ndarmage / openbs Goto Github PK

Chains consist of a set of data to express the decay and transmutation channels linking the nuclides. It could be very useful to have a tool for plotting the chains by a block diagram.

It is recommended to use the latest nuclear and decay data from JEFF or ENDF, in order to replace the first available and unofficial libraries.

There are currently two points whose execution is taking considerable time, when running the main module OpenBS.py. A discussion to improve both the methodology and the implementation is needed.

Contrary to Chiba et al. 2015, changes in the matrix associated to the ODEs system are determined by 1st order Taylor expansion where derivatives are estimated by incremental ratios. This requires the calculation of flux and rates in both unperturbed and perturbed conditions, leading potentially to longer calculation. Specifically, it is:
[ \Delta M = \frac{\partial M}{\partial N_i} \cdot \Delta N_i
= \frac{\partial M}{\partial \phi} \frac{\partial \phi}{\partial N_i} \cdot \Delta N_i.
]
The use of 1st order GPT won't need quantities at perturbed conditions.

The second point is about the calculation of the adjoint nuclide density vectors. Our implementation follows Chiba's derivation with the projection of the perturbed ODEs equations on the nuclide importance function. This derivation assumes that the matrix M is constant in time within each time step, thus requiring explicit solvers for the initial (or final) value problem. The backwards explicit solution for the nuclide importance forces the use of several calls to solve_ivp in each time step. Since the flux is already known along the evolution in time, we could evolve our method to solve for the nuclide importance on longer time frames, with a time-dependent M^T (see Eq. 7 of Chiba's article).

Parallelism by multiprocessing shows bad performances with the current implementation (v1.5.0). Processes are spawned on Win OS, while they're forked in posix system by default. Spawning forces copying of input arguments, which degrades the performances.

The spectrum of the nonlinear B1 homogeneous problem has been resolved by recurring to the approximation of the nonlinear polynomial eigenvalue problem. This method should be resumed in a short note aimed fro publication on a peer-reviewed journal.

As a complement, it would be interesting to investigate the extension to the general BN form, still in the infinite homogeneous problem.

Verify implementation and results from previous works performed during the student internship.