Smooth zero-contact-angle solutions to a thin-film equation around the steady state

In the simplest case of a linearly degenerate mobility, we view the thin-film equation as a classical free boundary problem. Our focus is on the regularity of solutions and of their free boundary in the “complete wetting” regime, which prescribes zero slope at the free boundary. In order to rule out of the analysis possible changes in the topology of the positivity set, we zoom into the free boundary by looking at perturbations of the stationary solution. Our strategy is based on a priori energy-type estimates which provide “minimal” conditions on the initial datum under which a unique global solution exists. In fact, this solution turns out to be smooth for positive times and to converge to the stationary solution for large times. As a consequence, we obtain smoothness and large-time behavior of the free boundary.     

Fluorescent Vesicles Consisting of Galactose‐based Amphiphilic Copolymers with a π‐Conjugated Sequence Self‐assembled in Water

Fluorescent vesicles considered as a mimic of natural primitive cells are prepared from poly(3‐hexylthiophene)‐block‐poly(3‐O‐methacryloyl‐D‐galactopyranose) P3HT‐b‐PMAGP copolymers. The unique characteristic of such vesicular nanostructures is their architecture, which comprises a hydrophobic π‐conjugated P3HT wall stabilized by a hydrophilic PMAGP interface featuring glucose units. The results of this work offer a very efficient and straightforward method for engineering well‐controlled fluorescent nanoparticles (without the addition of dyes), which provide an excellent support to the study of carbohydrate‐protein interactions.

     

Fragmentation of 370 MeV/n 20Ne and 470 MeV/n 24Mg in light targets

Total charge-changing cross sections and cross sections for the production of projectile-like fragments were determined for fragmentation reactions induced by 370 MeV/n ²⁰Ne ions in water and lucite, and 490 MeV/n ²⁴Mg ions in polyethylene, carbon and aluminum targets sandwiched with CR-39 plastic nuclear track detectors. An automated microscope system and a track-to-track matching algorithm were used to count and recognize the primary and secondary particles. The measured cross sections were then compared with published cross sections and predictions of different models. Two models and the three-dimensional Monte Carlo Particle Heavy Ion Transport Code System (PHITS) were used to calculate total charge-changing cross sections. Both models agreed within a few percent for the system ²⁴Mg + CH₂, however a deviation up to 20% was observed for the systems ²⁰Ne + H₂O and C₅H₈O₂, when using one of the models. For all the studied systems, PHITS systematically underestimated the total charge-changing cross section. It was also found that the partial fragmentation cross sections for ²⁴Mg + CH₂ measured in present and earlier works deviated up to 20% for Z = 6–11. Measured cross sections for the production of fragments (Z = 4–9) for ²⁰Ne + H₂O and C₅H₈O₂ were compared with predictions of three different semi-empirical models and JQMD which is used in the PHITS code. The calculated cross sections differed from the measured data by 10–90% depending on which fragment and charge was studied, and which model was used.     

Atom transfer radical polymerization of sodium2‐acrylamido‐2‐methylpropanesulfonate

The first example of well‐controlled atom transfer radical polymerization (ATRP) of a permanently charged anionic acrylamide monomer is reported. ATRP of sodium 2‐acrylamido‐2‐methylpropanesulfonate (NaAMPS) was achieved with ethyl 2‐chloropropionate (ECP) as an initiator and the CuCl/CuCl₂/tris(2‐dimethylaminoethyl)amine (Me₆TREN) catalytic system. The polymerizations were carried out in 50:50 (v/v) N,N‐dimethylformamide (DMF)/water mixtures at 20 °C. Linear first‐order kinetic plots up to a 92% conversion for a target degree of polymerization of 50 were obtained with [ECP]/[CuCl]/[CuCl₂]/[Me₆TREN] = 1:1:1:2 and [AMPS] = 1 M. The molecular weight increased linearly with the conversion in good agreement with the theoretical values, and the polydispersities decreased with increasing conversion, reaching a lower limit of 1.11. The living character of the polymerization was confirmed by chain‐extension experiments. Block copolymers with N,N‐dimethylacrylamide and N‐isopropylacrylamide were also prepared. The use of a DMF/water mixed solvent should make possible the synthesis of new amphiphilic ionic block copolymers without the use of protecting group chemistry. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4446–4454, 2005     

Activity coefficients from the emf of liquid membrane cells V. alkaline earth hexacyanoferrates (III) in aqueous solutions at 25°C

The relative mean activity coefficients of the M₃[Fe(CN)₆]₂ salts, M=Mg, Ca, Sr, Ba, are measured down to about 5×10^–6 mol-kg^–1 using the liquid membrane cell method. In the dilute region these salts display negative instead of positive deviations from the limiting law, contrary to Debye-Hückel's theory predictions. An indirect method based on auxiliary emf measurements in MCl₂, K₃Fe(CN)₆ and KCl, rather than a theory-assisted direct extrapolation to zero of the relative activity coefficients, is used to identify the actual values of the activity coefficients. The data are compared with Mayer's theory, ion-pair theory and numerical integration of the Poisson-Boltzmann equation. Best-fit coefficients of Pitzer's equation which meet the activity coefficients of the M₃[Fe(CN)₆]₂ salts to be reproduced, are reported.     

First results of the CAKE experiment

We present the preliminary results of the cosmic abundances below the knee energies (CAKE) experiment for the study of the primary cosmic-ray composition and for the search of exotic particles in the primary cosmic radiation. CAKE uses CR39^® and Lexan nuclear track detectors, which were calibrated with beams of 158 AGeV Pb ions and 1 AGeV Fe ions at the CERN and BNL accelerators, respectively. Results based on the analysis of a first data sample are shown.     

A Free Boundary Problem of Fourth Order: Classical Solutions in Weighted Hölder Spaces

We prove short-time existence and uniqueness of classical solutions in weighted Hölder spaces for the thin-film equation with linear mobility, zero contact angle, and compactly supported initial data. We furthermore show regularity of the free boundary and optimal regularity of the solution in terms of the regularity of the initial data. Our approach relies on Schauder estimates for the operator linearized at the free boundary, obtained through a variant of Safonov's method that is solely based on energy estimates.