Detection of small buried objects: asymptotic factorization and MUSIC

In this work, we consider a simple model problem for the electromagnetic exploration of small perfectly conducting objects buried within the lower halfspace of an unbounded two–layered background medium. In possible applications, such as, e.g., humanitarian demining, the two layers would correspond to air and soil. Moving a set of electric devices parallel to the surface of ground to generate a time–harmonic field, the induced field is measured within the same devices. The goal is to retrieve information about buried scatterers from these data. In mathematical terms, we are concerned with the analysis and numerical solution of the inverse scattering problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two–layered background medium from near field measurements of time–harmonic electromagnetic waves. For this purpose, we first study the corresponding direct scattering problem in detail and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero. Then, we use this expansion to justify a noniterative MUSIC–type reconstruction method for the solution of the inverse scattering problem. We propose a numerical implementation of this reconstruction method and provide a series of numerical experiments.

A sampling method for detecting buried objects using electromagnetic scattering

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scattering theory for this particular set-up.

Multifunctional water-soluble phosphorus dendrimers

Dendrimers are polymeric macromolecules with a regularly branched structure and are synthesised in an iterative fashion. Due to their monodispersity, well-defined shape and extremely high functionality, dendrimers are ideal nano-sized objects for functional and biocompatible surface coatings, biosensing and biomedicine. This dissertation describes the synthesis of ten novel water-soluble phosphorus containing dendrimers and their application in different biological and biomimetic systems. The dendrimers can be divided into two classes; the first type contains either a ferrocene at the core or 24 ferrocenes in the branches. They showed reversible reduction-oxidation behaviour and might be applied in electronic multilayered architectures. Dendrimers of the second class carry a dithiolane functionalised core that can strongly bind to noble metals, like gold substrates. Although such dendrimer coated substrates were unable to tether defect-free lipid bilayer membranes, the coatings were successfully applied for culturing Human Osteoblast cells. The cell adhesion to a coating of polycationic dendrimers was so strong that cell division could not take place, specifically evoking apoptosis. The polyanionic dendrimers, however, promoted excellent cell adhesion and proliferation. Therefore, the practical application of such macromolecular architectures can be envisioned, such as in dendrimer coatings for tissue engineering and or medical implants.