5 research outputs found
Molecular simulation from modern statistics: Continuous-time, continuous-space, exact
In a world made of atoms, the computer simulation of molecular systems, such
as proteins in water, plays an enormous role in science. Software packages that
perform these computations have been developed for decades. In molecular
simulation, Newton's equations of motion are discretized and long-range
potentials are treated through cutoffs or spacial discretization, which all
introduce approximations and artifacts that must be controlled algorithmically.
Here, we introduce a paradigm for molecular simulation that is based on modern
concepts in statistics and is rigorously free of discretizations,
approximations, and cutoffs. Our demonstration software reaches a break-even
point with traditional molecular simulation at high precision. We stress the
promise of our paradigm as a gold standard for critical applications and as a
future competitive approach to molecular simulation.Comment: 19 pages, 4 figures; 18 pages supplementary materials, 1
supplementary figur
Hard-disk computer simulations -- a historic perspective
We discuss historic pressure computations for the hard-disk model performed
since 1953, and compare them to results that we obtain with a powerful
event-chain Monte Carlo and a massively parallel Metropolis algorithm. Like
other simple models in the sciences, such as the Drosophila model of biology,
the hard-disk model has needed monumental effort to be understood. In
particular, we argue that the difficulty of estimating the pressure has not
been fully realized in the decades-long controversy over the hard-disk
phase-transition scenario. We present the physics of the hard-disk model, the
definition of the pressure and its unbiased estimators, several of which are
new. We further treat different sampling algorithms and crucial criteria for
bounding mixing times in the absence of analytical predictions. Our definite
results for the pressure, for up to one million disks, may serve as benchmarks
for future sampling algorithms. A synopsis of hard-disk pressure data as well
as different versions of the sampling algorithms and pressure estimators are
made available in an open-source repository.Comment: 21 pages, 13 figures, open-source repositor
JeLLyFysh-Version1.0 — a Python application for all-atom event-chain Monte Carlo
47 pages, 17 figuresInternational audienceWe present JeLLyFysh-Version1.0, an open-source Python application for event-chain Monte Carlo (ECMC), an event-driven irreversible Markov-chain Monte Carlo algorithm for classical N-body simulations in statistical mechanics, biophysics and electrochemistry. The application's architecture closely mirrors the mathematical formulation of ECMC. Local potentials, long-ranged Coulomb interactions and multi-body bending potentials are covered, as well as bounding potentials and cell systems including the cell-veto algorithm. Configuration files illustrate a number of specific implementations for interacting atoms, dipoles, and water molecules