The structure of unicellular maps, and a connection between maps of positive genus and planar labelled trees

A unicellular map is a map which has only one face. We give a bijection between a dominant subset of rooted unicellular maps of given genus and a set of rooted plane trees with distinguished vertices. The bijection applies as well to the case of labelled unicellular maps, which are related to all rooted maps by Marcus and Schaeffer’s bijection. This gives an immediate derivation of the asymptotic number of unicellular maps of given genus, and a simple bijective proof of a formula of Lehman and Walsh on the number of triangulations with one vertex. From the labelled case, we deduce an expression of the asymptotic number of maps of genus g with n edges involving the ISE random measure, and an explicit characterization of the limiting profile and radius of random bipartite quadrangulations of genus g in terms of the ISE.     

Decay of Solutions to a Linear Viscous Asymptotic Model for Water Waves

The authors discuss a linear viscous asymptotic model for water waves and the decay rate of solutions towards the equilibrium.     

Collective increase of first impression bias

We propose a simple model of first impression bias (FIB), where agents tend to ignore features which contradict their initial view. We consider a population of agents which are all in contact with a media, communicating randomly chosen features of an object. In some cases, we observe on simulations that FIB is significantly more frequent when the agents interact with each other than when they are only in contact with the media. We design an analytical aggregated model of the global agent‐based model behavior, which helps to explain the higher number of FIB due to the interactions. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Congested traffic dynamics, weak flows and very degenerate elliptic equations

Starting from a model of traffic congestion, we introduce a minimal-flow-like variational problem whose solution is characterized by a very degenerate elliptic PDE. We precisely investigate the relations between these two problems, which can be done by considering some weak notion of flow for a related ODE. We also prove regularity results for the degenerate elliptic PDE, which enables us in some cases to apply the DiPerna–Lions theory.     

Pushing the Lewis Acidity Boundaries of Boron Compounds With Non‐Planar Triarylboranes Derived from Triptycenes

Bending the planar trigonal boron center of triphenylborane by connecting its aryl rings with carbon or phosphorus linkers gave access to a series of 9‐boratriptycene derivatives with unprecedented structures and reactivities. NMR spectroscopy and X‐ray diffraction of the Lewis adducts of these non‐planar boron Lewis acids with weak Lewis base revealed particularly strong covalent bond formation. The first Lewis adduct of a trivalent boron compounds with the Tf₂N^? anion illustrates the unrivaled Lewis acidity of these species. Increasing the pyramidalization of the boron center and using a cationic phosphonium linker resulted in an exceptional enhancement of Lewis acidity. Introduction of a phosphorus and a boron atom at each edge of a triptycene framework, allowed access to new bifunctional Lewis acid‐base 9‐phospha‐10‐boratriptycenes featuring promising reactivity for the activation of carbon‐halogen bonds.     

Vapor‐Phase Linker Exchange of the Metal–Organic Framework ZIF‐8: A Solvent‐Free Approach to Post‐synthetic Modification

Zeolitic imidazolate frameworks (ZIFs) are a sub‐class of metal–organic frameworks (MOFs). Although generally stable, ZIFs can undergo post‐synthetic linker exchange (PSLE) in solution under mild conditions. Herein, we present a novel, solvent‐free approach to post‐synthetic linker exchange through exposure to linker vapor.     

Non-isothermal oxidation and kinetic analysis of pure magnesium powder

Journal of Thermal Analysis and Calorimetry - With high energy densities, metals appear as innovative energy carriers. In the present study, magnesium powder is considered as fuel for energy...     

Convergence to SPDEs in Stratonovich Form

We consider the perturbation of parabolic operators of the form ∂ _t  + P(x, D) by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseudo-differential operator P(x, D), the perturbed parabolic equation admits a solution given by a Duhamel expansion. Moreover, as the correlation length of the potential vanishes, we show that the latter solution converges in distribution to the solution of a stochastic parabolic equation with multiplicative noise that should be interpreted in the Stratonovich sense. The theory of mild solutions for such stochastic partial differential equations is developed. The behavior described above should be contrasted to the case of dimensions larger than or equal to the order of the elliptic pseudo-differential operator P(x, D). In the latter case, the solution to the random equation converges strongly to the solution of a homogenized (deterministic) parabolic equation as is shown in [2]. A stochastic limit is obtained only for sufficiently small space dimensions in this class of parabolic problems.     

Boroxol Rings in Liquid and Vitreous B2O3 from First Principles

We investigate the structural and vibrational properties of glassy B2O3 using first-principles molecular dynamics simulations. In particular, we determine the boroxol rings fraction f for which there is still no consensus in the literature. Two numerical models containing either a low or a high level of boroxol rings are tested against a gamut of experimental probes (static structure factor, Raman, 11B and 17O NMR data). We show that only the boroxol-rich model (f=75%) can reproduce the full set of observables. Total-energy calculations show that at the glass density, boroxol-rich structures are favored by about 6 kcal/(mol boroxol). Finally, the liquid state is explored in the 2,000-4,000 K range and a reduction of f to 10%-20% is obtained.