#Taylor series based integrator for contact hamiltonian flows

We provide the code that supports the numerical simulation reported in the manuscript A thermostat algorithm generating target ensembles.

The code is based on the package TaylorSeries.jl.

It is organized as follows.

The src folder contains the file ContactIntegrator.jl. This file defines the module ContactIntegrator that exports the main function contacthointegration! that performs the core of the simulation.

The module is imported in the script contact_taylor.jl which takes certain values for the parameters (see below), performs the numerical integration and generates a .hdf5 file which is saved in the HDF5 folder with the name given by the user (asked by the script).

The parameters reside in the file parameters.yaml and the users may modify it for their convenience.

Finally, the folder notebooks contains a jupyter notebook which illustrates how to manipulate the HDF5 data to generate the kind of figures displayed in the paper.

##Usage

Clone this repository with the following command in a UNIX terminal

~$ git clone https://github.com/dapias/ContactFlowsTaylor.git

Then move into the created folder and execute the script. To do that you may proceed in one of the three different following ways

1. In a UNIX terminal type

~$ julia contact_taylor.jl

2. In a UNIX terminal execute julia as

~$ julia

This command opens the Julia REPL. And then type the following command

julia> include("contact_taylor.jl")

3. Open a Jupyter Notebook and type in a cell

include("contact_taylor.jl")

Requirements

General

Julia. It may be downloaded from its webpage

Particular

The following packages are needed for the adequate execution of the program

• TaylorSeries
• HDF5
• YAML
• PyPlot (optional, it is used in the notebook)

To add a package type the following command in the Julia REPL.

julia> Pkg.add("PackageName")

###Miscellaneous (Runge-Kutta)

In the folder RungeKutta, the same field was integrated using the 4th order adaptive Runge-Kutta adaptive solver with the Dormand-Prince method implemented in the Package ODE.jl. It can be checked that the claim of the manuscript does not depend on the method of integration by analyzing the results of the Runge-Kutta integration. However, for this procedure there is a systematic numeric error that even though it is small it tends to grow up with time. It can be analyzed following the evolution of the invariant quantity.

###Authors

Diego Tapias (Facultad de Ciencias, UNAM) diego.tapias@nucleares.unam.mx

Alessandro Bravetti (Instituto de Ciencias Nucleares, UNAM) bravetti@correo.nucleares.unam.mx

2015.