The Reaction Admissibility Graph defines which clusters exist. Integration needs them packed into one contiguous state vector \(y \in \mathbb{R}^{N_{eq}}\). The StateLayout in state_layout.py is the map

(block, local index)  <->  global ODE index

A StateLayout is an ordered list of named Block objects. Blocks are added with add_discrete(), add_bin_moment(), add_scalar() and add_aux(), and the layout is closed with freeze(). After that, offset(), slice() and index() return the position of a block or of one of its entries, N_eq is the total number of equations, and describe() prints the layout.

State vectors of the C++ solver

The C++ solver uses the layouts below. \(I\) and \(V\) are the largest tracked SIA and vacancy cluster sizes.

Discrete equations, fission cascade (helium Case 2):

y[0..I-1]       SIA clusters c_n, n = 1..I
y[I..I+V-1]     vacancy clusters and bubbles c_m, m = 1..V
y[I+V]          total helium in cavities
y[I+V+1]        free helium c_h

The number of equations is \(I + V + 2\).

Discrete equations, fusion cascade (helium Case 1):

y[0..I-1]       SIA clusters c_n
y[I..I+V-1]     vacancy clusters and bubbles c_m
y[I+V..I+2V-1]  helium content Q_m of each cavity class
y[I+2V]         free helium c_h

The number of equations is \(I + 2V + 1\).

The free-helium entry is omitted when helium is treated in the quasi-steady state, which removes one equation in both cases.

With the bin-moment equations the sizes up to \(i_{discrete}\) and \(v_{discrete}\) keep one ODE per size, and the larger sizes are grouped into logarithmic bins that carry \(P\) moments each. The number of equations is

\[ N_{eq} = i_{discrete} + P\,I_{bin} + v_{discrete} + P\,V_{bin} + n_{He} . \]

The header comment of radcluster_code/cpp_utils/core/parameters.h lists these layouts in full.

See also: State-space reductions, Solver parameter file