2021

MacKay, Robert S. (2021) National Grid frequency trace. [Dataset]

Burby, J. W., Kallinikos, N. and MacKay, Robert S. (2021) Approximate symmetries of guiding-centre motion. Journal of Physics A: Mathematical and Theoretical, 54 (12). 125202. doi:10.1088/1751-8121/abe58a

2020

MacKay, Robert S., Johnson, S. and Sansom, B. (2020) How directed is a directed network? Royal Society Open Science , 7 (9). 201138. doi:10.1098/rsos.201138

Burby, J. W., Kallinikos, N. and MacKay, Robert S. (2020) Some mathematics for quasi-symmetry. Journal of Mathematical Physics, 61 (9). 093503. doi:10.1063/1.5142487

MacKay, Robert S. (2020) Incomplete pairwise comparison. Mathematics Today, 134 .

MacKay, Robert S. (2020) Differential forms for plasma physics. Journal of Plasma Physics . doi:10.1017/S0022377819000928 (In Press)

Burby, J. W., Kallinikos, N. and MacKay, Robert S. (2020) Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria. Physics of Plasmas . (In Press)

MacKay, Robert S. (2020) Sustainable energy storage - with hot air, cold air and liquid air. Contemporary Physics, 61 (1). pp. 1-11. doi:10.1080/00107514.2020.1794380

Davison, A. R., Beale, N., Battey, H. and MacKay, Robert S. (2020) An unethical optimisation principle. Royal Society Open Science . (In Press)

2018

MacKay, Robert S. (2018) Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow. Regular and Chaotic Dynamics, 23 (6). pp. 797-802. doi:10.1134/S1560354718060126

MacKay, Robert S. (2018) Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow. Regular and Chaotic Dynamics, 23 (6). pp. 797-802. doi:10.1134/S1560354718060126

Baesens, Claude and MacKay, Robert S. (2018) Simplest bifurcation diagrams for monotone families of vector fields on a torus. Nonlinearity, 31 (6). 2928. doi:10.1088/1361-6544/aab6e2

MacKay, Robert S. and Robinson, J. D. (2018) Aggregation of Markov flows I : theory. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 376 (2118). doi:10.1098/rsta.2017.0232

MacKay, Robert S. (2018) Management of complex dynamical systems. Nonlinearity, 31 (2). R52. doi:10.1088/1361-6544/aa952d

2017

Webborn, Ellen and MacKay, Robert S. (2017) A stability analysis of thermostatically-controlled loads for power system frequency control. Complexity, 2017 . 5031505. doi:10.1155/2017/5031505

MacKay, Robert S., Kenna, R., Low, Robert J. and Parker, S. (2017) Data for Calibration with confidence : a principled method for panel assessment. [Dataset]

MacKay, Robert S., Kenna, R., Low, R. J. and Parker, S. (2017) Calibration with confidence : a principled method for panel assessment. Royal Society Open Science , 4 (2). 160760. doi:10.1098/rsos.160760

MacKay, Robert S. (2017) Mode conversion in the cochlea? Transactions of Mathematics and Its Applications, 1 (1). tnx002. doi:10.1093/imatrm/tnx002

(2017) Frontiers of chaotic advection. Reviews of Modern Physics, 89 (2). 025007 . doi:10.1103/RevModPhys.89.025007

2016

Flatley, Lisa, MacKay, Robert S. and Waterson, Michael (2016) Optimal strategies for operating energy storage in an arbitrage or smoothing market. Journal of Dynamics and Games, 3 (4). pp. 371-398. doi:10.3934/jdg.2016020

2015

Thornby, John Albert, MacKay, Robert S. and Williams, M. A. (2015) Mathematical principles for the design of isostatic mount systems for dynamic structures. IMA Journal of Applied Mathematics, 80 (6). pp. 1837-1854. doi:10.1093/imamat/hxv020

Garvey, S. D., Eames, P. C., Wang, J. H., Pimm, A. J., Waterson, M., MacKay, Robert S., Giulietti, M., Flatley, Lisa, Thomson, M., Barton, J., Evans, David, Busby, J. and Garvey, J. E. (2015) On generation-integrated energy storage. Energy Policy, 86 . pp. 544-551. doi:10.1016/j.enpol.2015.08.001

2014

Flatley, Lisa, MacKay, Robert S. and Waterson, Michael (2014) Optimal strategies for operating energy storage in an arbitrage market. Working Paper. Coventry: University of Warwick. Department of Economics. Warwick economics research papers series (TWERPS), Volume 2014 (Number 1048). (Unpublished)

MacKay, Robert S. and Strub, Dayal C. (2014) Bifurcations of transition states : morse bifurcations. Nonlinearity, Volume 27 (Number 5). pp. 859-895. doi:10.1088/0951-7715/27/5/859

Bujorianu, Manuela and MacKay, Robert S. (2014) Complex systems techniques for cyber-physical systems. In: CyPhy '14 , Berlin, 14 - 17 Apr 2014 . Published in: CyPhy '14 Proceedings of the 4th ACM SIGBED International Workshop on Design, Modeling, and Evaluation of Cyber-Physical Systems Pages 27-30 pp. 27-30. ISBN 9781450328715 . doi:10.1145/2593458.2593460

2013

Baesens, Claude and MacKay, Robert S. (2013) Analysis of a scenario for chaotic quantal slowing down of inspiration. The Journal of Mathematical Neuroscience, Volume 3 (Number 1). Article number 18. doi:10.1186/2190-8567-3-18

Baesens, C. and MacKay, Robert S. (2013) Interaction of two systems with saddle-node bifurcations on invariant circles : I. Foundations and the mutualistic case. Nonlinearity, Volume 26 (Number 12). pp. 3043-3076. doi:10.1088/0951-7715/26/12/3043

Baesens, Claude, Chen, Yi-Chiuan and MacKay, Robert S. (2013) Abrupt bifurcations in chaotic scattering : view from the anti-integrable limit. Nonlinearity, Volume 26 (Number 9). pp. 2703-2730. doi:10.1088/0951-7715/26/9/2703

2012

San Miguel, M., Johnson, J. H., Kertész, János, Kaski, K., Díaz-Guilera, A., MacKay, Robert S., Loreto, V., Érdi, P. and Helbing, D. (2012) Challenges in complex systems science. The European Physical Journal Special Topics, Vol.214 (No.1). pp. 245-271. doi:10.1140/epjst/e2012-01694-y

(2012) The FuturICT education accelerator. The European Physical Journal Special Topics, Vol.214 (No.1). pp. 215-243. doi:10.1140/epjst/e2012-01693-0

2011

MacKay, Robert S. and Rourke, C. P. (2011) Natural observer fields and redshift. Journal of Cosmology, Vol.15 . pp. 6079-6099.

MacKay, Robert S. (2011) Existence of invariant circles for infinitely renormalisable area-preserving maps. In: Peixoto, Mauricio Matos and Pinto, Alberto Adrego and Rand, D. A. (David A.), (eds.) Dynamics, Games and Science I. Springer proceedings in mathematics, Vol.1 . Berlin ; Heidelberg ; New York: Springer, pp. 631-636. ISBN 9783642114564

Diakonova, M. and MacKay, Robert S. (2011) Mathematical examples of space-time phases. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol.21 (No.8). pp. 2297-2304. doi:10.1142/S0218127411029793

MacKay, Robert S. and Rourke, Colin (2011) Natural observer fields and redshift. Journal of Cosmology, Vol.15 . pp. 6079-6099.

MacKay, Robert S. (2011) Robustness of Markov processes on large networks. Journal of Difference Equations and Applications, Vol.17 (No.8). pp. 1155-1167. doi:10.1080/10236190902976889

Pinheiro, D. and MacKay, Robert S. (2011) An overview of the behaviour of a scattering map for the dynamics of two interacting particles in a uniform magnetic field. In: Machado, J. A. Tenreiro and Luo, Albert C. J. and Barbosa, Ramiro S. and Silva, Manuel F. and Figueiredo, Lino B., (eds.) Nonlinear Science and Complexity. New York: Springer, pp. 375-379. ISBN 9789048198832

2010

Sanders, Redland, Thornby, John Albert, Attridge, Alex, Hyde-Moxon, R., MacKay, Robert S., Stott, C., Williams, M. A. and Young, Ken W. (2010) Characteristics, accuracy and reverification of robotised articulated arm CMMs. In: 26th Coordinate Metrology Society Conference, Reno, Nevada, 20-24 July 2010. Published in: CMSC Online Archive ISSN 2328-6075.

Ball, Robin, Diakonova, Marina and MacKay, Robert S. (2010) Quantifying emergence in terms of persistent mutual information. Advances in Complex Systems, Vol.13 (No.3). pp. 327-338. doi:10.1142/S021952591000258X

MacKay, Robert S. (2010) Langevin equation for slow degrees of freedom of Hamiltonian systems. In: Thiel, Marco and Kurths, Jürgen and Romano, M. Carmen and Károlyi, György and Moura, Alessandro, (eds.) Nonlinear dynamics and chaos : advances and perspectives. Understanding complex systems . Heidelberg ; New York: Springer, pp. 89-102. ISBN 9783642046292

MacKay, Robert S. (2010) Review of Facts and speculations in cosmology, by Narlikar, J. V. and Burbidge, G. Contemporary Physics, Vol.51 (No.2). pp. 178-180. ISSN 0010-7514

MacKay, Robert S. (2010) Review of The correspondence of Isaac Newton, volume V, 1709–1713, by Hall, A.R. and Tilling, L., eds. Contemporary Physics, Vol.51 (No.5). pp. 463-464. ISSN 0010-7514

2009

Thornby, John Albert, Attridge, Alex, Johnson, T., MacKay, Robert S., Sanders, R., Stott, C., Williams, M. A. and Young, Ken W. (2009) Simulation, modelling and development of the metris RCA. In: 25th Coordinate Metrology Society Conference, Louisville, Kentucky, 20-24 July 2009. Published in: CMSC Online Archive ISSN 2328-6075.

2008

Pinheiro, D. and MacKay, Robert S. (2008) Interaction of two charges in a uniform magnetic field : II. spatial problem. Journal of Nonlinear Science, Vol.18 (No.6). pp. 615-666. doi:10.1007/s00332-008-9022-1

Pelinovsky, Dmitry, Schneider, Guido and MacKay, Robert S. (2008) Justification of the lattice equation for a nonlinear elliptic problem with a periodic potential. Communications in Mathematical Physics, Vol.284 (No.3). pp. 803-831. doi:10.1007/s00220-008-0640-0

MacKay, Robert S. (2008) Nonlinearity in complexity science. Nonlinearity, Vol.21 (No.12). T273-T281. doi:10.1088/0951-7715/21/12/T03

Yamapi, R. and MacKay, Robert S. (2008) Stability of synchronization in a shift-invariant ring of mutually coupled oscillators. Discrete and Continuous Dynamical Systems. Series B, Volume 10 (Number 4). pp. 973-996. doi:DOI:10.3934/dcdsb.2008.10.973

MacKay, Robert S. (2008) Review of Theories of molecular reaction dynamics : the microscopic foundations of chemical kinetics, by Henriksen, N.E. and Hansen, F.Y. Contemporary Physics, Vol.49 (No.6). pp. 462-464. ISSN 0010-7514

MacKay, Robert S. (2008) A steady mixing flow with no-slip boundaries. In: CCT'07 conference, Marseille, France, 4-8 Jun 2007. Published in: Chaos, Complexity and Transport : Theory and Applications Proceedings of the CCT '07 pp. 55-68. doi:10.1142/9789812818805_0004

2007

Celletti, Alessandra and MacKay, Robert S. (2007) Regions of nonexistence of invariant tori for spin-orbit models. Chaos, Vol.17 (No.4). Article: 043119. doi:10.1063/1.2811880

Baesens, C. and MacKay, Robert S. (2007) Erratum to “Discommensuration theory and shadowing in Frenkel–Kontorova models” by C. Baesens and R.S. MacKay [Physica D 216 (2006) 179–184]. Physica D: Nonlinear Phenomena, Vol.229 (No.1). p. 96. doi:10.1016/j.physd.2007.03.012

Baesens, C. and MacKay, Robert S. (2007) Resonances for weak coupling of the unfolding of a saddle-node periodic orbit with an oscillator. Nonlinearity, Vol.20 (No.5). pp. 1283-1298. doi:10.1088/0951-7715/20/5/012

2006

MacKay, Robert S. (2006) Cerbelli and Giona's map is pseudo-Anosov and nine consequences. Journal of Nonlinear Science, Vol.16 (No.4). pp. 415-434. doi:10.1007/s00332-005-0743-0

Pinheiro, D. and MacKay, Robert S. (2006) Interaction of two charges in a uniform magnetic field: I. Planar problem. Nonlinearity, Vol.19 (No.8). pp. 1713-1745. doi:10.1088/0951-7715/19/8/002

MacKay, Robert S. and MacKay, D. J. C. (2006) Ergodic pumping: A mechanism to drive biomolecular conformation changes. In: Conference on Nonlinear Physics - Condensed Matter, Dynamical Systems and Biophysics, Inst Henri Poincare, Paris, FRANCE, MAY 30-31, 2005. Published in: Physica D: Nonlinear Phenomena, Volume 216 (Number 1). pp. 220-234. ISSN 0167-2789. doi:10.1016/j.physd.2006.02.006

Dauxois, Thierry, MacKay, Robert S. and Tsironis, George (2006) Preface - Serge Aubry. Physica D: Nonlinear Phenomena, Volume 216 (Number 1). VII-IX. doi:10.1016/j.physd.2006.02.001

Bolotin, S and MacKay, Robert S. (2006) Nonplanar second species periodic and chaotic trajectories for the circular restricted three-body problem. Celestial Mechanic & Dynamical Astronomy, Volume 94 (Number 4). pp. 433-449. doi:10.1007/s10569-006-9006-0

1989

MacKay, Robert S., Meiss, J. D. and Stark, J. (1989) Converse KAM theory for symplectic twist maps. NONLINEARITY, 2 (4). pp. 555-570. doi:10.1088/0951-7715/2/4/004

Kim, Seunghwan, MacKay, Robert S. and Guckenheimer, J. (1989) Resonance regions for families of torus maps. NONLINEARITY, 2 (3). pp. 391-404. doi:10.1088/0951-7715/2/3/001

1988

MacKay, Robert S. and van Zeijts, J. B. J. (1988) Period doubling for bimodal maps: a horseshoe for a renormalisation operator. NONLINEARITY, 1 (1). pp. 253-277.