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Features: Faculty Insights


Colm-cille Caulfield is the new Head of the Department of Applied Mathematics and Theoretical Physics (DAMTP). He tells us about his research, the strengths of DAMTP, and the Department's vision for building on them.

Understanding turbulence

Caulfield is an expert in stratified turbulence. This wild and chaotic motion of fluids of varying density is considered one of the hardest problems of classical physics, and it creates practical problems across a huge range of industries. With his expertise on fluid dynamics, Caulfield has worked on anything from the hazards of gas releases at ferry ports to designing efficient air conditioning systems and deciding on the optimal placement of wind farms.

"It's very important to build on the traditional strengths of Cambridge, while always having your eyes up to think about the next thing to do."Colm-cille Caulfield

The aim of this part of Caulfield's work is to make the industrial processes involved more efficient — not just in terms of cost and time but, in these days of the climate crisis, also in terms of their environmental impact. "[Such optimisation] very often is a fluid dynamical question," he explains. "How can I perturb the flow, or control the flow in a particular way, to achieve a particular objective."

The other component of Caulfield's research is in an area where humans can't exert any direct control at all: he is collaborating with Earth scientists and oceanographers to try and understand the large scale circulation in the oceans. What is being circulated here is heat: because the Sun heats up the ocean much more at the equator than it does at the poles, and because water moves around, petawatts of heat are continually being transferred around the global oceans.

Amazingly, even turbulence that occurs on the scale of centimetres can affect this large scale circulation — it is this variety of scales that makes turbulence into such a difficult mathematical problem. Things become even more complex when you take account of the fact that the ocean contains "parcels" of fluid with different densities, due to different temperatures or different levels of salt content, for example. The mixing of fluids of varying densities leads to complicated energy pathways, which are only poorly understood, but play an important role in our predictions of the evolving climate system.

"The reason why a mathematician will be interested in fluid mechanics, in particular when the flow can be turbulent, is that [you have] a beautiful non-linear system, with a very rich range of different phenomena that can happen," Caulfield explains. "To try and extract the key physical processes is a really interesting modelling problem and it's a really interesting problem in understanding the properties of solutions of partial differential equations. And it also has a direct relevance for the global climate system or [in the case of industrial processes] for reducing the amount of carbon emissions we put into the atmosphere."

DAMTP and big data

Besides pen-and-paper mathematics and numerical simulations, an important role in Caulfield's work is played by experimental and observational data. In this sense Caulfield's field, like almost all other areas of human life, has recently experienced a revolution: the advent of big data. "The next decade will be an enormously exciting period, both for applied mathematics and for theoretical physics," he says. "One of the reasons it is so exciting is the access to [vast amounts of] data that allows us to produce new mathematical models and interpret the world."

On the applied mathematics side, the powers of mathematical algorithms which can extract information from huge data streams, for example through machine learning, open up near endless possibilities: from improving health care provisions or industrial processes to producing better climate models or driving on the advance of quantum computers.

The theoretical physics side of DAMTP stands to benefit equally. "The gravitational wave data, the data coming out of CERN, the amazing explosion in observational astronomy, [present] a huge opportunity for theoretical physics to really probe further in understanding the physical world."

Caulfield's vision for DAMTP sees it firmly linked into this new age of big data. On the one hand this means continually reviewing the teaching syllabus, a "live system" as Caulfield calls it, to see how cutting edge research conducted by the members of DAMTP can be integrated. "There are such opportunities to build on the strong grounding we have here of the traditional, rigorous mathematical training to then also point [the students] to these new areas where their mathematical skills will be enormously valuable."

On the research side, taking advantage of the rich ground now being offered to applied mathematics and theoretical physics means continually evolving the emphasis of research being done at DAMTP. "My role is, not to be an imperial leader, but somebody who is committed to consulting widely with my colleagues, for it to emerge in a collegiate fashion what we think the appropriate future directions are," he says.

"It's very important to build on the traditional strengths of Cambridge, while always having your eyes up to think about the next thing to do. We don't want to be following fashions, we want to set the agenda. I think we are managing to do that, but it's a continual process of critical self-evaluation."

Keeping it mixed

Caulfield is no stranger to Cambridge. He completed the famous Part III and his PhD here and has been working at DAMTP since 2005 on a joint appointment with the BP Institute for Multiphase Flow.

But he has also experienced the international aspect of mathematical research. Born in Coventry to Irish parents, he completed his undergraduate degree at the University of Ulster at Coleraine, and has held positions in Canada, Japan, and the US.

As far as DAMTP is concerned, this international dimension presents one of the challenges Caulfield sees lying ahead. "A real strength of this department is how incredibly international it is," he says. "[One of the challenges is] to ensure that we still maintain that openness and that opportunity for people to come from all over, and contribute, and feel welcome and included. Speaking personally, I have written papers with people from twenty different nationalities, from New Zealand to Chile. I think it's just amazing that we have all this international [collaboration]. That is something we need to ensure we manage to maintain."

Diversity in a more general sense, including of gender and socio-economic background, presents the other main challenge Caulfield is determined to take on. "We are very committed to [diversity and inclusion] and we are doing a wide range of things to try and enhance diversity in all cohorts within [the department]," he says. "It's about getting over the incorrect [perception] of elitism and [express] that everybody is welcome here: from all over the world, and from any background. The only qualification required is to really, really love maths. That's the challenge — to communicate this piece of information."

Luckily Caulfield won't have to take on these challenges on his own, or from scratch. He will be building on the work of his predecessor, Nigel Peake, as well as previous Heads of Department. "I have huge shoes to fill, yet I am looking forward to the challenge," he says.

In addition, Caulfield will have the support of a committed staff. "We have a fantastic cohort of people in this department at every stage," he says. "Laboratory technicians, administrative staff, support staff, are all committed to this great enterprise we have. Senior academic staff are really pushing back the boundaries of research while mentoring an amazing cohort of early career researchers."

"Some of the most important breakthroughs happen in the collegial [coffee and tea times]. This buzzing environment of enthusiasm for mathematics is combined with world class teaching, informed by and connected to the excitement of the research that is going on. This collaborative [sense of] 'we're all in it together, we all love mathematics' is the thing that really excites me."