Ring Dark Solitons in Toroidal Bose-Einstein Condensates

In this Thesis, we study various aspects of ring dark solitons (RDSs) in quasi-two-dimensional toroidally trapped Bose-Einstein condensates, focussing on atomic realisations thereof. Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localized soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments. It is also currently well known that in dimensions higher than one, (ring) dark solitons are susceptible, in general, to an irreversible decay into vortex-antivortex pairs through the snake instability. We show that the snake instability is caused by an unbalanced quantum pressure across the soliton's notch, linking the instability to the Bogoliubov-de Gennes spectrum. In particular, if the angular symmetry is maintained (or the toroidal trapping is restrictive enough), we show that the RDS is stable (long-lived with a lifetime of order seconds) in two dimensions. Furthermore, when the decay does take place, we show that the snake instability can in fact be reversible, and predict a previously unknown revival phenomenon for the original (many-)RDS system: the soliton structure is recovered and all the point-phase singularities (i.e. vortices) disappear. Eventually, however, the decay leads to an example of quantum turbulence; a quantum example of the laminar-to-turbulent type of transition.

Application of Carbon Nanotubes in Rotating Electrical Machines

Demand for increased energy efficiency has put an immense need for novel energy efficient systems. Electrical machines are considered as a much matured technology. Further improvement in this technology needs of finding new material to incorporate in electrical machines. Progress of carbon nanotubes research over the latest decade can open a new horizon in this aspect. Commonly known as ‘magic material’, carbon nanotubes (CNTs) have promising material properties that can change considerably the course of electrical machine design. It is believed that winding material based on carbon nanotubes create the biggest hope for a giant leap of modern technology and energy efficient systems. Though carbon nanotubes (CNTs) have shown amazing properties theoretically and practically during the latest 20 years, to the best knowledge of the author, no research has been carried out to find the future possibilities of utilizing carbon nanotubes as conductors in rotating electrical machines. In this thesis, the possibilities of utilizing carbon nanotubes in electrical machines have been studied. The design changes of electrical machine upon using carbon nanotubes instead of copper have been discussed vividly. A roadmap for this carbon nanotube winding machine has been discussed from synthesis, manufacturing and operational points of view.

Printed platforms for paper-based analytical applications

Paper-based analytical technologies enable quantitative and rapid analysis of analytes from various application areas including healthcare, environmental monitoring and food safety. Because paper is a planar, flexible and light weight substrate, the devices can be transported and disposed easily. Diagnostic devices are especially valuable in resourcelimited environments where diagnosis as well as monitoring of therapy can be made even without electricity by using e.g. colorimetric assays. On the other hand, platforms including printed electrodes can be coupled with hand-held readers. They enable electrochemical detection with improved reliability, sensitivity and selectivity compared with colorimetric assays. In this thesis, different roll-to-roll compatible printing technologies were utilized for the fabrication of low-cost paper-based sensor platforms. The platforms intended for colorimetric assays and microfluidics were fabricated by patterning the paper substrates with hydrophobic vinyl substituted polydimethylsiloxane (PDMS) -based ink. Depending on the barrier properties of the substrate, the ink either penetrates into the paper structure creating e.g. microfluidic channel structures or remains on the surface creating a 2D analog of a microplate. The printed PDMS can be cured by a roll-ro-roll compatible infrared (IR) sintering method. The performance of these platforms was studied by printing glucose oxidase-based ink on the PDMS-free reaction areas. The subsequent application of the glucose analyte changed the colour of the white reaction area to purple with the colour density and intensity depending on the concentration of the glucose solution. Printed electrochemical cell platforms were fabricated on paper substrates with appropriate barrier properties by inkjet-printing metal nanoparticle based inks and by IR sintering them into conducting electrodes. Printed PDMS arrays were used for directing the liquid analyte onto the predetermined spots on the electrodes. Various electrochemical measurements were carried out both with the bare electrodes and electrodes functionalized with e.g. self assembled monolayers. Electrochemical glucose sensor was selected as a proof-of-concept device to demonstrate the potential of the printed electronic platforms.

Hyperbolic Type Geometries in Subdomains

This Licentiate thesis deals with hyperbolic type geometries in planar subdomains. It is known that hyperbolic type distance is always greater in a subdomain than in the original domain. In this work we obtain certain lower estimates for hyperbolic type distances in subdomains in terms of hyperbolic type distances of the original domains. In particular the domains that we consider are cyclic polygons and their circumcircles, sectors and supercircles.

Artificial reflecting structures based on metamaterials

This thesis studies metamaterial-inspired mirrors which provide the most general control over the amplitude and phase of the reflected wavefront. The goal is to explore practical possibilities in designing fully reflective electromagnetic structures with full control over reflection phase. The first part of the thesis describes a planar focusing metamirror with the focal distance less than the operating wavelength. Its practical applicability from the viewpoint of aberrations when the incident angle deviates from the normal one is verified numerically and experimentally. The results indicate that the proposed focusing metamirror can be efficiently employed in many different applications due to its advantages over other conventional mirrors. In the second part of the thesis a new theoretical concept of reflecting metasurface operation is introduced based on Huygens’ principle. This concept in contrast to known approaches takes into account all the requirements of perfect metamirror operation. The theory shows a route to improve the previously proposed metamirrors through tilting the individual inclusions of the structure at a chosen angle from normal. It is numerically tested and the results demonstrate improvements over the previous design.