Orbital frustration at the origin of the magnetic behavior in LiNiO2

We report on the ESR, magnetization and magnetic susceptibility measurements performed over a large temperature range, from 1.5 to 750 K, on high-quality stoichiometric LiNiO2. We find that this compound displays two distinct temperature regions where its magnetic behavior is anomalous. With the help of a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that below T_of ~ 400 K, an orbitally-frustrated state characteristic of the triangular lattice is established. This then gives a solution to the long-standing controversial problem of the magnetic behavior in LiNiO2.Comment: 5 pages, 5 figures, RevTex, accepted in PR

Feller property and infinitesimal generator of the exploration process

We consider the exploration process associated to the continuous random tree (CRT) built using a Levy process with no negative jumps. This process has been studied by Duquesne, Le Gall and Le Jan. This measure-valued Markov process is a useful tool to study CRT as well as super-Brownian motion with general branching mechanism. In this paper we prove this process is Feller, and we compute its infinitesimal generator on exponential functionals and give the corresponding martingale

Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction

A new cell primo-culture method for freshwater benthic diatom communities

A new cell primo-culture method was developed for the benthic diatom community isolated from biofilm sampled in rivers. The approach comprised three steps: (1) scraping biofilm from river pebbles, (2) diatom isolation from biofilm, and (3) diatom community culture. With a view to designing a method able to stimulate the growth of diatoms, to limit the development of other microorganisms, and to maintain in culture a community similar to the original natural one, different factors were tested in step 3: cell culture medium (Chu No 10 vs Freshwater “WC” medium modified), cell culture vessel, and time of culture. The results showed that using Chu No 10 medium in an Erlenmeyer flask for cell culture was the optimal method, producing enough biomass for ecotoxicological tests as well as minimising development of other microorganisms. After 96 h of culture, communities differed from the original communities sampled in the two rivers studied. Species tolerant of eutrophic or saprobic conditions were favoured during culture. This method of diatom community culture affords the opportunity to assess, in vitro, the effects of different chemicals or effluents (water samples andindustrial effluents) on diatom communities, as well as on diatom cells, from a wide range of perspectives

A Formally Verified Floating-Point Implementation of the Compact Position Reporting Algorithm

The Automatic Dependent Surveillance-Broadcast (ADS-B) system allows aircraft to communicate their current state, including position and velocity information, to other aircraft in their vicinity and to ground stations. The Compact Position Reporting (CPR) algorithm is the ADS-B module responsible for the encoding and decoding of aircraft positions. CPR is highly sensitive to computer arithmetic since it heavily relies on functions that are intrinsically unstable such as floor and modulo. In this paper, a formally-verified double-precision floating-point implementation of the CPR algorithm is presented. The verification proceeds in three steps. First, an alternative version of CPR, which reduces the floating-point rounding error is proposed. Then, the Prototype Verification System (PVS) is used to formally prove that the ideal real-number counterpart of the improved algorithm is mathematically equivalent to the standard CPR definition. Finally, the static analyzer Frama-C is used to verify that the double-precision implementation of the improved algorithm is correct with respect to its operational requirement. The alternative algorithm is currently being considered for inclusion in the revised version of the ADS-B standards document as the reference implementation of the CPR algorithm

Size-dependent spinodal and miscibility gaps for intercalation in nano-particles

Using a recently-proposed mathematical model for intercalation dynamics in phase-separating materials [Singh, Ceder, Bazant, Electrochimica Acta 53, 7599 (2008)], we show that the spinodal and miscibility gaps generally shrink as the host particle size decreases to the nano-scale. Our work is motivated by recent experiments on the high-rate Li-ion battery material LiFePO4; this serves as the basis for our examples, but our analysis and conclusions apply to any intercalation material. We describe two general mechanisms for the suppression of phase separation in nano-particles: (i) a classical bulk effect, predicted by the Cahn-Hilliard equation, in which the diffuse phase boundary becomes confined by the particle geometry; and (ii) a novel surface effect, predicted by chemical-potential-dependent reaction kinetics, in which insertion/extraction reactions stabilize composition gradients near surfaces in equilibrium with the local environment. Composition-dependent surface energy and (especially) elastic strain can contribute to these effects but are not required to predict decreased spinodal and miscibility gaps at the nano-scale

Maïdo observatory: a new high-altitude station facility at Reunion Island (21° S, 55° E) for long-term atmospheric remote sensing and in situ measurements

Since the nineties, atmospheric measurement systems have been deployed at Reunion Island, mainly for monitoring the atmospheric composition in the framework of NDSC/NDACC (Network for the Detection of <i>Stratospheric</i> Change/Network for the Detection of Atmospheric Composition Change). The location of Reunion Island presents a great interest because there are very few multi-instrumented stations in the tropics and particularly in the southern hemisphere. In 2012, a new observatory was commissioned in Maïdo at 2200 m above sea level: it hosts various instruments for atmospheric measurements, including lidar systems, spectro-radiometers and in situ gas and aerosol measurements. <br><br> This new high-altitude Maïdo station provides an opportunity:<br> 1. to improve the performance of the optical instruments above the marine boundary layer, and to open new perspectives on upper troposphere and lower stratosphere studies;<br> 2. to develop in situ measurements of the atmospheric composition for climate change surveys, in a reference site in the tropical/subtropical region of the southern hemisphere;<br> 3. to offer trans-national access to host experiments or measurement campaigns for focused process studies