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Prof. Pep Español
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Statistical Mechanics behind Coarse-grained Models
There is a great interest from an economic perspective to simulate
complex fluid systems of industrial and technological importance.
A simulation allows to get insight on the processing of materials and
propose new directions for design without the expensive and time
consuming experimentation in a laboratory. However, computer
equipment is also a limited resource and there is also a need for
developing simulation models that allow to capture the essential
features of the materials with the minimum of computational units. The
process of representing a system with fewer degrees of freedom than
those actually present in the system is what we call coarse-graining.
Of course, several questions readily appear: Is there a general method
for coarse-graining? Is it always possible to coarse-grain a system?
How to ensure thermodynamic consistency in a coarse-grained model?
In the lectures we will attempt to answer these questions by reviewing
the general concepts behind coarse-graining from the point of view of
non-equilibrium statistical mechanics. Levels of description,
relevant variables, and time scales provide the conceptual framework
in order to formulate models for complex fluids. These models can be
"derived" microscopically by using a general projection operator that
allows one to obtain the equations of motion for the coarse-grained
variables. The general projection operator framework will be reviewed
and the recent development known as GENERIC will be presented. The
GENERIC structure strongly restricts the form of the dynamic equations
for coarse-grained models. It actually allows one to input the minimum
physical insight about the system of interest into the construction of
coarse-grained models for such systems while respecting the
thermodynamic consistency of the model. We will illustrate how to use
the GENERIC formalism in order to design discrete models for complex
fluids. As particular examples, the Smoothed Particle Dynamics and
Dissipative Particle Dynamics models will be presented. We will show
how, guided by the GENERIC formalism, one can generalize these models
in a consistent way in order to simulate viscoelastic fluids,
transport of pollutants, liquid-vapour systems, and binary mixtures.
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