After decades of experimental investigation, the dynamics howindividual cellsmove or deform-perfectly orchestrated for the creation and proliferation of tissue - remain partly unknown. In most recent years, the use of computational models, also called in silico experiments, has become a focus of interest. Due to their flexible scaling, compared to classical in vivo and in vitro studies, simulations can give important insights in the dynamics of cellular structures. We investigate Multi-Phasefield models for cellular structures, a versatile approach, capable of capturing complex changes in cell shape. Furthermore, it gives large flexibility in the modeling of cell-cell interactions and subcellular details like the propulsion machinery. The dynamics how these motility mechanisms create complex movement patterns on the tissue scale, will be a particular focus of this thesis. We compare four essentially different ways to introduce activity in Multi-Phasefield models, from movement driven by a random walk or the macroscopic shape of each cell towards a description of the subcellular machinery using either a polar or a nematic approach. For the different propulsion models, we investigate a variety of phenomena. Starting from the observation that the polar model creates collective motion, we observe that the resulting alignments resemble those of passive systems, expressed in Lewis’ and Aboav-Weaire’s law. Furthermore, we study a transition between solid and liquid state of the tissue, known to be important for many developmental processes. Additionally, we analyze the occurring patterns in the cellular alignment and flow, for systems in both confluence and confinement. Afterwards, we investigate the alignment of cell deformations with methods known from nematic structures. This reveals how the different propulsion mechanisms cause contractile or extensile behavior, classified by the movement of topological defects and the distribution of strain in their vicinity. At the end of this thesis, we show two extensions of themodels, capable of including growth and division of cells and generalizations towards curved manifolds as computational domains. Furthermore, we give an outlook on a possible roadmap for the future of Multi-Phasefield models in the description of cellular structures and their potential for a better understanding of the dynamics in the creation of life.

This work describes two phase field models for the simulation of the interface evolution between a LiCoO2 cathode (LCO) and a Li7La3Zr2O12 solid electrolyte (LLZO) in a Li-metal/LLZO/LCO battery during high temperature sintering. In these conditions atomic species tend to diffuse into the opposing material, creating an intermediate layer of mixed composition which resists the movement of lithium ions. This undesired effect prevents the resulting solid-state battery to achieve its theoretical performances and needs to be avoided. The first model is an adaptation of the work of J. M. Hu et alii [1] for a similar interface problem encountered between yttria-stabilized zirconia electrolytes (YSZ) and lanthanum-strontium-manganite cathodes (LSM) in solid oxide fuelcells (SOFC), while the second is based on the work of D. A. Cogswell [2][3] for phase separation in metal alloys, extended to include electrostatic effects due to internal charge unbalances and externally applied electric fields. Animplementation of the latter is however lacking, and the interested reader is encouraged to build one up on the theoretical framework presented in this paper. In the conclusion section it is possible to find insights on how to prevent the interfacial diffusion between LCO and LLZO with reference to experimental attempts and simulations, as well as future directions for the development of the models.

We present a phase-field crystal model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the microscopic density field. We showcase the model capabilities via selected numerical investigations which focus on the prototypical growth of two-dimensional crystals from the melt, resulting in faceted shapes and dendrites. This work sets the grounds for a comprehensive mesoscale model of solidification including thermal expansion.