Old List of Publications
(until 2017, by year)
2017
[34] B. P. Murray, M. D. Bustamante 2017 Energy flux enhancement, intermittency and turbulence via Fourier triad phase dynamics in 1D Burgers equation. arXiv:1705.08960
2016
[33] D. Lucas, M. D. Bustamante, M. Perlin 2016 Precession resonance in water waves. arXiv:1608.04241
[32] M. Buzzicotti, B. P. Murray, L. Biferale, M. D. Bustamante 2016 Phase and precession evolution in the Burgers equation. Eur. Phys. J. E 39, 3; pdf arXiv:1509.04450
[31] R. M. Mulungye, D. Lucas, M. D. Bustamante 2016 Atypical late-time singular regimes accurately diagnosed in stagnation-point-type solutions of 3D Euler flows. J. Fluid Mech. 788, R3; pdf arXiv:1508.03328
[30] M. Perlin, M. D. Bustamante 2016 A Robust Quantitative Comparison Criterion of Two Signals based on the Sobolev Norm of Their Difference. J. Eng. Math. 101, 115; DOI:10.1007/s10665-016-9849-7; pdf
arXiv:1412.6977
2015
[29] M. D. Bustamante, S. V. Nazarenko 2015 Derivation of the Biot-Savart equation from the nonlinear Schrodinger equation, Phys. Rev. E 92, 053019; pdf arXiv:1507.07806
[28] R. M. Mulungye, D. Lucas, M. D. Bustamante 2015 Symmetry-plane model of 3D Euler flows and mapping to regular systems to improve blowup assessment using numerical and analytical solutions, J. Fluid Mech. 771, 468; pdf arXiv:1411.6324
2014
[27] M. D. Bustamante, B. Quinn, D. Lucas 2014 Robust energy transfer mechanism via precession resonance in nonlinear turbulent wave systems, Phys. Rev. Lett. 113, 084502;
[Paper: pdf] [Supplemental Material: Mathematica 9.0 file pdf file] arXiv:1404.7833
[26] M. D. Bustamante, K. L. Harper, S. V. Nazarenko, B. Quinn 2014, Zonostrophy and other quadratic invariants in drift and QG wave turbulence, in Zonal Jets, eds. Boris Galperin and Peter Read, CUP;
2013
[25] M. D. Bustamante, U. Hayat, P. Lynch, B. Quinn 2013 Counting of discrete Rossby/drift wave resonant triads (again). Preprint: arXiv:1309.5513
[24] M. D. Bustamante, U. Hayat, P. Lynch, B. Quinn 2013a Counting of discrete Rossby/drift wave resonant triads. Preprint: arXiv:1309.0405
[23] M. D. Bustamante, B. Quinn 2013, Robust energy transfer mechanism and critically balanced turbulence via non-resonant triads in nonlinear wave systems.
Preprint: arXiv:1305.5517 Supplemental Material: Mathematica 8.0 file
[22] J. Harris, C. Connaughton, M. D. Bustamante 2013 Percolation transition in the kinematics of nonlinear resonance broadening in Charney-Hasegawa-Mima model of Rossby wave turbulence, New Journal of Physics 15, 083011; pdf arXiv:1212.5336
[21] K. L. Harper, M. D. Bustamante, S. V. Nazarenko 2013 Quadratic invariants for discrete clusters of weakly interacting waves, J. Phys. A: Math. Theor. 46, 245501; pdf arXiv:1212.3156 IOP Highlights of 2013 collection
[20] M. D. Bustamante, U. Hayat 2013 Complete classification of discrete resonant Rossby/drift wave triads on periodic domains, Commun. Nonlinear Sci. Numer. Simulat. 18, 2402–2419; pdf arXiv:1210.2036
[19] P. Lynch, M. D. Bustamante 2013 Quaternion Solution for the Rock'n'roller: Box Orbits, Loop Orbits and Recession, Regular & Chaotic Dynamics 18, 166–183; pdf arXiv:1207.6022
[18] M. E. Brachet, M. D. Bustamante, G. Krstulovic, P. D. Mininni, A. Pouquet, D. Rosenberg 2013 Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries, Phys. Rev. E 87, 013110; pdf arXiv:1206.6372
2012
[17] R. M. Kerr, M. D. Bustamante 2012, Exploring symmetry plane conditions in numerical Euler solutions, in Mathematical Aspects of Fluid Mechanics, eds. J. C. Robinson, J. L. Rodrigo and W. Sadowski, CUP; pdf
[16] J. Harris, M. D. Bustamante, C. Connaughton 2012 Externally forced triads of resonantly interacting waves: Boundedness and integrability properties, Commun. Nonlinear Sci. Numer. Simulat. 17, 4988–5006; pdf arXiv:1201.2867
[15] M. D. Bustamante, M. Brachet 2012 On the interplay between the BKM theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem, Phys. Rev. E 86, 066302; pdf arXiv:1112.1571
2011
[14] M. D. Bustamante 2011 3D Euler equations and ideal MHD mapped to regular systems: Probing the finite-time blowup hypothesis, Physica D 240, 1092–1099; pdf arXiv:1007.2587
[13] E. Kartashova, M. D. Bustamante 2011 Resonance clustering in wave turbulent regimes: Integrable dynamics, Commun. Comput. Phys. 10, 1211–1240; pdf arXiv:1002.4994
< 2010
[12] P. Lynch, M. D. Bustamante 2009 Precession and recession of the rock'n'roller, J. Phys A: Math. Theor. 42, 425203; IOP Select pdf Animation of the Rock'n'Roller
[11] M. D. Bustamante, E. Kartashova 2009a Effect of the dynamical phases on the nonlinear amplitudes' evolution, EPL 85, 34002; pdf arXiv:0901.2354v1
[10] M. D. Bustamante, E. Kartashova 2009 Dynamics of nonlinear resonances in Hamiltonian systems, EPL 85, 14004; pdf arXiv:0805.0358v3
[9] J. D. Gibbon, M. D. Bustamante, R. M. Kerr 2008 The three-dimensional Euler equations: singular or non-singular? Nonlinearity 21, T123–T129; pdf
[8] M. D. Bustamante, R. M. Kerr 2008 3D Euler about a 2D Symmetry Plane, Physica D 237, 1912–1920; pdf arXiv:0802.3369v1
[7] M. D. Bustamante, J.F. van Diejen, A.C. De la Maza 2008 Norm formulas for the Bethe ansatz on root systems of small rank, J. Phys. A: Math. Theor. 41, 025202; pdf
[6] C. Cartes, M. D. Bustamante, A. Pouquet, M. Brachet 2009 Capturing reconnection phenomena using generalized Eulerian-Lagrangian description in Navier-Stokes and resistive MHD, Fluid Dyn. Res. 41, 011404; pdf arXiv:0804.3602v1
[5] C. Cartes, M. D. Bustamante, M. Brachet 2007 Generalized Eulerian-Lagrangian description of Navier-Stokes dynamics, Phys. Fluids 19, 077101; pdf
[4] C. Chevalier, M. D. Bustamante, F. Debbasch 2007 Thermal statistical ensembles of black holes, Physica A: Statistical and Theoretical Physics 376, 293–307; pdf
[3] M. D. Bustamante, S.A. Hojman 2003 Lagrangian structures, integrability and chaos for 3D dynamical equations, J. Phys. A: Math. Gen. 36, 151–160; pdf hep-th/0208189
[2] M. D. Bustamante, S.A. Hojman 2003 Multi-Lagrangians, hereditary operators and Lax pairs for the Korteweg-de Vries positive and negative hierarchies, J. Math. Phys. 44 (10), 4652–4671; pdf hep-th/0301152
[1] O. Maldonado, D. Gottlieb, M. D. Bustamante, J. Roessler 1999 Transversal effect in a metal-to-metal interface, Phys. Stat. Sol. (b) 214, 315–325; pdf