Development of orientation during electrospinning of fibres of poly(ε-caprolactone)

We explore the influence of a rotating collector on the internal structure of poly(ε-caprolactone) fibres electrospun from a solution in dichloroethane. We find that above a threshold collector speed, the mean fibre diameter reduces as the speed increases and the fibres are further extended. Small-angle and wide-angle X-ray scattering techniques show a preferred orientation of the lamellar crystals normal to the fibre axis which increases with collector speed to a maximum and then reduces. We have separated out the processes of fibre alignment on the collector and the orientation of crystals within the fibres. There are several stages to this behaviour which correspond to the situations (a) where the collector speed is slower than the fibre spinning rate, (b) the fibre is mechanically extended by the rotating collector and (c) where the deformation leads to fibre fracture. The mechanical deformation leads to a development of preferred orientation with extension which is similar to the prediction of the pseudo-affine deformation model and suggests that the deformation takes place during the spinning process after the crystals have formed.

A wide-angle X-ray study of the development of molecular orientation in crosslinked natural rubber

Molecular orientation parameters have been measured for the non-crystalline component of crosslinked natural rubber samples deformed in uniaxial tension as a function of the extension ratio and of temperature. The orientation parapeters 〈P2(cosα)〉 and 〈P4(cosα)〉 were obtained by an analysis of the anisotropy of the wide-angle X-ray scattering functions. For the measurements made at high temperatures the level of crystallinity detected was negligible and the orientation-strain behaviour could be compared directly with the predictions of molecular models of rubber elasticity. The molecular orientation behaviour with strain was found to be at variance with the estimates of the affine model particularly at low and moderate strains. Extension of the crosslinked rubber at room temperature led to strain-crystallization and measurements of both the molecular orientation of the non-crystalline chains and the degree of crystallinity during extension and relaxation enabled the role of the crystallites in the deformation process to be considered in detail. The intrinsic birefringence of the non-crystalline component was estimated, through the use of the 〈P2(cosα)〉 values obtained from X-ray scattering measurements, to be 0.20±0.02.

Coupling between mesogenic units and polymer backbone in side-chain liquid crystal polymers and elastomers

The levels of alignment of the mesogenic units and of the polymer backbone trajectory for polyacrylate based nematic side-chain liquid crystal polymers and elastomers were evaluated by using wide angle X-ray and small angle neutron scattering procedures. The X-ray scattering measurements show that substantial levels of preferred orientation of the mesogenic units may be introduced through magnetic fields for uncrosslinked polymers and through mechanical extension for liquid crystal elastomers. Small angle neutron scattering measurements show that for highly aligned samples an anisotropic polymer backbone trajectory is observed in which the envelope is slightly extended by ∼ 10% in the direction parallel to the axis of alignment of the mesogenic units. The sense of this coupling differs from that recorded for other uncrosslinked side-chain liquid crystal polymers. Possible mechanisms to account for this anisotropy and its relationship to the properties of liquid crystal elastomers are discussed. The observed deformation behaviour of the liquid crystal elastomer is non-affine and this appears to confirm the dominating influence of the liquid crystal order of the side chains on the mechanical properties of these novel networks.

The determination of molecular orientation in uniaxially compressed PMMA by X-ray scattering

A procedure is presented for obtaining full molecular orientation information from wide angle X-ray scattering patterns of deformed non-crystalline polymers. The method is based on the analysis of experimental and calculated scattering patterns into their spherical harmonics. The results obtained for PMMA are compared with values predicted by the pseudo affine and affine deformation schemes.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

An ASIFT-based local registration method for satellite imagery

Imagery registration is a fundamental step, which greatly affects later processes in image mosaic, multi-spectral image fusion, digital surface modelling, etc., where the final solution needs blending of pixel information from more than one images. It is highly desired to find a way to identify registration regions among input stereo image pairs with high accuracy, particularly in remote sensing applications in which ground control points (GCPs) are not always available, such as in selecting a landing zone on an outer space planet. In this paper, a framework for localization in image registration is developed. It strengthened the local registration accuracy from two aspects: less reprojection error and better feature point distribution. Affine scale-invariant feature transform (ASIFT) was used for acquiring feature points and correspondences on the input images. Then, a homography matrix was estimated as the transformation model by an improved random sample consensus (IM-RANSAC) algorithm. In order to identify a registration region with a better spatial distribution of feature points, the Euclidean distance between the feature points is applied (named the S criterion). Finally, the parameters of the homography matrix were optimized by the Levenberg–Marquardt (LM) algorithm with selective feature points from the chosen registration region. In the experiment section, the Chang’E-2 satellite remote sensing imagery was used for evaluating the performance of the proposed method. The experiment result demonstrates that the proposed method can automatically locate a specific region with high registration accuracy between input images by achieving lower root mean square error (RMSE) and better distribution of feature points.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

Horo-tight spheres in hyperbolic space

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

The Bullough-Dodd model coupled to matter fields

The Bullough-Dodd model is an important two-dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac-Moody algebra A(2)((2)). The one- and two-soliton solutions as well as the breathers are constructed explicitly. We also consider integrable extensions of the Bullough-Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using a hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons. (C) 2008 Elsevier B.V. All rights reserved.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Term structure dynamics and no-arbitrage under the Taylor rule

A determinação da taxa de juros estrutura a termo é um dos temas principais da gestão de ativos financeiros. Considerando a grande importância dos ativos financeiros para a condução das políticas econômicas, é fundamental para compreender a estrutura que é determinado. O principal objetivo deste estudo é estimar a estrutura a termo das taxas de juros brasileiras, juntamente com taxa de juros de curto prazo. A estrutura a termo será modelado com base em um modelo com uma estrutura afim. A estimativa foi feita considerando a inclusão de três fatores latentes e duas variáveis ​​macroeconômicas, através da técnica Bayesiana da Cadeia de Monte Carlo Markov (MCMC).

Essays in macroeconomics and public finance

Esta tese dedica-se ao estudo dos sistemas tributários. Eu investigo como um sistema tributário afeta as escolhas dos indivíduos e consequentemente os recursos do país. Eu mostro como um sistema tributário induz as escolhas das pessoas, determinado assim as alocações de trabalho, produto e consumo da economia. No primeiro e segundo capítulo eu examino a taxação sobre os indivíduos, enquanto que no terceiro e quarto capítulos analiso a incidîncia tributária sobre os diferentes agentes da sociedade. No capítulo um, eu examino o sistema tributário ótimo, seguindo Mirrlees (1971) e Saez (2001). Eu mostro como seria este sistema tributário no Brasil, país com profunda desigualdade de renda entre os indivíduos. Ademais, eu investigo o sistema tributário afim, considerado uma alternativa entre os sistemas atual e o ótimo. No segundo capítulo eu analiso o sistema tributário conhecido como sacríficio igual. Mostro como o sistema tribuária derivado por Young (1987), redesenhado por Berliant and Gouveia (1993), se comporta no teste de eficiência derivado por Werning (2007). No terceiro e quarto capítulo eu examino como propostas de reforma tribuária afetariam a economia brasileira. No capítulo três investigo como uma reforma tributária atingiria as diferentes classes socias. No capítulo quatro, eu estudo as melhores direções para uma reforma tributária no Brasil, mostrando qual arranjo de impostos é menos ineficiente para o país. Por fim, investigo os efeitos de duas propostas de reforma tributária sobre a economia brasileira. Explicito quais os ganhos de produto e bem estar de cada proposta. Dedico especial atenção aos ganhos/perdas de curto prazo, pois estes podem inviabilizar uma reforma tributária, mesmo esta gerando ganhos de longo prazo.