductivity and magnetism in Ba(1-x)K(x)Fe2As2

It is widely believed that, in contrast to its electron-doped counterparts, the hole-doped compound Ba(1-x)K(x)Fe(2)As(2) exhibits a mesoscopic phase separation of magnetism and superconductivity in the underdoped region of the phase diagram. Here, we report a combined high-resolution x-ray powder diffraction and volume-sensitive muon spin rotation study of Ba(1-x)K(x)Fe(2)As(2) showing that this paradigm does not hold true in the underdoped region of the phase diagram (0≤x≤0.25). Instead we find a microscopic coexistence of the two forms of order. A competition of magnetism and superconductivity is evident from a significant reduction of the magnetic moment and a concomitant decrease of the magnetoelastically coupled orthorhombic lattice distortion below the superconducting phase transition.