Non-equilibrium Soft Matter

The diverse field of soft matter that comprises of many phenomena that we observe in nature and our daily life are inherently non-equilibrium processes. Further, these processes are influenced by multiple dynamical mechanisms that are intrinsically-coupled. Examples include the formation of a ring-shaped stain when coffee or tea is spilt, the migration of cells during wound healing, the flocking of birds, the motion of chloroplasts in plant cells, the taxis of microorganisms in response to external stimuli, and reaction rates in chemical reactions depending on evolving local concentrations, among others. The non-equilibrium nature of these processes makes them challenging to understand, but it is crucial to mathematically account for this out-of-equilibrium behavior in order to arrive at a quantitative model of the process being considered. More interestingly, this out-of-equilibrium nature can lead to new emergent physical, chemical, and biological dynamics that is not present in the basic mechanisms that are being coupled. This course discusses the salient concepts and features of non-equilibrium soft matter physics, and the associated mathematical tools required to model them. While there can be a multitude of approaches to study non-equilibrium soft matter, the focus in this course is a hydrodynamical approach to characterize transport and rate processes such as diffusion and convection, biochemical reactions, individual and collective motion of cells, and mechanical deformation. Special attention is paid to microbial motility, advection-diffusion systems, and elasticity in complex geometries while borrowing key concepts and tools from fluid dynamics, statistical physics, and fracture mechanics.

Non-equilibrium soft matter is 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 the relevant parameters to obtain insights into the non-equilibrium nature of the process and its rate-limiting factors. For the modeling part, Jupyter notebooks will be used. Extensive computer modeling will not be a part of the course. Starter notebooks will be provided, and the students will be expected to tinker with the various control parameters. The course fits in line with the other soft matter courses offered by PCC and also the Molecular Life Sciences MSc degree program, but can also be taken with a working knowledge of multivariable calculus.

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

• Incorporate and apply concepts of non-equilibrium physics on different kinds of soft matter systems
• Assess relevant modeling parameters, rate-limiting factors, time and length scales
• Develop a clear understanding of concepts underlying the coupling of non-equilibrium physical processes
• Analyze and evaluate the results of computer modeling in the context of the underlying theory

Assumed Knowledge:
PCC20806 Soft Matter, PCC41306 Advanced Soft Matter