A view from infinity of the uniform infinite planar quadrangulation

We introduce a new construction of the Uniform Infinite Planar Quadrangulation (UIPQ). Our approach is based on an extension of the Cori-Vauquelin-Schaeffer mapping in the context of infinite trees, in the spirit of previous work. However, we release the positivity constraint on the labels of trees which was imposed in these references, so that our construction is technically much simpler. This approach allows us to prove the conjectures of Krikun pertaining to the "geometry at infinity" of the UIPQ, and to derive new results about the UIPQ, among which a fine study of infinite geodesics.Comment: 39 pages, 11 figure

Corrosion inhibition of 2024 aluminium alloy by sodium decanoate

The present study concerns the corrosion protection of the aluminium alloy (AA) 2024 by sodium decanoate (a long-carbon-chain carboxylate). This compound-type is known to form hydrophobic films on the metal surface. The characterization of the inhibition mechanisms was studied for different experimental conditions (pH, NaCl concentrations) by using electrochemical techniques. Special attention was paid to the action of the carboxylate on the intermetallic particles by performing local electrochemical impedance measurements on a model system (Al/Cu couple). The decanoate afforded high protection to the AA2024 both by preventing chloride ion attack of the oxide layer and by limiting galvanic coupling between the intermetallic particles and the surrounding matrix. A passivation effect of the compound was also shown

Structural Dependence of the Molecular Mobility in the Amorphous Fractions of Polylactide

Fragility index and cooperativity length characterizing the molecular mobility in the amorphous phase are for the first time calculated in drawn polylactide (PLA). The microstructure of the samples is investigated from wide-angle X-ray scattering (WAXS) whereas the amorphous phase dynamics are revealed from broadband dielectric spectroscopy (BDS) and temperature-modulated differential scanning calorimetry (TMDSC). The drawing processes induce the decrease of both cooperativity and fragility with the orientation of the macromolecules. Post-drawing annealing reveals an unusual absence of correlation between the evolutions of cooperativity length and fragility. The cooperativity length remains the same compared to the drawn sample while a huge increase of the fragility index is recorded. By splitting the fragility index in a volume contribution and an energetic contribution, it is revealed that the amorphous phase in annealed samples exhibits a high energetic parameter, even exceeding the amorphous matrix value. It is assumed that the relaxation process is driven in such a way that the volume hindrance caused by the thermomechanical constraint is compensated by the acceleration of segmental motions linked to the increase of degrees of freedom. This result should also contribute to the understanding of the constraint slackening in the amorphous phase during annealing of drawn PLA, which causes among others the decrease of its barrier properties

Corrosion protection of AA2024 sealed anodic layers using the hydrophobic properties of carboxylic acids

The present study investigates the use of carboxylic acids as a post-treatment for sealed AA2024 anodised in tartaric–sulphuric acid electrolyte. Four monocarboxylic acids with different carbon chain lengths were tested ((CH3–(CH2)n–COOH with n=4, 8, 12 and 16). Hydrophobic surface properties after the posttreatment were characterized by contact angle measurements. Electrochemical impedance spectroscopy (EIS) was performed to assess the ability of the four carboxylic acids to form protective films. It was shown that stearic acid (n=16) used in its pure molten state was the most efficient. The organic film formed very rapidly (under 5 min) and contributed to the enhancement of the protection in terms of corrosion resistance of the sealed anodic layers. EIS measurements showed the presence of the organic films on the specimen surface

A derived isometry theorem for constructible sheaves on R\mathbb{R}

Persistent homology has been recently studied with the tools of sheaf theory in the derived setting by Kashiwara and Schapira, after J. Curry has made the first link between persistent homology and sheaves. We prove the isometry theorem in this derived setting, thus expressing the convolution distance of sheaves as a matching distance between combinatorial objects associated to them that we call graded barcodes. This allows to consider sheaf-theoretical constructions as combinatorial, stable topological descriptors of data, and generalizes the situation of persistence with one parameter. To achieve so, we explicitly compute all morphisms in $D^b_{\mathbb{R} c}(\textbf{k}_\mathbb{R})$, which enables us to compute distances between indecomposable objects. Then we adapt Bjerkevik's stability proof to this derived setting. As a byproduct of our isometry theorem, we prove that the convolution distance is closed, give a precise description of connected components of $D^b_{\mathbb{R} c}(\textbf{k}_\mathbb{R})$and provide some explicit examples of computation of the convolution distance