Dr Mike Jeffrey

M.Sc., Ph.D.(Bristol)

Current positions

Associate Professor in Engineering Mathematics
School of Engineering Mathematics and Technology

Contact

Press and media

Many of our academics speak to the media as experts in their field of research. If you are a journalist, please contact the University’s Media and PR Team:

Edit profile

Research interests

Geometrical Asymptotics. Although the bulk of the world satisfies nice simple rules laid down from Descartes, to Newton, Hamilton, through to Dirac, the really interesting structures are born from the outer fringes of these theories - sonic booms, rainbows, ripples on ponds, wave-particle or wave-ray dualities. On these fringes the theories break down, but in their wake, beautiful geometry reveals intricate physical phenomena, such as swirling Mach cones in helicopter noise, the speed-of-light caustic in a high energy synchrotron, cusps, whiskers and complex rays in conical diffraction; ...
Grazing Catastrophes. The theory of dynamical systems with discontinuities, such as friction, switching, or impact, is young and growing. At the heart of most theories is the assymption of smoothness, but from the squeal of brakes to the rattle of a fan blade, it is clear that in the real world things rarely run smoothly. These events are discontinuous, they involve sudden changes and loss of reversibility, and occur whenever two systems come into contact. Mathematics was not built to handle discontinuities, so we treat the interaction ad hoc, we look at the "before" and "after" in isolation, then stitch things back together later. But perhaps nature is not so malicious. Perhaps not everything is lost when a system jumps. By studying orbits that "graze" discontinuities - that almost jump but not quite - we hope to get to the heart of discontinuity.
From nonsmooth to slow-fast - Discontinuity Asymptotics. What does the borderland between a system with a discontinuity, and a system with a sudden (slow-fast) change, look like? Experimental laws of the second type are incredibly complicated. Theoretical equations of the first type are too idealistically simple. Somewhere between them are the bifurcations and the catastrophes that define real world events everywhere from engineering to physiology, where contact between systems takes place much more quickly than changes in the systems themselves, but hugely affects their dynamics. I am interested in a nonsingular understanding of singular perturbation theory: a geometrical relationship between nonsmooth and slow-fast systems.

Our people

Dr Mike Jeffrey

Current positions

Associate Professor in Engineering Mathematics

Contact

Press and media

Research interests

Projects and supervisions

Research projects

Resolving discontinuities in the behaviour of dynamical systems

Principal Investigator

Managing organisational unit

Dates

When Worlds Collide: the asymptotics of interacting systems (Career Acceleration Fellowship)

Principal Investigator

Managing organisational unit

Dates

Thesis supervisions

Routes to Indeterminacy in Nonsmooth Systems

Supervisors

Publications

Recent publications

Classification of Filippov type 3 singular points in planar bimodal piecewise smooth systems

Elementary catastrophes underlying bifurcations of vector fields and PDEs

Perturbation and determinacy of nonsmooth systems

The hidden sensitivity of non-smooth dynamics

Underlying catastrophes

Thesis

Conical Diffraction: Complexifying Hamilton's Diabolical Legacy

Supervisors

Award date

Related people

Dr Martin Homer

Dr Robert Szalai

Professor John Hogan

Dr Cameron Hall