Dr. Ashley P. Willis
Senior Lecturer of Applied Mathematics
Room H12,
Hicks Building
School of Mathematics and Statistics
+44 (0)114 2223746
a.p.willis /a/ sheffield.ac.uk
Office hours: I'm usually in H12 or around.
Please email to be sure.
2010/18-present: Lecturer/Senior Lecturer, School of Mathematics & Statistics, University of Sheffield, U.K.
Collaborator's pages
Elena Marensi
, EPSRC Research Assocate, Sheffield,
Optimization in Fluid Mechanics
;
Marc Avila
Bremen;
Predrag Cvitanović
Georgia Tech
(
chaosbook.org
);
Yohann Duguet
LIMSI, Paris;
Dave Gubbins
Leeds;
Yongyun Hwang
Imperial;
Rich Kerswell
DAMTP, Cambridge;
Jeorge Peixinho
PIMM, Paris.
Sheffield Fluid Dynamics Group
SoMaS Applied Mathematics Seminars
Some of my work:
A
Jacobian-free Newton-Krylov (JFNK) code
for finding solutions of high-dimensional nonlinear equations
(or low-dimensional if you like!).
I've written a
Double pendulum android app:
with two double-pendula side-by-side,
it is specifically designed to show how initially similar
states diverge - the chaotic system exhibits sensitivity to initial conditions (SIC).
It also shows how the chaotic paths follow particular repeating
patterns,
periodic orbits.
Publications can be found on my
Google Scholar page
or here:
Publications + preprints
A description of the mathematics behind the following videos can be found
here.
PhDs:
I am looking for motivated students
who would like to
apply and broaden their mathematical skills.
As the focus of my projects is usually
on the development of mathematical methods and the study of dynamical systems,
I expect you to be familiar with differential equations
and vector calculus, but you do not need to have taken advanced courses
on fluids.
The modelling of fluid flows is perhaps the traditional
test-bed for the development of new methods.
Often, even simple-looking setups exhibit all sorts
of interesting phenomena, and
our understanding of nature is greatly
enhanced through numerical simulation and experiments.
I am particularly interested in the appearance of
turbulence in fluid flows,
and in modelling flows in the interior of planets. The latter is
usually responsible for the generation of planetary magnetic fields.
For further information please contact me.
The following links to snippets of my work may also be of interest:
Turbulence.
Dynamos.
Please note that all PhD applications must be made
through the university system:
School info on PhD places.
University of Sheffield
S3 7RH, U.K.
2008-10: EU Marie Curie Fellow (PI), Laboratoire d'Hydrodynamique (LadHyX), Ecole Polytechnique, Paris, France
2005-08: EPSRC Research Associate, School of Mathematics, University of Bristol, U.K.
2002-05: NERC Research Fellow (RA), School of Earth Sciences, University of Leeds, U.K.
2002: PhD Applied Mathematics, Newcastle University, U.K.