(Inside Science) -- The recent fires in Australia showcased the destructive power of a raging wall of flames. As climate change increases the chances of frequent and devastating wildfires around our planet, researchers are looking for ways to better predict and fight the blazes. They have a surprising ally: the mathematics of waves.
Forest fires are an example of a less obvious corner of wave research that deals with what’s known as an excitable medium. Electrical signals in the heart and rust spreading across metal are other examples of such waves.
“What makes the waves in excitable systems very different is the fact that you have a stable resting state that can be excited, but takes time to recover from the excitement,” said Paul Sutcliffe, a mathematician from the University of Durham in the U.K.
Scientists around the world are working to better understand the mathematics of these unique waves -- research that could one day help save lives.
Spreading like wildfire
Because excitable media take time to recover after a wave passes, two waves in such a system would eliminate each other instead of passing through each other like sound waves or water waves. A forest fire cannot return to a previously burnt spot until the trees have grown back. The firefighting tactic of controlled burning, also known as backburning, is a real-life application that takes advantage of this property.
“Fire managers need to know if they start a burn here, would that help? Or will it get out of control?” said Tom Fletcher, a forest fire researcher from Brigham Young University in Provo, Utah. “Another big thing is firefighter safety -- what happens if there's a wind change, if they have an escape route, and how close can they be to active flames.”
Right now, firefighters mostly rely on empirical models for fighting wildfire. Compared to computer programs that simulate the complex physics of a wildfire, empirical models make predictions by referencing past data, for example by looking up how fast the fire front usually moves when the wind is this strong and the slope this steep.
Firefighters choose to use empirical models over physically based models for good reasons.
“One takes 20 minutes on a laptop and one takes a week on a supercomputer,” said Fletcher.
However, only the physically based models can teach us about the complex physics of wildfire.
Fire Dynamics Simulator (FDS) Simulation of a Wildfire. Credit: NIST
“We need them for exploring physical phenomena. For example, understanding why sometimes a fire doesn’t burn with a uniform flame front but kind of fingers through the vegetation, or perhaps showing where the smoke might go,” said Fletcher.
By considering a multitude of factors, such as the topology, the type of vegetation, the wind speed, and the moisture content of the soil, these physically based models can help predict how climate change may affect wildfire risks in the future and save lives.
Another potentially lifesaving example of the importance of understanding waves in excitable media can be found in the heart.
Serious as a heart attack
Our heart is made of muscle cells that contract and relax according to the electric signal sent out by specialized cells that act as a natural pacemaker. As these electrically triggered contractions ripple through the heart as excitable waves, abnormalities in the heart can alter their shape.
“These waves are one of the mechanisms that we know that can initiate tachycardia and fibrillation,” said Flavio Fenton, a physicist from the Georgia Institute of Technology in Atlanta. Tachycardia and fibrillation are both medical conditions related to irregular heartbeats and can be life-threatening if left untreated.
But just like one can’t burn down a forest in the name of wildfire research, in vivo experiments to study the physics of abnormal electric waves in the human heart is out of the question.
“It’s a bit difficult for you to convince someone to do an experiment that’s going to give them a heart attack,” said Sutcliffe.
Luckily, researchers can use geometrically analogous systems to study these waves. In a paper published in Physical Review Letters, Sutcliffe and his colleagues used chemical reactions instead of electric signals to explore the geometry of abnormal waves associated with irregular heartbeats.
They placed obstacles in a petri dish and observed how the wavefront of a chemical reaction curled around the obstacle and transformed from concentric ripples into spirals, which, if you use your imagination, may look like a pair of spinning eyes on asmiley face.
“If you have some scar tissue in your heart that the wave’s trying to get through, but [the cells] can't contract as the wave comes past, the wave can curl around and form a spiral,” said Sutcliffe.
Spiral waves in a dish, sped up by about 120 times. Credit: Cincotti et al., Physical Review Letters
Since a spiral wave propagates differently from the normal pacemaker signal, it can cause the heart to beat irregularly.
“Because it's very hard to measure and study these waves in a clinical setting, these studies over the years have become more and more appreciated by cardiologists,” said Fenton.
The road ahead
In the future, a better understanding of spiral waves may lead to safer and less invasive ways to treat different forms of arrhythmia. Optogenetics -- the idea that light can be used to control cell behaviors -- has helped spawn the idea of a light-based defibrillator for treating the condition, and researchers have already had some success testing early prototypes on mice.
“Instead of shocking the whole heart, it may be possible to just have a light treatment -- by shining a light with a particular frequency on your heart that would fix your heartbeat,” said Sutcliffe.
As for fighting wildfires, researchers are working to develop more comprehensive models for studying the physics of wildfires. They are also trying to simplify the simulation codes while maintaining their accuracy and reliability, so that these tools can be practical for firefighters as well.
"[Firefighters] want to know when they light a backfire to create a burned area in front of a wildfire, if the burned area is sufficient to stop the wildfire from spreading,” said Fletcher. “Also, they want to know if the temperature would get too intense when the fires intersect that the organic material in the soil is destroyed, and perhaps other ecological effects.”
Originally, the people who studied wave models were mostly just mathematicians, Fenton said. “But because of the applications to many other fields, now you have cardiologists, biomedical engineers, physicists and mathematicians, all working on this. It’s a very interdisciplinary field.”