A first order phase transition with non-constant density

We introduce a new model for first order phase transitions accounting for non-constant densities of the phases during the process. The resulting initial and boundary value problem for a PDE system is recovered by thermodynamical principles. The resulting system presents some singularities and strong nonlinearities accounting for internal constraints, ensuring in particular the positivity of the pressure and the temperature. Physical consistency for the order parameter comes from a maximum principle argument. Existence of a weak solution is proved by a regularization-passage to the limit procedure.     

All‐in‐One Cellulose Nanocrystals for 3D Printing of Nanocomposite Hydrogels

Cellulose nanocrystals (CNCs) with >2000 photoactive groups on each can act as highly efficient initiators for radical polymerizations, cross‐linkers, as well as covalently embedded nanofillers for nanocomposite hydrogels. This is achieved by a simple and reliable method for surface modification of CNCs with a photoactive bis(acyl)phosphane oxide derivative. Shape‐persistent and free‐standing 3D structured objects were printed with a mono‐functional methacrylate, showing a superior swelling capacity and improved mechanical properties.     

Enantiomeric and Diastereomeric Self‐Assembled Multivalent Nanostructures: Understanding the Effects of Chirality on Binding to Polyanionic Heparin and DNA

A family of four self‐assembling lipopeptides containing Ala‐Lys peptides attached to a C₁₆ aliphatic chain were synthesised. These compounds form two enantiomeric pairs that bear a diastereomeric relationship to one another (C₁₆‐l ‐Ala‐l ‐Lys/C₁₆‐d ‐Ala‐d ‐Lys) and (C₁₆‐d ‐Ala‐l ‐Lys/C₁₆‐l ‐Ala‐d ‐Lys). These diastereomeric pairs have very different critical micelle concentrations (CMCs). The self‐assembled multivalent (SAMul) systems bind biological polyanions as a result of the cationic lysine groups on their surfaces. For heparin binding, there was no significant enantioselectivity, but there was a binding preference for the diastereomeric assemblies with lower CMCs. Conversely, for DNA binding, there was significant enantioselectivity for systems displaying d ‐lysine ligands, with a further slight preference for attachment to l ‐alanine, with the CMC being irrelevant.     

Bifurcations and stability of amplitude modulated planar oscillations of an orbiting string with internal resonances

Nonlinear free transversal oscillations of an orbiting string satellite system are analyzed. They are governed by two partial integro-differential equations with quadratic nonlinearities. The system is weakly nonlinear but in practice works in conditions of nearly simultaneous internal resonance. The ability of truncated models to capture specific phenomena is discussed. By limiting the investigation to the planar motion with a one prevailing component perturbed out-of-plane, two different models with three modes in primary and secondary resonance are adopted. For increasing levels of the system energy, fundamental and bifurcated paths of fixed points are obtained and their stability is investigated. Moreover, periodically amplitude modulated planar motions and their stability for out-of-plane disturbances are studied.