Esmae Woods

Post Doctoral Researcher · University of Cambridge

Focus - Markov Chains 2024 – Present

Computational mathematician working on Monte Carlo methods for neutron transport, contributing to the development of SCONE — the Stochastic Calculator Of the Neutron transport Equation built at Cambridge. My work analyses how criticality simulations converge: Fourier analysis of fission-matrix acceleration, zeta-eigenvalue methods for faster criticality searches, and models of particle clustering in heterogeneous systems. PhD on state-reduction techniques for Markov chains in large ill-conditioned systems.

Body of work

4 items

Year

Publication 2025 · Dec

Fourier analysis of fission matrix convergence acceleration

Nuclear Science and Engineering · with Zi Liang Tan & Paul Cosgrove

Uses Fourier analysis to show analytically how the fission matrix accelerates convergence of Monte Carlo simulations — furthering understanding of when fission-matrix acceleration should be used. Follow-on projects exploring further effects of fission-matrix acceleration have branched from this work.

Linked · DOI Fission matrix Convergence analysis

Algorithm 2026 · in progress

Zeta-eigenvalue convergence for faster criticality searches

SCONE development · with Valeria Raffuzzi

Analysis of zeta-eigenvalue Monte Carlo simulations converging to a critical density — a new algorithm that could substantially reduce the computation time of density-criticality searches. Internal analytics and code exist; open-access convergence results on benchmark systems are the next milestone.

› Conference paper “Convergence of Monte Carlo Zeta Eigenvalue Simulations” (with V. Raffuzzi) submitted to PHYSOR 2026.
› Invited ANSWERS seminar “Short-cutting criticality searches with the zeta-eigenvalue equations” (May 2025), following a first presentation at ANSWERS 2024.

Asserted Criticality Zeta eigenvalue In progress

Model 2026 · in progress

Modelling clustering in heterogeneous systems

Correlation & path decomposition in spatial branching

A mathematical model predicting how many particles a Monte Carlo simulation needs before clustering artefacts disappear in a simple heterogeneous system — helping users choose particle counts with confidence. Preliminary mathematics and code exist; a journal paper validating the maths against simulations is planned.

Asserted Clustering Spatial branching In progress

Integration pathway 2024 → present

Shorter density-criticality searches for industry codes

Nuclear industry · ANSWERS community

Industry users need shorter density-criticality searches. The zeta-eigenvalue algorithm converges to a critical density with fewer criticality searches, and industry awareness is being built through the ANSWERS seminar series while remaining convergence challenges are resolved.

Impact trajectory

Algorithm built

Industry aware

Validated

Integration

› Presented at ANSWERS seminars in 2024 and May 2025 — the industry channel for UK criticality codes.

Asserted Integration Criticality

Output over time

2024 — 2026

2024

2025

2026

Research

Joined MaThRad · SCONE thread

ANSWERS invited seminar (May)

Fission-matrix paper published in NSE (Dec)

PHYSOR 2026 paper · submitted

Zeta-eigenvalue algorithm · target Apr

Clustering model paper · target Apr

Collab

Impact

ANSWERS 2024 · industry awareness