Skip

UCD Search

 
 
 
Facebook Twitter Linked In
 

UCD School of Mathematics and Statistics

Scoil na nEolaíochtaí Matamaitice UCD

News Archive

HED: The maths of going to extremes (09/07/13)

Large earthquakes and devastating hurricanes are thankfully relatively rare events. But understanding more about the maths behind such extreme events could help to improve how we can predict them - and it may even help with the more mundane weather forecast too. Dr Miguel D. Bustamante is looking at the maths behind low-probability events using the model of colliding vortices in fluids such as air and water, and the work feeds into the wider field of ‘extreme events’, as he explains....

“Mathematically speaking there are situations where you can define extreme events like rogue waves or freak waves, or tsunamis, hurricanes - and they have to do with events which have a small probability to occur,” he says. “Hurricanes have a small probability and big earthquakes have a small probability, and it is possible to put them under the same umbrella.” 

Extreme events can appear because systems are not linear, explains Dr Bustamante, who is a Senior Lecturer at UCD School of Mathematical Sciences. “You start with smooth initial conditions and then the behaviours are not simple, it leads to turbulence,” he says. “So we have been studying the dynamics of a turbulent system - vortices colliding in a fluid - as a model.”   

By numerically simulating how these vortices collide and react and by looking to predict ‘singularity’ where the object can no longer be mathematically defined, it’s possible to analyse physics that would be too impractical or costly to access with experiments, he notes. “Understanding the singularity is important - if you can predict when one is coming then you would be able to understand an extreme event is coming.” 

Through his work on the vortex model, Dr Bustamante has now presented a new way to mathematically look at the singularity problem: he reformed co-ordinates to look at the velocity field divided by the maximum vorticity and found that this simplified the equations needed. He is now working on implementing numerical simulations of these equations in two and three dimensions, and he hopes the work will enable more capable computer programmes for predicting extreme events without the need for more computing power. 

“You just need to write a new code in the mapped co-ordinates and you would gain a lot in precision,” says Dr Bustamante, whose research is funded through Science Foundation Ireland. And describes how the underlying approach could ultimately be used to help inform analyses of weather, climate, earthquakes and volcanoes: “It means improving the prediction power at the same computing cost - that would be the promise we hope.”

Dr Miguel D. Bustamante, Senior Lecturer with UCD School of Mathematical Sciences,was interviewed by freelance journalist Dr Claire O'Connell.

Miguel Bustamante

Original Article posted 08 July 2013

News Archive