# Stages WK

### From Werner KRAUTH

Here are a few practicals that are offered in my group for the second semester
of the 2013/14 year.

## Contents |

# Cluster algorithm for rods on the lattice (p-rods)

The goal of this practical is to develop a Monte Carlo algorithm for the simulation of fully packed ensembles of long rods on a lattice. A preliminary version of the algorithm has already been worked out, but some work remains to be done to reach a version of the program that could yield exploitable results.

See the literature:

A.Ghosh, D.Dhar, On the orientational ordering of long rods on a lattice. Europhysics Letters (EPL), 78(2), (2007) 20003.

A.Ghosh,D.Dhar and L. Jacobsen Random trimer tilings PHYSICAL REVIEW E 75, (2007) 011115

Mode: Stage de M2 (Master, two months)

Contact: Werner Krauth

# Event-chain algorithm in the NPT ensemble

New Monte Carlo algorithms breaking detailed balance have in recent years allowed to equilibrate much larger systems of dense liquids than before (event-chain Monte Carlo). Previously, these algorithms were formulated in the NVT ensemble, at constant volume. The goal of this project is to formulate an algorithm in the NPT ensemble, at constant pressure, and produce a proof-of-concept implementation. Possible applications include simulations in solid phases, and the search for densest hypersphere packings (dimension > 3). There, it has been conjectured recently that the densest packings are not crystals, but may be disordered.

Mode: Stage de M2 (Master, two months)

Contact: Werner Krauth, and Sebastian Kapfer

# Lattice-based jammed packings

Jammed sphere packings are model systems for granular matter. In a jammed packing, each particle is held in place by its neighbors such that the packing attains mechanical rigidity. An interesting subclass of jammed packings are Barlow packings which are based on the way a grocer stacks oranges (fcc/hcp lattice). Starting from a complete stack of oranges, how many can be removed until the packing is no longer stable? The loosest possible packings are expected to be ordered (as the most dense), with disordered configurations of vacancis at intermediate densities. The goal here is to develop a Monte Carlo algorithm for sampling the configuration space of this model.

Contact: Sebastian Kapfer (under the supervision of W. Krauth)

Mode: Stage de M2 (Master, two months)