# Teaching

## Phase Transitions in Active Matter

Collective behavior in suspensions of active (self-propelled) Brownian particles is the subject of much current research. Not only do these systems exhibit novel dynamics and phase behavior, they are also relevant for understanding self-organization phenomena in nature. While much of the interest in these systems has been driven by the introduction of new experimental model systems, theoretical studies of minimal active models have triggered a whole new branch of fundamental research in nonequilibrium statistical mechanics. In this course we learn

- Minimalist toy model of active sytems: Active Brownian Particles
- Mathematical modelling using Stochastic Calculus and Probabilistic approach (Fokker-Planck Equation)
- Physics of active Emulsions: active processes in droplets
- Collective behavior on a macroscopic scale
- Activity on nanoscale inside cells: biopolymer networks

Background: Basic knowledge of (classical) statistical mechanics and an open mind.

Evaluation: No exams. No assignments. Students will have opportunity to solve small research problems related to active matter.

Time and Location: Starting **15th October 2019**. TU Dresden, Zellescher Weg 17, Room BZW/A120/P

Lecturers: Dr. Christoph Weber and Dr. Abhinav Sharma

Top: Liquids exhibit local structuring as visible here in the shells around a central molecule (in red). The (scaled) density distribution around the central molecule is shown below; the pair correlation function which is a key quantity in the theories of liquids. Only at sufficiently large distances the pair correlation function approaches one, i.e, the density approaches the bulk value.

## Statistical Mechanics of Liquids

Understanding the behaviour of liquids is of great importance for physics, chemistry, biology and technology. However, the liquid state remains, in some sense, the most mysterious form of matter. The challenge to the theorist is to predict from the intermolecular forces the microstructure and macroscopic properties (e.g. heat capacity, viscosity, surface tension) of the system. While there has been enormous progress since the pioneering work of van der Waals, there remain many open questions, particularly regarding interfacial phenomena and nonequilibrium states. In this course we learn

- Imperfect gases: Virial expansion. What makes liquids different from gases?
- Distribution functions in liquids: Pair-Correlation function
- Integral equations for the pair correlation function: Percus-Yevick closure, potential of mean force, superposition approximation
- Perturbation theories of liquids: attractive interactions as weak perturbation, Zwanzig theory, Weeks-Chandlers-Anderson theory
- Density Functional Theory: powerful tool to study equilibrium properties of fluids
- Hands-on: Computation of the pair correlation (in python), pressure, and energy of a fluid using the Percus-Yevick closure.

Background: Basic knowledge of (classical) statistical mechanics and an open mind.

Evaluation: No exams. Six assignments. Students will have opportunity to solve small research problems related to active matter.

Time and Location: Summer Semesters at TU Dresden

Lecturers: Dr. Abhinav Sharma and Hidde Vuijk