Na atomic order, Co charge disproportionation and magnetism in Nax_{x}CoO2_{2} for large Na contents

We have synthesized and characterized four different stable phases of Na ordered Na$_{x}$CoO$_{2}$, for $0.65<x<0.8$. Above 100 K they display similar Curie-Weiss susceptibilities as well as ferromagnetic $q=0$ spin fluctuations in the CoO$_{2}$ planes revealed by $^{23}$Na NMR data. In all phases from $^{59}$Co NMR data we display evidences that the Co disproportionate already above 300 K into non magnetic Co$^{3+}$ and magnetic $\approx$Co$^{3.5+}$ sites on which holes delocalize. This allows us to understand that metallic magnetism is favored for these large Na contents. Below 100 K the phases differentiate, and a magnetic order sets in only for $x\gtrsim 0.75$ at $T_{N}=$22 K. We suggest that the charge order also governs the low $T$ energy scales and transverse couplings

59Co NMR study of the Co states in superconducting and anhydrous cobaltates

$^{59}$Co NMR spectra in oriented powders of Na$_{0.35}$CoO$_{2}$ and in its hydrated superconducting phase (HSC) Na$_{0.35}$CoO$_{2}$,1.3H$_{2}$O reveal a single electronic Co state with identical $T$ independent NMR shift tensor. These phases differ markedly from Na$_{0.7}$CoO$_{2}$, in which we resolve 3 types of Co sites. The large T variation of their spin susceptibilities $\chi ^{s}$ and the anisotropy of the orbital susceptibility $\chi ^{orb}$ allow us to conclude that charge disproportionation occurs, in a non magnetic Co$^{3+}$ and two magnetic sites with about 0.3 and 0.7 holes in the $t_{2g}$ multiplet. The data are consistent with those for the single Co site in the anhydrous and HSC phase assuming the expected Co$^{3.65+}$ charge.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let

Some stationary properties of a QQ-ball in arbitrary space dimensions

Introducing new physically motivated ans\"{a}tze, we explore both analytically and numerically the classical and absolute stabilities of a single $Q$-ball in an arbitrary number of spatial dimensions $D$, working in both the thin and thick wall limits.Comment: 35 pages, 32 figures; added references, corrected typo

The reversibility of sea ice loss in a state-of-the-art climate model

Rapid Arctic sea ice retreat has fueled speculation about the possibility of threshold (or ‘tipping point’) behavior and irreversible loss of the sea ice cover. We test sea ice reversibility within a state-of-the-art atmosphere–ocean global climate model by increasing atmospheric carbon dioxide until the Arctic Ocean becomes ice-free throughout the year and subsequently decreasing it until the initial ice cover returns. Evidence for irreversibility in the form of hysteresis outside the envelope of natural variability is explored for the loss of summer and winter ice in both hemispheres. We find no evidence of irreversibility or multiple ice-cover states over the full range of simulated sea ice conditions between the modern climate and that with an annually ice-free Arctic Ocean. Summer sea ice area recovers as hemispheric temperature cools along a trajectory that is indistinguishable from the trajectory of summer sea ice loss, while the recovery of winter ice area appears to be slowed due to the long response times of the ocean near the modern winter ice edge. The results are discussed in the context of previous studies that assess the plausibility of sea ice tipping points by other methods. The findings serve as evidence against the existence of threshold behavior in the summer or winter ice cover in either hemisphere

Mathematics and Morphogenesis of the City: A Geometrical Approach

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of traditional models from random graphs, complex networks theory or stochastic geometry takes into account geometrical, functional and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division / extension of space. We propose a dynamical model that mimics this logic and which from simple general rules and a few parameters succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.Comment: 13 pages, 13 figure

Poly(thiophenes) derivatized with linear and macrocyclic polyethers: from cation detection to molecular actuation

The association of linear or macrocyclic polyethers with the electronic properties of the π-conjugated polythiophene backbone leads to functional conducting polymers that exhibit metal cation dependent electronic properties. Based on this concept, various classes of cation sensors have been proposed and investigated for almost two decades. The interactions of metal cations with linear or macrocyclic polyether functional groups lead to modifications of the electronic properties of the π-conjugated backbone through various mechanisms including direct electronic effects on a single conjugated chain, collective electrochemical processes, or conformational changes. Conjugated polymers and oligomers representative of these various processes are discussed with an emphasis on recent examples of derivatized conjugated systems in which the interactions between metal cations and polyether groups serve as driving force to create molecular motion in conjugated systems