A geometric approach to stationary defect solutions in one space dimension

In this manuscript, we consider the impact of a small jump-type spatial heterogeneity on the existence of stationary localized patterns in a system of partial dierential equations in one spatial dimension...

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

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.

Refinements and developments on the stratospheric dust database and classification scheme

Greater than 750 individual particles have now been selected from collection flags housed in the JSC Cosmic Dust Curatorial Facility and most have been documented in the Cosmic Dust Catalogs [1]. As increasing numbers of particles are placed in Cosmic Dust Collections, and a greater diversity of particles are introduced to the stratosphere through natural and man-made processes (e.g. decaying orbits of space debris [2]), there is an even greater need for a classification scheme to encompass all stratospheric particles rather than only extraterrestrial particles. The fundamental requirements for a suitable classification scheme have been outlined in earlier communications [3,4]. A quantitative survey of particles on collection flag W7017 indicates that there is some bias in the number of samples selected within a given category for the Cosmic Dust Catalog [5]. However, the sample diversity within this selection is still appropriate for the development of a reliable classification scheme. In this paper, we extend the earlier works on stratospheric particle classification to include particles collected during the period May 1981 to November 1983.

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.

The impact of orbital errors on the estimation of satellite clock errors and PPP

Precise satellite orbit and clocks are essential for providing high accuracy real-time PPP (Precise Point Positioning) service. However, by treating the predicted orbits as fixed, the orbital errors may be partially assimilated by the estimated satellite clock and hence impact the positioning solutions. This paper presents the impact analysis of errors in radial and tangential orbital components on the estimation of satellite clocks and PPP through theoretical study and experimental evaluation. The relationship between the compensation of the orbital errors by the satellite clocks and the satellite-station geometry is discussed in details. Based on the satellite clocks estimated with regional station networks of different sizes (∼100, ∼300, ∼500 and ∼700 km in radius), results indicated that the orbital errors compensated by the satellite clock estimates reduce as the size of the network increases. An interesting regional PPP mode based on the broadcast ephemeris and the corresponding estimated satellite clocks is proposed and evaluated through the numerical study. The impact of orbital errors in the broadcast ephemeris has shown to be negligible for PPP users in a regional network of a radius of ∼300 km, with positioning RMS of about 1.4, 1.4 and 3.7 cm for east, north and up component in the post-mission kinematic mode, comparable with 1.3, 1.3 and 3.6 cm using the precise orbits and the corresponding estimated clocks. Compared with the DGPS and RTK positioning, only the estimated satellite clocks are needed to be disseminated to PPP users for this approach. It can significantly alleviate the communication burdens and therefore can be beneficial to the real time applications.

Tetragonal bismuth bilayer: A stable and robust quantum spin hall insulator

Topological insulators (TIs) exhibit novel physics with great promise for new devices, but considerable challenges remain to identify TIs with high structural stability and large nontrivial band gap suitable for practical applications. Here we predict by first-principles calculations a two-dimensional (2D) TI, also known as a quantum spin Hall (QSH) insulator, in a tetragonal bismuth bilayer (TB-Bi) structure that is dynamically and thermally stable based on phonon calculations and finite-temperature molecular dynamics simulations. Density functional theory and tight-binding calculations reveal a band inversion among the Bi-p orbits driven by the strong intrinsic spin-orbit coupling, producing a large nontrivial band gap, which can be effectively tuned by moderate strains. The helical gapless edge states exhibit a linear dispersion with a high Fermi velocity comparable to that of graphene, and the QSHphase remains robust on a NaCl substrate. These remarkable properties place TB-Bi among the most promising 2D TIs for high-speed spintronic devices, and the present results provide insights into the intriguing QSH phenomenon in this new Bi structure and offer guidance for its implementation in potential applications.