We will consider the scenario of the co-rotation of a fluid star (in specific, a neutron star) and a black hole. The neutron star (or primary)is assumed to have constant angular velocity. The tidal effects on the primary are investigated. First, the centrally condensed approximation is applied, where both bodies are considered as point sources. In the second treatment, the primary is treated as an incompressible and homogeneous fluid mass, which in addition to its own gravity is subject to centrifugal and Coriolis forces, derived from fluid motions. The black hole (or secondary) is treated as a rigid sphere and can be regarded as a point mass. The equilibrium figure is derived. The problem is then adapted to include vorticity and a pseudo-Newtonian potential. The coalescence of neutron star - black hole binaries and their importance to gravitational wave detection is also discussed. / Mathematical Sciences / M. Sc. (Applied Mathematics)

No description available.

In recent years, advances in deep optical, and especially deep near-infrared imaging with the Hubble Space Telescope (HST) and wide-field ground-based telescopes such as VISTA, have revolutionized our understanding of the cosmological evolution of galaxies and supermassive black-holes (as manifest through active galactic nuclei; AGN). In particular, the dynamic range provided by the survey `wedding cake' of available HST+ground-based optical/IR data offers new opportunities to push the meaningful statistical study of galaxy and AGN evolution out to high redshifts. Much recent attention has focused, unsurprisingly, on using these new data to push studies of galaxy formation back to within a billion years of the Big Bang, and exploring the role of young galaxies in driving cosmic hydrogen reionization during the crucial era corresponding to redshifts z ≃ 6-10. However, these data have not been as thoroughly exploited at intermediate redshifts, and have only recently been used to explore black-hole/AGN evolution. In this thesis I utilise the latest deep optical/near-infrared imaging and spectroscopy to explore three key facets of cosmological evolution. First, I present a new, robust measurement of the evolving rest-frame ultraviolet (UV) galaxy luminosity function (LF) over the key redshift range from z ≃ 2 to z ≃ 4. My results are based on the high dynamic range provided by combining the Hubble Ultra Deep Field (HUDF), CANDELS/GOODS-South, and UltraVISTA/COSMOS surveys. I utilise the unparalleled multi-frequency photometry available in this survey `wedding cake' to compile complete galaxy samples at z ≃ 2; 3; 4 via photometric redshifts (calibrated against the latest spectroscopy). This study is important as the peak of star-formation is shown to happen within a redshift range z = 2 - 4 and determining the exact epoch that the galaxies were forming most of their stars depends significantly on the UV luminosity density which requires robust measurements of the galaxy UV luminosity function and its accurate parameterization. My new determinations of the UV LF extend from M1500 ≃ -22 (AB mag) down to M1500 =-14.5, -15.5 and -16 at z ≃2, 3 and 4 respectively (thus reaching ≃ 3-4 magnitudes fainter than previous blank-field studies at z ≃ 2 - 3). At z ≃ 2 - 3 I find a much shallower faint-end slope (α = -1:32 ± 0:03) than the steeper values (α ≃ -1:7) reported in the literature, and show that this new measurement is robust. By z ≃ 4 the faint-end slope has steepened slightly, to α = -1:43 ± 0:04, and I show that these measurements are consistent with the overall evolutionary trend from z = 0 to z = 8. I then calculate the UV luminosity density (and hence unobscured star-formation density) and show that it peaks at z ≃ 2:5 - 3, when the Universe was ≃ 2:5 Gyr old. Second, I have used these data to revisit the possibility that X-ray AGN played a significant role in cosmic hydrogen reionization which is one of the major processes in the formation of the Universe we see today. Hence, it is really important to understand this phenomenon thoroughly by studying the properties of sources capable of ionising photons, such as star-forming galaxies and high redshift AGNs. Although most recent studies have suggested that the emerging population of young star-forming galaxies can bathe the Universe in sufficient high-energy photons to complete reionization by z ≃ 6, some authors have reasserted the potentially important role of high-redshift AGN in the hydrogen reionization process. In an effort to clarify this situation, I reinvestigate a claimed sample of 22 X-ray detected active galactic nuclei (AGN) at redshifts z > 4, which has reignited the debate as to whether young galaxies or AGN reionized the Universe. These sources lie within the GOODS-S/CANDELS field, and I examine both the robustness of the claimed X-ray detections (within the Chandra 4Ms imaging) and perform an independent analysis of the photometric redshifts of the optical/infrared counterparts. I confirm the reality of only 15 of the 22 reported X-ray detections, and moreover find that only 12 of the 22 optical/infrared counterpart galaxies actually lie robustly at z > 4. I recalculate the evolving far-UV (1500Å) luminosity density produced by AGN at high redshift, and find that it declines rapidly from z ≃ 4 to z ≃ 6, in agreement with several other recent studies of the evolving AGN luminosity function. The associated rapid decline in inferred hydrogen-ionizing emissivity contributed by AGN falls an order-of-magnitude short of the level required to maintain hydrogen ionization at z ≃ 6. I conclude that AGNs make a very minor contribution to cosmic hydrogen reionization. Finally, I have utilized the deep optical/near-infrared survey data to explore the prevalence of quenched/passive galaxies at high redshift. Applying a robust method to isolate passive galaxies from star-forming galaxies is the key to improving our understanding of the quenching process. Focusing primarily on the deep HUDF data-set, I have revisited the effectiveness of simple colour-colour (UVJ) selection techniques in isolating robust samples of quenched galaxies, and find that dust plays a more important role in this selection process than has been previously appreciated. Through careful SED fitting I successfully isolate a sample of apparently dust-free quiescent galaxies in the redshift range 0:5 < z < 4:5 but (at least in the HUDF) fail to find any galaxy which has remained truly quiescent for > 1 Gyr. I conclude by focusing on the properties of a refined/robust sample of apparently quenched galaxies at z > 3, and in particular establishing the contribution of quenched galaxies to stellar-mass density at early times. I conclude with a summary of my findings, and a brief discussion of the most promising avenues for future advances with the next generation of facilities, such as the James Webb Space Telescope (JWST).

Magister Scientiae - MSc / Solar energy generation arises as a result of direct conversion of sunlight into electricity a by solar cell; which is mainly made up of a semiconducting material incorporated into a system. It is emerging as one of the most reliable and cost efficient renewable energy sources. Within the solar field, organic bulk heterojunction photovoltaic cells have proved of being able to have a great impact in the future years; mainly due to the easy processability of the active layer and substrate, their cost effectiveness and above all, a good power conversion efficiency associated to the close 3-dimensional interpenetrating network that is generated from blending donor and acceptor semiconducting materials together in a bulk heterojunction active layer. In this research work, we therefore report on the study of a newly developed organic bulk heterojunction active layer based on a blend of a star-copolymer generation 1 poly(propylenethiophenoimine)-co-poly(ethylenedioxythiophene) (G1PPT-co-PEDOT) as donor material with N,N-diisopropylnaphthalene diimide (NDI) as acceptor material. Both materials were chemically synthesized. The synthesis of G1PPT-co-PEDOT started first by the functionalization of generation 1 poly(propyleneimine) tetramine, G1PPI into G1PPT by condensation reaction in the presence of 2-thiophene carboxaldehyde under Nitrogen gas followed by the copolymerization of G1PPT with ethylene dioxythiophene (EDOT) monomer in the presence of ammonium persulfate, (NH4)2S2O8 as oxidant. On the other hand, NDI was also synthesized via condensation reaction of 1,4,5,8-naphthalene tetracarboxylic dianhydride in the presence of two (2) equivalences of N,N-diisopropylamine at 110 oC overnight in DMF. Both materials were characterized using FT-IR, UV-Vis spectroscopy, Fluorescence spectroscopy, Voltammetry, HRSEM microscopy and XRD. Based on the cyclic voltammetry and UV-Vis results, we were able to calculate the HOMO, LUMO and band gap energy (Eg) values of both the donor and acceptor to be -4.03 eV, -6.287 eV and 2.25 eV for iii the donor G1PPT-co-PEDOT respectively and -4.302 eV, -7.572 eV and 3.27 eV for the acceptor respectively. From these results, the energy diagram for both donor and acceptor was drawn and it comes out that the separation between the HOMO of the donor and the LUMO of the acceptor ΔEg = 1.985 eV, the ideal value for a good donor-acceptor combination. Also the offset energy that is, the energy difference between the LUMO of the donor and the LUMO of the acceptor is 0.302 eV.

Este trabalho apresenta o resultado da aplicação do Método dos Volumes Finitos, adotado pelo software comercial Star-CCM+ na simulação para o regime permanente de escoamentos turbulentos incompressíveis e compressíveis sobre seções de aerofólios. Para o caso incompressível modelam-se seções do aerofólio NACA 0012 com ângulo de ataque zero. Para o caso compressível, uma seção do aerofólio supercrítico OAT15A em pequeno ângulo de ataque é modelada. Os domínios computacionais são discretizados por malhas não estruturadas de células poliédricas ou por malhas estruturadas de geração hiperbólica para diferentes topologias e parâmetros construtivos determinados pela estimativa de grandezas do fenômeno físico, como a altura da primeira camada de células quadrilaterais junto à parede. A qualidade e adequação dessas malhas para as simulações são verificadas por estudo de dependência quanto ao nível de refinamento e também quanto à posição do contorno onde o escoamento é livre no caso de escoamento compressível. Na metodologia de verificação, o índice de convergência de malha GCI e a ordem observada de convergência do método (dos Volumes Finitos) são obtidos para três níveis de refinamento com o propósito de selecionar uma malha de trabalho que concilie precisão e esforço computacional com os recursos disponíveis. As simulações são conduzidas para dois modelos de turbulência – o modelo Spalart-Allmaras e o modelo k-ω/SST. Os resultados obtidos pela aplicação desses modelos são interpretados sob o ponto de vista fenomenológico e comparados com os resultados experimentais disponíveis em literatura. / The Finite Volumes Method adopted by the commercial software Star-CCM+ is applied to the simulation of the steady state regime of incompressible and compressible turbulent flows over selected airfoil’s sections. The physical model used with the incompressible flow case is a NACA 0012 airfoil section at zero angle of attack. The ONERA’s OAT15A supercritical airfoil section at small angle of attack applies to the compressible flow case. The computational domains are discretized by structured and unstructured meshes for different topologies and far field configurations. The structured meshes are of the quadrilateral type with hyperbolic node distribution whilst the unstructured meshes use polyhedral cells. The grids are generated by applying a methodology where estimates of the flow variables are used as input for the grid’s constructive parameters like the near wall cell thickness. Grid dependency studies are carried out in order to verify the grid’s quality and suitability to represent the physical phenomena. The grid’s asymptotic convergence index GCI and its observed order of convergence are evaluated for three refinement levels and far field position for the compressible flow cases. The objective is to select the most suitable grid taking into account the accuracy requirements and the computational resources available. The one-equation Spalart-Allmaras turbulence model and the two-equation k-ω/SST turbulence models are used. The numerical results are discussed from the physical point of view and compared with the experimental ones available in literature.

Orientador: Prof. Dr. Vladislav Kupriyanov / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2015. / No presente trabalho estudamos as consequências físicas da não-comutatividade dependente da posição e rotacionalmente invariante em duas dimensões [x, y] = iq f (x2 + y2), usando a teoria de perturbações em mecânica quântica e considerando os modelos exatamente solúveis como o oscilador harmônico isotrópico e o problema de Landau. Nós demonstramos a consistência da abordagem proposta, em particular, derivamos a versão não-comutativa da equação de continuidade e mostramos que a probabilidade é conservada na nossa abordagem. Pesquisamos três formas gerais diferentes para a f (r): constante, monomial de r2 e exponencial Gaussiana. Obtendo resultados diversos de acordo com as características específicas de cada f (e. g. a potência do monomio, largura da Gaussiana). Para a maior parte das escolhas da f , temos encontrado quebra da degenerescência. / In the present work we study the physical consequences of the position dependent rotationally invariant noncommutativity in two dimensions [x, y] = iq f (x2 + y2), using the perturbation theory in quantum mechanics and considering the exactly solvable models in standard quantum mechanics: isotropic harmonic oscillator and Landau problem. We demonstrate the consistency of the proposed approach, in particular, we derive the noncommutative continuity equation and show that the probability is conserved in our approach. We investigate three different general forms of f (r): constant, monomial of r2 and Gaussian exponential. Obtaining diverse results according to specific characteristics of each f (e. g. monomial power and Gaussian width). Degeneracy breaking is found in most of the cases.

Este trabalho apresenta o resultado da aplicação do Método dos Volumes Finitos, adotado pelo software comercial Star-CCM+ na simulação para o regime permanente de escoamentos turbulentos incompressíveis e compressíveis sobre seções de aerofólios. Para o caso incompressível modelam-se seções do aerofólio NACA 0012 com ângulo de ataque zero. Para o caso compressível, uma seção do aerofólio supercrítico OAT15A em pequeno ângulo de ataque é modelada. Os domínios computacionais são discretizados por malhas não estruturadas de células poliédricas ou por malhas estruturadas de geração hiperbólica para diferentes topologias e parâmetros construtivos determinados pela estimativa de grandezas do fenômeno físico, como a altura da primeira camada de células quadrilaterais junto à parede. A qualidade e adequação dessas malhas para as simulações são verificadas por estudo de dependência quanto ao nível de refinamento e também quanto à posição do contorno onde o escoamento é livre no caso de escoamento compressível. Na metodologia de verificação, o índice de convergência de malha GCI e a ordem observada de convergência do método (dos Volumes Finitos) são obtidos para três níveis de refinamento com o propósito de selecionar uma malha de trabalho que concilie precisão e esforço computacional com os recursos disponíveis. As simulações são conduzidas para dois modelos de turbulência – o modelo Spalart-Allmaras e o modelo k-ω/SST. Os resultados obtidos pela aplicação desses modelos são interpretados sob o ponto de vista fenomenológico e comparados com os resultados experimentais disponíveis em literatura. / The Finite Volumes Method adopted by the commercial software Star-CCM+ is applied to the simulation of the steady state regime of incompressible and compressible turbulent flows over selected airfoil’s sections. The physical model used with the incompressible flow case is a NACA 0012 airfoil section at zero angle of attack. The ONERA’s OAT15A supercritical airfoil section at small angle of attack applies to the compressible flow case. The computational domains are discretized by structured and unstructured meshes for different topologies and far field configurations. The structured meshes are of the quadrilateral type with hyperbolic node distribution whilst the unstructured meshes use polyhedral cells. The grids are generated by applying a methodology where estimates of the flow variables are used as input for the grid’s constructive parameters like the near wall cell thickness. Grid dependency studies are carried out in order to verify the grid’s quality and suitability to represent the physical phenomena. The grid’s asymptotic convergence index GCI and its observed order of convergence are evaluated for three refinement levels and far field position for the compressible flow cases. The objective is to select the most suitable grid taking into account the accuracy requirements and the computational resources available. The one-equation Spalart-Allmaras turbulence model and the two-equation k-ω/SST turbulence models are used. The numerical results are discussed from the physical point of view and compared with the experimental ones available in literature.

The Great Observatories Origins Deep Survey North (GOODS-N) field, first surveyed by the HST, has been observed across numerous wavebands revealing populations of both Star Forming Galaxies (SFG) and Active Galactic Nuclei (AGN) over wide ranges of luminosities. It has been surmised that the evolution in the star forming population appears to diverge from that in the AGN population leading to a domination of SFGs at low flux densities. The number of starbursts can only be disentangled from the entire population if each source can be classified individually, which usually requires high angular resolution imaging. This is the motivation behind the e-MERLIN Galaxy Evolution survey, e-MERGE, which expands the depth of high resolution radio imaging in the GOODS-N field to increase the number of potentially classifiable sources. By use of wide-field imaging techniques, including a new high-speed mapping tool, together with a new semi-empirical primary beam-shape model for the e-MERLIN array, a deep wide-field high-resolution map is derived. This is the widest and deepest contiguous imaging yet obtained from e-MERLIN and JVLA observations, and yet contains less than 25% of the e-MERLIN data so far observed. The majority of the objects are shown to exhibit extended structure, and the angular size distribution place the median size around 1.2 arcsec, peaking between 0.5 and 0.7 arcsec. Automated algorithms are utilised to facilitate a new probabilistic classification tool based on multi-parameter correlations. 248 sources could be classified using the tool, each deriving a probability of AGN or SFG rather than forcing a binary category. Linear sizes of star-formation dominated sources are determined to lie in a range of 4 - 11 kpc, within the optical extent of galaxies. Differential source counting based on probabilistic classifications reveals that an increase in the luminosity evolution of SFGs is likely, although an apparent upturn in AGN may also exist to some lesser degree at low flux densities. The thesis establishes a clear roadmap for the remainder of the e-MERGE survey and a path to determine the star formation rate history of the Universe.

In the present work we study the problem of reconstructing a graph from its closed neighbourhood list. We will explore this problem, formulated by V. Sós, from the point of view of the fixed parameter complexity. We study the graph reconstruction problem in a more general setting, when the reconstructed graph is required to belong to some special graph class. In the present work we prove that this general problem lies in the complexity class FPT, when parametrized by the treewidth and maximum degree of the reconstructed graph, or by the number of certain special induced subgraphs if the reconstructed graph is 2-degenerate. Also, we prove that the graph reconstruction problem lies in the complexity class XP when parametrized by the vertex cover number. Finally, we prove mutual independence of the results

Neste trabalho nós estudamos alguns sistemas de spins e vértices exatamente solúveis em duas dimensões. A solubilidade exata está ligada ao fato de existirem soluções não triviais das equações de fatorização, o que nos permite obter a energia livre no limite termodinâmico. Introduzimos e resolvemos pelo método de espalhamento inverso, um modelo de dez vértices assimétrico com dois e três estados nas ligações. Obtemos o diagrama de fases e mostramos que o sistema exibe uma transição de fase de primeira ordem. Analisamos um modelo de oito vértices de férmions livres e propomos uma nova relação funcional que nos permite calcular a energia livre por vértice. Mostramos que este sistema de vértices corresponde ao modelo de Ising na rede Union Jack. Apresentamos um método de solução de modelos de spin em redes triangulares a partir da solução do mesmo modelo na rede quadrada. O método se aplica sempre que o modelo de spins envolver interação de primeiros vizinhos e satisfizer a relação triângulo-estrela. Estendemos para a rede triangular, as soluções autoduais de Fateev e Zamolodchikov para a rede quadrada, de modelos de spin com simetria Z(N). Analisamos as conjecturas existentes sobre a criticalidade do modelo de Potts definido na rede de Kagomé. Baseados na simetria e nas degenerescências dessa rede conjecturamos uma expressão para a sua linha crítica. / We study some spin and vertex systems which are exactly solvable in two dimensions. The exact solubility is connected to the existence of non trivial solutions of the factorization equations which allow us to determine the free energy in the thermodynamic limit. We introduce and solve by the inverse scattering method, a ten vertex model with two and three states on the links. We get the phase diagram of the system and show that it exhibits a first order phase transition. Analysing a free fermion eight vertex model, we propose a new functional relation which permit us to get the free energy per vertex. We also show that this system is equivalent to the Ising model in a Union Jack lattice. We present a method to solve spin models on triangular lattices from the known solution of the same model on square lattices. The method applies whenever the model involves first neighbours interactions and satisfies the star triangle relation. We extend to the triangular lattice the self dual solutions of Fateev and Zamolodchikov for Z(N) invariant spin systems. We also analyse the conjectures made before for the critical Potts model on a Kagomé lattice. Based on symmetry and on the collapses of this lattice we conjecture an expression for their critical line.