# Workshop: "Current challenges in complex materials: modelling and analysis"

**Dates:** January 9 - 13, 2023**Venue:** HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Irene Fonseca (Carnegie Mellon), Valeriy Slastikov (Bristol), Arghir Zarnescu (BCAM)

Many recent and spectacular technological advances are driven by the developments of novel complex materials with extraordinary and unique features. The adequate mathematical models are essential for the discovery and systematical study of the properties of these complex materials. There exists a number of well-accepted models for complex materials with well-understood mathematical challenges, for instance Oseen-Frank and Landau-de Gennes models for liquid crystals, Landau-Lifschitz and Brown models for magnetic materials, to name just a few. However, contemporary active investigations in physics, for instance, focus on heterogeneous or layered materials where multiple components with different properties are combined at appropriate scales. The main aim of this workshop is to bring together mathematicians and scientists working in various areas of materials science and applied mathematics in order to identify the main challenges posed by the modelling and analysis of complex materials.

Click here for the schedule

Click here for the abstract

Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.

# Video Recordings

# Day 1

Felix Otto: Bias in the Representative Volume Element method: periodize the ensemble instead of its realizations

Anne Bernand-Mantel: Skyrmion theory in magnetic thin films: the role of non-local magnetic dipolar interaction

Giacomo Canevari: A free-discontinuity problem for smectic liquid crystals

Zhiyuan Geng: Liquid crystal droplets and a nonlocal free boundary problem

Massimiliano Morini: Capillary surfaces and a model of nanowire growth

# Day 2

Radu Ignat: Separation and interaction energy between domain walls in a nonlocal model coming from micromagnetics

Giovanni Di Fratta: Curved thin-film limits of chiral Dirichlet energies

Michele Ruggeri: Numerical methods for antiferromagnetic and ferrimagnetic materials

Xian Chen: Two tier compatibility conditions for phase transforming polycrystals

# Day 3

Bianca Stroffolini: A 2D model for ferronematics with weak coupling

Razvan Dumitru Ceuca: Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study

# Day 4

Adriana Garroni: Variational approach for grain boundaries

Annika Bach: Emergence of topological singularities in the antiferromagnetic XY-model on the triangular lattice

Dmitry Golovaty: Tetrahedral frame fields via constrained third order symmetric tensors

# Day 5

Amit Acharya: Dynamics of line defects

Xavier Lamy: Generation of vortices in the Ginzburg Landau heat flow

Likhit Ganedi: Phase Separation in Heterogeneous Fluids

Theresa Simon: The elastica functional as the critical Gamma-limit of the screened Gamow model