Ab Initio study of magnetic interactions in the KCuF3 and K2CuF4 low-dimensional Systems

The ab initio cluster model approach has been used to study the electronic structure and magnetic coupling of KCuF3 and K2CuF4 in their various ordered polytype crystal forms. Due to a cooperative Jahn-Teller distortion these systems exhibit strong anisotropies. In particular, the magnetic properties strongly differ from those of isomorphic compounds. Hence, KCuF3 is a quasi-one-dimensional (1D) nearest neighbor Heisenberg antiferromagnet whereas K2CuF4 is the only ferromagnet among the K2MF4 series of compounds (M=Mn, Fe, Co, Ni, and Cu) behaving all as quasi-2D nearest neighbor Heisenberg systems. Different ab initio techniques are used to explore the magnetic coupling in these systems. All methods, including unrestricted Hartree-Fock, are able to explain the magnetic ordering. However, quantitative agreement with experiment is reached only when using a state-of-the-art configuration interaction approach. Finally, an analysis of the dependence of the magnetic coupling constant with respect to distortion parameters is presented.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

Covalently Interconnected Three- Dimensional Graphene Oxide Solids

The creation of three-dimensionally engineered nanoporous architectures via covalently interconnected nanoscale building blocks remains one of the fundamental challenges in nanotechnology. Here we report the synthesis of ordered, stacked macroscopic three-dimensional (3D) solid scaffolds of graphene oxide (GO) fabricated via chemical cross-linking of two-dimensional GO building blocks. The resulting 3D GO network solids form highly porous interconnected structures, and the controlled reduction of these structures leads to formation of 3D conductive graphene scaffolds. These 3D architectures show promise for potential applications such as gas storage; CO2 gas adsorption measurements carried out under ambient conditions show high sorption capacity, demonstrating the possibility of creating new functional carbon solids starting with two-dimensional carbon layers

Studies on collective excitations of quasi-two-dimensional Bose-Einstein condensate

Theory Division Department of Physics

Optimal Sub-Pixel arrangements and coding for ultra-high resolution three-dimensional OLED displays

Information display technology is a rapidly growing research and development field. Using state-of-the-art technology, optical resolution can be increased dramatically by organic light-emitting diode - since the light emitting layer is very thin, under 100nm. The main question is what pixel size is achievable technologically? The next generation of display will considers three-dimensional image display. In 2D , one is considering vertical and horizontal resolutions. In 3D or holographic images, there is another dimension – depth. The major requirement is the high resolution horizontal dimension in order to sustain the third dimension using special lenticular glass or barrier masks, separate views for each eye. The high-resolution 3D display offers hundreds of more different views of objects or landscape. OLEDs have potential to be a key technology for information displays in the future. The display technology presented in this work promises to bring into use bright colour 3D flat panel displays in a unique way. Unlike the conventional TFT matrix, OLED displays have constant brightness and colour, independent from the viewing angle i.e. the observer's position in front of the screen. A sandwich (just 0.1 micron thick) of organic thin films between two conductors makes an OLE Display device. These special materials are named electroluminescent organic semi-conductors (or organic photoconductors (OPC )). When electrical current is applied, a bright light is emitted (electrophosphorescence) from the formed Organic Light-Emitting Diode. Usually for OLED an ITO layer is used as a transparent electrode. Such types of displays were the first for volume manufacture and only a few products are available in the market at present. The key challenges that OLED technology faces in the application areas are: producing high-quality white light achieving low manufacturing costs increasing efficiency and lifetime at high brightness. Looking towards the future, by combining OLED with specially constructed surface lenses and proper image management software it will be possible to achieve 3D images.

Transport properties of one-dimensional, disordered two-band systems

We have studied the transport properties of disordered one-dimensional two-band systems. The model includes a narrow d band hybridised with an s band. The Landauer formula was used in the case of a very narrow d band or in the case of short chains. The results were compared with the localisation length of the wavefunctions calculated by the transfer matrix method, which allows the use of very lang chains, and an excellent agreement was obtained.

High-Speed Semiconductor Lasers based on Low-Dimensional Active Materials for Optical Telecommunication

The scope of this work is the fundamental growth, tailoring and characterization of self-organized indium arsenide quantum dots (QDs) and their exploitation as active region for diode lasers emitting in the 1.55 µm range. This wavelength regime is especially interesting for long-haul telecommunications as optical fibers made from silica glass have the lowest optical absorption. Molecular Beam Epitaxy is utilized as fabrication technique for the quantum dots and laser structures. The results presented in this thesis depict the first experimental work for which this reactor was used at the University of Kassel. Most research in the field of self-organized quantum dots has been conducted in the InAs/GaAs material system. It can be seen as the model system of self-organized quantum dots, but is not suitable for the targeted emission wavelength. Light emission from this system at 1.55 µm is hard to accomplish. To stay as close as possible to existing processing technology, the In(AlGa)As/InP (100) material system is deployed. Depending on the epitaxial growth technique and growth parameters this system has the drawback of producing a wide range of nano species besides quantum dots. Best known are the elongated quantum dashes (QDash). Such structures are preferentially formed, if InAs is deposited on InP. This is related to the low lattice-mismatch of 3.2 %, which is less than half of the value in the InAs/GaAs system. The task of creating round-shaped and uniform QDs is rendered more complex considering exchange effects of arsenic and phosphorus as well as anisotropic effects on the surface that do not need to be dealt with in the InAs/GaAs case. While QDash structures haven been studied fundamentally as well as in laser structures, they do not represent the theoretical ideal case of a zero-dimensional material. Creating round-shaped quantum dots on the InP(100) substrate remains a challenging task. Details of the self-organization process are still unknown and the formation of the QDs is not fully understood yet. In the course of the experimental work a novel growth concept was discovered and analyzed that eases the fabrication of QDs. It is based on different crystal growth and ad-atom diffusion processes under supply of different modifications of the arsenic atmosphere in the MBE reactor. The reactor is equipped with special valved cracking effusion cells for arsenic and phosphorus. It represents an all-solid source configuration that does not rely on toxic gas supply. The cracking effusion cell are able to create different species of arsenic and phosphorus. This constitutes the basis of the growth concept. With this method round-shaped QD ensembles with superior optical properties and record-low photoluminescence linewidth were achieved. By systematically varying the growth parameters and working out a detailed analysis of the experimental data a range of parameter values, for which the formation of QDs is favored, was found. A qualitative explanation of the formation characteristics based on the surface migration of In ad-atoms is developed. Such tailored QDs are finally implemented as active region in a self-designed diode laser structure. A basic characterization of the static and temperature-dependent properties was carried out. The QD lasers exceed a reference quantum well laser in terms of inversion conditions and temperature-dependent characteristics. Pulsed output powers of several hundred milli watt were measured at room temperature. In particular, the lasers feature a high modal gain that even allowed cw-emission at room temperature of a processed ridge wave guide device as short as 340 µm with output powers of 17 mW. Modulation experiments performed at the Israel Institute of Technology (Technion) showed a complex behavior of the QDs in the laser cavity. Despite the fact that the laser structure is not fully optimized for a high-speed device, data transmission capabilities of 15 Gb/s combined with low noise were achieved. To the best of the author`s knowledge, this renders the lasers the fastest QD devices operating at 1.55 µm. The thesis starts with an introductory chapter that pronounces the advantages of optical fiber communication in general. Chapter 2 will introduce the fundamental knowledge that is necessary to understand the importance of the active region`s dimensions for the performance of a diode laser. The novel growth concept and its experimental analysis are presented in chapter 3. Chapter 4 finally contains the work on diode lasers.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Magnetic interactions between transition metal impurities and clusters mediated by low-dimensional metallic hosts: A first principles theoretical investigation

The magnetic properties and interactions between transition metal (TM) impurities and clusters in low-dimensional metallic hosts are studied using a first principles theoretical method. In the first part of this work, the effect of magnetic order in 3d-5d systems is addressed from the perspective of its influence on the enhancement of the magnetic anisotropy energy (MAE). In the second part, the possibility of using external electric fields (EFs) to control the magnetic properties and interactions between nanoparticles deposited at noble metal surfaces is investigated. The influence of 3d composition and magnetic order on the spin polarization of the substrate and its consequences on the MAE are analyzed for the case of 3d impurities in one- and two-dimensional polarizable hosts. It is shown that the MAE and easy- axis of monoatomic free standing 3d-Pt wires is mainly determined by the atomic spin-orbit (SO) coupling contributions. The competition between ferromagnetic (FM) and antiferromagnetic (AF) order in FePtn wires is studied in detail for n=1-4 as a function of the relative position between Fe atoms. Our results show an oscillatory behavior of the magnetic polarization of Pt atoms as a function of their distance from the magnetic impurities, which can be correlated to a long-ranged magnetic coupling of the Fe atoms. Exceptionally large variations of the induced spin and orbital moments at the Pt atoms are found as a function of concentration and magnetic order. Along with a violation of the third Hund’s rule at the Fe sites, these variations result in a non trivial behavior of the MAE. In the case of TM impurities and dimers at the Cu(111), the effects of surface charging and applied EFs on the magnetic properties and substrate-mediated magnetic interactions have been investigated. The modifications of the surface electronic structure, impurity local moments and magnetic exchange coupling as a result of the EF-induced metallic screening and charge rearrangements are analysed. In a first study, the properties of surface substitutional Co and Fe impurities are investigated as a function of the external charge per surface atom q. At large inter-impurity distances the effective magnetic exchange coupling ∆E between impurities shows RKKY-like oscillations as a function of the distance which are not significantly affected by the considered values of q. For distances r < 10 Å, important modifications in the magnitude of ∆E, involving changes from FM to AF coupling, are found depending non-monotonously on the value and polarity of q. The interaction energies are analysed from a local perspective. In a second study, the interplay between external EF effects, internal magnetic order and substrate-mediated magnetic coupling has been investigated for Mn dimers on Cu(111). Our calculations show that EF (∼ 1eV/Å) can induce a switching from AF to FM ground-state magnetic order within single Mn dimers. The relative coupling between a pair of dimers also shows RKKY-like oscillations as a function of the inter-dimer distance. Their effective magnetic exchange interaction is found to depend significantly on the magnetic order within the Mn dimers and on their relative orientation on the surface. The dependence of the substrate-mediated interaction on the magnetic state of the dimers is qualitatively explained in terms of the differences in the scattering of surface electrons. At short inter-dimer distances, the ground-state configuration is determined by an interplay between exchange interactions and EF effects. These results demonstrate that external surface charging and applied EFs offer remarkable possibilities of manipulating the sign and strength of the magnetic coupling of surface supported nanoparticles.

An O(N) Algorithm for Three-Dimensional N-Body Simulations

We develop an algorithm that computes the gravitational potentials and forces on N point-masses interacting in three-dimensional space. The algorithm, based on analytical techniques developed by Rokhlin and Greengard, runs in order N time. In contrast to other fast N-body methods such as tree codes, which only approximate the interaction potentials and forces, this method is exact ?? computes the potentials and forces to within any prespecified tolerance up to machine precision. We present an implementation of the algorithm for a sequential machine. We numerically verify the algorithm, and compare its speed with that of an O(N2) direct force computation. We also describe a parallel version of the algorithm that runs on the Connection Machine in order 0(logN) time. We compare experimental results with those of the sequential implementation and discuss how to minimize communication overhead on the parallel machine.

Multisensor Modeling Underwater with Uncertain Information

This thesis develops an approach to the construction of multidimensional stochastic models for intelligent systems exploring an underwater environment. It describes methods for building models by a three- dimensional spatial decomposition of stochastic, multisensor feature vectors. New sensor information is incrementally incorporated into the model by stochastic backprojection. Error and ambiguity are explicitly accounted for by blurring a spatial projection of remote sensor data before incorporation. The stochastic models can be used to derive surface maps or other representations of the environment. The methods are demonstrated on data sets from multibeam bathymetric surveying, towed sidescan bathymetry, towed sidescan acoustic imagery, and high-resolution scanning sonar aboard a remotely operated vehicle.

Three-Dimensional Motion Estimation Using Shading Information in Multiple Frames

A new formulation for recovering the structure and motion parameters of a moving patch using both motion and shading information is presented. It is based on a new differential constraint equation (FICE) that links the spatiotemporal gradients of irradiance to the motion and structure parameters and the temporal variations of the surface shading. The FICE separates the contribution to the irradiance spatiotemporal gradients of the gradients due to texture from those due to shading and allows the FICE to be used for textured and textureless surface. The new approach, combining motion and shading information, leads directly to two different contributions: it can compensate for the effects of shading variations in recovering the shape and motion; and it can exploit the shading/illumination effects to recover motion and shape when they cannot be recovered without it. The FICE formulation is also extended to multiple frames.