Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.

Investigations on Nonlinear and Radiative Properties of Certain Phatonic Materials

Light in its physical and philosophical sense has captured the imagination of human mind right from the dawn of civilization. The invention of lasers in the 60’s caused a renaissance in the field of optics. This intense, monochromatic, highly directional radiation created new frontiers in science and technology. The strong oscillating electric field of laser radiation creates a. polarisation response that is nonlinear in character in the medium through which it passes and the medium acts as a new source of optical field with alternate properties. It was in this context, that the field of optoelectronics which encompasses the generation, modulation, transmission etc. of optical radiation has gained tremendous importance. Organic molecules and polymeric systems have emerged as a class of promising materials of optoelectronics because they offer the flexibility, both at the molecular and bulk levels, to optimize the nonlinearity and other suitable properties for device applications. Organic nonlinear optical media, which yield large third-order nonlinearities, have been widely studied to develop optical devices like high speed switches, optical limiters etc. Transparent polymeric materials have found one of their most promising applicationsin lasers, in which they can be used as active elements with suitable laser dyes doped in it. The solid-matrix dye lasers make possible combination of the advantages of solid state lasers with the possibility of tuning the radiation over a broad spectral range. The polymeric matrices impregnated with organic dyes have not yet widely used because of the low resistance of the polymeric matrices to laser damage, their low dye photostability, and low dye stability over longer time of operation and storage. In this thesis we investigate the nonlinear and radiative properties of certain organic materials and doped polymeric matrix and their possible role in device development

Inversão de momentos de fonte em métodos potenciais

A inversão de momentos de fonte gravimétrica tridimensional é analisada em duas situações. Na primeira se admite conhecer apenas a anomalia. Na segunda se admite conhecer, além da anomalia, informação a priori sobre o corpo anômalo. Sem usar informação a priori, mostramos que é possível determinar univocamente todo momento, ou combinação linear de momentos, cujo núcleo polinomial seja função apenas das coordenadas Cartesianas que definem o plano de medida e que tenha Laplaciano nulo. Além disso, mostramos que nenhum momento cujo núcleo polinomial tenha Laplaciano não nulo pode ser determinado. Por outro lado, informação a priori é implicitamente introduzida se o método de inversão de momentos se baseia na aproximação da anomalia pela série truncada obtida de sua expansão em multipolos. Dado um centro de expansão qualquer, o truncamento da série impõe uma condição de regularização sobre as superfícies equipotenciais do corpo anômalo, que permite estimar univocamente os momentos e combinações lineares de momentos que são os coeficientes das funções-bases da expansão em multipolos. Assim, uma distribuição de massa equivalente à real é postulada, sendo o critério de equivalência especificado pela condição de ajuste entre os campos observado e calculado com a série truncada em momentos de uma ordem máxima pré-estabelecida. Os momentos da distribuição equivalente de massa foram identificados como a solução estacionária de um sistema de equações diferenciais lineares de 1a. ordem, para a qual se asseguram unicidade e estabilidade assintótica. Para a série retendo momentos até 2a. ordem, é implicitamente admitido que o corpo anômalo seja convexo e tenha volume finito, que ele esteja suficientemente distante do plano de medida e que a sua distribuição espacial de massa apresente três planos ortogonais de simetria. O método de inversão de momentos baseado na série truncada (IMT) é adaptado para o caso magnético. Para este caso, mostramos que, para assegurar unicidade e estabilidade assintótica, é suficiente pressupor, além da condição de regularização, a condição de que a magnetização total tenha direção e sentido constantes, embora desconhecidos. O método IMT baseado na série de 2a. ordem (IMT2) é aplicado a anomalias gravimétricas e magnéticas tridimensionais sintéticas. Mostramos que se a fonte satisfaz as condições exigidas, boas estimativas da sua massa ou vetor momento de dipolo anômalo total, da posição de seu centro de massa ou de momento de dipolo e das direções de seus três eixos principais são obtidas de maneira estável. O método IMT2 pode falhar parcialmente quando a fonte está próxima do plano de medida ou quando a anomalia tem efeitos localizados e fortes de um corpo pequeno e raso e se tenta estimar os parâmetros de um corpo grande e profundo. Definimos por falha parcial a situação em que algumas das estimativas obtidas podem não ser boas aproximações dos valores verdadeiros. Nas duas situações acima descritas, a profundidade do centro da fonte (maior) e as direções de seus eixos principais podem ser erroneamente estimadas, embora que a massa ou vetor momento de dipolo anômalo total e a projeção do centro desta fonte no plano de medida ainda sejam bem estimados. Se a direção de magnetização total não for constante, o método IMT2 pode fornecer estimativas erradas das direções dos eixos principais (mesmo se a fonte estiver distante do plano de medida), embora que os demais parâmetros sejam bem estimados. O método IMT2 pode falhar completamente se a fonte não tiver volume finito. Definimos por falha completa a situação em que qualquer estimativa obtida pode não ser boa aproximação do valor verdadeiro. O método IMT2 é aplicado a dados reais gravimétricos e magnéticos. No caso gravimétrico, utilizamos uma anomalia situada no estado da Bahia, que se supõe ser causada por um batólito de granito. Com base nos resultados, sugerimos que as massas graníticas geradoras desta anomalia tenham sido estiradas na direção NNW e adelgaçadas na direção vertical durante o evento compressivo que causou a orogênese do Sistema de Dobramentos do Espinhaço. Além disso, estimamos que a profundidade do centro de massa da fonte geradora é cerca de 20 km. No caso magnético, utilizamos a anomalia de um monte submarino situado no Golfo da Guiné. Com base nos resultados, estimamos que o paleopolo magnético do monte submarino tem latitude 50°48'S e longitude 74°54'E e sugerimos que não exista contraste de magnetização expressivo abaixo da base do monte submarino.

Hard X-ray photoemission study of the Fabre salts (TMTTF)(2)X (X = SbF6 and PF6)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cyclically-arranged, storm-controlled, prograding lithosomes in Messinian terrigenous shelves (Bajo Segura Basin, western Mediterranean)

This work focuses on a Messinian shallow-marine terrigenous unit, termed the La Virgen Formation, which forms part of the sedimentary infill of the Bajo Segura Basin (Betic margin of the western Mediterranean). This formation was deposited during a high sea level phase prior to the onset of the Messinian Salinity Crisis. Stratigraphically, it comprises a prograding stack of sandstone lithosomes alternating with marly intervals (1st-order cyclicity). These lithosomes are characterized by a homoclinal geometry that tapers distally, and interfinger with pelagic sediments rich in planktonic and benthic microfauna (Torremendo Formation). An analysis of sedimentary facies of each lithosome reveals a repetitive succession of sandy storm beds (tempestites), occasionally amalgamated, which are separated by thin marly layers (2nd-order cyclicity). Each storm bed contains internal erosional surfaces (3rd-order cyclicity) that delimit sets of laminae. Two categories of storm beds have been differentiated. The first one includes layers formed below storm wave base (SWB), characterized by traction structures associated to unidirectional flows (scoured base, planar lamination, and parting lineation). The second category consists of layers deposited above the SWB which display typical high regime oscillatory flow structures (swaley and hummocky cross lamination). In both cases, the ichnological record is characterized by an oligotypic association of Ophiomorpha nodosa, which can be interpreted as the result of allochthonous tracemakers (crustaceans) transported during storm events together with the sediment. The benthic microfauna in the marly intervals that separate the sandstone lithosomes (1st-order cyclicity) indicates that the storm ebb surges were deposited at depths ranging from those of inner shelf settings (with Elphidium spp. and Cibicides lobatulus) to those of outer shelf (with Valvulineria complanata and Uvigerina cylindrica). At the distal end of the sandstone lithosomes, the planktonic microfauna is characterized by a high content of taxa indicative of warm-oligotrophic waters (Globigerinoides obliquus and Globigerinoides bulloideus). In contrast, in the marly intervals, the microfauna is dominated by species typical of cold-eutrophic waters (Globigerina and Neogloboquadrina). This alternation of planktic foraminiferal assemblages is interpreted as being the expression of climatic cycles, in which every episode of progradation of tempestite-dominated lithosomes corresponds to maximum insolation and warm waters, whereas episodes of marly deposition correspond to minimal insolation and cold waters. The 1st-order cyclicity recorded in the La Virgen Formation, in a context of terrigenous storm-dominated shelf, corresponds to sapropel/homogeneous marl cycles formed in a pelagic basin (Torremendo Fm). These cycles in pelagic sediments are commonplace throughout the Mediterranean during the Messinian and reflect precession orbital changes: repeated periods of maximum insolation – minimum precession (sapropels) and minimal insolation – maximum precession (homogeneous marls). The fact that the example of terrigenous unit studied herein is coetaneous with the well-developed reef complexes in the Mediterranean basins points out the importance of sediment supply in the formation of large-scale sandy lithosomes. This is a crucial aspect to understanding reservoir genesis as well as lateral stratigraphic relationships with potential seal and/or source rocks.

Advanced fibre gratings fabricated in standard and infrared glass fibres by ultraviolet and near-infrared-femtosecond lasers

In this thesis, I describe studies on fabrication, spectral characteristics and applications of tilted fibre gratings (TFGs) with small, large and 45° tilted structures and novel developments in fabrication of fibre Bragg gratings (FBGs) and long period gratings (LPGs) in normal silica and mid-infrared (mid-IR) glass fibres using near-IR femtosecond laser. One of the major contributions presented in this thesis is the systematic investigation of structures, inscription methods and spectral, polarisation dependent loss (PDL) and thermal characteristics of TFGs with small (<45°), large (>45°) and 45° tilted structures. I have experimentally characterised TFGs, obtaining relationships between the radiation angle, central wavelength of the radiation profile, Bragg resonance and the tilt angle, which are consistent with theoretical simulation based on the mode-coupling theory. Furthermore, thermal responses have been measured for these three types of TFGs, showing the transmission spectra of large and 45° TFGs are insensitive to the temperature change, unlike the normal and small angle tilted FBGs. Based on the distinctive optical properties, TFGs have been developed into interrogation system and sensors, which form the other significant contributions of the work presented in this thesis. The 10°-TFG based 800nm WDM interrogation system can function not just as an in-fibre spectrum analyser but also possess refractive index sensing capability. By utilising the unique polarisation properties, the 81 °-TFG based sensors are capable of sensing the transverse loading and twisting with sensitivities of 2.04pW/(kg/m) and 145.90pW/rad, repectively. The final but the most important contribution from the research work presented in this thesis is the development of novel grating inscription techniques using near-IR femtosecond laser. A number of LPGs and FBGs were successfully fabricated in normal silica and mid-IR glass fibres using point-by-point and phase-mask techniques. LPGs and 1st and 2nd order FBGs have been fabricated in these mid-IR glass fibres showing resonances covering the wavelength range from 1200 to 1700nm with the strengths up to 13dB. In addition, the thermal and strain sensitivities of these gratings have been systematically investigated. All the results from these initial but systematic works will provide useful function characteristics information for future fibre grating based devices and applications in mid-IR range.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Full-dimensional analytical ab initio potential energy surface of the ground state of HOI

Extensive ab initio calculations using a complete active space second-order perturbation theory wavefunction, including scalar and spin-orbit relativistic effects with a quadruple-zeta quality basis set were used to construct an analytical potential energy surface (PES) of the ground state of the [H, O, I] system. A total of 5344 points were fit to a three-dimensional function of the internuclear distances, with a global root-mean-square error of 1.26 kcal mol(-1). The resulting PES describes accurately the main features of this system: the HOI and HIO isomers, the transition state between them, and all dissociation asymptotes. After a small adjustment, using a scaling factor on the internal coordinates of HOI, the frequencies calculated in this work agree with the experimental data available within 10 cm(-1). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3615545]

Coherent molecular solitons in Bose-Einstein condensates

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEG, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output. [S0031-9007(98)07283-4].

Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments

We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic chi((2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze superchemistry dynamics.

Quantitative analysis of the time courses of enzyme-catalyzed reactions

The catalytic properties of enzymes are usually evaluated by measuring and analyzing reaction rates. However, analyzing the complete time course can be advantageous because it contains additional information about the properties of the enzyme. Moreover, for systems that are not at steady state, the analysis of time courses is the preferred method. One of the major barriers to the wide application of time courses is that it may be computationally more difficult to extract information from these experiments. Here the basic approach to analyzing time courses is described, together with some examples of the essential computer code to implement these analyses. A general method that can be applied to both steady state and non-steady-state systems is recommended. (C) 2001 academic Press.

Efficient Implementation Of A Single-Precision Floating-Point Arithmetic Unit on FPGA

This paper presents a single precision floating point arithmetic unit with support for multiplication, addition, fused multiply-add, reciprocal, square-root and inverse squareroot with high-performance and low resource usage. The design uses a piecewise 2nd order polynomial approximation to implement reciprocal, square-root and inverse square-root. The unit can be configured with any number of operations and is capable to calculate any function with a throughput of one operation per cycle. The floatingpoint multiplier of the unit is also used to implement the polynomial approximation and the fused multiply-add operation. We have compared our implementation with other state-of-the-art proposals, including the Xilinx Core-Gen operators, and conclude that the approach has a high relative performance/area efficiency. © 2014 Technical University of Munich (TUM).

Hierarchical wrinkling on elastometric Janus spheres

Hierarchical wrinkling on elastomeric Janus spheres is permanently imprinted by swelling, for different lengths of time, followed by drying the particles in an appropriate solvent. First-order buckling with a spatial periodicity (lambda(11)) of the order of a few microns and hierarchical structures comprising of 2nd order buckling with a spatial periodicity (lambda(12)) of the order of hundreds of nanometers have been obtained. The 2nd order buckling features result from a Grinfeld surface instability due to the diffusion of the solvent and the presence of sol molecules.

The three main marine depositional cycles of the Neogene of Portugal

The present work follows a stratigraphic model for the marine Neogene of Portugal based on the definition of three main marine sedimentary cycles. Conceptually the I, II and III Neogene Cycles can be defined as 2nd order sedimentary sequences with duration ranging from 5 to 8 Ma. The I Neogene Cycle is fully represented only in the Lower Tagus Basin. Ranging from the Early Aquitanian to the Late Burdigalian the I Neogene Cycle testify a transgressive episode in the region of Lisbon and Setúbal Peninsula. Rapid lateral facies variations suggest a shallowmarine basin. This cycle ends with an important Late Burdigalian tectonic compressive event expressed by uplift of the surrounding areas and deformation affecting the Early Miocene deposits of the Arrábida Chain. The II Neogene Cycle includes thick sedimentary sequences covering Paleozoic and Mesozoic formations in the Algarve and Alvalade-Melides regions and it extends as far north as Santarém in the Lower Tagus Basin. Mainly controlled by global eustasy, it was generated by the important positive eustatic trend that characterized the Middle Miocene worldwide to which the Portuguese continental margin acted more or less passively. This cycle ended with a second and the most important compression event starting after the end of the Serravallian affecting the entire Portuguese onshore and shelf areas. This led to an important depositional hiatus of marine sediments for more than 2.5 Ma. During the Early and the Middle Tortonian occurred the clockwise rotation of the Guadalquivir Basin. The thickmarine units deposited afterwards in this basin produced a litostatic load, which seems to have induced subsidence farther west resuming the Neogene marine sedimentation in the Cacela region (Eastern Algarve), during the Late Tortonian. This marks the beginning of the III Neogene Cycle. To the north, in the Sado Basin (Alvalade-Melides region), a similar depositional sequence starts its sedimentation during the Messinian. Further north, in the Pombal-Caldas da Rainha region, marine sedimentation started during the Late Pliocene (Piacenzian). The migration in time, from south to north for the beginning of the marine sedimentation of this cycle is interpreted as reflecting a visco-elastic propagation of the deformation from the Betic chain northwards.

An RF LC Q-enhanced CMOS iter using integrated inductors with layout optimization

Dissertação apresentada para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia