Arnold, V. I. & Avez, A. 1989 Ergodic Problems of Classical Mechanics. Addison-Wesley.
Alvarez, M. M., Arratia, P. E. & Muzzio, F. J. 2002 a Laminar mixing in eccentric stirred tank systems. Can. J. Chem. Engng 80, 546–557.
Alvarez, M. M., Shinbrot, T., Zalc, J. & Muzzio, F. J. 2002 b Practical chaotic mixing. Chem. Engng Sci. 17, 3749–3753.
Balasuriya, S. 2005 Optimal perturbation for enhanced chaotic transport. Physica D 202, 155–176.
Beigie, D., Leonard, A. & Wiggins, S. 1994 Invariant manifold templates for chaotic advection. Chaos Solitons Fractals 4, 749–868.
Boyland, P. L., Aref, H. & Stremler, M. A. 2000 Topological fluid mechanics of stirring. J. Fluid Mech. 403, 277–304.
Cerbelli, S., Vitacolonna, V., Adrover, A. & Giona, M. 2004 Eigenvalue–eigenfunction analysis of infinitely fast reactions and micromixing regimes in regular and chaotic bounded flows. Chem. Engng Sci. 59, 2125–2144.
Devaney, R. 1989 An Introduction to Chaotic Dynamical Systems. 2nd edn. Perseus Books.
D'Alessandro, D., Dahleh, M. & Mezić, I. 1999 Control of mixing in fluid flow: A maximum entropy approach. IEEE Trans. Aut. Contr. 44, 1852–1863.
Fountain, G. O., Khakhar, D. V. & Ottino, J. M. 1997 Visualization of three-dimensional chaos. Science 31, 683–686.
Franjione, J. G. & Ottino, J. M. 1992 Symmetry concepts for geometric analysis of mixing flows. Phil. Trans. R. Soc. Lond. A 338, 301–323.
Giona, M., Cerbelli, S. & Adrover, A. 2002 Geometry of reaction interfaces in chaotic flows. Phys. Rev. Lett. 88, 024501 I–IV.
Giona, M., Cerbelli, S., & Vitacolonna, V. 2004 a Universality and imaginary potentials in advection–diffusion equations in closed flows. J. Fluid Mech. 513, 221–237.
Giona, M., Adrover, A., Cerbelli, S. & Vitacolonna, V. 2004 b Spectral properties and transport mechanisms of partially chaotic bounded flows in the presence of diffusion. Phys. Rev. Lett. 92, 114101 I–IV.
Harvey, A. D. III, Wood, S. P. & Leng, D. E. 1997 Experimental and computational study of multiple impeller flows. Chem. Engng Sci. 52, 1479–1491.
Hobbs, D. M., & Muzzio, F. J. 1998 Optimization of a static mixer using dynamical systems techniques. Chem. Engng Sci. 53, 3199–3213.
Hobbs, D. M., Alvarez, M. M. & Muzzio, F. J. 1997 Mixing in globally chaotic flows: A self-similar process. Fractals 5, 395–425.
Katok, A. & Hasselblatt, B. 1995 Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press.
Lamberto, D. J., Muzzio, F. J., Swanson, P. D. & Tonkovich, A. L 1996 Using time-dependent RPM to enhance mixing in stirred vessels. Chem. Engng Sci. 51, 733–741.
Liu, W. & Haller, G. 2004 Inertial manifolds and completeness of eigenmodes for unsteady magnetic dynamos. Physica D 194, 297–319.
Liu, M., Muzzio, F. J. & Peskin, R. L. 1994 a Quantification of mixing in aperiodic chaotic flows. Chaos Solitons Fractals 4, 869–893.
Liu, M., Peskin, R. L., Muzzio, F. J., & Leong, C. W. 1994 b Structure of the stretching field in chaotic cavity flows. AIChE J. 40, 1273–1286.
Mathew, C., Mezić, I., & Petzold, L. 2005 A multiscale measure for mixing. Physica D 211, 23–46.
Mathew, C., Mezić, I., Grivopoulos, S., Vaidya, U. & Petzold, L. 2007 Optimal control of mixing in Stokes fluid flows. J. Fluid Mech. 580, 261–281.
Metcalfe, G., Rudman, M., Brydon, A., Graham, L. J. W. & Hamilton, R. 2005 Composing chaos: An experimental and numerical study of an open duct mixing flow. AIChE J. 52, 9–28.
Noack, B. R., Mezić, I., Tadmor, G. & Banaszuk, A. 2004 Optimal mixing in recirculation zones. Phys. Fluids 16, 867–888.
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos and Transport. Cambridge University Press.
Ottino, J. M. & Wiggins, S. 2004 a Designing optimal micromixers. Science 305, 485–486.
Ottino, J. M. & Wiggins, S. 2004 b Introduction: Mixing in microfluidics. Phil. Trans. R. Soc. Lond. A 362, 923–935.
Rice, M., Hall, J., Papadakis, G. & Yanneskis, M. 2006 Investigation of laminar flow in a stirred vessel at low Reynolds numbers. Chem. Engng Sci. 61, 2762–2770.
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 An analytic study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347–394.
Sharma, A. & Gupte, N. 1997 Control methods for problems of mixing and coherence in chaotic maps and flows. Pramana J. Phys. 488, 231–248.
Stremler, M. A., Haselton, F. R. & Aref, H. 2004 Designing for chaos: Applications of chaotic advection at the microscale. Phil. Trans. R. Soc. Lond. A 362, 1019–1036.
Tabeling, P. 2005 Introduction to Microfluidics. Oxford University Press.
Tabeling, P., Chabert, M., Dodge, A., Jullien, C. & Okkels, F. 2004 Chaotic mixing in cross-channel micromixer. Phil. Trans. R. Soc. Lond. 362, 987–1000.
Tay, F. E. H. 2002 Microfluidics and BioMEMS Applications. Kluwer.
Thiffeault, J. L., Doering, C. R. & Gibbon, J. D. 2004 A bound on mixing efficiency for the advection–diffusion equation. J. Fluid Mech. 521, 105–114.
Thiffeault, J.-L. & Finn, M. D. 2006 Topology, braids and mixing in fluids. Phil. Trans. R. Soc. Lond. A 364, 3251–3266.
Toussaint, V., Carriere, P., & Raynal, F. 1995 A numerical Eulerian approach to mixing by chaotic advection. Phys. Fluids 7, 2587–2600.
Toussaint, V., Carriere, P., Scott, J. & Gence, J. N. 2000 Spectral decay of a passive scalar in chaotic mixing. Phys. Fluids 12, 2834–2844.
Vikhansky, A. 2002 a Enhancement of laminar mixing by optimal control methods. Chem. Engng Sci. 57, 2719–2725.
Vikhansky, A. 2002 b Control of stretching rate in time-periodic chaotic flows. Phys. Fluids 14, 2752–2756.
Wiggins, S. & Ottino, J. M. 2004 Foundations of chaotic mixing. Phil. Trans. R. Soc. Lond. A 362, 937–970.
Wojtkowski, M. 1981 A model problem with the coexistence of stochastic and integrable behavior. Commun. Math. Phys. 80, 453–464.
Xia, H. M., Shu, C., Wan, S. Y. M. & Chen, Y. T. 2006 Influence of the Reynolds number on chaotic mixing in a spatially periodic micromixer and its characterization using dynamical system techniques. J. Micromech. Microengng 16, 53–61.
Zalc, J. M., Szalai, E. S. & Muzzio, F. J. 2003 Mixing dynamics in the SMX static mixer as a function of injection location and flow ratio. Polym. Engng Sci. 43, 875–890.