Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Self-sustained clusters and ergodicity breaking in spin models

Self-sustained spin clusters are analytically linked to ergodicity breaking in fully connected Ising and Sherrington-Kirkpatick (SK) models, relating the less understood spin space to the well understood state space. This correspondence is established through the absence of clusters in the paramagnetic phase, the presence of one dominant cluster in the Ising ferromagnet, and the formation of nontrivial clusters in SK spin glass. Yet unobserved phenomena are also revealed such as a first order phase transition in cluster sizes in the SK ferromagnet. The method could be adapted to investigate other spin models. © 2013 American Physical Society.

[Fe(μ-btzmp)2(btzmp)2](ClO4)2:a doubly-bridged 1D spin-transition bistetrazole-based polymer showing thermal hysteresis behaviour

The reaction of btzmp (1,2-bis(tetrazol-1-yl)-2-methylpropane) with Fe(ClO4)2 generates a 1D polymeric species, [Fe(μ-btzmp)2(btzmp)2](ClO4)2, showing a steep spin transition (T½↑ = 136 K and T ½↓ = 133 K) with a 3 K thermal hysteresis. The crystal structure at 100 and 200 K reveals that, in contrast to other bistetrazole based spin-transition systems such as [Fe(endi)3](BF4)2 and [Fe(btzp)3](ClO4)2, the present compound has only two ligands bridging the metallic centres, while the other two coordination positions are occupied by two mono-coordinated (non-bridging) btzmp ligands. This peculiarity confers an unprecedented crystal packing in the series of 1D bistetrazole based polymers. The change in spin state is accompanied by an order/disorder transition of the ClO4- counterion. A careful examination of the structural changes occurring upon the spin transition indicates that this order/disorder is most likely affected by the modification of the [tetrazole-centroid]-ND-Fe angle (which is typical of bistetrazole spin-transition materials). Apart from X-ray analysis, also magnetic susceptibility, Mössbauer and UV-vis spectroscopies have been used to characterise the HS and the LS states of [Fe(µ-btzmp)2(btzmp)2](ClO4)2. © The Royal Society of Chemistry.

Insights into the influence of solvent polarity on the crystallization of poly(ethylene oxide) spin-coated thin films via in situ grazing incidence wide-angle X-ray scattering

Controlling polymer thin-film morphology and crystallinity is crucial for a wide range of applications, particularly in thin-film organic electronic devices. In this work, the crystallization behavior of a model polymer, poly(ethylene oxide) (PEO), during spin-coating is studied. PEO films were spun-cast from solvents possessing different polarities (chloroform, THF, and methanol) and probed via in situ grazing incidence wide-angle X-ray scattering. The crystallization behavior was found to follow the solvent polarity order (where chloroform < THF < methanol) rather than the solubility order (where THF > chloroform > methanol). When spun-cast from nonpolar chloroform, crystallization largely followed Avrami kinetics, resulting in the formation of morphologies comprising large spherulites. PEO solutions cast from more polar solvents (THF and methanol) do not form well-defined highly crystalline morphologies and are largely amorphous with the presence of small crystalline regions. The difference in morphological development of PEO spun-cast from polar solvents is attributed to clustering phenomena that inhibit polymer crystallization. This work highlights the importance of considering individual components of polymer solubility, rather than simple total solubility, when designing processing routes for the generation of morphologies with optimum crystallinities or morphologies.

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

A facile spin-cast route for cation exchange of multilayer perpendicularly-aligned nanorod assemblies

A facile spin cast route was developed to convert perpendicularly aligned nanorod assemblies of cadmium chalcogenides into their silver and copper analogues. The assemblies are rapidly cation exchanged without affecting either the individual rod dimensions or collective superlattice order extending over several multilayers.

Non-Gaussian distribution of collective operators in quantum spin chains

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions. Interestingly, we show that the distributions for different system sizes collapse on thesame curve after scaling for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii–Kosterlitz–Thouless type. We propose and analyse the feasibility of an experimental reconstruction of the distribution using light–matter interfaces for atoms in optical lattices or in optical resonators.

Research-based spin-offs as agents of knowledge dissemination: evidence from the analysis of innovation networks

The paper addresses the role played by research-based spin-offs (RBSOs) as knowledge dissemination mechanisms, through their position in knowledge networks. For this purpose the paper analyses the formal networks established by the Portuguese RBSOs in the context of publicly funded research, technology and pre-commercial product development projects, and investigates their configuration along two levels. At organisational level, in order to understand whether RBSOs extend their reach beyond the academic sphere; and if they do, whether they relate with similar firms or connect to organisations located downstream in the knowledge value chain, and which is their position in networks involving both research organisations and other firms. At spatial level, in order to understand whether RBSOs extend their reach beyond the region where they are created, thus potentially acting as connectors between diverse regions. The analysis starts from the population of RBSOs created in Portugal until 2007 (387) and identifies those that have established formal technological relationships as part of projects funded by all the programmes launched in the period 1993-2012. As a result, the analysis encompasses 192 collaborative projects and involves 82 spin-offs and 281 partners, of which only 20% are research organisations, the remaining being other firms and a variety of other user organisations. The results, although still preliminary, provide some insights into the knowledge networking behaviour of the RBSOs. As expected, research organisations are a central actor in spin-offs’ networks, being the sole partner for some of them. But half of the RBSOs have moved beyond the academic sphere, being frequently a central element in tripartite technological relationships between research and other organisations and occupying an intermediation position in the network, thus potentially acting as facilitators in knowledge circulation and transformation. Also as expected, RBSOs are predominantly located in the main metropolitan areas and tend to relate with organisations similarly located. But while geographical proximity emerges as important in the choice of partners, in about half of the cases, RBSOs knowledge networks have extended beyond regional boundaries. Given their central position in the network this suggests a role as connectors across regions that will be explored in subsequent research.

Research-based spin-offs as agents of knowledge dissemination: evidence from the analysis of innovation networks

The paper addresses the role played by research-based spin-offs (RBSOs) as knowledge dissemination mechanisms, through their position in knowledge networks. For this purpose the paper analyses the formal networks established by Portuguese RBSOs, in the context of publicly funded research, technology and pre-commercial product development projects, and investigates their configuration across two levels. At organisational level, in order to understand whether RBSOs extend their reach beyond the academic sphere; and if they do, whether they connect to organisations located downstream in the knowledge value chain, and which is their position in networks involving both research organisations and other firms. At spatial level, in order to understand whether RBSOs extend their reach beyond the region where they are created, thus potentially acting as connectors between diverse regions. The analysis starts from the population of RBSOs created in Portugal until 2007 (327 firms) and identifies those that have established formal technological relationships, as part of projects funded by all the relevant programmes launched in the period 1993-2012. As a result, the analysis encompasses 192 collaborative projects and involves 82 spin-offs and 281 partners, of which only 20% are research organisations, the remaining being other firms and a variety of other downstream organisations. The results, although still preliminary, provide some insights into the knowledge networking behaviour of the RBSOs. As expected, research organisations are a central actor in spin-offs’ networks, being the sole partner for some of them. But half of the RBSOs have moved beyond the academic sphere, being frequently a central element in tripartite technological relationships between research and other organisations, and occupying an intermediation position in the network, thus potentially acting as facilitators in knowledge circulation and transformation. Also as expected, RBSOs are predominantly located in the main metropolitan areas and tend to relate with organisations similarly located. But while geographical proximity emerges as important in the choice of partners, in about half of the cases, RBSOs knowledge networks have extended beyond regional boundaries. Given their central position in the network, this suggests a role as connectors across regions that will be explored in subsequent research.

Thermal activation, long-range ordering, and topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, are ubiquitous in nature and display many rich phenomena and novel physics. Artificial spin ices (ASIs), arrays of lithographically patterned Ising-like single-domain magnetic nanostructures, are highly tunable systems that have proven to be a novel method for studying the effects of frustration and associated properties. The strength and nature of the frustrated interactions between individual magnets are readily tuned by design and the exact microstate of the system can be determined by a variety of characterization techniques. Recently, thermal activation of ASI systems has been demonstrated, introducing the spontaneous reversal of individual magnets and allowing for new explorations of novel phase transitions and phenomena using these systems. In this work, we introduce a new, robust material with favorable magnetic properties for studying thermally active ASI and use it to investigate a variety of ASI geometries. We reproduce previously reported perfect ground-state ordering in the square geometry and present studies of the kagome lattice showing the highest yet degree of ordering observed in this fully frustrated system. We consider theoretical predictions of long-range order in ASI and use both our experimental studies and kinetic Monte Carlo simulations to evaluate these predictions. Next, we introduce controlled topological defects into our square ASI samples and observe a new, extended frustration effect of the system. When we introduce a dislocation into the lattice, we still see large domains of ground-state order, but, in every sample, a domain wall containing higher energy spin arrangements originates from the dislocation, resolving a discontinuity in the ground-state order parameter. Locally, the magnets are unfrustrated, but frustration of the lattice persists due to its topology. We demonstrate the first direct imaging of spin configurations resulting from topological frustration in any system and make predictions on how dislocations could affect properties in numerous materials systems.

ENZYME-FREE UBIQUITIN LIGATION. FROM NATIVE CHEMICAL LIGATION AND SPIN LABELING TO DIMERIZATION BY INTER-UBIQUITIN MIMICKING LINKAGE AND PH-DEPENDENT CONFORMATIONAL SWITCH

The delicate balance between the production and disposal of proteins is vital for the changes required in the cell to respond to given stimulus. Ubiquitination is a protein modification with a range of signaling outcomes when ubiquitin is attached to a protein through a highly ordered enzymatic cascade process. Understanding ubiquitination is a growing field and nowadays the application of chemical reactions allows the isolation of quantitative materials for structural studies. Therefore, in this dissertation it is described some of these suitable chemical methodologies to produce an isopeptide bond toward the polymerization of ubiquitin bypassing the enzymatic control with the purpose of showing if these chemical modifications have a direct impact on the structure of ubiquitin. First, the possibility of incorporating non-natural lysine analogs known as mercaptolysines into the polypeptide chain of Ubiquitin was explored when they were attached to ubiquitin by native chemical ligation at its C terminus. The sulfhydryl group was used for the attachment of a paramagnetic label to map the surface of ubiquitin. Second, the condensation catalyzed by silver nitrate was used for the dimer assembly. In particular, the main focus was on examining whether orthogonal protection and deprotection of each monomer have an impact on the reaction yield, since the synthetic strategy has been previously attempted successfully. Third, the formation of ubiquitin dimers was approached by building an inter-ubiquitin linkage mimicking the isopeptide bond with two approaches, the classic disulfide exchange as well as the thiol-ene click reaction by thermal initiation in aqueous conditions. After assembling the dimeric units, they were studied by Nuclear Magnetic Resonance, in order to establish a conformational state profile which depends on the pH conditions. The latter is a very important concept since some ligands have a preferred affinity when the protein-protein hydrophobic patches are in close proximity.

Venture Capital for University Spin-Outs Companies in the context of University-based Entrepreneurial Ecosystems: an International Comparison

The objectives are, firstly, to identify the role of the university-focused intermediaries, specifically University-focused Venture Capital Firms (UVCs), in order to explain how they interact at the early stage of University Spin-out Companies (USOs) creation, particularly regarding knowledge sharing. Secondly, to analyse whether they change their position once the USO is developed, in the context of the dynamics of a university-based entrepreneurial ecosystem.

Critical behavior of the three-dimensional Ising spin glass

We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L520) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a KosterlitzThouless phase transition. Precise values for the ν and ƞ critical exponents are also presented.

Effects of spin on high-energy radiation from accreting black holes

Observations of jets in X-ray binaries show a correlation between radio power and black hole spin. This correlation, if confirmed, points toward the idea that relativistic jets may be powered by the rotational energy of black holes. In order to examine this further, we perform general relativistic radiative transport calculations on magnetically arrested accretion flows, which are known to produce powerful jets via the Blandfordâ Znajek (BZ) mechanism. We find that the X-ray and γ-ray emission strongly depend on spin and inclination angle. Surprisingly, the high-energy power does not show the same dependence on spin as the BZ jet power, but instead can be understood as a redshift effect. In particular, photons observed perpendicular to the spin axis suffer little net redshift until originating from close to the horizon. Such observers see deeper into the hot, dense, highly magnetized inner disk region. This effect is largest for rapidly rotating black holes due to a combination of frame dragging and decreasing horizon radius. While the X-ray emission is dominated by the near horizon region, the near-infrared (NIR) radiation originates at larger radii. Therefore, the ratio of X-ray to NIR power is an observational signature of black hole spin.