From Queue to Core · Birth-Death Processes and the Stochastic Foundations of Reactor Kinetics.

I followed the same Leanpub-style logic as your NEXUS-1 page: strong opening question, clear bridge for the target reader, “under the hood” explanation, transparent boundary, and reader positioning. (Leanpub)

About the Book

Have you ever looked at a reactor-kinetics screen and wondered why the equations have the shape they do?

You see neutron power, delayed-neutron precursor groups, reactivity, Doppler feedback, moderator feedback, xenon poisoning, and a live numerical solver. The deterministic behaviour looks smooth and continuous. But underneath that smooth curve stands a more fundamental stochastic picture: neutrons are born, removed, counted, and lost through a chain of random events.

From Queue to Core is written to make that hidden bridge visible.

This book explains how the classical birth–death process from queueing theory and continuous-time Markov chains can be used as a disciplined stochastic foundation for understanding reactor kinetics. It does not claim that a reactor is literally a queue. Instead, it uses the birth–death process as a clean mathematical language for neutron-population dynamics: births correspond to fission-created neutrons, deaths correspond to absorption or leakage, and criticality becomes the balance between creation and removal.

The book then walks carefully from that stochastic picture toward the deterministic six-group point-kinetics model used in NEXUS-1. Along the way, it explains the master equation, extinction probability, startup intuition, delayed-neutron groups, mean-field collapse, feedback effects, and the difference between what a stochastic model can claim and what a deterministic engineering solver can claim.

This is a theoretical companion to the NEXUS-1 demonstrator, but it remains practical in spirit. The reader is not only shown equations; the book also includes worked examples, representative NEXUS-1 constants, interpretable comparison tables, and C# algorithms that implement the ideas step by step: a birth–death Monte Carlo path, a master-equation approximation, and a compact point-kinetics-style solver.

What This Book Covers

From Queue to Core develops the bridge in stages:

• why queueing theory is useful here, and where the analogy stops;
• how a birth–death process becomes a continuous-time Markov chain;
• how neutron populations can be interpreted as stochastic populations;
• why criticality, extinction, and startup are naturally probabilistic ideas;
• how delayed neutrons turn a prompt chain into a controllable reactor;
• how the master equation collapses into deterministic point kinetics;
• how the NEXUS-1 kinetics engine fits into this theoretical structure;
• how stochastic and deterministic models differ in meaning, cost, and claim;
• how the ideas can be implemented in clear, educational C# code.

What Is Under the Hood?

The book connects several layers that are often kept separate:

The stochastic layer
A reactor chain begins as a population process. Individual neutrons appear and disappear randomly. The birth–death model makes that population explicit.

The probability layer
The master equation tracks the probability of every possible neutron population. It is richer than a single trajectory, but also more expensive.

The deterministic layer
Point kinetics tracks the mean behaviour of the neutron population and delayed-neutron precursor groups. This is the layer that becomes practical for a live simulator.

The feedback layer
Doppler feedback, moderator feedback, xenon poisoning, and control input explain why reactor kinetics is not just exponential growth or decay. Feedback turns a chain into a regulated physical system.

The implementation layer
The C# appendix shows how the models can be translated into interpretable algorithms. The purpose is not reactor-control software; the purpose is executable understanding.

Who This Book Is For

This book is for software engineers, C#/.NET developers, systems architects, control engineers, mathematically curious readers, and advanced learners who want to understand the mathematical parentage of the NEXUS-1 kinetics engine.

You do not need to be a nuclear engineer to read it. Some familiarity with probability, differential equations, or simulation helps, but the book is written with the same NEXUS-1 teaching rule used throughout the series: explain the bridge before asking the reader to cross it.

Honest Boundary

This book is not a nuclear-safety manual, not a validated neutronics code, not certified simulation software, and not operational guidance for any real facility. NEXUS-1 remains a browser-based educational demonstrator. The value of this book is conceptual, mathematical, and architectural: it shows how stochastic thinking, deterministic reactor kinetics, and readable software implementation can be connected without pretending that the model is more than it is.

At its heart, From Queue to Core is about one idea:

A deterministic reactor-kinetics curve is not magic. It is the visible engineering shadow of a deeper stochastic chain.

This book is warmly dedicated to my good friend Alekos, with gratitude for his friendship, encouragement, and presence along the journey of turning difficult ideas into written form.

Author: Grigorios Kyriakos Agathangelidis
Greek name: Γρηγόριος Κυριάκος Αγαθαγγελίδης
Also searchable as: Αγαθαγγελίδης Γρηγόριος, Αγαθαγγελιδης Γρηγοριος, Grigorios Agathangelidis.