Dynamic coarse-graining of non-linear systems

What is it about?

We are generally interested in numerically studying the properties of soft matter, which includes distinct materials such as plastics, glasses, colloidal suspensions (e.g., milk) but also biological systems such as bacterial suspensions and biofilms. Due to limited computational resources, such studies, however, often have to rely on coarse graining. This is the process of removing microscopic degrees of freedom to find models that are computationally much more efficient but still allow for realistic simulations of static and dynamic characteristics. While structural properties in coarse-grained models can be described and reconstructed by effective potentials, the description of dynamics is even more complex. It requires the introduction of additional dissipative and thermal forces to compensate for the systematic removal of degrees of freedom. One of the open questions in this field is how non-linearities in the underlying system influence form and dynamics of the coarse-grained model. In this work, we investigate a system in thermal equilibrium using analytical theory, linear and non-linear projection operator formalisms, and computer simulations for a detailed analysis of the impact of such non-linearities. Our study highlights some open challenges and possible solutions in dynamic coarse graining.

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Photo by WrongTog on Unsplash

Photo by WrongTog on Unsplash

Why is it important?

Chemical and biological soft matter systems are governed by processes on very different time scales, and the behavior on longer time scales can depend on short-time dynamics. Performing computer simulations thus can turn out to be prohibitively slow. Summarizing the influence of solvent molecules via generalized Langevin dynamics is a possible and approved way to handle this dilemma. It usually relies on the assumption of harmonic interactions between all particles. This, however, is not always justified: There is a plethora of soft matter and biological systems in which non-linear dynamics are essential, including deeply supercooled liquids, polymer melts, tracers in solutions of filaments, and hydrogels.

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