wendy

A one-dimensional gravitational N-body code.

Overview

wendy solves the one-dimensional gravitational N-body problem to machine precision with an efficient algorithm [O(log N) / particle-collision]. Alternatively, it can solve the problem with approximate integration, but with exact forces.

Author

Jo Bovy (University of Toronto): bovy - at - astro - dot - utoronto - dot - ca

Installation

Install the latest release using

pip install wendy

or clone/fork/download the repository and install using

sudo python setup.py install

or locally using

python setup.py install --user

The behavior of the parallel sorting algorithm used when setting sort='parallel' in the approximate version of the N-body code (approx=True) is controlled by a few compilation-time variables: PARALLEL_SERIAL_SORT_SWITCH, which sets the length of an array below which the serial sort is used, PARALLEL_SERIAL_MERGE_SWITCH, which sets the length of an array below which a serial merge is used (as part of the mergesort sorting algorithm used), and PARALLEL_SORT_NUM_THREADS, the number of threads used in the parallel sorting algorithm. By default, these are set to PARALLEL_SERIAL_MERGE_SWITCH=10000, PARALLEL_SERIAL_MERGE_SWITCH=50000, and PARALLEL_SORT_NUM_THREADS=32, which appear to work well. Significant speed-ups can be obtained by optimizing these for your system and specific problem. They can be set to different values by running, e.g.,

export CFLAGS="$CFLAGS -D PARALLEL_SERIAL_SORT_SWITCH=10 -D PARALLEL_SERIAL_MERGE_SWITCH=10 -D PARALLEL_SORT_NUM_THREADS=2"

before compiling the code (if you are trying to change them, make sure to force a re-compilation by removing the build/ directory).

Usage

Use wendy.nbody to initialize a generator object for initial (x,v) with masses m. The generator then returns the state of the system at equally-spaced time intervals:

g= wendy.nbody(x,v,m,0.05) # delta t = 0.05
next_x, next_v= next(g) # at t=0.05
next_x, next_v= next(g) # at t=0.10
...

The generator initialization with wendy.nbody has options to (a) solve the problem exactly or not using approx=, (b) include an external harmonic oscillator potential omega^2 x^2 / 2 with omega= (both for exact and approximate solutions), and (c) include an arbitrary external force F(x,t) (using ext_force=, only for the approximate solution).

Examples

• Phase mixing and violent relaxation in one dimension: example notebook (run locally to see movies, or view on nbviewer)

• A self-gravitating, sech² disk: example notebook (run locally to see movies, or view on nbviewer)

• The Gaia phase-space spiral: example notebook (run locally to see movies, or view on nbviewer)

• Adiabatic contraction: example notebook (run locally to see movies, or view on nbviewer)

• Adiabatic vs. non-adiabatic energy injection for an exponential disk: example notebook (run locally to see movies, or view on nbviewer)

• wendy scaling with particle number: example notebook (view on nbviewer)