- Melting in two dimensions
- Irreversible Monte Carlo algorithms (Event-chain Monte Carlo)
- Minkowski tensors and other shape metrics
- Granular Matter from the Statistical Physics perspective
- Stochastic geometry

Dr. Sebastian Kapfer

Theoretische Physik 1

Staudtstr. 7

91058 Erlangen

Germany

Office: Building B3, Room 02.573

Phone: +49 9131 85 28448

Fax: +49 9131 85 28444

Email: sebastian.kapfer@fau.de

The study the mixing time, that is, the time to equilibrium from a worst-case initial condition. For the first time, we report the exact scalings of the mixing time for an array of reversible and irreversible Markov chains. We can connect the dynamical universality classes of the 1D hard-sphere model to known classes for the TASEP, but we also find a new class both on the continuum and on the lattice. The new class mixes faster than all known classes and corresponds to the Event-chain algorithm.

Using simulated annealing, we explored the locally densest packing motifs of aspherical particles, generalizing the well-known kissing problem. Depending on the particle aspect ratio, different optimal structures are observed. In extended disordered packings of frictionless particles, knowledge of the minimal packing volume allows us to apply k-Gamma theory. Moreover, we find that approximate icosahedral clusters are found in random packings, while the optimal local structures for more aspherical particles are not formed.

In recent work with M. Michel and W. Krauth, I introduced a new paradigm to construct Monte Carlo algorithms of the event-chain type for generic interactions. These algorithms break several of the fundamental principles of Metropolis Monte Carlo algorithm: they obey global balance instead of detailed balance, are free of rejections, intrinsically generate cooperative cluster moves, and evolve the system along a continuous time coordinate! Algorithms of this type can significantly reduce autocorrelation times in MC computations. Intriguingly, the factorized acceptance rule also allows us to rigorously include long-range interactions such as Coulomb forces without the conventional Ewald summation. This significantly improves the scaling with system size, permitting access to larger system sizes.

The reference implementation can be found on Github.

Quasicrystals include additional degrees of freedom (phasons) over the ones known from periodic crystals (phonons). How these lead to new kinds of topological defects is currently being investigated.

Postscript code for driving a lasercutter to produce the above puzzle.

Some programs that I wrote or contributed to over the years:

Fabian Schaller's online Minkowski tensor computation

postlhc: Manyparticle Monte Carlo code implementing the cell-veto and event-chain algorithms

sphmink: compute 3D spherical Minkowski tensors

Papaya: compute 2D Minkowski tensors

Karambola: compute 3D Minkowski tensors (with Fabian Schaller)

Erpel: a voxel-based finite element code for elastic properties of porous media

voxelsurface: computes a voxelized representation from a triangulated surface

Let me know if you want to reuse any of this, I'm glad to help!

Voxelized sheet and network solids from our Biomaterials article

A PDF version of my PhD thesis