Superdiffusive transport and energy localization in disordered granular crystals

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

doi:10.1103/PhysRevE.93.022902

Title: Superdiffusive transport and energy localization in disordered granular crystals

Journal Article · Fri Feb 12 00:00:00 EST 2016 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.93.022902· OSTI ID:1234648

Martinez, Alejandro J. ^[1]; Kevrekidis, Panagiotis G. ^[2]; Porter, Mason A. ^[1]

Univ. of Oxford, Oxford (United Kingdom)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition. Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m^~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1234648

Alternate ID(s):: OSTI ID: 1237989

Report Number(s):: LA-UR-14-28911; PLEEE8; TRN: US1600511

Journal Information:: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics; ISSN 1539-3755

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 24 works

Citation information provided by
Web of Science

References (88)

Transport and Anderson localization in disordered two-dimensional photonic lattices Schwartz, Tal; Bartal, Guy; Fishman, Shmuel Nature, Vol. 446, Issue 7131 https://doi.org/10.1038/nature05623	journal	March 2007
Direct observation of Anderson localization of matter waves in a controlled disorder Billy, Juliette; Josse, Vincent; Zuo, Zhanchun Nature, Vol. 453, Issue 7197 https://doi.org/10.1038/nature07000	journal	June 2008
Anderson localization of a non-interacting Bose–Einstein condensate Roati, Giacomo; D’Errico, Chiara; Fallani, Leonardo Nature, Vol. 453, Issue 7197 https://doi.org/10.1038/nature07071	journal	June 2008
Excitations of One-Dimensional Bose-Einstein Condensates in a Random Potential Gurarie, V.; Refael, G.; Chalker, J. T. Physical Review Letters, Vol. 101, Issue 17 https://doi.org/10.1103/PhysRevLett.101.170407	journal	October 2008
Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals Conti, C.; Fratalocchi, A. Nature Physics, Vol. 4, Issue 10 https://doi.org/10.1038/nphys1035	journal	August 2008
Disordered Lattice Solitons Efremidis, Nikolaos K.; Hizanidis, Kyriakos Physical Review Letters, Vol. 101, Issue 14 https://doi.org/10.1103/PhysRevLett.101.143903	journal	October 2008
Localization of ultrasound in a three-dimensional elastic network Hu, Hefei; Strybulevych, A.; Page, J. H. Nature Physics, Vol. 4, Issue 12 https://doi.org/10.1038/nphys1101	journal	October 2008
Speckle Instability: Coherent Effects in Nonlinear Disordered Media Grémaud, Benoît; Wellens, Thomas Physical Review Letters, Vol. 104, Issue 13 https://doi.org/10.1103/PhysRevLett.104.133901	journal	March 2010
Absence of Diffusion in Certain Random Lattices Anderson, P. W. Physical Review, Vol. 109, Issue 5 https://doi.org/10.1103/PhysRev.109.1492	journal	March 1958
Localization: theory and experiment Kramer, B.; MacKinnon, A. Reports on Progress in Physics, Vol. 56, Issue 12 https://doi.org/10.1088/0034-4885/56/12/001	journal	December 1993
Nonlinear lattice waves in heterogeneous media Laptyeva, T. V.; Ivanchenko, M. V.; Flach, S. Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 49 https://doi.org/10.1088/1751-8113/47/49/493001	journal	November 2014
Anderson localization in QCD-like theories Giordano, Matteo; Kovács, Tamás G.; Pittler, Ferenc International Journal of Modern Physics A, Vol. 29, Issue 25 https://doi.org/10.1142/S0217751X14450055	journal	October 2014
Dynamics of Heterogeneous Materials Nesterenko, Vitali F. Shock Wave and High Pressure Phenomena https://doi.org/10.1007/978-1-4757-3524-6	book	January 2001
Solitary waves in the granular chain Sen, S.; Hong, J.; Bang, J. Physics Reports, Vol. 462, Issue 2 https://doi.org/10.1016/j.physrep.2007.10.007	journal	June 2008
Non-linear waves in lattices: past, present, future Kevrekidis, P. G. IMA Journal of Applied Mathematics, Vol. 76, Issue 3 https://doi.org/10.1093/imamat/hxr015	journal	April 2011
Granular crystals: Nonlinear dynamics meets materials engineering Porter, Mason A.; Kevrekidis, Panayotis G.; Daraio, Chiara Physics Today, Vol. 68, Issue 11 https://doi.org/10.1063/PT.3.2981	journal	November 2015
The Anderson localization problem, the Fermi–Pasta–Ulam paradox and the generalized diffusion approach Kuzovkov, V. N. Physica Scripta, Vol. 84, Issue 6 https://doi.org/10.1088/0031-8949/84/06/065002	journal	November 2011
Delocalization of wave packets in disordered nonlinear chains Skokos, Ch.; Krimer, D. O.; Komineas, S. Physical Review E, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevE.79.056211	journal	May 2009
Erratum: Delocalization of wave packets in disordered nonlinear chains [Phys. Rev. E 79 , 056211 (2009)] Skokos, Ch.; Krimer, D. O.; Komineas, S. Physical Review E, Vol. 89, Issue 2 https://doi.org/10.1103/PhysRevE.89.029907	journal	February 2014
Dynamical thermalization of disordered nonlinear lattices Mulansky, Mario; Ahnert, Karsten; Pikovsky, Arkady Physical Review E, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevE.80.056212	journal	November 2009
Nonlinear waves in disordered diatomic granular chains Ponson, Laurent; Boechler, Nicholas; Lai, Yi Ming Physical Review E, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevE.82.021301	journal	August 2010
Wave propagation in random granular chains Manjunath, Mohith; Awasthi, Amnaya P.; Geubelle, Philippe H. Physical Review E, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevE.85.031308	journal	March 2012
Frequency filtering in disordered granular chains Lawney, Brian P.; Luding, Stefan Acta Mechanica, Vol. 225, Issue 8 https://doi.org/10.1007/s00707-014-1130-4	journal	June 2014
Energy transport in one-dimensional disordered granular solids Achilleos, V.; Theocharis, G.; Skokos, Ch. Physical Review E, Vol. 93, Issue 2 https://doi.org/10.1103/PhysRevE.93.022903	journal	February 2016
Energy transport in one- and two-dimensional anharmonic lattices with isotopic disorder Bourbonnais, Roch; Maynard, Roger Physical Review Letters, Vol. 64, Issue 12 https://doi.org/10.1103/PhysRevLett.64.1397	journal	March 1990
Anderson localization and solitonic energy transport in one-dimensional oscillatory systems Zavt, G. S.; Wagner, M.; Lütze, A. Physical Review E, Vol. 47, Issue 6 https://doi.org/10.1103/PhysRevE.47.4108	journal	June 1993
Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals Daraio, C.; Nesterenko, V. F.; Herbold, E. B. Physical Review E, Vol. 73, Issue 2 https://doi.org/10.1103/PhysRevE.73.026610	journal	February 2006
Solitary waves in a chain of beads under Hertz contact Coste, C.; Falcon, E.; Fauve, S. Physical Review E, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevE.56.6104	journal	November 1997
Solitonlike pulses in perturbed and driven Hertzian chains and their possible applications in detecting buried impurities Sen, Surajit; Manciu, Marian; Wright, James D. Physical Review E, Vol. 57, Issue 2 https://doi.org/10.1103/PhysRevE.57.2386	journal	February 1998
Shocks in non-loaded bead chains with impurities Hascoët, E.; Herrmann, H. J. The European Physical Journal B, Vol. 14, Issue 1 https://doi.org/10.1007/s100510050119	journal	February 2000
Nondestructive identification of impurities in granular medium Hong, Jongbae; Xu, Aiguo Applied Physics Letters, Vol. 81, Issue 25 https://doi.org/10.1063/1.1522829	journal	December 2002
Localized breathing modes in granular crystals with defects Theocharis, G.; Kavousanakis, M.; Kevrekidis, P. G. Physical Review E, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevE.80.066601	journal	December 2009
Wave localization in strongly nonlinear Hertzian chains with mass defect Job, Stéphane; Santibanez, Francisco; Tapia, Franco Physical Review E, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevE.80.025602	journal	August 2009
Anomalous Wave Reflection at the Interface of Two Strongly Nonlinear Granular Media Nesterenko, V. F.; Daraio, C.; Herbold, E. B. Physical Review Letters, Vol. 95, Issue 15 https://doi.org/10.1103/PhysRevLett.95.158702	journal	October 2005
Energy Trapping and Shock Disintegration in a Composite Granular Medium Daraio, C.; Nesterenko, V. F.; Herbold, E. B. Physical Review Letters, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevLett.96.058002	journal	February 2006
Decorated, Tapered, and Highly Nonlinear Granular Chain Doney, Robert; Sen, Surajit Physical Review Letters, Vol. 97, Issue 15 https://doi.org/10.1103/PhysRevLett.97.155502	journal	October 2006
Pulse propagation in decorated granular chains: An analytical approach Harbola, Upendra; Rosas, Alexandre; Romero, Aldo H. Physical Review E, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevE.80.051302	journal	November 2009
Highly nonlinear solitary waves in heterogeneous periodic granular media Porter, Mason A.; Daraio, Chiara; Szelengowicz, Ivan Physica D: Nonlinear Phenomena, Vol. 238, Issue 6 https://doi.org/10.1016/j.physd.2008.12.010	journal	April 2009
Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap Herbold, E. B.; Kim, J.; Nesterenko, V. F. Acta Mechanica, Vol. 205, Issue 1-4 https://doi.org/10.1007/s00707-009-0163-6	journal	April 2009
Stationary shocks in periodic highly nonlinear granular chains Molinari, Alain; Daraio, Chiara Physical Review E, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevE.80.056602	journal	November 2009
New family of solitary waves in granular dimer chains with no precompression Jayaprakash, K. R.; Starosvetsky, Yuli; Vakakis, Alexander F. Physical Review E, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevE.83.036606	journal	March 2011
Solitary waves in a general class of granular dimer chains Jayaprakash, K. R.; Vakakis, Alexander F.; Starosvetsky, Yuli Journal of Applied Physics, Vol. 112, Issue 3 https://doi.org/10.1063/1.4740060	journal	August 2012
Nonlinear Resonances Leading to Strong Pulse Attenuation in Granular Dimer Chains Jayaprakash, K. R.; Starosvetsky, Yuli; Vakakis, Alexander F. Journal of Nonlinear Science, Vol. 23, Issue 3 https://doi.org/10.1007/s00332-012-9155-0	journal	December 2012
Exact solution to the problem of nonlinear pulse propagation through random layered media and its connection with number triangles Sokolow, Adam; Sen, Surajit Annals of Physics, Vol. 322, Issue 9 https://doi.org/10.1016/j.aop.2007.05.004	journal	September 2007
Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals Chen, A. -Li; Wang, Yue-Sheng Physica B: Condensed Matter, Vol. 392, Issue 1-2 https://doi.org/10.1016/j.physb.2006.12.004	journal	April 2007
Optimal Design of Composite Granular Protectors Fraternali, Fernando; Porter, Mason A.; Daraio, Chiara Mechanics of Advanced Materials and Structures, Vol. 17, Issue 1 https://doi.org/10.1080/15376490802710779	journal	December 2009
Universal Power-Law Decay of the Impulse Energy in Granular Protectors Hong, Jongbae Physical Review Letters, Vol. 94, Issue 10 https://doi.org/10.1103/PhysRevLett.94.108001	journal	March 2005
Generation and control of sound bullets with a nonlinear acoustic lens Spadoni, A.; Daraio, C. Proceedings of the National Academy of Sciences, Vol. 107, Issue 16 https://doi.org/10.1073/pnas.1001514107	journal	April 2010
Highly nonlinear waves' sensor technology for highway infrastructures Khatri, Devvrath; Daraio, Chiara; Rizzo, Piervincenzo The 15th International Symposium on: Smart Structures and Materials & Nondestructive Evaluation and Health Monitoring, SPIE Proceedings https://doi.org/10.1117/12.775848	conference	April 2008
Strongly nonlinear waves in a chain of Teflon beads Daraio, C.; Nesterenko, V. F.; Herbold, E. B. Physical Review E, Vol. 72, Issue 1 https://doi.org/10.1103/PhysRevE.72.016603	journal	July 2005
Granular acoustic switches and logic elements Li, Feng; Anzel, Paul; Yang, Jinkyu Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms6311	journal	October 2014
Energy equipartition in two-dimensional granular systems with spherical intruders Szelengowicz, I.; Hasan, M. A.; Starosvetsky, Y. Physical Review E, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevE.87.032204	journal	March 2013
Nonlinear mixed solitary—Shear waves and pulse equi-partition in a granular network Zhang, Yijing; Hasan, M. Arif; Starosvetsky, Yuli Physica D: Nonlinear Phenomena, Vol. 291 https://doi.org/10.1016/j.physd.2014.10.005	journal	January 2015
Destruction of Anderson Localization by a Weak Nonlinearity Pikovsky, A. S.; Shepelyansky, D. L. Physical Review Letters, Vol. 100, Issue 9 https://doi.org/10.1103/PhysRevLett.100.094101	journal	March 2008
Chaotic destruction of Anderson localization in a nonlinear lattice Tietsche, S.; Pikovsky, A. EPL (Europhysics Letters), Vol. 84, Issue 1 https://doi.org/10.1209/0295-5075/84/10006	journal	September 2008
KAM tori in 1D random discrete nonlinear Schrödinger model? Johansson, M.; Kopidakis, G.; Aubry, S. EPL (Europhysics Letters), Vol. 91, Issue 5 https://doi.org/10.1209/0295-5075/91/50001	journal	September 2010
The crossover from strong to weak chaos for nonlinear waves in disordered systems Laptyeva, T. V.; Bodyfelt, J. D.; Krimer, D. O. EPL (Europhysics Letters), Vol. 91, Issue 3 https://doi.org/10.1209/0295-5075/91/30001	journal	August 2010
Delocalization induced by nonlinearity in systems with disorder García-Mata, Ignacio; Shepelyansky, Dima L. Physical Review E, Vol. 79, Issue 2 https://doi.org/10.1103/PhysRevE.79.026205	journal	February 2009
Energy spreading in strongly nonlinear disordered lattices Mulansky, M.; Pikovsky, A. New Journal of Physics, Vol. 15, Issue 5 https://doi.org/10.1088/1367-2630/15/5/053015	journal	May 2013
Pseudo-two-dimensional random dimer lattices Naether, U.; Mejía-Cortés, C.; Vicencio, R. A. Physics Letters A, Vol. 379, Issue 12-13 https://doi.org/10.1016/j.physleta.2015.01.032	journal	June 2015
Highly nonlinear solitary waves in chains of ellipsoidal particles Ngo, Duc; Khatri, Devvrath; Daraio, Chiara Physical Review E, Vol. 84, Issue 2 https://doi.org/10.1103/PhysRevE.84.026610	journal	August 2011
Highly nonlinear solitary waves in chains of cylindrical particles Khatri, Devvrath; Ngo, Duc; Daraio, Chiara Granular Matter, Vol. 14, Issue 1 https://doi.org/10.1007/s10035-011-0297-9	journal	December 2011
Observation of Two-Wave Structure in Strongly Nonlinear Dissipative Granular Chains Rosas, Alexandre; Romero, Aldo H.; Nesterenko, Vitali F. Physical Review Letters, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevLett.98.164301	journal	April 2007
Model for Dissipative Highly Nonlinear Waves in Dry Granular Systems Vergara, Lautaro Physical Review Letters, Vol. 104, Issue 11 https://doi.org/10.1103/PhysRevLett.104.118001	journal	March 2010
Discrete breathers — Advances in theory and applications Flach, Sergej; Gorbach, Andrey V. Physics Reports, Vol. 467, Issue 1-3 https://doi.org/10.1016/j.physrep.2008.05.002	journal	October 2008
Asymptotic solution for solitary waves in a chain of elastic spheres Chatterjee, Anindya Physical Review E, Vol. 59, Issue 5 https://doi.org/10.1103/PhysRevE.59.5912	journal	May 1999
Phase compactons Pikovsky, Arkady; Rosenau, Philip Physica D: Nonlinear Phenomena, Vol. 218, Issue 1 https://doi.org/10.1016/j.physd.2006.04.015	journal	June 2006
Dark breathers in granular crystals Chong, C.; Kevrekidis, P. G.; Theocharis, G. Physical Review E, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevE.87.042202	journal	April 2013
Damped-driven granular chains: An ideal playground for dark breathers and multibreathers Chong, C.; Li, F.; Yang, J. Physical Review E, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevE.89.032924	journal	March 2014
Localizing Energy Through Nonlinearity and Discreteness Campbell, David K.; Flach, Sergej; Kivshar, Yuri S. Physics Today, Vol. 57, Issue 1 https://doi.org/10.1063/1.1650069	journal	January 2004
Absence of localization in a random-dimer model Dunlap, David H.; Wu, H-L.; Phillips, Philip W. Physical Review Letters, Vol. 65, Issue 1 https://doi.org/10.1103/PhysRevLett.65.88	journal	July 1990
Anomalous localization in low-dimensional systems with correlated disorder Izrailev, F. M.; Krokhin, A. A.; Makarov, N. M. Physics Reports, Vol. 512, Issue 3 https://doi.org/10.1016/j.physrep.2011.11.002	journal	March 2012
Localization in paired correlated random binary alloys Evangelou, S. N.; Wang, A. Z. Physical Review B, Vol. 47, Issue 20 https://doi.org/10.1103/PhysRevB.47.13126	journal	May 1993
Energy transport in one-dimensional harmonic chains Datta, P. K.; Kundu, K. Physical Review B, Vol. 51, Issue 10 https://doi.org/10.1103/PhysRevB.51.6287	journal	March 1995
Asymptotic energy profile of a wave packet in disordered chains Lepri, S.; Schilling, R.; Aubry, S. Physical Review E, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevE.82.056602	journal	November 2010
High order symplectic integrators for perturbed Hamiltonian systems Laskar, Jacques; Robutel, Philippe Celestial Mechanics and Dynamical Astronomy, Vol. 80, Issue 1, p. 39-62 https://doi.org/10.1023/A:1012098603882	journal	January 2001
Thermal conduction in classical low-dimensional lattices Lepri, S. Physics Reports, Vol. 377, Issue 1 https://doi.org/10.1016/S0370-1573(02)00558-6	journal	April 2003
Disorder-enhanced nonlinear delocalization in segmented waveguide arrays Heinrich, Matthias; Keil, Robert; Lahini, Yoav New Journal of Physics, Vol. 14, Issue 7 https://doi.org/10.1088/1367-2630/14/7/073026	journal	July 2012
Enhanced distribution of a wave-packet in lattices with disorder and nonlinearity Naether, Uta; Rojas-Rojas, Santiago; Martínez, Alejandro J. Optics Express, Vol. 21, Issue 1 https://doi.org/10.1364/OE.21.000927	journal	January 2013
The fragmentation of a line of balls by an impact Hinch, E. J.; Saint–Jean, S. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 455, Issue 1989 https://doi.org/10.1098/rspa.1999.0447	journal	September 1999
Localization in a nonlinear disordered system Rasmussen, K. Ø; Cai, D.; Bishop, A. R. Europhysics Letters (EPL), Vol. 47, Issue 4 https://doi.org/10.1209/epl/i1999-00405-1	journal	August 1999
Localization in one-dimensional chains with Lévy-type disorder Zakeri, Sepideh S.; Lepri, Stefano; Wiersma, Diederik S. Physical Review E, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevE.91.032112	journal	March 2015
Threshold for Chaos and Thermalization in the One-Dimensional Mean-Field Bose-Hubbard Model Cassidy, Amy C.; Mason, Douglas; Dunjko, Vanja Physical Review Letters, Vol. 102, Issue 2 https://doi.org/10.1103/PhysRevLett.102.025302	journal	January 2009
Absence of Wave Packet Diffusion in Disordered Nonlinear Systems Kopidakis, G.; Komineas, S.; Flach, S. Physical Review Letters, Vol. 100, Issue 8 https://doi.org/10.1103/PhysRevLett.100.084103	journal	February 2008
Heat Conduction in Chains of Nonlinear Oscillators Lepri, Stefano; Livi, Roberto; Politi, Antonio Physical Review Letters, Vol. 78, Issue 10 https://doi.org/10.1103/PhysRevLett.78.1896	journal	March 1997
Self-trapping transition in nonlinear cubic lattices Naether, Uta; Martínez, Alejandro J.; Guzmán-Silva, Diego Physical Review E, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevE.87.062914	journal	June 2013
Soliton mobility in disordered lattices Sun, Zhi-Yuan; Fishman, Shmuel; Soffer, Avy Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.040903	journal	October 2015
Discrete Breathers in One-Dimensional Diatomic Granular Crystals Boechler, N.; Theocharis, G.; Job, S. Physical Review Letters, Vol. 104, Issue 24 https://doi.org/10.1103/PhysRevLett.104.244302	journal	June 2010

Cited By (7)

Direct measurement of superdiffusive energy transport in disordered granular chains Kim, Eunho; Martínez, Alejandro J.; Phenisee, Sean E. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-03015-3	journal	February 2018
Elastic Wannier-Stark ladders and Bloch oscillations in 1D granular crystals Shi, Xiaotian; Chaunsali, Rajesh; Wu, Ying Journal of Applied Physics, Vol. 123, Issue 10 https://doi.org/10.1063/1.5011664	journal	March 2018
Quasiperiodic granular chains and Hofstadter butterflies Martínez, Alejandro J.; Porter, Mason A.; Kevrekidis, P. G. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2127 https://doi.org/10.1098/rsta.2017.0139	journal	July 2018
Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices Senyange, B.; Manda, B. Many; Skokos, Ch. Physical Review E, Vol. 98, Issue 5 https://doi.org/10.1103/physreve.98.052229	journal	November 2018
Chaos and Anderson localization in disordered classical chains: Hertzian versus Fermi-Pasta-Ulam-Tsingou models Ngapasare, A.; Theocharis, G.; Richoux, O. Physical Review E, Vol. 99, Issue 3 https://doi.org/10.1103/physreve.99.032211	journal	March 2019
Nonlinear Coherent Structures in Granular Crystals Chong, C.; Porter, Mason A.; Kevrekidis, P. G. arXiv https://doi.org/10.48550/arxiv.1612.03977	text	January 2016
Elastic Wannier-Stark Ladders and Bloch Oscillations in 1D Granular Crystals Shi, Xiaotian; Chaunsali, Rajesh; Wu, Ying arXiv https://doi.org/10.48550/arxiv.1711.00511	text	January 2017

Similar Records

Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

Journal Article · Fri Jul 15 00:00:00 EDT 2011 · Physical Review. A · OSTI ID:1234648

Lugan, P; Sanchez-Palencia, L

Effects of gravity and nonlinearity on the waves in the granular chain

Journal Article · Fri Jun 01 00:00:00 EDT 2001 · Physical Review E · OSTI ID:1234648

Hong, Jongbae; Xu, Aiguo

Breathers in a locally resonant granular chain with precompression

Journal Article · Thu Sep 01 00:00:00 EDT 2016 · Physica. D, Nonlinear Phenomena · OSTI ID:1234648

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; +1 more

Related Subjects

36 MATERIALS SCIENCE
97 MATHEMATICS AND COMPUTING

Title: Superdiffusive transport and energy localization in disordered granular crystals

Citation Formats

References (88)

Cited By (7)

Similar Records

Related Subjects