Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

Branes and supersymmetric quantum field theories

Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories.

One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don’t know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories.

First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.

Cosmological consequences of dark matter interactions and vacuum fluctuations

This thesis is divided into two parts: interacting dark matter and fluctuations in cosmology. There is an incongruence between the properties that dark matter is expected to possess between the early universe and the late universe. Weakly-interacting dark matter yields the observed dark matter relic density and is consistent with large-scale structure formation; however, there is strong astrophysical evidence in favor of the idea that dark matter has large self-interactions. The first part of this thesis presents two models in which the nature of dark matter fundamentally changes as the universe evolves. In the first model, the dark matter mass and couplings depend on the value of a chameleonic scalar field that changes as the universe expands. In the second model, dark matter is charged under a hidden SU(N) gauge group and eventually undergoes confinement. These models introduce very different mechanisms to explain the separation between the physics relevant for freezeout and for small-scale dynamics.

As the universe continues to evolve, it will asymptote to a de Sitter vacuum phase. Since there is a finite temperature associated with de Sitter space, the universe is typically treated as a thermal system, subject to rare thermal fluctuations, such as Boltzmann brains. The second part of this thesis begins by attempting to escape this unacceptable situation within the context of known physics: vacuum instability induced by the Higgs field. The vacuum decay rate competes with the production rate of Boltzmann brains, and the cosmological measures that have a sufficiently low occurrence of Boltzmann brains are given more credence. Upon further investigation, however, there are certain situations in which de Sitter space settles into a quiescent vacuum with no fluctuations. This reasoning not only provides an escape from the Boltzmann brain problem, but it also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere during slow-roll inflation, suggesting that eternal inflation is much less common than often supposed. Instead, decoherence occurs during reheating, so this analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation.

Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

Lattice anomalies and magnetic states in Fe_5Si_3-Mn_5Si_3 alloys

The lattice anomalies and magnetic states in the (Fe_100-xMn_x)₅Si₃ alloys have been investigated. Contrary to what was previously reported, results of x-ray diffraction show a second phase (α') present in Fe-rich alloys and therefore strictly speaking a complete solid solution does not exist. Mössbauer spectra, measured as a function of composition and temperature, indicate the presence of two inequivalent sites, namely 6(g) site (designated as site I) and 4(d) (site II). A two-site model (TSM) has been introduced to interpret the experimental findings. The compositional variation of lattice parameters a and c, determined from the x-ray analysis, exhibits anomalies at x = 22.5 and x = 50, respectively. The former can be attributed to the effect of a ferromagnetic transition; while the latter is due to the effect of preferential substitution between Fe and Mn atoms according to TSM.

The reduced magnetization of these alloys deduced from magnetic hyperfine splittings has been correlated with the magnetic transition temperatures in terms of the molecular field theory. It has been found from both the Mössbauer effect and magnetization measurements that for composition 0 ≤ x ˂ 50 both sites I and II are ferromagnetic at liquid-nitrogen temperature and possess moments parallel to each other. In the composition range 50 ˂ x ≤ 100 , the site II is antiferromagnetic whereas site I is paramagnetic even at a temperature below the bulk Néel temperatures. In the vicinity of x = 50 however, site II is in a state of transition between ferromagnetism and antiferromagnetism. The present study also suggests that only Mn in site II are responsible for the antiferromagnetism in Mn₅Si₃ contrary to a previous report.

Electrical resistance has also been measured as a function of temperature and composition. The resistive anomalies observed in the Mn-rich alloys are believed to result from the effect of the antiferromagnetic Brillouin zone on the mobility of conduction electrons.

Analysis on the spin reorientation of GdFeCo/DyFeCo exchange-coupled double-layer films

In this paper, GdFeCo/DyFeCo exchange-coupled double-layer films used for center aperture type magnetically induced super resolution were investigated through experiments and theoretical calculation. The samples were prepared by magnetron sputtering method. The polar Kerr effect was measured to prove the spin reorientation of the readout layer. Theoretical study of magnetization profiles was performed on the basis of the mean-field theory and the continuum model. The theoretical results showed that the magnetization orientation of the readout layer changed gradually from in-plane to out-of-plane with the rise of the temperature. Theoretical analysis explained the experimental results successfully. (c) 2005 Elsevier B.V. All rights reserved.

Síntese e estudo das propriedades luminescentes do SrGa2O4 dopado com íons de Cr3+

Amostras policristalinas de Sr(Ga1-xCrx)2O4 com x = 0,01 foram estequiometricamente preparadas pela mistura dos materiais em pó SrCO3, Ga2O3 e Cr2O3. A estrutura cristalina da amostra dopada foi analisada pelas medidas de difração de raios-X. O padrão de difração revelou uma única fase relacionada a fase monoclínica do SrGa2O4. Os dados foram ajustados usando o Método de Rietveld para refinamento de estruturas e os parâmetros da rede foram determinados. A luminescência do íon de Cr3+ na rede do SrGa2O4 foi investigada pelas espectroscopias de excitação e emissão a temperatura ambiente, através das quais verificamos que os íons de Cr3+ estão localizados em dois sítios diferentes. Os espectros de emissão apresentam bandas largas associadas à transição eletrônica 4T2(4F) → 4A2(4F) para ambos os sítios. Estes resultados são analisados pela teoria de campo cristalino e o parâmetro de campo cristalino Dq e os parâmetros de Racah B e C são determinados pelas posições das bandas de excitação. A partir destes parâmetros determinamos um campo cristalino forte para ambos os sítios. Além disto, foram realizadas medidas de espectroscopia fotoacústica que confirmaram as transições identificadas e estimadas nos espectros de excitação.

Possible antigravity regions in F (R) theory?

We construct an F(R) gravity theory corresponding to the Weyl invariant two scalar field theory. We investigate whether such F (R) gravity can have the antigravity regions where the Weyl curvature invariant does not diverge at the Big Bang and Big Crunch singularities. It is revealed that the divergence cannot be evaded completely but can be much milder than that in the original Weyl invariant two scalar field theory. (C) 2014 The Authors. Published by Elsevier B.V.

Caracterização óptica e estrutural de materiais isolantes dopados com metais de transição do grupo do ferro

O objetivo deste trabalho foi a investigação das propriedades ópticas e estruturais de materiais isolantes contendo metais de transição do grupo do ferro como impurezas substitucionais. As técnicas usadas para o estudo de amostras MgGa2O4, MgGa2O4 + B- Ga2O3 e ZnGa2O4 dopadas com Cr3+e Fe3+ foram: fotoluminescência, excitação, difração de raios-X, espalhamento de nêutrons, método de Rietveld para o refinamento da estrutura e espectroscopia fotoacústica. Estas técnicas permitem a determinação da coordenação do sítio impureza, a atribuição das transições de energia, o cálculo dos parâmetros de energia e a determinação de propriedades cristalográficas. As amostras apresentam largas bandas de energia nas regiões do visível e do infravermelho. Estas transições indicam a relevância deste estudo pelo interesse tecnológico na obtenção de novos materais com bandas sintonizáveis. No primeiro capítulo apresentamos uma introdução à teoria de campo cristalino. No segundo capítulo apresentamos medidas de fotoluminescência e excitação do MgGa2O4 dopado com 0,1, 0,5, 1,0 e 5,0 % de Cr3+ a 77 K e temperatura ambiente. No terceiro capítulo usamos fotoluminescência, excitação, espalhamento de nêutrons, difração de raios X, fotoacústica e método de refino de Rietveld para analisar o sistema MgGa2O4 + B-Ga2O3 contendo 0,1, 0,5, 1,0 e 5,0 % de Cr3+. No quarto capítulo mostramos resultados de fotoacústica para o ZnGa2O4 dopado com 5% e 10% de Fe3+.

Processos estocásticos em teoria de campos e aplicação ao universo inflacionário

É conhecido que derivações microscópicas obtidas através de métodos de teoria quântica de campos (TQC) podem conduzir a complicadas equações de movimento (EdM) que possuem um termo dissipativo com memória e um termo de ruído colorido. Um caso particularmente interessante é o modelo que escreve a interação entre um sistema e um banho térmico a temperatura T. Motivado por isso, usamos uma prescrição que nos permite reescrever EdMs não-markovianas semelhantes as obtidas em TQC em termos de um sistema de equações locais, para então confrontarmos a solução desse sistema com a solução aproximada usada correntemente na literatura, a chamada aproximação markoviana. A pergunta chave a qual se pretende responder aqui é: dado um conjunto de parâmetros que descrevem o modelo, a aproximação markoviana é suficientemente boa para descrever a dinâmica do sistema se comparada a dinâmica obtida atravéS da EdM não-markoviana? Além disso, consideramos uma versão linear da ELG de forma que pudéssemos determinar o nível de confiança da nossa metodologia numérica, procedimento este realizado comparando-se a solução analítica com a solução numérica. Como exemplo de aplicação prática do tema discutido aqui, comparamos a evolução não-markoviana do inflaton com a evolução markoviana do mesmo num modelo de universo primordial denominado inflação não-isentrópica (warm inflation).

Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field.

We investigate the evolution of localized blobs of swirling or buoyant fluid in an infinite, inviscid, electrically conducting fluid. We consider the three cases of a strong imposed magnetic field, a weak imposed magnetic field, and no magnetic field. For a swirling blob in the absence of a magnetic field, we find, in line with others, that the blob bursts radially outward under the action of the centrifugal force, forming a thin annular vortex sheet. A simple model of this process predicts that the vortex sheet thins exponentially fast and that it moves radially outward with constant velocity. These predictions are verified by high-resolution numerical simulations. When an intense magnetic field is applied, this phenomenon is suppressed, with the energy and angular momentum of the blob now diffusing axially along the magnetic field lines, converting the blob into a columnar structure. For modest or weak magnetic fields, there are elements of both types of behavior, with the radial bursting dominating over axial diffusion for weak fields. However, even when the magnetic field is very weak, the flow structure is quite distinct to that of the nonmagnetic case. In particular, a small but finite magnetic field places a lower bound on the thickness of the annular vortex sheet and produces an annulus of counter-rotating fluid that surrounds the vortex core. The behavior of the buoyant blob is similar. In the absence of a magnetic field, it rapidly develops the mushroomlike shape of a thermal, with a thin vortex sheet at the top and sides of the mushroom. Again, a simple model of this process predicts that the vortex sheet at the top of the thermal thins exponentially fast and rises with constant velocity. These predictions are consistent with earlier numerical simulations. Curiously, however, it is shown that the net vertical momentum associated with the blob increases linearly in time, despite the fact that the vertical velocity at the front of the thermal is constant. As with the swirling blob, an imposed magnetic field inhibits the formation of a vortex sheet. A strong magnetic field completely suppresses the phenomenon, replacing it with an axial diffusion of momentum, while a weak magnetic field allows the sheet to form, but places a lower bound on its thickness. The magnetic field does not, however, change the net vertical momentum of the blob, which always increases linearly with time.

Does the orbital degeneracy play any role in the high thermopower of lamellar cobaltites?

This article investigates the role of the CoO6 octahedron distortion on the electronic properties and more particularly on the high value of the Seebeck coefficient in the BiCaCoO lamellar cobaltites. Our measurements provide clues indicating that the t2g orbital degeneracy lifting has to be considered to account for the observed high temperature limit of the thermopower. They also provide experimental arguments for locating the a1g and eg′ orbitals levels on the energy scale, through the compression of the octahedron. These results are in agreement with recent ab initio calculation including the electronic correlations and concluding for the inversion of these levels as compared to the expectation from the crystal field theory. © 2007 American Institute of Physics.

High resolution direct measurement of temperature distribution in silicon nanophotonics devices.

Following the miniaturization of photonic devices and the increase in data rates, the issues of self heating and heat removal in active nanophotonic devices should be considered and studied in more details. In this paper we use the approach of Scanning Thermal Microscopy (SThM) to obtain an image of the temperature field of a silicon micro ring resonator with sub-micron spatial resolution. The temperature rise in the device is a result of self heating which is caused by free carrier absorption in the doped silicon. The temperature is measured locally and directly using a temperature sensitive AFM probe. We show that this local temperature measurement is feasible in the photonic device despite the perturbation that is introduced by the probe. Using the above method we observed a significant self heating of about 10 degrees within the device.

Fabrication and analysis of 2x2 thermo-optic SOI waveguide switch with low power consumption and fast response by anisotropy chemical etching

A low power consumption 2 x 2 thermo-optic switch with fast response was fabricated on silicon-on-insulator by anisotropy chemical etching. Blocking trenches were etched on both sides of the phase-shifting arms to shorten device length and reduce power consumption. Thin top cladding layer was grown to reduce power consumption and switching time. The device showed good characteristics, including a low switching power of 145 mW and a fast switching speed of 8 +/- 1 mus, respectively. Two-dimensional finite element method was applied to simulate temperature field in the phase-shifting arm instead of conventional one-dimensional method. According to the simulated result, a new two-dimensional index distribution of phase-shifting arm was determined. Consequently finite-difference beam propagation method was employed to simulate the light propagation in the switch, and calculate the power consumption as well as the switching speed. The experimental results were in good agreement with the theoretical estimations. (C) 2004 Elsevier B.V. All rights reserved.