Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems

We consider a general Euler-Korteweg-Poisson system in R ³, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-in-time weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which the Cauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Székelyhidi.     

Fibril Structure Demonstrates the Role of Iodine Labelling on a Pentapeptide Self-Assembly

Iodination has long been employed as a successful labelling strategy to gain structural insights into proteins and other biomolecules via several techniques, including Small Angle X-ray Scattering, Inductively Coupled Plasma Mass Spectrometer (ICP-MS), and single-crystal crystallography. However, when dealing with smaller biomolecular systems, interactions driven by iodine may significantly alter their self-assembly behaviour. The engineering of amyloidogenic peptides for the development of ordered nanomaterials has greatly benefitted from this possibility. Still, to date, iodination has exclusively been applied to aromatic residues. In this work, an aliphatic bis-iodinated amino acid was synthesized and included into a custom pentapeptide, which showed enhanced fibrillogenic behaviour. Peptide single crystal X-ray structure and powder X-ray diffraction on its dried water solution demonstrated the key role of iodine atoms in promoting intermolecular interactions that drive the peptide self-assembly into amyloid fibrils. These findings enlarge the library of halogenated moieties available for directing and engineering the self-assembly of amyloidogenic peptides.     

Interactions at the outside faces of calix

Attractive pi-pi interactions between two of the four outside cavity faces of 1,3-bis-pyridylmethylcalix[4]arene (1) and both faces of 1,4-diiodotetrafluorobenzene (2a) form infinite one-dimensional non-covalent ribbons where the two modules alternate. These ribbons are cross-linked by electron donor-acceptor interactions between picolyl nitrogen atoms of calixarene 1 in one chain and iodine atoms of perfluoroarene 2a in another chain and the two-dimensional supramolecular network 3a is formed. A similar behaviour is also shown by 1,4-dibromotetrafluorobenzene (2b). The halogen bonding and the attractive pi-pi interactions occur in directions which are nearly orthogonal each other. Diiodotetrafluorobenzene, being involved in both these interactions, appears to be a particularly interesting tecton. The ability of electron-poor arenes to elicit the exo-receptor potential of calixarene module by connecting their outside faces through pi-pi interactions may be developed as a new and general binding protocol in calixarene self-assembly processes.     

A Quasi-Neutral Limit in a Hydrodynamic Model for Charged Fluids

 The combined quasineutral and relaxation time limit for a bipolar hydrodynamic model is considered. The resulting limit problem is a nonlinear diffusion equation describing a neutral fluid. We make use of various entropy functions and the related entropy productions in order to obtain strong enough uniform bounds. The necessary strong convergence of the densities is obtained by using a generalized version of the “div-curl” Lemma and monotonicity methods.     

Organic fluorine compounds: a great opportunity for enhanced materials properties

Interactions of "organic fluorine" have gained great interest not only in the context of crystal engineering, but also in the systematic design of functional materials. The first part of this tutorial review presents an overview on interactions known by organic fluorine. This involves π-π(F), C-F···H, F···F, C-F···π(F), C-F···π, C-F···M(+), C-F···C=O and anion-π(F) interactions, as well as other halogen bonds. The effect of the exchange of H vs. F is discussed by means of several examples and a short introduction to the young field of "fluorous" chemistry is given. The second part is dedicated to numerous applications of fluorine and fluorous interactions. It is shown how application of fluorination is used to enable a number of reactions, to improve materials properties and even open up new fields of research.     

Metadynamics study of a β-hairpin stability in mixed solvents

Understanding the molecular mechanisms that allow some organisms to survive in extremely harsh conditions is an important achievement that might disclose a wide range of applications and that is constantly drawing the attention of many research fields. The high adaptability of these living creatures is related to the presence in their tissues of a high concentration of osmoprotectants, small organic, highly soluble molecules. Despite osmoprotectants having been known for a long time, a full disclosure of the machinery behind their activity is still lacking. Here we describe a computational approach that, taking advantage of the recently developed metadynamics technique, allows one to fully describe the free energy surface of a small β-hairpin peptide and how it is affected by an osmoprotectant, glycine betaine (GB) and for comparison by urea, a common denaturant. Simulations led to relevant thermodynamic information, including how the free energy difference of denaturation is affected by the two cosolvents; unlike urea, GB caused a considerable increase of the folded basin stability, which transposes into a higher melting temperature. NMR experiments confirmed the picture derived from the theoretical study. Further molecular dynamics simulations of selected conformations allowed investigation into deeper detail the role of GB in folded state protection. Simulations of the protein in GB solutions clearly showed an excess of osmoprotectant in the solvent bulk, rather than in the protein domain, confirming the exclusion from the protein surface, but also highlighted interesting features on its interactions, opening to new scenarios besides the classic "indirect mechanism" hypothesis.     

Temperature and pressure dependence of secondary process in an epoxy system

Dielectric spectroscopy as a function of temperature and pressure was used to study the secondary relaxation in poly [(phenyl glycidyl ether)-co-formaldehyde] at hydrostatic pressure up to 600 MPa and at different temperatures between 315 and 243 K. From the analysis of the isothermal measurements, we observe that the activation volume of the secondary relaxation has nonmonotonic temperature dependence with a maximum at the temperature of the glass transition at ambient pressure. An interpretation in terms of mean hole volume dispersion is proposed based on literature data. Moreover, from isobaric data, we studied the effect of pressure on activation entropy and enthalpy of the secondary relaxation evidencing its local nature but also the presence of a certain complexity of the motion, which supports the idea that this process reflects the motion of a large part of the molecule.