Date: 2019/June/10th-14th (5 days)

Time: 10-14, with a lunch break 12-13.

Note on June 12, 14:15-18 because of PhD defense

__Teachers__

Ikuya Kinefuchi, Junichiro Shiomi (University of Tokyo)

Please find more details below.

__Intended Learning outcome__

After completing this course the student should manage to:

– identify the different scales of a thermo-fluid problem and their mutual interactions

– discuss and perform simple first principles (quantum) calculations.

– discuss lattice dynamics of atoms, molecules, or crystals under classical and quantum statistics.

– describe how to upscale transport properties (diffusivity, thermal conductivity, viscosity)

– describe coarse-grained modelling and multiscale simulations for fluid and thermal properties.

– discuss application of the atomistic to mesoscales simulations to fluid and thermal phenomena at various scales (e.g. evaporation, condensation, transport in narrow pores, wetting, heat conduction in nanostructures)

__Course main content__

Simulations at various scales from atomistic to mesoscales have become important in fluid and thermal science and engineering, particularly to understand phenomena involving multi-scales as in any interfacial flows. The lecture aims to provide basic knowledge and practical experience in standard and non-standard calculations of matter and phenomena at various scales related to fluid dynamics and heat transfer, ranging from first-principles calculations of electron levels/bands and interatomic force to dissipative particle dynamics simulations of mesoscale heat and mass transport.

__Eligibility__

The course assumes that the students have an undergraduate knowledge of Thermodynamics.

__Examination__

Project work with final presentation in groups of 2. Oral exam.

PRO1 – Project, 3. Grade scale: P, F

TEN1 – Examination, 2, grade scale: P, F

__Syllabus and program:__

Lecture program (17 hours)

H1: Basics of quantum physics (minimum level), approximation of Schrodinger equation, molecular orbital theory and bonds, energy levels, interatomic forces and fields

H2: First principles calculations, density functional theory, various approximations (local density, single electron, adiabatic etc)

H3: Hands-on: calculations of total energy, electronic levels/bands, and force constants.

H4: Lattice dynamics, lattice vibration and dispersions

H5: Various statistics (Fermi-Dirac , Bose-Einstein, Maxwell-Boltzmann)

H6: Hands-on: calculation of phonon bands of crystals,

H7: Basics of statistical mechanics (minimum level)

H8: Molecular dynamics (algorithm, thermodynamic properties, ensembles)

H9: Linear response theory, Einstein’s relations for transport properties (diffusivity, viscosity, thermal conductivity).

H10: Non-equilibrium molecular dynamics for transport properties

H11: Hands-on: calculations of transport properties of a simple fluid (or a more complex system)

H12: Introduction to the dissipative particle dynamics (equation of motion, fluctuation-dissipation theorem)

H13: Conventional interaction models for liquids, polymers, etc.

H14: Implementation issues (time integration algorithm, boundary conditions, etc.), evaluation of mechanical and thermodynamic properties

H15: Reverse coarse-graining strategy (force matching method, reverse Monte Carlo method, iterative Boltzmann inversion method)

H16: Forward coarse-graining strategy (Mori-Zwanzig projection operator method), multiscale / hybrid simulations

H17: Hands-on: calculation of the shear viscosity of a simple fluid (optional: determination of the phase diagram for a block copolymer melt)