A generalisation of de la Vallée-Poussin procedure to multivariate approximations

Advances in Computational Mathematics - Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data....     

Control over Nanostructures and Associated Mesomorphic Properties of Doped Self‐Assembled Triarylamine Liquid Crystals

We have synthesized a series of triarylamine‐cored molecules equipped with an adjacent amide moiety and dendritic peripheral tails in a variety of modes. We show by ¹H NMR and UV/Vis spectroscopy that their supramolecular self‐assembly can be promoted in solution upon light stimulation and radical initiation. In addition, we have probed their molecular arrangements and mesomorphic properties in the bulk by integrated studies on their film state by using differential scanning calorimetry (DSC), variable‐temperature polarizing optical microscopy (VT‐POM), variable‐temperature X‐ray diffraction (VT‐XRD), and atomic force microscopy (AFM). Differences in the number and the disposition of the peripheral tails significantly affect their mesomorphic properties associated with their lamellar‐ or columnar‐packed nanostructures, which are based on segregated stacks of the triphenylamine cores and the lipophilic/lipophobic periphery. Such structural tuning is of interest for implementation of these soft self‐assemblies as electroactive materials from solution to mesophases.     

Diffusion of Gold Nanoparticles in Inverse Opals Probed by Heterodyne Dynamic Light Scattering

The diffusive behavior of nanoparticles inside porous materials is attracting a lot of interest in the context of understanding, modeling, and optimization of many technical processes. A very powerful technique for characterizing the diffusive behavior of particles in free media is dynamic light scattering (DLS). The applicability of the method in porous media is considered, however, to be rather difficult due to the presence of multiple sources of scattering. In contrast to most of the previous approaches, the DLS method was applied without ensuring matching refractive indices of solvent and porous matrix in the present study. To test the capabilities of the method, the diffusion of spherical gold nanoparticles within the interconnected, periodic nanopores of inverse opals was analyzed. Despite the complexity of this system, which involves many interfaces and different refractive indices, a clear signal related to the motion of particles inside the porous media was obtained. As expected, the diffusive process inside the porous sample slowed down compared to the particle diffusion in free media. The obtained effective diffusion coefficients were found to be wave vector-dependent. They increased linearly with increasing spatial extension of the probed particle concentration fluctuations. On average, the slowing-down factor measured in this work agrees within combined uncertainties with literature data.

     

Comparison of fast field-cycling magnetic resonance imaging methods and future perspectives

ABSTRACT

Fast field-cycling (FFC) nuclear magnetic resonance relaxometry is a well-established method to determine the relaxation rates as a function of magnetic field strength. This so-called nuclear magnetic relaxation dispersion gives insight into the underlying molecular dynamics of a wide range of complex systems and has gained interest especially in the characterisation of biological tissues and diseases. The combination of FFC techniques with magnetic resonance imaging (MRI) offers a high potential for new types of image contrast more specific to pathological molecular dynamics. This article reviews the progress in FFC-MRI over the last decade and gives an overview of the hardware systems currently in operation. We discuss limitations and error correction strategies specific to FFC-MRI such as field stability and homogeneity, signal-to-noise ratio, eddy currents and acquisition time. We also report potential applications with impact in biology and medicine. Finally, we discuss the challenges and future applications in transferring the underlying molecular dynamics into novel types of image contrast by exploiting the dispersive properties of biological tissue or MRI contrast agents.