Initial Commit.

Created as_toroidal project to include the evolution of a purely
toroidal field under the assumption of axial simmetry.
Completed finite difference code

as_toroidal.cpp now performs a finite difference simulation, but there
is not a practical mechanism yet to display the results. A conservative
code is next on the todo list.
Created conservative code and generated results logs

Current code fails both in its finite difference and conservative
versions. To compile with one or the other, the compiler variable
conservative must be defined. Currently the conservative code blows up
shortly after it starts, independent of the initial conditions, while
the finite difference version, although it does not explode, it produces
an enourmously asymmetric behavior between south and north pole, and
complete irregularity in its values, which is unphysical.
Fixed diff. eq. for conservative case, still explodes

The equation used both for the finite difference and conservative
schemes had errors in its derivation. After fixing them on the
conservative case, code still explodes. Problems arise at the center of
the star, and are due to the resistive terms, in particular the ones
expressing flux in theta. Probably a functional dependance for the
resistivity is needed, rather than a constant value.
Replaced all floats with doubles
Fix boundary issues with cons. code, and allow for a minimun r

-	Erased restrictions on the boundaries, they completely disconnected the
boundaries from the rest of the points immediately causing
discontinuities.
-	Allowed the definition of an rmin, under which the field is not
present.
Use midpoint values for chi in the conservative scheme

-	Solve immediately for the midvalues of chi for the conservative
	schemes, instead of getting them as an average.
Several changes, conservative code now seems to work

-	Corrected error in conservative code, sin(2*theta) was used
due to an error in the code, which produced discontinuities in the
equator. It now seems to work (at least it does not explode).
-	Implemented a corrected version for the finite difference
scheme. However, it seems to be very unstable.
-	Updated the way results are logged, everytime "plotSteps" timesteps
pass, the data is logged in a way readable by gnuplot to produce color
maps for B in the entire star.
Corrected value of function chi

Previously, an erroneous and radial form for the function chi was used.
This has been corrected now, and the new function preserves the form
(1-x**2) for the density.
Corrected conservative code to consider non-radial chi

Previous version of the code erroneously used a radial profile for chi.
This has been fixed in the conservative code. The finite difference code
though requires fixing.
Included notes

Added a tex file together with the pdf it produces, describing the
equations and the code used.
Erased thmin option

Eliminated the option to choose a minimun theta in which the field is
restricted. This was used just to haste testing of the code, and is now
unnecesary.
Added input through command line.

Input parameters for the simulation are now given through the command
line, and saved to a file (params.dat) inside the results folder. Output files have
also been changed, and are no longer compatible with gnuplot. Idea is to
create python scripts with matplotlib to create the required output.
Included output plotter

Created the script plotter.py, which uses matplotlib to plot the output
of as_toroidal. This script reads the params.dat file in the output and
extracts from there the required info. It's output is a set of pngs,
which can be transformed into a movie using mencoder with the command:

mencoder "mf://*.png" -mf fps=10 -o test.avi -ovc lavc -lavcopts
vcodec=msmpeg4v2:vbitrate=800

independent of the initial values, the MF seems to aquire a skewed
shape, and then collapses along a "line". Not sure if its just a
numerical issue.
Use equilibrium initial conditions

Constructed a MF such that beta=beta(chi), which is an equilibrium.
However, it still blows up in the simulations.
Optimizations done to the plotter

Modified the plotter script so it solves the correspondance between the
spherical and the cartesian grid only once, and not for each plot. This
obvious optimization significantly enhances the performance.
Erased pieces of incomplete finite difference code

Eliminated the use of the compiler constant "conservative" which was
used to compile either the conservative, or the finite difference code.
The finite difference code was not correctly implemented, and the
conservative code has a better prospect.
Function dchiValue was also a remnant form the fd code
Several changes, things work now!!

-Bugfix: Corrected hall terms. fluxes in theta where missing a minus sign,causing all my sorrow...
-Optimization: Solve all common factors once at the beggining
-Optimization: Solve fluxes once instead of twice, i.e. only solving the
"forward" fluxes in the grid.
-Change: Use the fundamental Ohm eigenmode as initial condition. The messy wxm file included is a wxmaxima script to help solve this initial conditions.
-Change: Use constant density.
-Change: Increase resolution of plots made by plotter.py
Uncomment hall terms