# School of Mathematics

## Dr Rob J Sturman

Associate Professor

Applied Mathematics

### Contact details

Room: 9.24

Tel: +44 (0)113 3435139

Email: R.Sturman @ leeds.ac.uk

### Keywords

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

## Current postgraduate students

Patrick Wright (2014)

## Publications

**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

DOI:10.1007/978-3-319-42402-6_13

View abstract

**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

DOI:10.1137/130934076

View abstract

**Springham J, Sturman RJ** Polynomial decay of correlations in linked-twist maps *Ergodic Theory and Dynamical Systems*, 2012

View abstract

**Sturman R** A dynamical systems approach to musical tuning *Dynamical Systems*, **27**, 131-143, 2012

DOI:10.1080/14689367.2012.656300

View abstract

**Sturman R** The role of discontinuities in mixing *Advances in Applied Mechanics*, **45**, 51-90, 2012

DOI:10.1016/B978-0-12-380876-9.00002-1

View abstract

**Sturman RJ, Springham J** Rate of Chaotic Mixing and Boundary Behavior *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, 2012

View abstract

**Juarez G, Lueptow RM, Ottino JM, Sturman R, Wiggins S** Mixing by cutting and shuffling *EPL-EUROPHYS LETT*, **91**, 2010

DOI:10.1209/0295-5075/91/20003

**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

DOI:10.1017/S002211200800075X

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

DOI:10.1002/smll.200600361

**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

DOI:10.1063/1.1769111

**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

DOI:10.1016/j.physd.2004.02.002

**Ashwin P, Field M, Rucklidge AM, Sturman R** Phase resetting effects for robust cycles between chaotic sets *Chaos*, **13**, 973-981, 2003

DOI:10.1063/1.1586531

View abstract

**Ashwin P, Sturman R** Decelerating defects and non-ergodic critical behaviour in a unidirectionally coupled map lattice *PHYS LETT A*, **309**, 423-434, 2003

DOI:10.1016/S0375-9601(03)00245-7

**Ashwin P, Rucklidge AM, Sturman R** Cycling attractors of coupled cell systems and dynamics with symmetry In *Synchronization: Theory and Application*, 5-23, 2003

View abstract

**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

DOI:10.1103/PhysRevE.66.035201

View abstract

**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

View abstract

**Sturman R, Wiggins S** Eulerian indicators for predicting and optimizing mixing quality *New Journal of Physics*, **11**,

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