Low-molecular-weight gels: from the rational design to the application of versatile soft materials

Low-molecular-weight (LMW) gels are a versatile class of soft materials that gained increasing interest over the last few decades. They are made of a small percentage, often lower than 1.0 %, of organic molecules called gelators, dispersed in a liquid medium. Such molecules have a molecular weight usually lower than 1 kDa. The gelator molecules start to interact after the addition of a trigger, and form fibres, whose entanglement traps the solvent through capillary forces. A plethora of LMW gelators have been designed, including short peptides. Such gelators present several advantages: the synthesis is easy and can be easily scaled up; they are usually biocompatible and biodegradable; the gelation phenomenon can be rationalised by making small variation on the peptide scaffold; they find application in several fields. In this thesis, an overview of several peptide based LMW gels is presented. In each study, the gelation conditions were carefully studied, and the final materials were thoroughly investigated. First, the gelation ability of a fluorinated phenylalanine was assessed, to understand how the presence of a rigid moiety and the presence of fluorine may influence the gelation. In this context, a method for the dissolution of sensitive gelators was studied. Then, the control over the gel formation was studied both over time and space, taking advantage of either the pH-annealing of the gel or the reaction-diffusion of a hydrolysing reagent. Some gels were probed for various applications. Due to their ability of trapping water and organic solvents, we used gels for trapping pollutants dissolved in water, as well as a medium for the controlled release of either fragrances or bioactive compounds. Finally, the interaction of the gel matrix with a light-responsive molecule was assessed to understand wether the gel properties or the interaction of the additive with light were affected.

Pattern recognition analysis on heavy ion reaction data

One of the problems in the analysis of nucleus-nucleus collisions is to get information on the value of the impact parameter b. This work consists in the application of pattern recognition techniques aimed at associating values of b to groups of events. To this end, a support vec- tor machine (SVM) classifier is adopted to analyze multifragmentation reactions. This method allows to backtracing the values of b through a particular multidimensional analysis. The SVM classification con- sists of two main phase. In the first one, known as training phase, the classifier learns to discriminate the events that are generated by two different model:Classical Molecular Dynamics (CMD) and Heavy- Ion Phase-Space Exploration (HIPSE) for the reaction: 58Ni +48 Ca at 25 AMeV. To check the classification of events in the second one, known as test phase, what has been learned is tested on new events generated by the same models. These new results have been com- pared to the ones obtained through others techniques of backtracing the impact parameter. Our tests show that, following this approach, the central collisions and peripheral collisions, for the CMD events, are always better classified with respect to the classification by the others techniques of backtracing. We have finally performed the SVM classification on the experimental data measured by NUCL-EX col- laboration with CHIMERA apparatus for the previous reaction.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.