Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a class of non-smooth vector fields we provide necessary and sufficient conditions for the existence of closed poly-trajectorie. By means of a regularization process we prove that hyperbolic closed poly-trajectories are limit sets of a sequence of limit cycles of smooth vector fields. In our approach the Poincaré Index for non-smooth vector fields is introduced. © 2013 Springer Science+Business Media New York.

Análise da dinâmica de um sistema vibrante não ideal de dois graus de liberdade

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The geostationary orbit : a critical legal geography of space’s most valuable real estate

This chapter attends to the legal and political geographies of one of Earth's most important, valuable, and pressured spaces: the geostationary orbit. Since the first, NASA, satellite entered it in 1964, this small, defined band of Outer Space, 35,786km from the Earth's surface, and only 30km wide, has become a highly charged legal and geopolitical environment, yet it remains a space which is curiously unheard of outside of specialist circles. For the thousands of satellites which now underpin the Earth's communication, media, and data industries and flows, the geostationary orbit is the prime position in Space. The geostationary orbit only has the physical capacity to hold approximately 1500 satellites; in 1997 there were approximately 1000. It is no overstatement to assert that media, communication, and data industries would not be what they are today if it was not for the geostationary orbit. This chapter provides a critical legal geography of the geostationary orbit, charting the topography of the debates and struggles to define and manage this highly-important space. Drawing on key legal documents such as the Outer Space Treaty and the Moon Treaty, the chapter addresses fundamental questions about the legal geography of the orbit, questions which are of growing importance as the orbit’s available satellite spaces diminish and the orbit comes under increasing pressure. Who owns the geostationary orbit? Who, and whose rules, govern what may or may not (literally) take place within it? Who decides which satellites can occupy the orbit? Is the geostationary orbit the sovereign property of the equatorial states it supertends, as these states argued in the 1970s? Or is it a part of the res communis, or common property of humanity, which currently legally characterises Outer Space? As challenges to the existing legal spatiality of the orbit from launch states, companies, and potential launch states, it is particularly critical that the current spatiality of the orbit is understood and considered. One of the busiest areas of Outer Space’s spatiality is international territorial law. Mentions of Space law tend to evoke incredulity and ‘little green men’ jokes, but as Space becomes busier and busier, international Space law is growing in complexity and importance. The chapter draws on two key fields of research: cultural geography, and critical legal geography. The chapter is framed by the cultural geographical concept of ‘spatiality’, a term which signals the multiple and dynamic nature of geographical space. As spatial theorists such as Henri Lefebvre assert, a space is never simply physical; rather, any space is always a jostling composite of material, imagined, and practiced geographies (Lefebvre 1991). The ways in which a culture perceives, represents, and legislates that space are as constitutive of its identity--its spatiality--as the physical topography of the ground itself. The second field in which this chapter is situated—critical legal geography—derives from cultural geography’s focus on the cultural construction of spatiality. In his Law, Space and the Geographies of Power (1994), Nicholas Blomley asserts that analyses of territorial law largely neglect the spatial dimension of their investigations; rather than seeing the law as a force that produces specific kinds of spaces, they tend to position space as a neutral, universally-legible entity which is neatly governed by the equally neutral 'external variable' of territorial law (28). 'In the hegemonic conception of the law,' Pue similarly argues, 'the entire world is transmuted into one vast isotropic surface' (1990: 568) on which law simply acts. But as the emerging field of critical legal geography demonstrates, law is not a neutral organiser of space, but is instead a powerful cultural technology of spatial production. Or as Delaney states, legal debates are “episodes in the social production of space” (2001, p. 494). International territorial law, in other words, makes space, and does not simply govern it. Drawing on these tenets of the field of critical legal geography, as well as on Lefebvrian concept of multipartite spatiality, this chapter does two things. First, it extends the field of critical legal geography into Space, a domain with which the field has yet to substantially engage. Second, it demonstrates that the legal spatiality of the geostationary orbit is both complex and contested, and argues that it is crucial that we understand this dynamic legal space on which the Earth’s communications systems rely.

Analysis of regionally enhanced GPS orbit and clock solutions and contribution to improvement of real-time precise point positioning

This work experimentally examines the performance benefits of a regional CORS network to the GPS orbit and clock solutions for supporting real-time Precise Point Positioning (PPP). The regionally enhanced GPS precise orbit solutions are derived from a global evenly distributed CORS network added with a densely distributed network in Australia and New Zealand. A series of computational schemes for different network configurations are adopted in the GAMIT-GLOBK and PANDA data processing. The precise GPS orbit results show that the regionally enhanced solutions achieve the overall orbit improvements with respect to the solutions derived from the global network only. Additionally, the orbital differences over GPS satellite arcs that are visible by any of the five Australia-wide CORS stations show a higher percentage of overall improvements compared to the satellite arcs that are not visible from these stations. The regional GPS clock and Uncalibrated Phase Delay (UPD) products are derived using the PANDA real time processing module from Australian CORS networks of 35 and 79 stations respectively. Analysis of PANDA kinematic PPP and kinematic PPP-AR solutions show certain overall improvements in the positioning performance from a denser network configuration after solution convergence. However, the clock and UPD enhancement on kinematic PPP solutions is marginal. It is suggested that other factors, such as effects of ionosphere, incorrectly fixed ambiguities, may be the more dominating, deserving further research attentions.

Magnetic resonance imaging: An accurate, radiation-free, alternative to computed tomography for the primary imaging and three-dimensional reconstruction of the bony orbit

Purpose: To determine the extent to which the accuracy of magnetic resonance imaging (MRI) based virtual 3-dimensional (3D) models of the intact orbit can approach that of the gold standard, computed tomography (CT) based models. The goal was to determine whether MRI is a viable alternative to CT scans in patients with isolated orbital fractures and penetrating eye injuries, pediatric patients, and patients requiring multiple scans in whom radiation exposure is ideally limited. Materials and Methods: Patients who presented with unilateral orbital fractures to the Royal Brisbane and Women’s Hospital from March 2011 to March 2012 were recruited to participate in this cross-sectional study. The primary predictor variable was the imaging technique (MRI vs CT). The outcome measurements were orbital volume (primary outcome) and geometric intraorbital surface deviations (secondary outcome)between the MRI- and CT-based 3D models. Results: Eleven subjects (9 male) were enrolled. The patients’ mean age was 30 years. On average, the MRI models underestimated the orbital volume of the CT models by 0.50 0.19 cm3 . The average intraorbital surface deviation between the MRI and CT models was 0.34 0.32 mm, with 78 2.7% of the surface within a tolerance of 0.5 mm. Conclusions: The volumetric differences of the MRI models are comparable to reported results from CT models. The intraorbital MRI surface deviations are smaller than the accepted tolerance for orbital surgical reconstructions. Therefore, the authors believe that MRI is an accurate radiation-free alternative to CT for the primary imaging and 3D reconstruction of the bony orbit. �

Nature of dependence of spin-orbit splittings on atomic number

It has been shown that Dirac equation employing a constant value of the screening constant Z0 does not explain the variation of spin-orbit splittings of 2p and 3p levels with atomic number Z. A model which takes into account the variation of Z0 withZ is shown to satisfactorily predict the dependence of spinorbit splittings onZ.

Application of the Conjugate Gradient Method to a Problem on Minimum Time Orbit Transfer

This correspondence considers the problem of optimally controlling the thrust steering angle of an ion-propelled spaceship so as to effect a minimum time coplanar orbit transfer from the mean orbital distance of Earth to mean Martian and Venusian orbital distances. This problem has been modelled as a free terminal time-optimal control problem with unbounded control variable and with state variable equality constraints at the final time. The problem has been solved by the penalty function approach, using the conjugate gradient algorithm. In general, the optimal solution shows a significant departure from earlier work. In particular, the optimal control in the case of Earth-Mars orbit transfer, during the initial phase of the spaceship's flight, is found to be negative, resulting in the motion of the spaceship within the Earth's orbit for a significant fraction of the total optimized orbit transfer time. Such a feature exhibited by the optimal solution has not been reported at all by earlier investigators of this problem.

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Construction of Singer Subgroup Orbit Codes Based on Cyclic Difference Sets

A recent approach for the construction of constant dimension subspace codes, designed for error correction in random networks, is to consider the codes as orbits of suitable subgroups of the general linear group. In particular, a cyclic orbit code is the orbit of a cyclic subgroup. Hence a possible method to construct large cyclic orbit codes with a given minimum subspace distance is to select a subspace such that the orbit of the Singer subgroup satisfies the distance constraint. In this paper we propose a method where some basic properties of difference sets are employed to select such a subspace, thereby providing a systematic way of constructing cyclic orbit codes with specified parameters. We also present an explicit example of such a construction.