Kinetic theory of active matter: coarse-graining and invasion waves

Date

Feb 16, 2017

Time

3:00 PM - 4:00 PM

Speaker

Thomas Ihle

Affiliation

Ernst-Moritz-Arndt University Greifswald, Institute for Physics

Series

TUD ZIH Kolloquium

Language

en

Main Topic

Informatik

Other Topics

Physik, Informatik

Host

Ralph Müller-Pfefferkorn, Zentrum für Informationsdienste und Hochleistungsrechnen

Description

Models of self-driven agents similar to the Vicsek model are studied by means of kinetic theory. In these models, particles try to align their travel directions with the average direction of their neighbors plus some noise. At low noise, a globally ordered state of collective motion forms. These models have a discrete time step, consist of a simple streaming and collision step and are easily implemented on a computer.
A kinetic theory is derived from an exact equation for the N-particle probability density using Boltzmann’s approximation of Molecular Chaos. A coarse-graining procedure, called Chapman-Enskog expansion is performed to derive hydrodynamic equations from the kinetic theory.
The kinetic theory is also solved numerically by a Lattice-Boltzmann-like algorithm. Steep soliton-like waves are observed that lead to an abrupt jump of the global order parameter if the noise level is changed. The shape of the waves is shown to quantitatively agree within 3% with agent-based simulations at large particle speeds. At small densities and realistic particle speeds, the mean-field assumption of Molecular
Chaos is invalid near the onset of collective motion, and correlation and memory effects become relevant.
I will show how to self-consistently include correlation effects at the level of ring-kinetic theory. Instead of just one kinetic equation, an additional equation for the time evolution of the two-particle correlations will be derived. This equation is solved numerically for a homogeneous system and shown to be in excellent agreement with agent-based simulations in certain parameter ranges.
Thomas Ihle studierte Physik an der Universität Leipzig, wechselte 1991 als Diplomand an das Forschungszentrum Jülich und promovierte 1996 an der RWTH Aachen. Nach Postdoc-Aufenthalten in Paris, Grenoble, Minneapolis und Stuttgart wurde Prof. Ihle 2004 an die North Dakota State University berufen, wo er 2010 Tenure erhielt. 2015 erfolgte die Ernennung zum Professor an der Ernst-Moritz-Arndt Universität Greifswald. Hauptarbeitsgebiete sind kinetische Theorie und Computersimulation selbstgetriebener Teilchen, Entwicklung teilchenbasierter Algorithmen für komplexe Flüssigkeiten sowie Musterbildung beim Kristallwachstum.

Links

• http://tu-dresden.de/veranstaltungen/termin?id=TUD58a2baed496ca

Last modified: Feb 16, 2017, 8:41:20 AM