The structure theory of nilspaces I

This paper forms the first part of a series by the authors [GMV2,GMV3] concerning the structure theory of nilspaces of Antol\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of cubes $C^n(X)\subseteq X^{2^n}$, $n=1,2,\ldots$ satisfying some natural axioms. Antol\'in Camarena and Szegedy proved that from these axioms it follows that (certain) nilspaces are isomorphic (in a strong sense) to an inverse limit of nilmanifolds. The aim of our project is to provide a new self-contained treatment of this theory and give new applications to topological dynamics. This paper provides an introduction to the project from the point of view of applications to higher order Fourier analysis. We define and explain the basic definitions and constructions related to cubespaces and nilspaces and develop the weak structure theory, which is the first stage of the proof of the main structure theorem for nilspaces. Vaguely speaking, this asserts that a nilspace can be built as a finite tower of extensions where each of the successive fibers is a compact abelian group. We also make some modest innovations and extensions to this theory. In particular, we consider a class of maps that we term fibrations, which are essentially equivalent to what are termed fiber-surjective morphisms by Anatol\'in Camarena and Szegedy, and we formulate and prove a relative analogue of the weak structure theory alluded to above for these maps. These results find applications elsewhere in the project.Royal Societ

Results from a set of three-dimensional numerical experiments of a hot Jupiter atmosphere

We present highlights from a large set of simulations of a hot Jupiter atmosphere, nominally based on HD 209458b, aimed at exploring both the evolution of the deep atmosphere, and the acceleration of the zonal flow or jet. We find the occurrence of a super-rotating equatorial jet is robust to changes in various parameters, and over long timescales, even in the absence of strong inner or bottom boundary drag. This jet is diminished in one simulation only, where we strongly force the deep atmosphere equator-to-pole temperature gradient over long timescales. Finally, although the eddy momentum fluxes in our atmosphere show similarities with the proposed mechanism for accelerating jets on tidally-locked planets, the picture appears more complex. We present tentative evidence for a jet driven by a combination of eddy momentum transport and mean flow.Comment: 26 pages, 22 Figures. Accepted for publication in Astronomy and Astrophysic

Modeling and Dynamic Analysis of Paralleled dc/dc Converters With Master-Slave Current Sharing Control

A simple, application-oriented, transfer function model of paralleled converters employing Master-Slave Current-sharing (MSC) control is developed. Dynamically, the Master converter retains its original design characteristics; all the Slave converters are forced to depart significantly from their original design characteristics into current-controlled current sources. Five distinct loop gains to assess system stability and performance are identified and their physical significance is described. A design methodology for the current share compensator is presented. The effect of this current sharing scheme on 'system output impedance' is analyzed

Alkaline-Earth Derivatives of Diphenylphosphine-Borane

Treatment of β-diketiminato (BDI = HC{C(CH3)Ndipp)}2 where dipp = 2,6-iPr2C6H3) magnesium butyl [(BDI)MgBu] (I) and calcium hexamethyldisilazide [(BDI)Ca{N(SiMe3)2}] (II) complexes with equimolar quantities of diphenylphosphine-borane, Ph2PH·BH3, results in the formation of the respective alkaline earth (Ae) phosphidoborane derivatives [(BDI)Mg(Ph2PBH3)]2 (6a) and [(BDI)Ca(Ph2PBH3)] (7a). Although satisfactory single crystals of 7a could not be obtained, 6a was crystallographically characterized and both compounds display similar NMR spectra. The dimeric Ae-hydride complexes [(BDI)AeH]2 (IIIa, Ae = Mg; IIIb, Ae = Ca) react with substoichiometric quantities of Ph2PH·BH3, allowing the crystallization of the dimeric Mg and trimeric Ca phosphidoborane species [(BDI)Mg(H)(H3BPPh2)Mg(BDI)] (8) and [{(BDI)Ca}3(H)(H3BPPh2)2] (9). In the absence of coordinating Lewis bases, compounds 6a, 7a, 8, and 9 display dynamic solution-state behavior (in benzene and toluene), while addition of THF furnishes the monomeric adducts [(BDI)Mg(H3BPPh2)·THF] (6b) and [(BDI)Ca(H3BPPh2)·THF] (7b). Addition of Ph2PH·BH3 to compound 6a results in BH3 transfer to eliminate Ph2PH and generate the phosphinodiboronate complex [(BDI)Mg{(H3B)2PPh2}]2 (10) in preference to dehydrocoupling of the phosphidoborane and phosphine-borane reagents.</p

The structure theory of nilspaces ii: Representation as nilmanifolds

This paper forms the second part of a series by the authors [GMV1,GMV3] concerning the structure theory of nilspaces of Antol\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of cubes $C_n(X)\subseteq X^{2^n}$, $n=1,2,\ldots$ satisfying some natural axioms. From these axioms it follows that a nilspace can be built as a finite tower of extensions where each of the successive fibers is a compact abelian group. Our main result is a new proof of a result due to Antol\'in Camarena and Szegedy [CS12], stating that if each of these groups is a torus then $X$ is isomorphic (in a strong sense) to a nilmanifold $G/\Gamma$. We also extend the theorem to a setting where the nilspace arises from a dynamical system $(X,T)$. These theorems are a key stepping stone towards the general structure theorem in [GMV3] (which again closely resembles the main theorem of [CS12]). The main technical tool, enabling us to deduce algebraic information from topological data, consists of existence and uniqueness results for solutions of certain natural functional equations, again modelled on the theory in [CS12]

Modeling and Dynamic Analysis of Paralleled of dc/dc Converters with Master-Slave Current Sharing Control

A simple, application-oriented, transfer function model of paralleled converters employing Master-Slave Current-sharing (MSC) control is developed. Dynamically, the Master converter retains its original design characteristics; all the Slave converters are forced to depart significantly from their original design characteristics into current-controlled current sources. Five distinct loop gains to assess system stability and performance are identified and their physical significance is described. A design methodology for the current share compensator is presented. The effect of this current sharing scheme on 'system output impedance' is analyzed

The EU and Asia within an evolving global order: what is Europe? Where is Asia?

The papers in this special edition are a very small selection from those presented at the EU-NESCA (Network of European Studies Centres in Asia) conference on "the EU and East Asia within an Evolving Global Order: Ideas, Actors and Processes" in November 2008 in Brussels. The conference was the culmination of three years of research activity involving workshops and conferences bringing together scholars from both regions primarily to discuss relations between Europe and Asia, perceptions of Europe in Asia, and the relationship between the European regional project and emerging regional forms in Asia. But although this was the last of the three major conferences organised by the consortium, it in many ways represented a starting point rather than the end; an opportunity to reflect on the conclusions of the first phase of collaboration and point towards new and continuing research agendas for the future

The ELAIS Deep X-ray Survey

We present initial follow-up results of the ELAIS Deep X-ray Survey which is being undertaken with the Chandra and XMM-Newton Observatories. 235 X-ray sources are detected in our two 75 ks ACIS-I observations in the well-studied ELAIS N1 and N2 areas. 90% of the X-ray sources are identified optically to R=26 with a median magnitude of R=24. We show that objects which are unresolved optically (i.e. quasars) follow a correlation between their optical and X-ray fluxes, whereas galaxies do not. We also find that the quasars with fainter optical counterparts have harder X-ray spectra, consistent with absorption at both wavebands. Initial spectroscopic follow-up has revealed a large fraction of high-luminosity Type 2 quasars. The prospects for studying the evolution of the host galaxies of X-ray selected Type 2 AGN are considered.Comment: 9 pages, 5 figures, To appear in Proceedings of XXI Moriond Conference: "Galaxy Clusters and the High Redshift Universe Observed in X-rays", edited by D. Neumann, F.Durret, & J. Tran Thanh Va

The Limits of the Primitive Equations of Dynamics for Warm, Slowly Rotating Small Neptunes and Super Earths (article)

This is the author accepted manuscript. The final version is available from American Astronomical Society / IOP Publishing via the DOI in this record.The dataset associated with this article is located in ORE at: https://doi.org/10.24378/exe.1023We present significant differences in the simulated atmospheric flow for warm, tidally-locked small Neptunes and super Earths (based on a nominal GJ 1214b) when solving the simplified, and commonly used, primitive dynamical equations or the full Navier-Stokes equations. The dominant prograde, superrotating zonal jet is markedly different between the simulations which are performed using practically identical numerical setups, within the same model. The differences arise due to the breakdown of the so-called `shallow-fluid' and traditional approximations, which worsens when rotation rates are slowed, and day{night temperature contrasts are increased. The changes in the zonal advection between simulations solving the full and simplified equations, give rise to significant differences in the atmospheric redistribution of heat, altering the position of the hottest part of the atmosphere and temperature contrast between the day and night sides. The implications for the atmospheric chemistry and, therefore, observations need to be studied with a model including a more detailed treatment of the radiative transfer and chemistry. Small Neptunes and super Earths are extremely abundant and important, potentially bridging the structural properties (mass, radius, composition) of terrestrial and gas giant planets. Our results indicate care is required when interpreting the output of models solving the primitive equations of motion for such planets.Leverhulme TrustScience and Technology Facilities CouncilEuropean Research Counci