APRÈN. Portal de la producció docent del professorat de la UPC

Shells are generally defined as structures with fixed shapes that deform under applied loads. In common engineering contexts, a shell is a load-bearing element, that typically does not undergo considerable geometrical changes. Nevertheless, in some applications such as soft robotics, it is desired to engineer structural elements that morph. A morphing structure could either generate movement by the existence of mechanisms that are considered instabilities, or a power input into the system such as activity. Active nematics are a class of liquid crystals capable of performing mechanical power by transducing chemical energy. This work attempts to study an active nematic surface, whose activity is fueled by (elongated) living cells. Our bio-hybrid system is analogous to an active nematic surface as it reshapes upon actuation. Motivated by the experiments where elongated cells are patterned nematically onto a thin sheet, we study the reshaping of the shell intending to understand the relation between the input patterns of nematic cell orientation and the output shape. For this purpose, we combine the appropriate shell theories with active nematic models in a computational framework and derive a shell model with active tension along a nematic texture.

Modelling and simulating accretion growth by characterizing the prestrain as a function of time

Homeostasis is a process by which biological systems maintain stability in an evolving environment. However, homeostasis is far from being a static state. In rapidly self-renewing tissues such as the small intestine epithelium, most cells are replaced every few days, and during their lifespan undergo differentiation and migrate over long distances along gradients of cell shape and density. We model mathematically and computationally intestinal organoids, a simpler in-vitro system which captures the essential features of intestinal homeostasis. To model this system, we adopt a continuum hydrodynamic model where the system is described in terms of the cell number density and the concentration of morphogen Wnt. We provide a systematic derivation of the model, its numerical discretization, and examine its ability to self-organize into dynamical steady-states, which closely mimic the experimental observations in terms of cell density fields, velocity fields and division/extrusion patterns.

Nucleation is a very common process by which phase separation takes place in multicomponent liquid mixtures. Phase field models are usually applied to study phase separation, but they are insufficient to study nucleation events, since these transitions are thermally activated and require overcoming an energy barrier. To overcome this difficulty, we combined phase field models with the string method, a numerical scheme capable of finding transition pathways and critical states, to study nucleation in binary and ternary systems. Our model is able to capture homogeneous and heterogeneous nucleation both in binary and ternary systems. We validate our approach by comparing it with classical nucleation theory, valid in a sharp interface limit, and further examine and discuss the discrepancies between these two approaches. In the future this model can be applied to study more complex configurations, some of which are interesting from a biological point of view because they simulate protein separation in the intracellular fluid.

In this thesis, we will study the invasion of breast cancer into the tissue. This process involves many cellular and extracellular processes tightly coupled between them. In particular, in this work we focus on the mechanics of the extra-cellular matrix that forms part of this tissue and exhibits a mechanosensitive nature that is essential to understand the motility and invasion of cancer. We will focus on the mechanics of the collagen network, more precisely on a model for an elastic material that can account for different types of collagen networks, with varying concentration and properties. In order to capture the large deformations of the extracellular matrix, we need to go beyond linear elasticity and use a hyperelastic model. This study will be done using a C++ library called Hipelife, dedicated to the solving of finite element problems.

Euglenids are protists unicellular flagellates made of parallel proteinaceous strips and microtubules located underneath the plasma membrane, they exhibit a highly intriguing shape morphing mechanism that permits them to move through the media and for the feeding process. Inspired by this behaviour we develop a model to mimics the pellicle kinematics by linking the pellicle deformations and the mechanics of the rods by assuming a continuous surface made of adjacent rods. The computational model works by finding the shape configuration that minimizes the energy functional. We obtain a wide repertory of possible configurations using axisymmetric cylindrical surfaces and we obtain a reduce model for the case of inextensible rods. Additional actuation of pellicle shears should be studied to obtain a larger set of shape configurations mainly non-axisymmetrical. New numerical studies are needed to obtain smooth transitions between pairs of stable configurations.

Epithelial cells arrange into two-dimensional cohesive cell layers that perform very important mechanical functions during development and adult physiology. These layers and their cell constituents can be seen as structured materials. The goal of this thesis is to develop structural mechanics models of tissues (vertex models) based on the sub-cellular dynamics of the acto-myosin cytoskeleton. We expect to understand the effective viscoelastic properties of epithelial tissues in terms of the microscopic dynamics of the cytoskeleton.

Within cells, the cytoskeleton organizes into polymer networks with unique properties. At short time-scales, they behave elastically. However, due to molecular turnover, at longer time-scales they behave like viscous fluids in low Reynold limit. In addition to this, they are capable of actively developing tension, thanks to molecular motors using chemical energy . At the tissue scale, epithelial cell formed by monolayers can exhibit, in some regimes, a similar active fluid behavior. Contractile forces plays a key role in tissue, for example, in organ development, wound healing, remodeling of the newly synthesized connective tissue, and in sub-cellular level like cell elongation, contraction, rearrangements, cell adhesion, division, cell migration and furrow construction in cytokinesis. Furthermore, as a part of optogenetic technnique, the doped epithelial tissues experience contractility upon illumination. Motivated by this, in the present work we considered a monolayer of cells with illumination as an external power input defined as an tension pattern in space and time to engineer contractility patterns to transport material from one part of the tissue to another or to engineer morphogensis. Altogether, for the system at low Reynold's limit, governing equations of this compressible active visco-elastic model are developed using traditional continuum approach and Onsager's variational principle and solved using linear finite elements. The system is non-dimensionalized and the effect of each independent parameter on the system is analyzed. Finally, this model helps in examining the principles that govern the ability to remodel the material by applying space-time patterns of activity.

In this thesis we review some basic concepts of tensors and differential geometry and apply them to model the actin cortex, an active envelop that determines the shape and mechanical properties of animal cells. The model formalism invokes Onsager's variational principle. We study the cell response under a density gradient when we vary the rates of polymerization and depolymerization. Two different scenarios are observed: the cell recovers the equilibrium density, or the gradient increases giving rise to a stable-bleb shape. The transition between these two situations is also studied.

The goal of this Master's thesis is to provide a physical and mathematical model that attempts to describe the deformation process of hydrogels. Hydrogels are commonly defined as three dimensional networks of hydrophilic polymers with the ability to retain a large quantity of water. Nevertheless, describing the deformation process of hydrogels can be challenging. In this thesis, I expose a variational model that is obtained with the Onsager's principle. This principle provides an ideal setting for discretization and numerical analysis.

Nowadays, technology advances really fast and so does the generation of data. Almost all electronic devices are constantly generating and sharing a huge amount of data through the World Wide Web. Moreover, recent policies of open governments and data, are helping to make available this information for everybody that wants to take it and use it. The aim of using Big Data is to discover knowledge that is hidden behind thousands of rows of information. However, to find out the value of the data, it is necessary to use non-traditional methods able to deal with such amount of information. Furthermore, big cities have traffic problems and complex mobility patterns which need to be studied in depth to improve life conditions of citizens, reduce pollution and to create eco-friendly cities. This work is focused on the city of Barcelona and its bike-sharing system Bicing. The aim is to understand the mobility patterns of Bicing subscribers using Big Data. Treating Big Data requires of more resources than conventional problems. So that, setting a methodology to acquire, pre-process and treat the data has been necessary before proceeding with the analysis. In order to gain visibility out of the data, two different approaches have been followed. First of all, an exploratory analysis of the behaviour of the users of Bicing. On the other hand, a Principal Component Analysis has also been carried out to understand the data but also to reduce the dimensionality, hence the volume of the data necessary to provide acceptable results. To sum up, the present work is a particular example of the possibilities that Big Data offers in terms of gaining knowledge out of massive amounts of data. Moreover, it studies the patterns of Bicing subscribers during different periods of the day, week and year based on real data.

A fuel cell is an electrochemical device that has the ability to turn the chemical energy in a fuel directly into electricity with high e ciency. Inside the fuel cell, oxidation and reduction electrochemical reactions take place producing low-voltage current (DC) and heat. The former is used to do useful work while the latter is wasted or can be used in cogeneration applications. Fuel cells are usually compared with other energy convertors, like reciprocating engines or batteries. Batteries and fuel cells have the same operating principle, based on the electrochemical reactions at the anode and the cathode. The main di erence being that batteries store the reactant inside the cell instead of in a separate storage tank. There are di erent types of fuel cells depending on the materials used in the electrolytes, the substances that react in the anode and the cathode or the working temperature. The current work focuses on Polymer Electrolyte Membrane (PEM) fuel cells, which can work between -40 and 100 C and use hydrogen as fuel, oxygen as cathode reactant and Na on® as the electrolyte (Figure 1.1). The working principle of the PEM fuel cell is based on two electrochemical reactions. The process starts at the anode, where the hydrogen ows in the anode Gas Flow Channel (GFC) and di uses through the pores in the Gas Di usion Layer (GDL). Attached to the GDL is the Catalyst Layer (CL). The CL is made using a platinum-based ink which is painted on either the PEM or the GDL. The ink contains carbon, Pt and electrolyte. The resulting coating is a thin (about 10 m) porous layer. The Pt catalyses the rst reaction: the hydrogen oxidation reaction.H2 􀀀! 2H+ + 2e- (1.1) After this reaction, the next layer is the membrane which is made of Na on®. The membrane allows the protons to travel across its section but it is impermeable for the electrons and gases. The electrons have to go back through the GDL and the current collector (that act as the walls of the anode gas ow channel) in order to meet the protons at the other side of the membrane, thus generating the desired electric current. In the cathode, the oxygen ows in the cathode gas channels, di uses through the GDL and in the catalyst layer reacts with the protons from the membrane, performing the second reaction: 2H+ + 2e- + 1 2 O2 􀀀! 2H2OThe union of the anode GDL and CL, membrane and cathode CL and GDL is also known as Membrane Electrode Assembly (MEA). When fuelled with hydrogen, the fuel cell has zero emissions, since the only product of the electrochemical reaction is water and heat. The water generated in the reaction is one of the key factors in uencing the fuel cell performance. The membrane needs water in order to conduct the protons; if there is not enough water, the membrane dries out and the fuel cell cannot work any longer. Alternatively, if there is too much water, the pores in the CL and GDL ood preventing the reactant gases from di using through it. The exceeding water has therefore to be evacuated through the cathode gas channels. This is the starting point of the present work. There are three types of two-phase ow in the gas channels depending on di erent factors. Their names change depending on the author, however, these ows are usually known as droplet, lm and slug ow [2], as shown on Figure 1.2. The present work focuses on droplet ow and the conditions that lead to lm and slug ow. Since it is very di cult to develop an analytical equation for the shape of a water lm, the best way to proceed is the analysis of a single static and deformed droplet and then identify the conditions that lead to lm and slug ow formation. In addition, the area coverage of the formed droplets is another variable that needs to be considered, and this variable takes values from 0 to 1 only when the ow is identi ed as droplet ow.

The goal of this project is to explore the mechanics of lipid fluid membranes as found in biological and made-man systems through continuum models and numerical simulations. Traditionally, the focus has been on the equilibrium configurations of vesicles through minimization of the curvature energy subject to constraints. Here, the goal is to describe the time-evolution of out-of-equilibrium vesicle configurations, which are of relevance in biological systems. Towards this goal, an accurate description of the dissipative mechanisms is crucial, in particular the viscous dissipation induced by the 2D flow of lipids on the deforming surface that describes a vesicle [1]. The resulting equations can only be solved analytically in very simple settings. So the problem is solved numerically using a B-Spline description of the membrane vesicle. The dynamics are described using two types of viscosity: the L2 or Willmore viscosity and the inner flow viscosity. By comparing the evolution in time of the two systems, it is stated that the dynamics are clearly different. It is found that one describes better the physics of the system.