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Dr Rob J Sturman

Associate Professor
Applied Mathematics

Contact details

Room: 9.24
Tel: +44 (0)113 3435139
Email: R.Sturman @


Dynamical systems
Ergodic theory
Fluid mixing
Piecewise isometries

Research interests

I am interested in applying ideas from ergodic theory and dynamical systems to fluid mixing problems. Chaotic mixing in fluids has for a long time been studied from the topological viewpoint, with the existence of a horseshoe frequently pointing the way towards chaotic dynamics, and hence mixing. However, horseshoes are objects of zero volume, and as such do not guarantee that islands of unmixed fluid do not exist. Ergodic theory, and in particular linked twist maps, gives a framework in which mixing results on sets of positive (and even full) volume can be formulated. I have applied these ideas to a range of different physical situations, including DNA hybridisation chambers, channel flows and granular tumblers. I have recently become interested in the idea of mixing by cutting and shuffling.

Useful links

Personal homepage

Current postgraduate students

Patrick Wright (2014)


Christov IC; Lueptow RM; Ottino JM; Sturman R A parametric study of mixing in a granular flow a biaxial spherical tumbler. 181, 143-154 2016
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Christov IC, Lueptow RM, Ottino JM, Sturman R A study in three-dimensional chaotic dynamics: granular flow and transport in a bi-axial spherical tumbler SIAM Journal on Applied Dynamical Systems, 13, 901-943, 2014
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Springham J, Sturman RJ Polynomial decay of correlations in linked-twist maps Ergodic Theory and Dynamical Systems, 2012
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Sturman R A dynamical systems approach to musical tuning Dynamical Systems, 27, 131-143, 2012
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Sturman R The role of discontinuities in mixing Advances in Applied Mechanics, 45, 51-90, 2012
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Sturman RJ, Springham J Rate of Chaotic Mixing and Boundary Behavior Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2012
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Juarez G, Lueptow RM, Ottino JM, Sturman R, Wiggins S Mixing by cutting and shuffling EPL-EUROPHYS LETT, 91, 2010

Sturman R, Meier SW, Ottino JM, Wiggins S Linked twist map formalism in two and three dimensions applied to mixing in tumbled granular flows J FLUID MECH, 602, 129-174, 2008

Hertzsch JM, Sturman R, Wiggins S DNA microarrays: Design principles for maximizing ergodic, chaotic mixing SMALL, 3, 202-218, 2007

Sturman R; Ottino J; Wiggins S The mathematical foundations of mixing: the linked twist map as a paradigm in applications: micro to macro, fluids to solids. Cambridge University Press 2006

Ashwin P, Rucklidge AM, Sturman R Cycling chaotic attractors in two models for dynamics with invariant subspaces CHAOS, 14, 571-582, 2004

Ashwin P, Rucklidge AM, Sturman R Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory PHYSICA D, 194, 30-48, 2004

Ashwin P, Field M, Rucklidge AM, Sturman R Phase resetting effects for robust cycles between chaotic sets Chaos, 13, 973-981, 2003
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Ashwin P, Sturman R Decelerating defects and non-ergodic critical behaviour in a unidirectionally coupled map lattice PHYS LETT A, 309, 423-434, 2003

Ashwin P, Rucklidge AM, Sturman R Cycling attractors of coupled cell systems and dynamics with symmetry In Synchronization: Theory and Application, 5-23, 2003
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Ashwin P, Rucklidge AM, Sturman R Infinities of stable periodic orbits in systems of coupled oscillators Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), 66, pp.035201, 2002
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Sturman R, Stark J Semi-uniform ergodic theorems and applications to forced systems Nonlinearity, 13, 113-143, 2000

Sturman R Scaling of intermittent behaviour of a strange nonchaotic attractor Physics Letters, Section A: General, Atomic and Solid State Physics, 259, 355-365, 1999
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Sturman R, Wiggins S Eulerian indicators for predicting and optimizing mixing quality New Journal of Physics, 11,
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