Tutorial 2. Graphs and Networks for Complex Materials: Fundamental Concepts

ANCILLARYEVENT · MAR-2T · ID: MAR-2T

This is the first of a set of tutorials that provide a comprehensive dive into the basics of graph theory, network science and their implementations in materials science, biological sciences, and self-assembly processes. Emerging from graph theory and statistical thermodynamics, network science has profoundly influenced diverse fields—from physics to biology and social sciences. Combined with current knowledge of multifunctional materials and nanostructures, the foundational graph-based methods can reveal deep connections between complexity of structures, their functions and dynamics. Structural descriptors of complex materials combining order and disorder can replace crystal order parameter and provide a rapidly expanding toolbox for soft matter and advanced materials offering previously inaccessible functionalities, exemplified by biological and biomimetic nanocomposites. 

This first instalment of the tutorial will provide the mathematical, physical, and chemical foundations for graph-based methodologies in soft matter.  We will introduce key concepts and advances in this area.  Participants will delve into fundamental concepts of graphs and networks with the concomitant explanations how they offer an efficient and comprehensive description of complex materials, followed by physical dynamics on these networks and gels as a prime example where networks reveal essential materials properties. We will study intricate network structures inherent in advanced materials, demonstrating how network science provides a robust framework for predicting material behavior. 

Topics covered: 

• Introduction to Network Science  
• Graph Description of Complex Materials  
• Physical Dynamics on Networks   
• Gels as Complex Networks