Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth

We study the energy-critical focusing nonlinear Schrödinger equation with an energy-subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we give a sufficient and necessary condition for a solution to scatter, in the spirit of Kenig and Merle (Invent Math 166:645–675, 2006).     

Small cycle structure for words in conjugation invariant random permutations

We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive cyclic simplifications, the word $w$ still contains at least two different letters, then we get a universal limiting joint law for short cycles for the word in these permutations. These results can be seen as an extension of our previous work (Kammoun and Maïda. Electron. Commun. Probab. 2020;25:1-14.) from the product of permutations to any non-trivial word in the permutations and also as an extension of the results of Nica (Random Struct. Algorithms1994;5:703-730.) from uniform permutations to general conjugation invariant random permutations. In particular, we get optimal assumptions in the case of the commutator of two such random permutations.     

Poly(ester-amide)s Derived From Adipic Acid, 1,4-Butanediol and β-Alanine: Synthesis and Characterization

A series of polyesteramides (PEAs) differing in their amide/ester ratio, within a range of molar composition from 90/10 to 10/90, have been synthesized by a direct melt polycondensation of 1,4-butanediol, adipic acid and β-alanine. Their structure was fully characterized by FTIR and NMR spectroscopy. The resulting copolymers are amorphous, they are thermally stable to temperatures up to 330°C, and present increasing glass transition temperatures at increasing amide content.     

Evaluation of the inhibitive effect of benzotriazole on archeological bronze in acidic medium

An archaeological bronze artefact was a Punic coin excavated from the north east of Tunisia in 2001. The composition of the copper alloy revealed a content of 3.5 % of tin and 1.4 % of lead with the presence of some sulphur heterogeneity. The surface presents some roughnesses and cracks and is covered by a corrosion layer of 20–40 μm thickness. The use of benzotriazole (BTA) as an inhibitor has become a standard element for the preservation of cuprous-based metals. In order to investigate the behaviour of BTA in an acidic medium, an Electrochemical Impedance Spectroscopy (EIS) investigation was performed to characterize the electrochemical behaviour of the interface of the archaeological bronze sample/acidic medium without and with BTA addition. Impedance diagrams obtained at different immersion times show that the presence of the inhibitor prevents the diffusional process observed in the absence of BTA. The inhibition of the pre-polarized bronze surface revealed that the mechanism of action of the benzotriazole molecule in an acidic medium is governed by the chemisorption process.     

Extensional dynamics of viscoplastic filaments: II. Drips and bridges

A model for the dynamics of slender filaments of Herschel–Bulkley fluid is used to explore viscoplastic dripping under gravity and thinning under controlled extension (liquid bridges). The conditions required for fluid to yield are delineated, and the subsequent thinning and progression to pinch-off are tracked numerically. Calculations varying the dimensionless parameters of the problem are presented to illustrate the effect of surface tension, rheology, inertia (for dripping) and gravity. The theoretical solutions are compared with laboratory experiments using aqueous solutions of Carbopol and Kaolin suspensions. For drips and bridges, experiments with Carbopol are well matched by the theory, using a surface tension equal to that of water, even in situations when the fluid is not slender. Experiments with Kaolin do not compare well with theory for physically plausible values of the surface tension. Implications for rheometry and surface-tension inference are discussed.