Theoretical and numerical aspects of nuclear physisc project

Implementation of Bateman equation using Runge-Kutta method and matrix exponential method.

In this project we solve the Bateman's equations for a decay process that involves Iodine-135 and Xenon-135 numerically. In particular, Iodine-135 decays into Xenon-135 and the main process we see is a poison growing. The poisoning function represents how much Xenon-135 grows by Iodine-135 decay. If the thermal neutron flux $\phi$ is modified we can observe many curves one inside the other.

Numerical methods

The methods chosen for this code are fourth-order Runge-Kutta and the matrix exponential method. Runge-Kutta is an iterative method to compute the solution of a system of ODE; matrix exponential method does the same using a costant coefficient matrix and arrays inside which collecting the equations.

Plots

The plots inserted here want to show the different poisoning curves coming from the implementation of the two different methods. Poisoning plot coming from matrix exponential method, Runge-Kutta and the plotting of the ODE are collected as .png images inside the project folder. Their names are respectively: "poisoning_matrix.png", "poisoning_rk4.png" and "ode_matrix.png".

Math formulas

All of the math formulas are collected into the presentation file .pdf inserted in the project folder.

Python libraries

1. numpy;
2. matplotlib.pyplot;
3. scipy.linalg.expm;
4. tabulate.

Bibliography

The following link shows the reference I used to develop the project:

1. https://www.matec-conferences.org/articles/matecconf/pdf/2018/45/matecconf_icemp2018_01004.pdf
2. https://publications.sckcen.be/portal/files/1169036/Masterproef_Maren_Vranckx.pdf.