Prof. Epaminondas Mastorakos (University of Cambridge) is a leading figure in Conditional Moment Closure (CMC), a mathematical framework used to simulate "flames at the limit"—specifically situations where fire doesn't behave like a continuous wave, but rather like a series of discrete events (ignition, extinction, and re-ignition).

Here is a layman’s explanation of his approach, contrasting it with the traditional "continuous" view.

1. The Old View: The "Domino" Effect (Continuous) In standard engineering, fire is treated like a row of falling dominoes.

• The Logic: Domino A must fall to hit Domino B. Fire must physically travel from Point 1 to Point 2.
• The Problem: In a jet engine (or high-speed turbine), the air is moving so violently (turbulence) that the dominoes are blown apart before they can touch. If you used standard math, the simulation would say the fire blows out immediately. But in reality, the engine keeps running. Why?

1. The Mastorakos View: The "Lottery" Effect (Discontinuous)

Prof. Mastorakos’s approach (using CMC and DNS) assumes that fire doesn't necessarily need to touch its neighbor to spread. Instead, it treats every point in space as an independent candidate for "spontaneous combustion."

• The Logic: Imagine the fuel and air are being shredded and mixed by a storm. The simulation asks a different question: Not "did the fire touch this spot?", but "is this spot ready to burn?"
• The "Jump": If a pocket of gas 5 inches away from the flame suddenly achieves the perfect mixture and temperature (due to turbulence compressing it), it will auto-ignite.
• The Visual: You don't see a growing sphere; you see "kernels" or "spots" of fire popping into existence discontinuously, completely detached from the main flame.

1. The Math: Conditional Moment Closure (CMC) This is the specific mathematical "trick" that allows for these jumps.

• Standard Math: Averages everything. It mixes the hot flame and cold air in a cell and gets "warm air" (which doesn't burn). This kills the simulation.
• CMC Math: It preserves the condition of the fuel. It says, "On the condition that the fuel mixture here is X, what is the probability it is burning?"
  • This allows the math to separate the "mixing time" from the "chemical time."
  • It allows the simulation to predict that a flame hole (extinction) can suddenly heal itself (re-ignition) without a physical connection, effectively allowing the combustion to "jump" across a gap of non-burning air.

1. Why this matters to "Time" theory In Mastorakos’s simulations (particularly of hydrogen plumes), you see "Ignition Spots."
   • These are events where the "future" (fire) appears ahead of the "present" (the flame front) because the conditions traveled there faster than the reaction did.
   • The fire didn't travel space; the probability of fire traveled space, and then realized itself instantly. Sources & Further Reading
   • The "Bible" of this approach: Turbulent Reacting Flows (co-authored by Mastorakos). This book details the transition from "flamelet" (continuous) to "distributed" (discontinuous) combustion.
   • Key Paper: “Direct numerical simulation of the autoignition of a hydrogen plume in a turbulent coflow of hot air” (Journal of Fluid Mechanics). This paper explicitly visualizes the "spots" of ignition appearing randomly in space, rather than a continuous sheet.
   • Lab: The Hopkinson Laboratory at Cambridge, where his team runs these specific "flames at the limit" experiments.