Continuum Mechanics group

The Continuum Mechanics group at York consists of Professors Vladimir Vladimirov and Martin Bees and Dr Konstantin Ilin. It has strong links with the Mathematical Biology Group

The main research interests are:

Martin Bees: Bioconvection; bacterial swarming; chemically driven hydrodynamics instabilites; ecology & biocontrol; plankton patchiness and dynamics.

Zaq Coelho: Ergodic theory and dynamical systems.

Konstantin Ilin: Fluid mechanics; magnetohydrodynamics; stability theory.

Vladimir Vladimirov: Applied mathematics; fluid dynamics; stability theory; averaging methods; liquid crystals; biological fluid dynamics.





(in alphabetical order)

Professor Martin A. Bees
MA (Oxon) PhD (Leeds)
Mathematical Biology, Fluid Mechanics
+44 1904 32 2038
Dr Gustav W Delius
PhD (Stony Brook)
Stochastic Modelling in Mathematical Biology and Theoretical Ecology, Spatial Stochastic Processes, Quantum Field Theory, Integrable Systems, Quantum Groups
+44 1904 32 3077
Ilin, Konstantin
Dr Konstantin Ilin
PhD (Novosibirsk)
fluid mechanics, magnetohydrodynamics, stability theory
+44 1904 32 4149
Professor Vladimir Vladimirov
Diploma in Physics and Applied Mathematics (Novosibirsk University), PhD-Candidate of Science in Physics and Mathematics (Novosibirsk and Moscow), DrSci-Doctor of Sciences in Physics and Mathematics (Novosibirsk and Moscow)
Applied Mathematics and Fluid Dynamics with special interests in: Asymptotic and Averaging Methods, Vibrodynamics; Hydrodynamic Stability; Vortex Dynamics; Geophysical Fluid Dynamics; Magneto-Hydrodynamics (MHD); Liquid Crystals; Biological Fluid Dynamics.
+44 1904 32 3070



Vladimirov VA.  Submitted.  Scalar transport in oscillating flows. Journal of Fluid Mechanics.



Vladimirov VA.  2013.  Dumbbell micro-robot driven by flow oscillations. Journal of Fluid Mechanics. 717(Rapid publications, 2013):1-11. Abstract  Download: Acoustic-Robot-4.pdf (200.36 KB)


O'Malley S, Bees MA.  2012.  The orientation of swimming biflagellates in shear flows. Bulletin of Mathematical Biology. 74:232–55.


Williams CR, Bees MA.  2011.  A tale of three taxes. The Journal of Experimental Biology. 214:2398–408.
Williams CR, Bees MA.  2011.  Biology: Algal synchronized swimming. Nature Research Highlights. 474:544.
MacKay N.  2011.  Is air combat Lanchestrian? Phalanx: the Bulletin of Military Operations Research. 44(4):12-14.
Williams CR, Bees MA.  2011.  Photo-gyrotactic bioconvection. Journal of Fluid Mechanics. 678:41–86.

Fluid Dynamics

Reseach Topics

Fluid Dynamics is a well established and exciting area of research. As an academic subject it has its very deep fundamental (mathematical and physical) core and enormous number of applications to a wide range of natural phenomena ranging from swimming of microorganisms to airplane design, from weather forecast to astrophysics. The main current research topics of the Fluid Dynamics Group are


Please see the homepages of members of the group for more details.


[Under development]

Current research of the Group is focused mostly on Vibrodynamics

Vibrodynamics studies the behaviour of any  system (mechanical, physical, biological, etc.), which undergoes vibrations or oscillations and allows description in terms of slow changing (averaged) parameters and oscillating parameters. Our current research in Vibrodynamics includes the following topics:

What is Vibrodynamics?

Researchers in physics and mechanics know how useful, when studying any physical or mechanical system, to raise a question: what happens if we make it to vibrate? This question proved its productive and inspiring power in the long and impressive serious of discoveries, achieved in attempts to find the answer.

Michael Faraday (1830) put a glass of water on a vertically vibrating table. It led him to the renowned discoveries of the parametric resonance and the parametric excitation of surface waves.

Andrew Stephenson (1908) and Petr Kapitza (1951) applied the high frequency vibrations to the pivot of a pendulum. It led to the discovery of the dynamic stabilization of the `up side down’ pendulum. This result has been generalized to a broad class of systems. For instance, a similar idea was realized for the levitating of the charged particles in an oscillating electric field by Wolfgang Paul (1958) and Michail Miller (1958) (and was honoured with the Nobel Prize in Physics in 1989).

V.N.Chelomey (1956) considered a high frequency longitudinal force applied to a beam. He predicted the increasing of the effective stiffness of the beam (it is not well known in the West, that Chelomey was also a renown General Constructor of Russian missiles). This theoretical idea was tested in the laboratory experiments by David Acheson and Tom Mullin (1993).

Igor Simonenko and Svetlana Zenkovskaya (1966) raised a question what happens if a container with an inhomogeneous fluid (for instance, a pot of water heated from below) undergoes vibrations. The result was the discovery that the thermal convection can be controlled by vibrations. In particular, vertical vibrations can completely suppress all convective motions. Now the vibrational convection represents a wide and attractive research field with applications to the space technology and to microgravity phenomena.

John Littlewood and Dame Mary Cartwright (1957) considered the well known Van-der-Pol equations and analyzed their solutions for the periodically modulated coefficients. In physical terms it means that they considered a lamp generator with periodically modulated parameters. They found specific chaotic regimes in this system. It led to the discovery of a fundamental object of the modern dynamical system and chaos theory (the Smale horseshoe).

It should be emphasized, that from the mathematical viewpoint all listed effects and results are specific for the modulated systems and are impossible if equations do not contain oscillating factors (for the autonomous system). Theoretical developments of systems of equation containing oscillating factors form an active and important research area in mathematics. Simultaneously with the mathematical and theoretical developments, a very active process of the creation of various vibrational technical devices takes place. It is very important to emphasize here, that the attitude of engineers towards the vibrations has been under the drastic change: the old approach of treating vibrations as only a ‘bad’ and ‘harmful’ factor which should be avoided or suppressed has been changed to the productive use of vibrations (vibrational drilling and cutting, vibrational transport, etc.). It is true that the problem of suppressing of the already existing harmful vibrations is always urgent. However, we suppose that now it is timely to start the solving the problem how to use the existing (unavoidable) vibrations, like we use the energy of wind, rivers, and radiation of the Sun.

Studies of the vibrational effects in various (physical, mechanical, geophysical, biological, medical, technical, and economical) systems continue to bring new and impressive discoveries. These studies can be united under the name of Vibrodynamics. This term was coined in our group (V.A.Vladimirov, V.I.Yudovich, K.I.Ilin).

Vibrodynamics represents a really broad and interdisciplinary research area, since of any physical, mechanical, etc. system (after the exposing it to vibrations) becomes its subject. It is already well recognized that the organizing of the interdisciplinary efforts is the key for success in Vibrodynamics. This resulted for instance in the creation of the Laboratory for Vibrational Mechanics in St-Petersburg (Russia), and the Centre of Vibro-Impact Systems in Loughborough (UK).

Significant research in the theoretical Vibrodynamics has been undertaken at the Department of Mathematics, University of York under the leadership of Prof. V.A.Vladimirov, Prof V.I.Yudovich, and Dr.K.I.Ilin. During last few years the participants produced a number of sound results, which drastically simplified the theory in this area. A number of interesting problems, which were not accessible before, become solvable. Naturally, simplification of the theory brings a great deal of its generalization. What is even more important, this breakthrough in theory (as well as some pilot laboratory experiments) brought us the confidence that this area is very promising for the obtaining of interesting theoretical, experimental, and engineering results. This success allowed us to choose the most encouraging directions (we do understand now, what targets we should hit and able to hit!).  As the result of all these activities Vibrodynamics has been identified among the best research direction to concentrate the efforts of specialists in mechanics, mathematics, physics, chemistry anf many other areas of Sciences and Engineering.


Applied Mathematics Seminar

York's Applied Maths seminars cover a range of interests and research groups, from continuum mechanics to networks and nonlinear dynamics, and extending to applications in biology and chemistry.

The seminars take place on Mondays at 3.15 pm in ATB/037A.

Next talk:

Space-Time Liquid-Crystals: synchronization and fluctuations in active matter

Applied Mathematics Seminar
Date and time: 
April 27, 2015, 14:00 - 15:00
Prof Tanniemola B Liverpool (Bristol Uni)

Colonies of swimming bacteria, algae or spermatozoa are examples of active systems composed of interacting units that consume energy and collectively generate motion and mechanical stresses.  Due to the anisotropy of their interactions, these active particles can exhibit orientational order at high concentration and have been called “living liquid crystals".

Edited 15 Apr 2015 - 22:51 by dop502

Information on How to Reach the University is available. You can locate James College on the campus map. Please contact Martin Bees if you need further information.

Programme for this term

Date and timesort icon Title Speaker Room
January 12, 2015, 14:00 - 15:00 Predators, Prey and Prevalence Dr Andrew Bate (York) G/013
February 9, 2015, 14:00 - 15:00 Cassava disease: a clean seed solution Dr Finn Mcquaid (Rothamsted) W/301
February 16, 2015, 14:00 - 16:00 Microfluidic control for flagellated microswimmers Dr Vasiliy Kantsler (Warwick) W/301

Please note that this is an evolving programme. It is advisable to (re-load and) re-check the page shortly before each talk. (Mailing list TBD). 

See also the list of all Applied Mathematics talks.

iCal feed for this seminar

PhD projects

This page is under construction. Please check again soon.


Bioconvection; Biological Fluid Dynamics; Mathematical Ecology; Pattern formation. Martin Bees

I have several projects available.  PhD students can choose to get involved in experiemental work in my wet laboratory.

Project 1) Hydrodynamic interactions of swimming micro-organisms: from individuals to suspensions

Project 2) Biodiesel from algae

Project 3) Porous media, micro-organisms and gas exchange

Project 4) Morphological characterization of spatial patterns in bioconvection using integral geometry

Project 5) Biological control of agricultural pests

Project 6) Chemically induced hydrodynamic instabilities

Project 7) Mathematical physiology

Project 8) The ecology of plankton patchiness and the impact of turbulence

For further ideas and projects please see visit my hompage, or send an email.


Combat Modelling. Niall MacKay

A range of topics could be pursued, including dynamical-systems, stochastic and network models, of historical and contemporary (typically insurgent) conflict, and studies of the interplay between mathematical modelling and doctrine and organizational culture. MacKay has worked on mixed-force Lanchester models, dynamical models of insurgency, analysis of air combat data from the Battle of Britain, the US-Japanese Pacific air war and Korea, airpower theory and the development of RAF fighter doctrine, and naval war, both in the 'big gun' era and for the guided-missile age.