Coupled Processes in Soft and Active Matter

Many processes in Nature and our daily life are influenced by multiple mechanisms which are intrinsically-coupled. Examples include the formation of a ring-shaped stain when coffee is spilt, the migration of cells during wound healing, and reaction rates depending on evolving local concentrations, among others. The coupling of different mechanisms makes many processes challenging to understand, but it is crucial to take this coupling into account to arrive at an accurate quantitative model of the process. More interestingly, the coupling of dynamical processes can introduce new, emergent physical, chemical, and biological dynamics that is not present in the basic mechanisms that are being coupled. The course discusses the relevant concepts from soft matter physics, and the associated mathematical tools, to understand how processes can be coupled. Our focus is on transport and rate processes such as diffusion and convection, migration in electric fields, (bio)chemical reactions, individual and collective motion of cells, and mechanical deformation. Special attention is paid to hydrodynamics of swimming and microbial motility, advection-diffusion systems, and even elasticity in complex geometries. A selection is made from more advanced subjects such as fluid dynamics, statistical physics, and fracture — each creating a distinct class of coupled processes.

Coupled processes are often mathematically-complex. So we employ easy-to-use computer modeling approaches to explore the relevant mathematics. The modeling exercises are used for illustration and ‘playing around’ with coupled processes to obtain insight into the effects of the relevant parameters, the rate-limiting factors, and the time and length scales. For the modeling part, Jupyter notebooks will be used. Extensive computer programming will not be a part of the course, and is not required from the students. Starter notebooks will be provided, and the students will be expected to tinker with the various control parameters. The course fits in the line of other PCC courses on soft matter but can also be taken with a basic knowledge of multivariable calculus.

After successful completion of this course students are expected to be able to:

• relate and apply concepts of coupled processes in different kinds of soft matter systems;
• assess relevant modelling parameters, rate-limiting factors, time and length scales;
• demonstrate a clear understanding of concepts underlying the coupling of processes;
• analyse and evaluate the results of the computer modeling in the context of the underlying theory.

Assumed Knowledge:
PCC20806 Soft Matter