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.

     

Suppression of Liquid-Liquid Phase Separation and Aggregation of Antibodies by Modest Pressure Application

The high colloidal stability of antibody (immunoglobulin) solutions is important for pharmaceutical applications. Inert cosolutes, excipients, are generally used in therapeutic protein formulations to minimize physical instabilities, such as liquid–liquid phase separation (LLPS), aggregation and precipitation, which are often encountered during manufacturing and storage. Despite their widespread use, a detailed understanding of how excipients modulate the specific protein-protein interactions responsible for these instabilities is still lacking. In this work, we demonstrate the high sensitivity to pressure of globulin condensates as a suitable means to suppress LLPS and subsequent aggregation of concentrated antibody solutions. The addition of excipients has only a minor effect. The high pressure sensitivity observed is due to the fact that these flexible Y-shaped molecules create a considerable amount of void volume in the condensed phase, leading to an overall decrease in the volume of the system upon dissociation of the droplet phase by pressure already at a few tens of to hundred bar. Moreover, we show that immunoglobulin molecules themselves are highly resistant to unfolding under pressure, and can even sustain pressures up to about 6 kbar without conformational changes. This implies that immunoglobulins are resistant to the pressure treatment of foods, such as milk, in high-pressure food-processing technologies, thereby preserving their immunological activity.     

Comprehensive Characterization of Shredded Lithium-Ion Battery Recycling Material

Herein we report on an analytical study of dry-shredded lithium-ion battery (LIB) materials with unknown composition. Samples from an industrial recycling process were analyzed concerning the elemental composition and (organic) compound speciation. Deep understanding of the base material for LIB recycling was obtained by identification and analysis of transition metal stoichiometry, current collector metals, base electrolyte and electrolyte additive residues, aging marker molecules and polymer binder fingerprints. For reversed engineering purposes, the main electrode and electrolyte chemistries were traced back to pristine materials. Furthermore, possible lifetime application and accompanied aging was evaluated based on target analysis on characteristic molecules described in literature. With this, the reported analytics provided precious information for value estimation of the undefined spent batteries and enabled tailored recycling process deliberations. The comprehensive feedstock characterization shown in this work paves the way for targeted process control in LIB recycling processes.     

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.     

Measurement of the muon capture rate in hydrogen gas and determination of the proton's pseudoscalar coupling gP

The rate of nuclear muon capture by the proton has been measured using a new technique based on a time projection chamber operating in ultraclean, deuterium-depleted hydrogen gas, which is key to avoiding uncertainties from muonic molecule formation. The capture rate from the hyperfine singlet ground state of the microp atom was obtained from the difference between the micro(-) disappearance rate in hydrogen and the world average for the micro(+) decay rate, yielding Lambda(S)=725.0+/-17.4 s(-1), from which the induced pseudoscalar coupling of the nucleon, g(P)(q(2)=-0.88m(2)(micro))=7.3+/-1.1, is extracted.     

Quantum nonlocality and beyond: limits from nonlocal computation

We address the problem of "nonlocal computation," in which separated parties must compute a function without any individual learning anything about the inputs. Surprisingly, entanglement provides no benefit over local classical strategies for such tasks, yet stronger nonlocal correlations allow perfect success. This provides intriguing insights into the limits of quantum information processing, the nature of quantum nonlocality, and the differences between quantum and stronger-than-quantum nonlocal correlations.     

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.