Finite-length armchair graphene nanoribbons can behave as one dimensional topological materials, that may show edge states in their zigzag-terminated edges, depending on their width and termination. We show here a full solution of Tight-Binding graphene rectangles of any length and width that can be seen as either finite-length armchair or zigzag ribbons. We find exact analytical expressions for both bulk and edge eigen-states and eigen-energies. We write down exact expressions for the Coulomb interactions among edge states and introduce a Hubbard-dimer model to analyse the emergence and features of different magnetic states at the edges, whose existence depends on the ribbon length. We find ample room for experimental testing of our predictions in N = 5 armchair ribbons. We compare the analytical results with ab initio simulations to benchmark the quality of the dimer model and to set its parameters. A further detailed analysis of the ab initio Hamiltonian allows us to identify those variations of the Tight-Binding parameters that affect the topological properties of the ribbons.

We analyse the electrical response of narrow graphene nanogaps in search for transport signatures stemming from spin-polarized edge states. We find that the electrical transport across graphene nanogaps having perfectly defined zigzag edges does not carry any spin-related signature. We also analyse the magnetic and electrical properties of nanogaps whose electrodes have wedges that possibly occur in the currently fabricated nanogaps. These wedges can host spin polarized wedge low-energy states due to the bipartite nature of the graphene lattice. We find that these spin-polarized low-energy modes give rise to low-voltage signatures in the differential conductance and to distinctive features in the stability diagrams. These are caused by fully spin-polarized currents.

The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the ground-state exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. Many exact results, limits, and expansions about those limits are given in the Appendices.

Resumen del trabajo presentado al March Meeting of the American Physical Society, celebrado en New Orleans, Louisiana (USA) del 13 al 17 de marzo de 2017.

Resumen del trabajo presentado al American Physical Society March Meeting, celebrado en San Antonio, Texas (USA) del 2 al 6 de marzo de 2015.

This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.

Refractory wear and skull growth on the hearth walls and the bottom of the blast furnace have been researched. A series of thermocouples were installed in the hearth, and the temperature measurements were recorded in a structured query language every minute. A heat transfer model was used to study the temperature evolution and hearth wear profile using a commercial software package (MATLAB version 5.0) based on computational fluid dynamics. The location of the 1150 degrees C isotherm in the hearth lining has been calculated. An online monitoring tool was used to analyse the temperature distribution in the hearth and offers, to the plant operators, periodic information on the refractory state. Electromotive force (EMF) probes were installed in the hearth to estimate the variations in the liquid level in the hearth and to determine the thermal state (TS) evolution. Good correlation is seen between EMF and TS, and the EMF amplitudes in the different tapholes follow and even precede the local TS.

We analyze the low-voltage transport response of large molecular wires bridging graphene electrodes, where the molecules are physisorbed onto the graphene sheets by planar anchor groups. In our study, the sheets are pulled away to vary the gap length and the relative atomic positions. The molecular wires are also translated in directions parallel and perpendicular to the sheets. We show that the energy position of the Breit-Wigner molecular resonances is universal for a given molecule, in the sense that it is independent of the details of the graphene edges, gaps lengths, or of the molecule positions. We discuss the need to converge carefully the $k$ sampling to provide reasonable values of the conductance.

We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single-and double-site versions of the Anderson, Hubbard, and spinless fermion models. The exact exchange and correlation potentials keep the full nonlocal dependence on electron occupations. The analytic expressions allow us to compare the Kohn-Sham eigenstates of exact density functional theory with the many-body quasiparticle states of these correlated-electron systems. The exact Kohn-Sham spectrum describes correctly many of the nontrivial features of the many-body quasiparticle spectrum such as, for example, the precursors of the Kondo peak. However, we find that some pieces of the quasiparticle spectrum are missing because the many-body phase space for electron and hole excitations is richer.

We present an ab-initio analysis of the impact of edge shape and graphene-molecule anchor coupling on the electronic and transport functionalities of graphene-based molecular electronics devices. We analyze how Fano-like resonances, spin filtering and negative differential resistance effects may or may not arise by modifying suitably the edge shapes and the terminating groups of simple organic molecules. We show that the spin filtering effect is a consequence of the magnetic behavior of zigzag-terminated edges, which is enhanced by furnishing these with a wedge shape. The negative differential resistance effect is originated by the presence of two degenerate electronic states localized at each of the atoms coupling the molecule to graphene which are strongly affected by a bias voltage. The effect could thus be tailored by a suitable choice of the molecule and contact atoms if edge shape could be controlled with atomic precision.

We present a theoretical study of the magnetic properties of dicyclopentadienyl metallocene and phthalocyanine molecules, that contain the transition metal atoms M = Fe, Co, Ni, Cu, Zn, Ir, Pt and Au. Our most important prediction is that gold and copper molecules are magnetic. We find that the magnetism of these molecules is fairly unconventional: the gold atom itself is weakly magnetic or even non-magnetic. Its role is rather to induce magnetism in the surrounding carbon and nitrogen atoms, producing a sort of spin density wave.

The blast furnace is a countercurrent reactor in which a reducing gas is produced by coke gasification with the oxygen blown in via tuyeres. The reducing gas flows upwards, reducing the iron ores charged at the top of the furnace. It is a very complex process with many influencing and correlating factors. Its productivity is the quotient between possible gas throughput per unit of time and required specific gas generation for 1 tonne of hot metal obtained, and its permeability is a measure of the gas ability to pass through the bed of solid materials. The objective of 'high levels of injection of pulverised coal' is not only compatible with productivity, but also even necessary to increase blast furnace productivity. In this sense the helium tracing technique consists of injecting He at the tuyeres with its arrival at the blast furnace top being detected by a mass spectrometer. With this measurement it is possible to define the transfer time as the delay between the injection moment and the time when the helium concentration reaches 10% of the maximum detected level. Calculated variables from the measurements allow a concise characterisation of the blast furnace state. These gas transfer measurements can be considered as a new tool to evaluate the state of a furnace at a specific moment. The main advantage will be that by employing only one measurement it will be possible to evaluate the furnace state.

In the frame of this project two types of measurements were performed. While CRM, SIDMAR and CORUS focused on doing only transfer time measurements in order to characterize the radial gas distribution, ARCELOR RESEARCH, TKS and ACERALIA performed also concentration measurements aiming at detecting cross-flows and at assessing the BF shaft permeability. Both types of measurements seem to be able to give valuable information regarding the gas distribution of the furnace and could be complementary to each other. Helium tracing was developed as a more reliable tool for monitoring the gas distribution in a blast furnace, enabling to make gas transfer time measurements more continuously available. However, helium tracing was not the tool we expected. As lots of BF measurements helium tracing is not a sufficient tool to monitor the gas distribution in the blast furnace, giving all the information needed by the operator with a sufficient reliability and accuracy. It has to be regarded has a supplementary tool. Lack of consistency of the measurements makes that an advisory tool could not be well developed, so the assessment of the BF shaft permeability is rather poor / difficult. Making use of the He tracing measurements require a long term investigation. Also several R&D techniques were developed during this project: tuyere injection with uptake detection to look for gas distribution asymmetries, two tracing gases technique (TTGT), gas injection at different tuyeres, shaft injection and tuyere probe injection. All these techniques seem to give valuable information but to fully understand their significance more research is needed.

EMF in a blast furnace can be used to predict liquid level variations into the hearth. After the strong influence of some process parameters has been minimized, the variation of the EMF at the end of consecutive castings can be used as a criterion of liquid level variations. Currently this criterion is integrated in a mathematical model that sends messages to an on-line advisory tool.

At the beginning of the project the main emphasis was laid on the definition of the process requirements and on preliminary work in the labs and in the plants. In order to achieve the main objective of this project, online laser measurements of alkalis, zinc and lead in blast furnace top gas using the LIBS technique (Laser Induced Breakdown Spectroscopy), a measuring concept was developed that met all requirements of the partners involved. This included the design of a housing for the measuring equipment, a mechanical measuring probe and a laser measuring probe for laser measurements in different positions inside the top-gas pipes of the blast furnace plants. This was carried out in agreement with all partners and with special respect to the different constructional features of the 3 blast furnace plants involved, the requirements of the laser measuring technique itself as well as to saftey items during the measurements. The structure of the top gas pipes and the location of existing platforms were the main criteria for selecting the measuring sites. With this in mind, ThyssenKrupp Stahl (TKS-CS) chose BF #2 in Schwelgern and Rautaruukki Oyj (RR) BF #2 at Rautaruukki's Raahe steelworks. Aceralia (ACER) had the choice between BF A or B. In accordance with the measuring concept, the blast furnace plants prepared openings at the top gas pipes and verified the periphery which was necessary for the measurements, e.g. connections for electricity, gas and water supply. At the Institute of Ferrous Metallurgy of the RWTH Aachen (IEHK) a literature survey concerning the circulating elements in the blast furnace was carried out. The influence process of sodium, potassium, zinc, and lead on the blast furnaces were described. Laboratory rigs were set up at the research institutes IEHK, Fraunhofer Institut Lasertechnik (ILT) and the Institute of Electronic Structure & Laser of FORTH (IELS/FORTH) in order to prepare and to support the measurements in the blast furnace plants. The verification of the measuring method, the limits of detection of the elements and the measurement of calibration curves were of major importance here. Measurements were performed on reference materials as well as on different blast furnace flue dust samples which were provided by the steel plants. Different process conditions, e.g. gas velocity and pressure, particle density and gas composition and its influence on the detection of the elements of interest were investigated. The examination of the influence of the top gas pressure on the detection lines of the elements was of special interest and led to the use of a laser system with double pulse option by ILT. With the aid of laboratory experiments, the most prominent detection lines of the elements Na, K, Zn and Pb were established. Under the guidance of ILT a data pool containing all relevant technical data of the laser measuring equipment was compiled to specify the measuring equipment housing in agreement with all partners. Further investigations were carried out by ILT to determine the parameters for the design of the laser measuring probe and in particular of the measuring head. Most of the components of the laser measuring apparatus were specified and tested in the laboratory. The measuring concept which had been defined in the previous phase, was realised. TKS-CS set up the housing for the measuring equipment and constructed the mechanical measuring probe. In order to verify the functional suitability of the measuring system before starting the experiments at the blast furnace, a laboratory simulation rig was set up. This rig simulated a section of the blast furnace top gas pipe and allowed the examination of the original components under similar conditions to the blast furnace. First tests were made in order to test the handling of the movable probe when different pressures in the "top-gas pipe" are adjusted. Further on, the gas tightness of valves and stuffing boxes was examined.