Basic HTML Version
Annual Review
2010/11
16
Modelling the World
U
nderstanding and modelling how the
world works through applying one
simple mathematical formula would seem
to be the ultimate scientific fantasy.
It formed part of what John Nash, the brilliant
mathematician who won the Noble Prize for
Economics in 1994, and who was portrayed
by Russell Crowe in the film
A Beautiful Mind
,
attempted to do throughout his life.
The field of “Nonlinear Partial Differential
Equations” may by itself appear to be an
obscure mathematical pursuit - yet this high
aim is precisely what those working within it are
striving for.
Professor Gui-Qiang Chen, Professorial Fellow
of Keble and Oxford Professor of Partial
Differential Equations, is a world leader in
research in this field.
Academics and practitioners across an
enormous range of disciplines are recognising
the importance of these equations in enabling
them to model very precisely the cumulative
causes and effects of a vast array of individual
actions, both physical and social. Such models
are vital in fields such as engineering. To use
the simplest possible example, these equations
enable engineers to understand not only what
the effect one lorry load will have on the bridge
they are constructing, but also the impact of a
further lorry, not only separately on the bridge
but also on the effect the first lorry is having
– and so on, for a large number of separate
loads. Social scientists are also increasingly
using such equations to model mass human
behaviour. Professor Chen’s work allows for
much more finely tuned and sophisticated
calculations, making these equations even
more practically useful.
In Mathematics, a differential equation states
how a rate of change (a “differential”) in one
variable is connected to change in another.
Most simply, the equation might be
dy/dx = 2, which means that the rate of
change of the variable y with respect to the
variable x is 2. A partial differential equation
enables us to calculate the individual effects of
multiple variables separately. Nonlinear partial
differential equations – the most difficult and
useful, and the focus of Professor Chen’s work
– allow us to see what effects a change in one
variable will have on all the elements which
interact. It can also be seen as essentially the
modelling of the “butterfly effect”, whereby
a small change in just one thing can lead to
totally unexpected consequences.
Professor Chen dates his interest in this field
back to his childhood fascination with the
regular huge tidal surges that ended in the
Hangzhou bay near his hometown, Ningbo,
close to Shanghai in China. What specific
combination of forces and circumstances
resulted in this pattern of unnaturally large,
sometimes fatal, waves?
He similarly watched the regular shapes formed
by the huge flocks of migrating birds which
flew overhead. Could we understand how the
intricate movement of these groups happened,
and perhaps predict and model them?
Gui-Qiang Chen took a bachelor of science
degree from the prestigious Fudan University
in Shanghai, followed by a PhD from the
Chinese Academy of Sciences in Beijing.
After senior posts in New York and Chicago,
he began at the Oxford Centre for Nonlinear
Partial Differential Equations, with a Professorial
Fellowship at Keble, in 2009.
As a leader of the new Keble “Nonlinearity”
research cluster in development, Professor
Chen is a strong supporter of the Keble
Advanced Studies Centre plans and the
possibilities of interdisciplinary research in a
College setting. A widely applicable area such
as Nonlinear Partial Differential Equations is
tailor-made for productive collaborations.
With his co-founder of the Nonlinearity cluster,
Dr Apala Majumdar, Keble Research Fellow
in Applied Mathematics, Professor Chen
says of their group: “The behaviour of every
material object, with length scales ranging from
sub-atomic to astronomical and timescales
ranging from picoseconds to millennia, can be
modelled by partial differential equations or by
equations having similar features. Our aim is to
create awareness about the huge impact that
mathematical analysis and modelling can have
across the physical/life sciences and beyond.”