# Professor Andrew Archer, University of Loughborough

**Date**: Monday 22 October 2018, 15:00 – 16:00**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Seminars, Applied Mathematics**Cost**: Free

#### Professor Andrew Archer, University of Loughborough. Part of the applied mathematics seminar series.

Introduction to classical density functional theory (DFT) and dynamical density functional theory (DDFT)

In this talk I will give an introduction to classical^** density functional theory (DFT) and dynamical density functional theory (DDFT). DFT is a statistical-mechanical theory for the average density distribution of a system of classical particles in the presence of an external field. It is a microscopic theory, able to describe the structure even down to the scale of the individual particles. A typical problem that can be solved using DFT is to determine the density distribution of molecules in a liquid in the presence of a container wall. It can also describe solid phases of matter and the density distribution at the interface between a crystal coexisting with the liquid phase. In addition to yielding particle density distributions, DFT can also be used to obtain thermodynamic quantities such as free energies and interfacial tensions. DDFT is a generalisation of DFT, able to describe the non-equilibrium time evolution of the density profile. Originally developed for systems of Brownian particles with stochastic equations of motion, the formalism has been extended to describe many body systems evolving under Newton's equations of motion and also underdamped stochastic equations of motion.

^** Classical DFT should not be confused with quantum DFT, a related theory for the density distribution of electrons in matter. I will not discuss quantum DFT.