# Homogenization in the energy variable for a neutron transport model

## TL;DR

This paper studies the homogenization of the linear Boltzmann equation with highly heterogeneous energy-dependent parameters, revealing a memory effect and supporting findings with numerical experiments.

## Contribution

It introduces a two-scale convergence approach to homogenize energy-variable heterogeneity in neutron transport models, uncovering a memory effect in the limit.

## Key findings

- Homogenization induces a memory effect in the energy variable.
- Numerical experiments illustrate the homogenization results.
- The approach applies to highly heterogeneous optical parameters.

## Abstract

This article addresses the homogenization of linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit. We also provide some numerical experiments to illustrate our results. In the Appendix, we treat a related case of the harmonic oscillator.