Theoretical studies of microfluidics: "walking" drops and "melting" snowflakes.

The present PhD thesis summarizes two examples of research in microfluidics. Both times water was the subject of interest, once in the liquid state (droplets adsorbed on chemically functionalized surfaces), the other time in the solid state (ice snowflakes and their fractal behaviour). The first problem deals with a slipping nano-droplet of water adsorbed on a surface with photo-switchable wettability characteristics. Main focus was on identifying the underlying driving forces and mechanical principles at the molecular level of detail. Molecular Dynamics simulation was employed as investigative tool owing to its record of successfully describing the microscopic behaviour of liquids at interfaces. To reproduce the specialized surface on which a water droplet can effectively “walk”, a new implicit surface potential was developed. Applying this new method the experimentally observed droplet slippage could be reproduced successfully. Next the movement of the droplet was analyzed at various conditions emphasizing on the behaviour of the water molecules in contact with the surface. The main objective was to identify driving forces and molecular mechanisms underlying the slippage process. The second part of this thesis is concerned with theoretical studies of snowflake melting. In the present work snowflakes are represented by filled von Koch-like fractals of mesoscopic beads. A new algorithm has been developed from scratch to simulate the thermal collapse of fractal structures based on Monte Carlo and Random Walk Simulations (MCRWS). The developed method was applied and compared to Molecular Dynamics simulations regarding the melting of ice snowflake crystals and new parameters were derived from this comparison. Bigger snow-fractals were then studied looking at the time evolution at different temperatures again making use of the developed MCRWS method. This was accompanied by an in-depth analysis of fractal properties (border length and gyration radius) in order to shed light on the dynamics of the melting process.

Implicit computational complexity and probabilistic classes

The thesis applies the ICC tecniques to the probabilistic polinomial complexity classes in order to get an implicit characterization of them. The main contribution lays on the implicit characterization of PP (which stands for Probabilistic Polynomial Time) class, showing a syntactical characterisation of PP and a static complexity analyser able to recognise if an imperative program computes in Probabilistic Polynomial Time. The thesis is divided in two parts. The first part focuses on solving the problem by creating a prototype of functional language (a probabilistic variation of lambda calculus with bounded recursion) that is sound and complete respect to Probabilistic Prolynomial Time. The second part, instead, reverses the problem and develops a feasible way to verify if a program, written with a prototype of imperative programming language, is running in Probabilistic polynomial time or not. This thesis would characterise itself as one of the first step for Implicit Computational Complexity over probabilistic classes. There are still open hard problem to investigate and try to solve. There are a lot of theoretical aspects strongly connected with these topics and I expect that in the future there will be wide attention to ICC and probabilistic classes.

Extending Implicit Computational Complexity and Abstract Machines to Languages with Control

The Curry-Howard isomorphism is the idea that proofs in natural deduction can be put in correspondence with lambda terms in such a way that this correspondence is preserved by normalization. The concept can be extended from Intuitionistic Logic to other systems, such as Linear Logic. One of the nice conseguences of this isomorphism is that we can reason about functional programs with formal tools which are typical of proof systems: such analysis can also include quantitative qualities of programs, such as the number of steps it takes to terminate. Another is the possiblity to describe the execution of these programs in terms of abstract machines. In 1990 Griffin proved that the correspondence can be extended to Classical Logic and control operators. That is, Classical Logic adds the possiblity to manipulate continuations. In this thesis we see how the things we described above work in this larger context.

Probabilistic Recursion Theory and Implicit Computational Complexity

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene's partial recursive functions which includes, among initial functions, one that returns identity or successor with probability 1/2. We then prove the equi-expressivity of the obtained algebra and the class of functions computed by PTMs. In the the second part of the thesis we investigate the relations existing between our recursion-theoretical framework and sub-recursive classes, in the spirit of Implicit Computational Complexity. More precisely, endowing predicative recurrence with a random base function is proved to lead to a characterization of polynomial-time computable probabilistic functions.

Tailoring properties and functionalities of TiO2 and Ag nanoparticles involved in surfaces engineering processes

The functionalization of substrates through the application of nanostructured coatings allows to create new materials, with enhanced properties. In this work, the development of self-cleaning and antibacterial textiles, through the application of TiO2 and Ag based nanostructured coatings was carried out. The production of TiO2 and Ag functionalized materials was achieved both by the classical dip-padding-curing method and by the innovative electrospinning process to obtain nanofibers doped with nano-TiO2 and nano-Ag. In order to optimize the production of functionalized textiles, the study focused on the comprehension of mechanisms involved in the photocatalytic and antibacterial processes and on the real applicability of the products. In particular, a deep investigation on the relationship between nanosol physicochemical characteristics, nanocoating properties and their performances was accomplished. Self-cleaning textiles with optimized properties were obtained by properly purifying and applying commercial TiO2 nanosol while the studies on the photocatalytic mechanism operating in self-cleaning application demonstrated the strong influence of hydrophilic properties and of interaction surface/radicals on final performance. Moreover, a study about the safety in handling of nano-TiO2 was carried out and risk remediation strategies, based on “safety by design” approach, were developed. In particular, the coating of TiO2 nanoparticles by a SiO2 shell was demonstrated to be the best risk remediation strategy in term of biological response and preserving of photoreactivity. The obtained results were confirmed determining the reactive oxygen species production by a multiple approach. Antibacterial textiles for biotechnological applications were also studied and Ag-coated cotton materials, with significant anti-bacterial properties, were produced. Finally, composite nanofibers were obtained merging biopolymer processing and sol-gel techniques. Indeed, electrospun nanofibers embedded with TiO2 and Ag NPs, starting from aqueous keratin based formulation were produced and the photocatalytic and antibacterial properties were assessed. The results confirmed the capability of electrospun keratin nanofibers matrix to preserve nanoparticle properties.

Bone-implant interface. Evaluation of osteoblastic cells behavior on nanopatterned titanium surfaces: an in vitro analysis

Protein-adsorption occurs immediately following implantation of biomaterials. It is unknown at which extent protein-adsorption impacts the cellular events at bone-implant interface. To investigate this question, we compared the in-vitro outcome of osteoblastic cells grown onto titanium substrates and glass as control, by modulating the exposure to serum-derived proteins. Substrates consisted of 1) polished titanium disks; 2) polished disks nanotextured with H2SO4/H2O2; 3) glass. In the pre-adsorption phase, substrates were treated for 1h with αMEM alone (M-noFBS) or supplemented with 10%-foetal-bovine-serum (M-FBS). MC3T3-osteoblastic-cells were cultured on the pre-treated substrates for 3h and 24h, in M-noFBS and M-FBS. Subsequently, the culture medium was replaced with M-FBS and cultures maintained for 3 and 7days. Cell-number was evaluated by: Alamar-Blue and MTT assay. Mitotic- and osteogenic-activities were evaluated through fluorescence-optical-microscope by immunolabeling for Ki-67 nuclear-protein and Osteopontin. Cellular morphology was evaluated by SEM-imaging. Data were statistically analyzed using ANOVA-test, (p<0.05). At day3 and day7, the presence or absence of serum-derived proteins during the pre-adsorption phase had not significant effect on cell-number. Only the absence of FBS during 24h of culture significantly affected cell-number (p<0.0001). Titanium surfaces performed better than glass, (p<0.01). The growth rate of cells between day3 and 7 was not affected by the initial absence of FBS. Immunolabeling for Ki-67 and Osteopontin showed that the mitotic- and osteogenic- activity were ongoing at 72h. SEM-analysis revealed that the absence of FBS had no major influence on cell-shape. • Physico-chemical interactions without mediation by proteins are sufficient to sustain the initial phase of culture and guide osteogenic-cells toward differentiation. • The challenge is avoiding adsorption of ‘undesirables’ molecules that negatively impact on the cueing cells receive from surface. This may not be a problem in healthy patients, but may have an important role in medically-compromised-individuals in whom the composition of tissue-fluids is altered.