The Avogadro Constant for the Definition and Realization of the Mole

The International System of Units’ (SI) base unit of the quantity “amount of substance” is the mole (symbol: mol). After the revision of the SI to be implemented in 2019, when all SI units will be based solely on constants, the mole will be defined through a fixed value of the Avogadro constant N_A. One mole contains exactly 6.02214076 × 10²³ elementary entities, meaning the mole will no longer be linked to the kilogram. Currently, the mole is defined via the mass of exactly 0.012 kg of the ¹²C isotope which links it to the kilogram prototype. The history, changes, and implications of the revised definition of the mole are discussed here from the chemist's point of view. The ability to count entities such as atoms or molecules (precisely enough to enable a revision of the SI and preserve consistency of previous and future measurements) is crucial. This is achieved with the realization (Mise en Pratique) based on the X‐ray‐crystal density (XRCD) method (counting the atoms in a silicon sphere). The determination of N_A, focusing on the measurement of the molar mass of silicon highly enriched in the ²⁸Si isotope, with the lowest uncertainty so far, is presented.     

Enhancements in full‐field PIXE imaging—Large area elemental mapping with increased lateral resolution devoid of optics artefacts

The combination of a pn‐junction charge‐coupled device‐based pixel detector with a poly‐capillary X‐ray optics was installed and examined at the Helmholtz‐Zentrum Dresden‐Rossendorf. The set‐up is intended for particle‐induced X‐ray emission imaging to survey the trace elemental composition of flat/polished geological samples. In the standard configuration, a straight X‐ray optics (20 μm capillary diameter) is used to guide the emitted photons from the sample towards the detector with nearly 70 000 pixels. Their dimensions of 48 × 48 μm² are the main limitation of the lateral resolution. This limitation can be bypassed by applying a dedicated subpixel algorithm to recalculate the footprint of the photon's electron cloud in the detector. The lateral resolution is then mainly determined by the capillary's diameter. Nevertheless, images are still superimposed by the X‐ray optics pattern. The optics' capillaries are grouped in hexagonal bundles resulting in a reduced transmission of X‐rays in the boundary regions. This influence can be largely suppressed by combining a series of short measurements at slightly shifted positions using a precision stage and correcting the image data for this shifting. The use of a subpixel grid for the image reconstruction allows a further increase of the spatial resolution. This approach of image‐stacking and multiframe super‐resolution in combination with the subpixel correction algorithm is presented and illustrated with experimental data. Additionally, a flat‐field correction is shown to remove the remaining imaging inhomogeneity caused by non‐uniform X‐ray transmission. The described techniques can be used for all X‐ray spectrometry methods using an X‐ray camera to obtain high‐quality elemental images.     

Bound States in Yukawa Theory

A generalization of the Gell-Mann–Low Theorem is applied to lowest nontrivial order to bound state calculations in Yukawa theory. We present the solution of the corresponding effective Schrödinger equation for two-fermion bound states with the exchange of a massless boson. The complete low-lying bound state spectrum is obtained for fine structure constants below one and different ratios of the constituent masses. The consistency of the nonrelativistic and one-body limits is explicitly verified.     

A comprehensive study of classification methods for medical diagnosis

In this model study, we developed a method to distinguish between breast cancer cells and normal epithelial cells, which is in principal suitable for online diagnosis by Raman spectroscopy. Two cell lines were chosen as model systems for cancer and normal tissue. Both cell lines consist of epithelial cells, but the cells of the MCF‐7 series are carcinogenic, where the MCF‐10A cells are normal growing. An algorithm is presented for distinguishing cells of the MCF‐7 and MCF‐10A cell lines, which has an accuracy rate of above 99%. For this purpose, two classification steps are utilized. The first step, the so‐called top‐level classifier searches for Raman spectra, which are measured in the nuclei region. In the second step, a wide range of discriminant models are possible and these models are compared. The classification rates are always estimated using a cross‐validation and a holdout‐validation procedure to ensure the ability of the routine diagnosis to work in clinical environments. Copyright © 2009 John Wiley & Sons, Ltd.     

Facile Access to Hydroxy‐Functional Core–Shell Microspheres via Grafting of Ethylene Oxide by Anionic Ring‐Opening Polymerization

We present a facile access route to hydroxy‐functional narrow disperse microspheres of well‐defined grafting density (GD). Ethylene oxide has been grafted from highly crosslinked poly(divinyl benzene) microspheres by anionic ring‐opening polymerization using sec‐butyllithium as activator together with the phosphazene base t‐BuP₄. Initially, core microspheres have been prepared by precipitation polymerization utilizing divinyl benzene (DVB, 80 wt.‐%). The grafting of poly(ethylene oxide) (PEO) from the surface resulted in the formation of functional core–shell microspheres with hydroxy‐terminal end groups. The number average particle diameter of the grafted microspheres was 3.6 µm and the particle weight increased by 5.7%. The microspheres were characterized by SEM, FT‐IR spectroscopy, elemental analysis, and fluorescence microscopy. The surface GD (determined via two methods) was 1.65 ± 0.06 and 2.09 ± 0.08 chains · nm⁻², respectively.

     

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation

This work studies the spatio-temporal dynamics of a generic integral-differential equation subject to additive random fluctuations. It introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for Fokker-Planck equations, and studies analytically the systems’ stability near Turing bifurcations. In addition two types of fluctuation are studied, namely fluctuations uncorrelated in space and time, and global fluctuations, which are constant in space but uncorrelated in time. We show that the global fluctuations shift the Turing bifurcation threshold. This shift is proportional to the fluctuation variance. Applications to a neural field equation and the Swift-Hohenberg equation reveal the shift of the bifurcation to larger control parameters, which represents a stabilization of the system. All analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral-differential equation. To gain some insight into experimental manifestations, the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively.     

Scanning gate microscopy of a nanostructure where electrons interact

We show that scanning gate microscopy can be used for probing electron-electron interactions inside a nanostructure. We assume a simple model made of two noninteracting strips attached to an interacting nanosystem. In one of the strips, the electrostatic potential can be locally varied by a charged tip. This change induces corrections upon the nanosystem Hartree-Fock self-energies which enhance the fringes spaced by half the Fermi wavelength in the images giving the quantum conductance as a function of the tip position.