Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets

We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (constructed on a feasible open set of an IFS) and the general relations to the corresponding functionals for self-similar sets. In particular, we characterize the situation, when these functionals coincide. In this case, the Minkowski content and the fractal curvatures of a self-similar set can be expressed completely in terms of the volume function or curvature data, respectively, of the generator of the tiling. In special cases such formulas have been obtained recently using tube formulas and complex dimensions or as a corollary to results on self-conformal sets. Our approach based on the classical Renewal Theorem is simpler and works for a much larger class of self-similar sets and tilings. In fact, generator type formulas are obtained for essentially all self-similar sets, when suitable volume functions (and curvature functions, respectively) related to the generator are used. We also strengthen known results on the Minkowski measurability of self-similar sets, in particular on the question of non-measurability in the lattice case.     

Carbon‐Coated LiTi2(PO4)3: An Ideal Insertion Host for Lithium‐Ion and Sodium‐Ion Batteries

We report the extraordinary performance of carbon‐coated sodium super ion conductor (NASICON)‐type LiTi₂(PO₄)₃ as an ideal host matrix for reversible insertion of both Li and Na ions. The NASICON‐type compound was prepared by means of a Pechini‐type polymerizable complex method and was subsequently carbon coated. Several characterization techniques such as XRD, thermogravimetric analysis (TGA), field‐emission (FE) SEM, TEM, and Raman analysis were used to study the physicochemical properties. Both guest species underwent a two‐phase insertion mechanism during the charge/discharge process that was clearly evidenced from galvanostatic and cyclic voltammetric studies. Unlike that of Li (≈1.5 moles of Li), Na insertion exhibits better reversibility (≈1.59 moles of Na) while experiencing a slightly higher capacity fade (≈8 % higher than Li) and polarization (780 mV) than Li. However, excellent rate capability profiles were noted for Na insertion relative to its counterpart Li. Overall, the Na insertion properties were found to be superior relative to Li insertion, which makes carbon‐coated NASICON‐type LiTi₂(PO₄)₃ hosts attractive for the development of next‐generation batteries.     

Phase-Field Modeling of Hydraulic Fracture

Hydraulically driven fracture has gained more and more research activity in the last few years, especially due to the growing interest of the petroleum industry. Key challenge for a powerful simulation of this scenario is an effective modeling and numerical implementation of the behavior of the solid skeleton and the fluid phase, the mechanical coupling between the two phases as well as the incorporation of the fracture process. Existing models for hydraulic fracturing can be found for example in [1], where the crack path is predetermined, or in [2] who use a phase field fracture model in an elastic framework, however without incorporating the fluid flow. In this work we propose a new compact model structure for the Biot-type fluid transport in porous media at finite strains based on only two constitutive functions, that is the free energy function ψ and a dissipation potential ϕ that includes the incorporation of an additional Poiseuille-type fluid flow in cracks. This formulation is coupled to a phase field approach for fracture and is fully variational in nature, as shown in [3]. In contrast to formulations with a sharp-crack discontinuity, the proposed regularized approach has the main advantage of a straight-forward modeling of complex crack patterns including branching. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An improved rapid method for the determination of actinides in water

A new rapid method has been developed for the determination of Th, Pu, Np, U, Am and Cm isotopes in water samples of about 1 L. Actinides are pre-concentrated by co-precipitation with Ca phosphate, sequentially separated on stacked TEVA and TK221 cartridges and measured by alpha spectrometry. The TK221 extraction chromatographic resin contains i.e. CMPO and DGA extractants. It has been characterized by measuring the weight distribution ratios (D_w) of actinides which are higher than 1000 for all actinides in 3 M HNO₃. The method has been optimized, applied for the analysis of tap and seawater samples and validated by participating in an IAEA proficiency test. Chemical recoveries for all actinides are better than 50%. The method can be performed within one day.

     

Lensless diffractive imaging using tabletop coherent high-harmonic soft-X-ray beams

We present the first experimental demonstration of lensless diffractive imaging using coherent soft x rays generated by a tabletop soft-x-ray source. A 29 nm high harmonic beam illuminates an object, and the subsequent diffraction is collected on an x-ray CCD camera. High dynamic range diffraction patterns are obtained by taking multiple exposures while blocking small-angle diffraction using beam blocks of varying size. These patterns reconstruct to images with 214 nm resolution. This work demonstrates a practical tabletop lensless microscope that promises to find applications in materials science, nanoscience, and biology.     

Structure, scaling, and phase transition in the optimal transport network

The structure and properties of optimal networks depend on the cost functional being minimized and on constraints to which the minimization is subject. We show here two different formulations that lead to identical results: minimizing the dissipation rate of an electrical network under a global constraint is equivalent to the minimization of a power-law cost function introduced by Banavar et al. [Phys. Rev. Lett. 84, 4745 (2000)10.1103/PhysRevLett.84.4745]. An explicit scaling relation between the currents and the corresponding conductances is derived, proving the potential flow nature of the latter. Varying a unique parameter, the topology of the optimized networks shows a transition from a tree topology to a very redundant structure with loops; the transition corresponds to a discontinuity in the slope of the power dissipation.     

Improved CE(SDS)-CZE-MS method utilizing an 8-port nanoliter valve

Capillary sieving electrophoresis utilizing SDS (CE(SDS)) is one of the most applied methods for the analysis of antibody (mAb) size heterogeneity in the biopharmaceutical industry. Inadequate peak identification of observed protein fragments is still a major issue. In a recent publication, we introduced an electrophoretic 2D system, enabling online mass spectrometric detection of generic CE(SDS) separated peaks and identification of several mAb fragments. However, an improvement regarding system stability and handling of the approach was desired. Here, we introduce a novel 8-port valve in conjunction with an optimized decomplexation strategy. The valve contains four sample loops with increased distances between the separation dimensions. Thus, successively coinjection of solvent and cationic surfactant without any additional detector in the second dimension is enabled, simplifying the decomplexation strategy. Removal efficiency was optimized by testing different volumes of solvents as presample and cationic surfactant as postsample zone. 2D measurements of the light and heavy chain of the reduced NIST mAb with the 8-port valve and the optimized decomplexation strategy demonstrates the increased robustness of the system. The presented novel set-up is a step toward routine application of CE(SDS)-CZE-MS for impurity characterization of proteins in the biopharmaceutical field.     

Negishi Cross-Coupling Provides Alkylated Tryptophans and Tryptophan Regioisomers

Mild transition-metal catalysed cross-couplings enable direct functionalisation of biocatalytically halogenated tryptophans with alkyl iodides, representing a new alternative for late-stage derivatisations of halogenated aromatic amino acids. Moreover, this strategy enables preparation of (homo)tryptophan regioisomers in a simple two-step synthesis using a Pd-catalysed Negishi cross coupling. This method provides access to non-canonical constitutional surrogates of tryptophan, ready for use in peptide synthesis.     

1‐Factor and Cycle Covers of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. Any list of three 1‐factors induces a core of a cubic graph. We use results on the structure of cores to prove sufficient conditions for Berge‐covers and for the existence of three 1‐factors with empty intersection. Furthermore, if , then is an upper bound for the girth of G. We also prove some new upper bounds for the length of shortest cycle covers of bridgeless cubic graphs. Cubic graphs with have a 4‐cycle cover of length and a 5‐cycle double cover. These graphs also satisfy two conjectures of Zhang 18 . We also give a negative answer to a problem stated in 18 .