Doctor Andrew Burbanks

Recent Publications

 ORCiD: https://orcid.org/0000-0003-0685-6670

Papers

1. Burbanks AD, Osbaldestin AH, Thurlby JA,
   Rigorous bounds on the fractal dimension of the period-doubling attractor,
   In preparation, 2020.
2. Burbanks AD, Osbaldestin AH, Thurlby JA,
   Period-doubling renormalisation fixed points in unimodal maps of odd critical exponent,
   In preparation, 2020.
3. Cerasuolo M, Burbanks AD, Turner L,
   Multiscale modelling of neuroendocrine transdifferentiation in prostate cancer cells,
   In preparation, 2020.
4. Burbanks AD, Osbaldestin AH, Thurlby JA,
   Rigorous bounds on period-doubling renormalisation fixed-points in maps with critical point of degree 4,
   Submitted to Communications in Mathematical Physics, [arXiv:2006.13127], 2020. [ arXiv:2006.13127 ]
5. Wairegi A, Gamboa A, Burbanks AD, Lee EA, Farrelly D,
   Microscopic Superfluidity in 4He Clusters Stirred by a Rotating Impurity Molecule,
   Physical Review Letters, 112, 143401 (April 2014). [ doi:10.1103/PhysRevLett.112.143401 ]
6. Hennig D, Mulhern C, Burbanks AD, Schimansky-Geier L,
   Nonlinear response of a linear chain to weak driving,
   Physical Review E, 89, 012906 (January 2014). [ doi:10.1103/PhysRevE.89.012906 ]
7. Hennig D, Mulhern C, Burbanks AD,
   From strong chaos via weak chaos to regular behaviour: Optimal interplay between chaos and order,
   Physica D: Nonlinear Phenomena, 253, pp102-110, (June 2013). [ doi:10.1016/j.physd.2013.03.004 ]
8. Mulhern C, Hennig D, Burbanks AD,
   The coupled dynamics of two particles with different limit sets,,
   The European Physical Journal B, 86, 185, (April 2013). [ doi:10.1140/epjb/e2013-31114-5 ]
9. Banaji, M, Burbanks, AD,
   A graph theoretic condition for irreducibility of a set of cone preserving matrices,
   Linear Algebra and its Applications (2013). [ doi:10.1016/j.laa.2013.01.029 ]
10. Burbanks AD, Hennig D, Mulhern C, Osbaldestin AH,
    Explicit Construction of an Autonomous Hamiltonian System Exhibiting Continual Directed Flow,
    Physics Letters A, 376 (34), pp2283-2287, (2012). [ doi:10.1016/j.physleta.2012.05.051 ]
11. Mulhern C, Hennig D, Burbanks AD, Osbaldestin AH,
    Current reversals and current suppression in an open two degree of freedom system,
    Phys. Rev. E 83 (6), 066207 (2011). [ doi:10.1103/PhysRevE.83.066207 ]
12. Hennig D, Burbanks AD, Osbaldestin AH, Mulhern C,
    From Collective Periodic Running States to Completely Chaotic Synchronised States in Coupled Particle Dynamics,
    Chaos 21 (2), 023132 (2011). [ doi:10.1063/1.3594577 ]
13. Hennig D, Burbanks AD, Osbaldestin AH,
    Directed current in the Holstein system,
    Phys. Rev. E. 83 (3), 031121 (2011). [ doi:10.1103/PhysRevE.83.031121 ]
14. Hennig D, Burbanks AD, Osbaldestin AH, Mulhern C,
    Transient-chaos induced directed transport in a spatially-open Hamiltonian system,
    J. Phys. A: Math. Theor. 43 (34) 345101 (2010). [ doi:10.1088/1751-8113/43/34/345101 ]
15. Hennig D, Burbanks AD, Mulhern C, Osbaldestin AH,
    Emergence of continual directed flow in Hamiltonian systems,
    Physical Review E 82 (2), 026210 (2010). [ doi:10.1103/PhysRevE.82.026210 ]
16. Hennig D, Burbanks AD, Osbaldestin AH,
    Avalanches in a nonlinear oscillator chain in a periodic potential,
    Eur. Phys. J. Special Topics 187 (1), 145--156 (2010). [ doi:10.1140/epjst/e2010-01279-x ]
17. Hennig D, Burbanks AD, Osbaldestin AH,
    Directing particle transport in a two-dimensional periodic potential landscape,
    J. Chem. Phys. 375 (2-3), 492--502 (2010). [ doi:10.1016/j.chemphys.2010.03.018 ]
18. Hennig D, Burbanks AD, Osbaldestin AH,
    Directed transport of two interacting particles in a washboard potential,
    Physica D 238 (23-24), 2273-2281 (2009) 2273--2281. [ doi:10.1016/j.physd.2009.09.011 ]
19. Waalkens H, Burbanks AD, Wiggins S,
    Formula to compute the microcanonical volume of reactive initial conditions in transition state theory.
    J. Phys. A.: Math. Gen. 38, L759--L768, 2005. [ doi:10.1088/0305-4470/38/45/L03 ]
20. Waalkens H, Burbanks AD, Wiggins S,
    Efficient procedure to compute the microcanonical volume of initial conditions that lead to escape trajectories from a multi-dimensional potential well.
    Phys. Rev. Lett., 95, 084301, 2005. [ doi:10.1103/PhysRevLett.95.084301 ]
21. Waalkens H, Burbanks AD, Wiggins S,
    Escape from Planetary Neighbourhoods.
    Mon. Not. Royal Astron. Soc., 361, 763--775, 2005. [ doi:10.1111/j.1365-2966.2005.09237.x ]
22. Waalkens H, Burbanks AD, Wiggins S,
    Phase Space Conduits for Reaction in Multi-Dimensional Systems.
    J. Chem. Phys., 121 (13), 6207--6225, 2004. [ doi:10.1063/1.1789891 ]
23. Waalkens H, Burbanks AD, Wiggins S,
    A procedure to detect a new type of chaotic saddle; application to 3-d Hill's problem.
    J. Phys. A., 37 (24), L257--L265, 2004. [ doi:10.1088/0305-4470/37/24/L04 ]
24. Astakhov S, Burbanks AD, Farrelly D, Wiggins S,
    Chaos-Assisted Capture of Irregular Moons.
    Nature, 423, 264--267, 2003. [ doi:10.1038/nature01622 ]
25. Burbanks AD, Nussbaum R, Sparrow C,
    Extension of order-preserving maps on a cone.
    Proc. Royal Soc. Edinburgh, 133A, 35--59, 2003. [ doi:10.1017/S0308210500002274 ]
26. Burbanks AD, Nussbaum R, Sparrow C,
    Remarks on continuous extension of order-preserving homogeneous maps.
    Kybernetica, 39(2), 205--215, 2003.
27. Burbanks AD, Osbaldestin A, Stirnemann AH,
    Rigorous Bounds on the Hausdorff Dimension of Siegel disc boundaries.
    Communications in Mathematical Physics, 199(2), 417--439, 1998. [ doi:10.1007/s002200050507 ]
28. Burbanks AD, Osbaldestin A, Stirnemann AH,
    Fractal Dimension of Siegel Disc Boundaries.
    European Journal of Physics B, 4, 263--265, 1998. [ doi:10.1007/s100510050377 ]
29. Burbanks AD, Stirnemann AH,
    Hölder Continuous Siegel Disc Boundary Curves.
    Nonlinearity, 8 (6), 901--920, 1995. [ doi:10.1088/0951-7715/8/6/002 ]

Doctoral Thesis

1. Burbanks A,
   Renormalization for Siegel Discs.
   Ph.D. Thesis, Loughborough, 1997.

Conference Proceedings & Other Publications

1. Collins P, Burbanks AD, Wiggins S, Waalkens H, Schubert R,
   Background and Documentation of Software for Computing Hamiltonian Normal Forms,
   Laboratory for Advanced Computation in the Mathematical Sciences, University of Bristol, Report, 2008. [ online ]
2. Astakhov S, Burbanks AD, Farrelly D, Wiggins S,
   Dynamics of capture in the restricted three-body problem.
   Astronomical Society of the Pacific
   Order & Chaos in Stellar & Planetary Systems,
   CS-316, 2004. [ arXiv:astro-ph/0310618v1 ]
3. Burbanks AD, Sparrow C,
   Continuous extension of order-preserving homogeneous maps.
   Proc. IFAC Symposium, August 2001, Prague, Czech Republic. Max-Plus Algebras.
4. Burbanks AD, Sparrow C,
   Monotone homogeneous functions admit continuous extension.
   Statistical Laboratory, University of Cambridge, Research Report 1999-13.
5. Burbanks AD,
   Extracting beauty from Chaos.
   Public Awareness & Schools Support for Maths (PASS Maths/+plus), 9, Sep 1999.