Molecular spintronics using noncollinear magnetic molecules

We investigate the spin transport through strongly anisotropic noncollinear magnetic molecules and find that the noncollinear magnetization acts as a spin-switching device for the current. Moreover, spin currents are shown to offer a viable route to selectively prepare the molecular device in one of two degenerate noncollinear magnetic states. Spin-currents can be also used to create a non-zero density of toroidal magnetization in a recently characterized Dy_3 noncollinear magnet.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Numerical simulations of strong wind situations near the Mediteranean French Coast: comparison with FETCH data

A detailed analysis is made of some typical strong wind situations near the French Mediterranean coast. Special attention has been paid to the wind from the north-northwest in the Gulf of Lion, also called the mistral. The analysis is made from both the synoptic and mesoscale point of view with the aid of numerical simulations carried out with the Regional Atmospheric Modeling System (RAMS) to study the main atmospheric, climatic, and meteorological characteristics of this wind in the Gulf of Lion. Simulations were made with this model during the periods of 20-22 March and 24-26 March 1998. Afterward, a comparison was made with the meteorological measurements collected during the international Flux, Etat de la Mer et Te´le´de´tection en Condition de Fetch Variable (FETCH) campaign (Gulf of Lion, March-April 1998). The comparison between the simulated wind fields and the values measured by the coastal meteorological stations, an oceanographic buoy, and the ship Atalante at sea help to give full understanding of the complicated physical processes that characterize strong wind situations in coastal zone

Six vertex model with domain-wall boundary conditions in the Bethe-Peierls approximation

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice with partial domain-wall boundary conditions. We show that this rather simple approximation yields results that are remarkably close to the exact ones when these are known, and allows one to estimate the location of the phase boundaries with relative little effort in cases in which exact results are not available.Comment: 19 pages, 14 figure

Quasiflats in hierarchically hyperbolic spaces

The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the maximal dimension of a quasiflat. Examples for which the rank coincides with familiar quantities include: the dimension of maximal Dehn twist flats for mapping class groups, the maximal rank of a free abelian subgroup for right-angled Coxeter and Artin groups, and, for the Weil--Petersson metric, the rank is the integer part of half the complex dimension of Teichm\"{u}ller space. We prove that any quasiflat of dimension equal to the rank lies within finite distance of a union of standard orthants (under a mild condition satisfied by all natural examples). This resolves outstanding conjectures when applied to various examples. For mapping class group, we verify a conjecture of Farb; for Teichm\"{u}ller space we answer a question of Brock; for CAT(0) cubical groups, we handle special cases including right-angled Coxeter groups. An important ingredient in the proof is that the hull of any finite set in an HHS is quasi-isometric to a CAT(0) cube complex of dimension bounded by the rank. We deduce a number of applications. For instance, we show that any quasi-isometry between HHSs induces a quasi-isometry between certain simpler HHSs. This allows one, for example, to distinguish quasi-isometry classes of right-angled Artin/Coxeter groups. Another application is to quasi-isometric rigidity. Our tools in many cases allow one to reduce the problem of quasi-isometric rigidity for a given hierarchically hyperbolic group to a combinatorial problem. We give a new proof of quasi-isometric rigidity of mapping class groups, which, given our general quasiflats theorem, uses simpler combinatorial arguments than in previous proofs.Comment: 58 pages, 6 figures. Revised according to referee comments. This is the final pre-publication version; to appear in Duke Math. Jou

Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups

We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the mapping class group of a finite type surface: improving the bound from exponential to at most quadratic in the complexity of the surface. We also apply the main result to various other hierarchically hyperbolic groups and spaces. We also prove a small-cancellation result namely: if $G$ is a hierarchically hyperbolic group, $H\leq G$ is a suitable hyperbolically embedded subgroup, and $N\triangleleft H$ is "sufficiently deep" in $H$, then $G/\langle\langle N\rangle\rangle$ is a relatively hierarchically hyperbolic group. This new class provides many new examples to which our asymptotic dimension bounds apply. Along the way, we prove new results about the structure of HHSs, for example: the associated hyperbolic spaces are always obtained, up to quasi-isometry, by coning off canonical coarse product regions in the original space (generalizing a relation established by Masur--Minsky between the complex of curves of a surface and Teichm\"{u}ller space).Comment: Minor revisions in Section 6. This is the version accepted for publicatio

Cochlear Implant Outcomes and Genetic Mutations in Children with Ear and Brain Anomalies

Background. Specific clinical conditions could compromise cochlear implantation outcomes and drastically reduce the chance of an acceptable development of perceptual and linguistic capabilities. These conditions should certainly include the presence of inner ear malformations or brain abnormalities. The aims of this work were to study the diagnostic value of high resolution computed tomography (HRCT) and magnetic resonance imaging (MRI) in children with sensorineural hearing loss who were candidates for cochlear implants and to analyse the anatomic abnormalities of the ear and brain in patients who underwent cochlear implantation. We also analysed the effects of ear malformations and brain anomalies on the CI outcomes, speculating on their potential role in the management of language developmental disorders. Methods. The present study is a retrospective observational review of cochlear implant outcomes among hearing-impaired children who presented ear and/or brain anomalies at neuroimaging investigations with MRI and HRCT. Furthermore, genetic results from molecular genetic investigations (GJB2/GJB6 and, additionally, in selected cases, SLC26A4 or mitochondrial-DNA mutations) on this study group were herein described. Longitudinal and cross-sectional analysis was conducted using statistical tests. Results. Between January 1, 1996 and April 1, 2012, at the ENT-Audiology Department of the University Hospital of Ferrara, 620 cochlear implantations were performed. There were 426 implanted children at the time of the present study (who were <18 years). Among these, 143 patients (64 females and 79 males) presented ear and/or brain anomalies/lesions/malformations at neuroimaging investigations with MRI and HRCT. The age of the main study group (143 implanted children) ranged from 9 months and 16 years (average = 4.4; median = 3.0). Conclusions. Good outcomes with cochlear implants are possible in patients who present with inner ear or brain abnormalities, even if central nervous system anomalies represent a negative prognostic factor that is made worse by the concomitant presence of cochlear malformations. Common cavity and stenosis of the internal auditory canal (less than 2 mm) are negative prognostic factors even if brain lesions are absent

Upper Bounds to the Performance of Cooperative Traffic Relaying in Wireless Linear Networks

Wireless networks with linear topology, where nodes generate their own traffic and relay other nodes' traffic, have attracted increasing attention. Indeed, they well represent sensor networks monitoring paths or streets, as well as multihop networks for videosurveillance of roads or vehicular traffic. We study the performance limits of such network systems when (i) the nodes' transmissions can reach receivers farther than one-hop distance from the sender, (ii) the transmitters cooperate in the data delivery, and (iii) interference due to concurrent transmissions is taken into account. By adopting an information-theoretic approach, we derive analytical bounds to the achievable data rate in both the cases where the nodes have full-duplex and half-duplex radios. The expressions we provide are mathematically tractable and allow the analysis of multihop networks with a large number of nodes. Our analysis highlights that increasing the number of coop- erating transmitters beyond two leads to a very limited gain in the achievable data rate. Also, for half-duplex radios, it indicates the existence of dominant network states, which have a major influence on the bound. It follows that efficient, yet simple, communication strategies can be designed by considering at most two cooperating transmitters and by letting half-duplex nodes operate according to the aforementioned dominant state

Phase separation and critical percolation in bidimensional spin-exchange models

Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phase-separate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this dynamics first takes a system with equal density of the two species to a critical percolation state. We prove this claim and we determine the time-dependence of the growing length associated to this process with the scaling analysis of the statistical and morphological properties of the clusters of the two phases.Comment: 6 pages, 9 figure

An algorithm for constructing certain differential operators in positive characteristic

Given a non-zero polynomial $f$ in a polynomial ring $R$ with coefficients in a finite field of prime characteristic $p$, we present an algorithm to compute a differential operator $\delta$ which raises $1/f$ to its $p$th power. For some specific families of polynomials, we also study the level of such a differential operator $\delta$, i.e., the least integer $e$ such that $\delta$ is $R^{p^e}$-linear. In particular, we obtain a characterization of supersingular elliptic curves in terms of the level of the associated differential operator.Comment: 23 pages. Comments are welcom