vice.migration.specs.gas
========================

Type : ``migration_matrix``

Default: Zeroes (i.e. no gas migration)

The gas migration matrix. For a multizone simulation with N zones,
this is an NxN matrix.

This matrix is defined such that :math:`G_{ij}` represents the
mass fraction of gas that moves from the :math:`i`'th zone to the
:math:`j`'th zone in a 10 Myr time interval.

Allowed Types
-------------
* 	real number
	The fraction of gas that migrates in a 10 Myr time interval is
	constant, given by this value.
* 	<function>
	Must accept time in Gyr as the only parameter. The fraction of gas
	that migrates in a 10 Myr time interval varies with time, and is
	described by this function.

Notes
-----
The mass fraction of interstellar gas that migration from zone
:math:`i` to zone :math:`j` at a time :math:`t` is calculated via

.. math:: f_{ij}(t) = G_{ij}(t) \frac{\Delta t}{\text{10 Myr}}

The mass that migrates is then given by :math:`M_{g,i} f_{ij}(t)`,
where :math:`M_{g,i}` is the total mass of the interstellar medium in
zone :math:`i`.

This guarantees that the amount of gas that migrates in a given time
interval does not depend on the timestep size.

Example Code
------------
>>> import math
>>> import vice
>>> example = vice.migration.specs(3)
>>> example.gas[1][0] = 0.1
>>> def f(t):
	return math.exp(-t / 2)
>>> example.gas[0][1] = f
>>> example.gas
	MigrationMatrix{
		0 ---------> {0.0, <function f at 0x120588560>, 0.0}
		1 ---------> {0.1, 0.0, 0.0}
		2 ---------> {0.0, 0.0, 0.0}
	}