Estudo da estabilidade do movimento rotacional de satélites artificiais com variáveis canônicas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some remarks on the attractor behaviour in ELKO cosmology

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Métrica para definição de pontos estáveis utilizando-se da Análise de Robustez no posicionamento por ponto preciso

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A new approach on the stability analysis in ELKO cosmology

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite’s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical length is dynamically equivalent to the perturbation produced by an oblate central body on a mass-point satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite?s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical dimension is dynamically equivalent to the perturbation produced by an oblate central body on a masspoint satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Universal duality in a Luttinger liquid coupled to a generic environment

We study a Luttinger liquid (LL) coupled to a generic environment consisting of bosonic modes with arbitrary density-density and current-current interactions. The LL can be either in the conducting phase and perturbed by a weak scatterer or in the insulating phase and perturbed by a weak link. The environment modes can also be scattered by the imperfection in the system with arbitrary transmission and reflection amplitudes. We present a general method of calculating correlation functions under the presence of the environment and prove the duality of exponents describing the scaling of the weak scatterer and of the weak link. This duality holds true for a broad class of models and is sensitive to neither interaction nor environmental modes details, thus it shows up as the universal property. It ensures that the environment cannot generate new stable fixed points of the renormalization group flow. Thus, the LL always flows toward either conducting or insulating phase. Phases are separated by a sharp boundary which is shifted by the influence of the environment. Our results are relevant, for example, for low-energy transport in (i) an interacting quantum wire or a carbon nanotube where the electrons are coupled to the acoustic phonons scattered by the lattice defect; (ii) a mixture of interacting fermionic and bosonic cold atoms where the bosonic modes are scattered due to an abrupt local change of the interaction; (iii) mesoscopic electric circuits.

Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

I. Singular perturbation problems involving singular points and turning points. II. On the averaged Lagrangian technique for nonlinear dispersive waves

In Part I a class of linear boundary value problems is considered which is a simple model of boundary layer theory. The effect of zeros and singularities of the coefficients of the equations at the point where the boundary layer occurs is considered. The usual boundary layer techniques are still applicable in some cases and are used to derive uniform asymptotic expansions. In other cases it is shown that the inner and outer expansions do not overlap due to the presence of a turning point outside the boundary layer. The region near the turning point is described by a two-variable expansion. In these cases a related initial value problem is solved and then used to show formally that for the boundary value problem either a solution exists, except for a discrete set of eigenvalues, whose asymptotic behaviour is found, or the solution is non-unique. A proof is given of the validity of the two-variable expansion; in a special case this proof also demonstrates the validity of the inner and outer expansions.

Nonlinear dispersive wave equations which are governed by variational principles are considered in Part II. It is shown that the averaged Lagrangian variational principle is in fact exact. This result is used to construct perturbation schemes to enable higher order terms in the equations for the slowly varying quantities to be calculated. A simple scheme applicable to linear or near-linear equations is first derived. The specific form of the first order correction terms is derived for several examples. The stability of constant solutions to these equations is considered and it is shown that the correction terms lead to the instability cut-off found by Benjamin. A general stability criterion is given which explicitly demonstrates the conditions under which this cut-off occurs. The corrected set of equations are nonlinear dispersive equations and their stationary solutions are investigated. A more sophisticated scheme is developed for fully nonlinear equations by using an extension of the Hamiltonian formalism recently introduced by Whitham. Finally the averaged Lagrangian technique is extended to treat slowly varying multiply-periodic solutions. The adiabatic invariants for a separable mechanical system are derived by this method.

An Arbitrary Lagrangian Eulerian Method for Three-Phase Flows with Triple Junction Points

We present a moving mesh method suitable for solving two-dimensional and axisymmetric three-liquid flows with triple junction points. This method employs a body-fitted unstructured mesh where the interfaces between liquids are lines of the mesh system, and the triple junction points (if exist) are mesh nodes. To enhance the accuracy and the efficiency of the method, the mesh is constantly adapted to the evolution of the interfaces by refining and coarsening the mesh locally; dynamic boundary conditions on interfaces, in particular the triple points, are therefore incorporated naturally and accurately in a Finite- Element formulation. In order to allow pressure discontinuity across interfaces, double-values of pressure are necessary for interface nodes and triple-values of pressure on triple junction points. The resulting non-linear system of mass and momentum conservation is then solved by an Uzawa method, with the zero resultant condition on triple points reinforced at each time step. The method is used to investigate the rising of a liquid drop with an attached bubble in a lighter liquid.

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

Non-periodic quasi-stable nonlinear optical carrier pulses with sliding chirp-free points for transmission at 40 Gbit/s rate

In this paper, we demonstrate the possibility of reaching a quasi-stable nonlinear transmission regime with carrier pulses of 12.5 ps width in multi-channel 40 Gbit/s systems. The quasi-stable pulses that are presented in this work for the first time are not dispersion-managed solitons, and are indeed supported by a large normal span average dispersion and misbalanced optical amplification, and representing a new type of nonlinear carrier.

Use of 3D visualisation to enhance groundwater stable isotope data and its interpretation, Lockyer Valley, southeast Queensland

The use of stable isotope ratios δ18O and δ2H are well established in assessment of groundwater systems and their hydrology. The conventional approach is based on x/y plots and relation to various MWL’s, and plots of either ratio against parameters such as Clor EC. An extension of interpretation is the use of 2D maps and contour plots, and 2D hydrogeological vertical sections. An enhancement of presentation and interpretation is the production of “isoscapes”, usually as 2.5D surface projections. We have applied groundwater isotopic data to a 3D visualisation, using the alluvial aquifer system of the Lockyer Valley. The 3D framework is produced in GVS (Groundwater Visualisation System). This format enables enhanced presentation by displaying the spatial relationships and allowing interpolation between “data points” i.e. borehole screened zones where groundwater enters. The relative variations in the δ18O and δ2H values are similar in these ambient temperature systems. However, δ2H better reflects hydrological processes, whereas δ18O also reflects aquifer/groundwater exchange reactions. The 3D model has the advantage that it displays borehole relations to spatial features, enabling isotopic ratios and their values to be associated with, for example, bedrock groundwater mixing, interaction between aquifers, relation to stream recharge, and to near-surface and return irrigation water evaporation. Some specific features are also shown, such as zones of leakage of deeper groundwater (in this case with a GAB signature). Variations in source of recharging water at a catchment scale can be displayed. Interpolation between bores is not always possible depending on numbers and spacing, and by elongate configuration of the alluvium. In these cases, the visualisation uses discs around the screens that can be manually expanded to test extent or intersections. Separate displays are used for each of δ18O and δ2H and colour coding for isotope values.

Preparation and thermal energy storage properties of paraffin/calcined diatomite composites as form-stable phase change materials

A composite paraffin-based phase change material (PCM) was prepared by blending composite paraffin and calcined diatomite through the fusion adsorption method. In this study, raw diatomite was purified by thermal treatment in order to improve the adsorption capacity of diatomite, which acted as a carrier material to prepare shape-stabilized PCMs. Two forms of paraffin (paraffin waxes and liquid paraffin) with different melting points were blended together by the fusion method, and the optimum mixed proportion with a suitable phase-transition temperature was obtained through differential scanning calorimetry (DSC) analysis. Then the prepared composite paraffin was adsorbed in calcined diatomite. The prepared paraffin/calcined diatomite composites were characterized by the scanning electron microscope (SEM) and Fourier transformation infrared (FT-IR) analysis techniques. Thermal energy storage properties of the composite PCMs were determined by DSC method. DSC results showed that there was an optimum adsorption ratio between composite paraffin and calcined diatomite and the phase-transition temperature and the latent heat of the composite PCMs were 33.04 ◦C and 89.54 J/g, respectively. Thermal cycling test of composite PCMs showed that the prepared material is thermally reliable and chemically stable. The obtained paraffin/calcined diatomite composites have proper latent heat and melting temperatures, and show practical significance and good potential application value.

How stable is the well-being of Australian mothers who care for young children with special health care needs?

Ninety-seven percent of children who have special health care needs are cared for by their mothers. These mothers cite that their informal care work can be intrinsically rewarding, however, the role is not without substantial difficulties and consequences. We investigated differences in the health and well-being of mothers whose young children do and do not have special health care needs. Quantitative data are drawn from Growing Up in Australia: The Longitudinal Study of Australian Children. This study employs a matched-case control methodology to compare the experiences of a group of 292 mothers whose children are identified as having long term special health care needs to those mothers whose children are typically developing at two time points; Wave 1 (2004) and Wave 3 (2008). The findings support previous research that mothers of children with special health care needs have poorer general health and mental health than mothers whose children do not have special needs. Mothers of children with special health care needs also perceived life as more difficult. Longitudinally, this study also shows that maternal well-being remains relatively stable during the years when children are transitioning to formal schooling. Implications for policy makers, practitioners and early childhood professionals are discussed.