### CoMe Seminar Series

Lisandro Roldán, Andrea Collivadino and Jordi Barceló

Lisandro Roldán (Master in Numerical Methods in Engineering)

**Computational model for the chemo-mechanical mechanism in wound healing**

Wounds in multicellular tissue occur regularly through the lifetime of organisms, and the closure of these gaps is fundamental for their healthy development. Two important processes involved are the formation of an actomyosin ring and its active contraction. A mechanical continuum model for both of them is developed. The first one involves the coupling of transient calcium transport, with actin fibers and myosin motors recruitment and non-linear mechanics. For the second stage, the active deformation of the previously formed actomyosin cable is modeled.

Andrea Collivadino (Master in Advanced Mathematics and Mathematical Engineering)

**A variational approach in modelling hydrogels**

Hydrogels are defined as a cross-linked polymeric network that exhibits the ability to swell and retain a significant fraction of solvent. Hydrogels are capable of large and recoverable deformations and, as the solvent flows across the network, energy is dissipated. From these features, it follows that a successful model need to couple large deformations with mass transport and dissipation. The Onsager variational principle satisfies all these requirements. Moreover, it provides a convenient setting for performing numerical analysis and coupling different physics in the system. This is particularly convenient since hydrogels can exhibit responsive behavior to external stimuli such as pH, electricity, light, and many more.

Jordi Barceló

**High order finite element method for Stefan problem.**

The Stefan problem is a partial differential equation adapted to the case in which an interface can move with time. It describe the temperature distribution in a homogeneous medium undergoing a phase change, in this case water passing to ice. In this project I have used XFEM to solve the problem using a level set to define the interface. I have impose weak dirichlet boundary condition in the interface with Nitsche’s method and the update of the level set for each node has been done using the normal velocity of the closest point on the interface. Finally I have test the good convergence of the method.

Victoria Lang (Master in Advanced Mathematics and Mathematical Engineering)

**Numerical Modelling of the Electrophysiology of the Neuron**

The immediate goal of this master’s thesis is to examine the electrophysiology of the neuron and the consequences of imposing mechanical insults to neurons. Existing mathematical models, such as the Hodgkin-Huxley model of the neuron, form the basis for this study. Using mathematical models to describe biological processes has become increasingly important for the advantages that arise from this integration. Some of these advantages include: the development of computer-aided simulations prior to wet experiments, the ability to easily validate clinical results when the data coincide, and the ability to characterize and predict behaviors using mathematical principles. Moreover, the application of mathematics to biology makes way for more refined models that give deeper insights to the observations and theories scientists have made.