CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Nesta dissertaÃÃo, estudamos como se comporta o modelo do oscilador de Dirac, inserido em um sistema de dois nÃveis, ao interagir com o campo eletromagnÃtico externo, desconsiderando a quantizaÃÃo do campo (teoria semiclÃssica). Para tal, obtemos as funÃÃes de inversÃo de populaÃÃo de energia e de spin em trÃs situaÃÃes gerais: sem termos que violam a simetria de Lorentz; com a introduÃÃo de um termo CPT-Ãmpar que quebra a simetria vetorial de Lorentz; com a introduÃÃo de um termo CPT-Ãmpar que quebra a simetria de Lorentz por meio de um acoplamento axial. Em seguida, analisamos o caso especial da ressonÃncia entre o sistema e o campo incidente. Nesse caso, toda a influÃncia do oscilador de Dirac foi perdida e as funÃÃes de inversÃo de populaÃÃo de energia e de spin reduziram-se aos resultados encontrados na literatura cientÃfica.

In this thesis we are dealing with basic methods of theoretical physics focusing on quantum theory of gravity, that are: Hamilton-Dirac formalism for singular systems, Dirac`s method of quantizing systems with constraints and its mathematical formulation - refined algebraic quantization, representation of compact groups and representation of Lorentz group. We apply these methods to find eigenstates of Lorentz group and General linear group generators. We construct a physical Hilbert space on temporal part of 3+1 decomposition of Einstein-Cartan theory. Powered by TCPDF (www.tcpdf.org)

This diploma thesis is focused on preparation of perovskite methylammonium lead bromide thin film layers and also thin film layers of its precursors, namely methylammonium bromide and lead(II) bromide, by spin-coating from the solution; and optical characterisation of the prepared thin film layers by UV-VIS spectroscopy and spectroscopical ellipsometry. Methylammonium bromide does not absorb in visible nor ultraviolet region, the maximum absorption of lead(II) bromide occurred in ultraviolet region, methylammonium lead bromide absorbs in visible region. Optical band gaps were determined by Tauc method to (3,5 ± 0,1) eV for lead(II) bromide and 2,15 eV, respectively 2,25 eV for perovskite. Refractive indices and extinction coefficients were determined by ellipsometry in range of wavelengths from 290 nm to 830 nm and their dependence with layer thickness was discussed. Ellipsometry model used in this thesis consist on Tauc-Lorentz oscillators for methylammonium bromide, methylammonium lead bromide and partially for lead(II) bromide, which another part is formed by New Amorphous oscillator.

This work deals with modeling of progression of dielectric variables and mixture formulas for solution of properties of composite materials in dependency on frequency. Theoretical part of the work explains physical principles of polarisation mechanisms and influence on dielectric constant with changing temperature and frequency. In theoretical part processes inside the composite material, which is in electrical field are described. The work contains summary of mixture formulas and methods of their derivation. Program for use in education is a part of the work. It allows modelling of progression of dielectric variables in dependency on frequency and Cole-Cole circle diagram. In mixtures it allows modelling of frequency dependencies of dielectric constant in accordance to Maxwell's, Bőttcher's and Lichtenecker's mixture formulas.

Consider a domain Ω ⊂ RN with Lipschitz boundary and let d(x) = dist(x, ∂Ω). It is well known for p ∈ (1, ∞) that u ∈ W1,p 0 (Ω) if and only if u/d ∈ Lp (Ω) and ∇u ∈ Lp (Ω). Recently a new characterization appeared: it was proved that u ∈ W1,p 0 (Ω) if and only if u/d ∈ L1 (Ω) and ∇u ∈ Lp (Ω). In the author's bachelor thesis the condition u/d ∈ L1 (Ω) was weakened to the condition u/d ∈ L1,p (Ω), but only in the case N = 1. In this master thesis we prove that for N ≥ 1, p ∈ (1, ∞) and q ∈ [1, ∞) we have u ∈ W1,p 0 (Ω) if and only if u/d ∈ L1,q (Ω) and ∇u ∈ Lp (Ω). Moreover, we present a counterexample to this equivalence in the case q = ∞. 1

This thesis studies the volume of the unit ball of finite-dimensional Lorentz sequence spaces p,q n . Lorentz spaces are a generalisation of Lebesgue spaces with a quasinorm described by two parameters 0 < p, q ≤ ∞. The volume of the unit ball Bp,q n of a general finite-dimensional Lorentz space was so far an unknown quantity, even though for the Lebesgue spaces it has been well-known for many years. We present the explicit formula for Vol(Bp,∞ n ) and Vol(Bp,1 n ). We also describe the asymptotic behaviour of the n-th root of Vol(Bp,q n ) with respect to the dimension n and show that [Vol(Bp,q n )]1/n ≈ n−1/p for all 0 < p < ∞, 0 < q ≤ ∞. Furthermore, we study the ratio of Vol(Bp,∞ n ) and Vol(Bp n). We conclude by examining the decay of entropy numbers of embeddings of the Lorentz spaces.

The Lorentz group is a symmetry group on Minkowski space, and as such is central to studying the geometry of this and related spaces. The group therefore shows up also from physical considerations, such as trying to formulate quantum physics in anti-de Sitter space. In this thesis, the Lorentz group in 2+1 dimensions and its representations are investigated, and comparisons are made to the analogous rotation group. Firstly, all unitary irreducible representations are found and classified. Then, those representations are realised as the square-integrable, analytic functions on the unit circle and the unit disk, which turn out to correspond to the projective lightcone and the hyperbolic plane, respectively. Also, a way to realise a particular class of representations on 1+1-dimensional anti-de Sitter space is shown. / Lorentzgruppen är en symmetrigrupp på Minkowski-rum, och är således central för att studera geometrin i detta och relaterade rum. Gruppen dyker också därför upp från fysikaliska frågeställningar, såsom att försöka formulera kvantfysik i anti-de Sitter-rum. Denna uppsats undersöker Lorentzgruppen i 2+1 dimensioner och dess representationer, och jämför med den analoga rotationsgruppen. Först konstrueras och klassificeras alla unitära irreducibla representationer. Sedan realiseras dessa representationer som de analytiska funktioner på enhetscirkeln och enhetsskivan vars belopp i kvadrat är integrerbara. Det visar sig att denna cirkel respektive skiva svarar mot den projektiva ljuskonen respektive det hyperboliska planet. Dessutom visas att en särskild klass av representationer blir relevanta för att formulera kvantfysik i 1+1-dimensionellt anti-de Sitter-rum.

<p> Continuous Casting (CC) is an essential process in the steel industry to transform molten steel into solid product. This process begins with primary cooling (PC) where the molten steel is cooled, and the initial solidification begins. It is important to monitor the process of PC as defects such as thinning of the shell in the mold can lead to breakouts. Key parameters in PC are the mold design, casting condition, and steel composition. In the research conducted, key parameters for PC are investigated to analyze the impact on flow formation and solidification. To optimize mold design, angular taper to the narrow face can be employed to accommodate for any shell shrinkage. Utilizing computational fluid dynamics, a range of mold taper is simulated per the developed solidification model with defined temperature-dependent material properties. When simulated without a taper, significant air gap formation in the corners of the mold is visible due to thermal shrinkage of the shell. This air gap decreases the cooling rate due to the shell’s lack of contact with the cooling mold wall. A parametric study of mold taper ranging from no taper to 3° as well as change in casting conditions, superheat and casting speed, are conducted to analyze the impact of taper with respect to the casting conditions. Per the conditions applied, angular taper between 1° and 2° resulted into reduction of undercooling and overcooling in the corner of the mold which is subjected to cooling from the broad face and narrow face of the cool mold wall. The turbulent flow in the mold region was found to drastically influences the quality of steel produced during continuous casting. The flow itself can lead to surface defects or slag entrainment based on the formation. A high surface wave due to turbulence of the injected melt lead to fluctuations and the instability compromised the quality of the steel produced as well as entrained the slag. To regulate the flow, electromagnetic forces can be applied in the mold, dampening the local turbulent flow. As the electrically conductive molten steel interacts with the induced magnetic field, it reduced the velocity of the steel jet released from the ports of the submerged entry nozzle. Per the simulation-based study conducted increasing the EMBr strength from 2975G to 4350G reduced the peak surface wave height by 59.47% and volume of flux rate of decrease by 4.25%. Additionally, increasing the SEN depth from 110 mm to 350 mm increased the average wave height by 19% and volume of flux rate of decrease by 2.6%. Lastly, increasing the mold width from 1.067 m to 1.50m increased average wave height by 8.71% and volume of flux rate of decrease by 0.9%. </p>

No description available.

No description available.