**May 13, 2019 at 10:00 - May 17, 2019**
- BCAM

**Pep Español (UNED, Spain)**

**DATES:** 13-17 May 2019 (5 sessions)

**TIME:** 10:00 - 12:00 (a total of 10 hours)

**LOCATION:** BCAM Seminar room

In this course we present in detail the fundamentals of the theory of coarse-graining, explore different applications that range from thermodynamics of small systems to complex fluids (colloidal suspensions and other viscoelastic fluids), and describe particle-based simulation methodologies like DPD and SDPD for the simulation of complex fluids.

**PROGRAMME:**
**1. The microscopic level: **Classical Mechanics and Statistical Mechanics. Ergodicity, Irreversibility, Equilibrium. Probabilities in Phase space. Levels of description. The Maximum Entropy Principle.

**2. The CG dynamics: **The Stochastic Dynamics of Coarse Grained variables. Green's view of coarse-graining. The Zwanzig projection operator technique. The GENERIC framework. Einstein formula, small fluctuations. SDE for pedestrians. Near equilibrium and Mori theory of projection operators.

**3. The Theory of Coarse-Graining at work: **Thermodynamics of small systems. Colloids, Smoluchowski and Langevin descriptions. Discrete fluctuating hydrodynamics. Nanoparticles embedded in a fluid.

**4. Lagrangian fluid particles:** The continuum limit and the Lagrangian description. The DPD model. The SDPD model. The SDPD model for viscoelastic fluids.

**5. Blob Models of complex molecules: **Coarse-grained models for complex molecules. Isothermal models of complex molecules. Non-isothermal models.

**REFERENCES: **
[1] H. Grabert "Projection operator techniques in Non-equilibrium Statistical Mechanics" (Springer 1982)

[2] H.C. Öttinger "Beyond equilibrium Thermodynamics" (Wiley & sons 2005)

***Registration is free, but mandatory before May 10th: **To sign-up go to

https://bit.ly/2DguyZe and fill the registration form. Student grants are available. Please, let us know if you need support for travel and accommodation expenses when you fill the form.