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Journal articles on the topic 'Nonlinear lattice'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Toda, Morikazu, Yoshiko Okada, and Shinsuke Watanabe. "Nonlinear Dual Lattice." Journal of the Physical Society of Japan 59, no. 12 (December 15, 1990): 4279–85. http://dx.doi.org/10.1143/jpsj.59.4279.

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2

Shi, Xianling, Fangwei Ye, Boris Malomed, and Xianfeng Chen. "Nonlinear surface lattice coupler." Optics Letters 38, no. 7 (March 21, 2013): 1064. http://dx.doi.org/10.1364/ol.38.001064.

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3

Suárez, Alberto, and Jean Pierre Boon. "Nonlinear lattice gas hydrodynamics." Journal of Statistical Physics 87, no. 5-6 (June 1997): 1123–30. http://dx.doi.org/10.1007/bf02181275.

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4

Haq, S., A. B. Movchan, and G. J. Rodin. "Lattice Green’s Functions in Nonlinear Analysis of Defects." Journal of Applied Mechanics 74, no. 4 (August 20, 2006): 686–90. http://dx.doi.org/10.1115/1.2710795.

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A method for analyzing problems involving defects in lattices is presented. Special attention is paid to problems in which the lattice containing the defect is infinite, and the response in a finite zone adjacent to the defect is nonlinear. It is shown that lattice Green’s functions allow one to reduce such problems to algebraic problems whose size is comparable to that of the nonlinear zone. The proposed method is similar to a hybrid finite-boundary element method in which the interior nonlinear region is treated with a finite element method and the exterior linear region is treated with a boundary element method. Method details are explained using an anti-plane deformation model problem involving a cylindrical vacancy.

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5

Serra-Garcia, Marc, Miguel Molerón, and Chiara Daraio. "Tunable, synchronized frequency down-conversion in magnetic lattices with defects." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (July 23, 2018): 20170137. http://dx.doi.org/10.1098/rsta.2017.0137.

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We study frequency conversion in nonlinear mechanical lattices, focusing on a chain of magnets as a model system. We show that, by inserting mass defects at suitable locations, we can introduce localized vibrational modes that nonlinearly couple to extended lattice modes. The nonlinear interaction introduces an energy transfer from the high-frequency localized modes to a low-frequency extended mode. This system is capable of autonomously converting energy between highly tunable input and output frequencies, which need not be related by integer harmonic or subharmonic ratios. It is also capable of obtaining energy from multiple sources at different frequencies with a tunable output phase, due to the defect synchronization provided by the extended mode. Our lattice is a purely mechanical analogue of an opto-mechanical system, where the localized modes play the role of the electromagnetic field and the extended mode plays the role of the mechanical degree of freedom. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

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6

Pal, Raj Kumar, Federico Bonetto, Luca Dieci, and Massimo Ruzzene. "A study of deformation localization in nonlinear elastic square lattices under compression." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (July 23, 2018): 20170140. http://dx.doi.org/10.1098/rsta.2017.0140.

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The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where a variety of localized deformations were found depending on loading configuration, lattice parameters and boundary conditions. These studies are conducted on other lattice structures, with the objective of identifying and investigating minimal models that exhibit localization, hysteresis and path-dependent behaviour. To this end, we first consider a two-dimensional square lattice consisting of point masses connected by in-plane axial springs and vertical ground springs, which may be considered as a discrete description of an elastic membrane supported by an elastic substrate. Results illustrate that, depending on the relative values of the spring constants, the lattice exhibits in-plane or out-of-plane instabilities leading to localized deformations. This model is further simplified by considering the one-dimensional case of a spring–mass chain sitting on an elastic foundation. A bifurcation analysis of this lattice identifies the stable and unstable branches and sheds light on the mechanism of transition from affine deformation to global or diffuse deformation to localized deformation. Finally, the lattice is further reduced to a minimal four-mass model, which exhibits a deformation qualitatively similar to that in the central part of a longer chain. In contrast to the widespread assumption that localization is induced by defects or imperfections in a structure, this work illustrates that such phenomena can arise in perfect lattices as a consequence of the mode shapes at the bifurcation points. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

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7

Flint, Christopher, Armen Oganesov, George Vahala, Linda Vahala, and Min Soe. "Lattice algorithms for nonlinear physics." Radiation Effects and Defects in Solids 172, no. 9-10 (October 3, 2017): 737–41. http://dx.doi.org/10.1080/10420150.2017.1398251.

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8

Ke-pu, Lü, Duan Wen-shan, Zhao Jin-bao, Wang Ben-ren, and Wei Rong-jue. "Particular solitons in nonlinear lattice." Chinese Physics 9, no. 2 (February 2000): 81–85. http://dx.doi.org/10.1088/1009-1963/9/2/001.

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9

Watanabe, Shinsuke. "Wave Modulation in Nonlinear Lattice." Journal of the Physical Society of Japan 58, no. 6 (June 15, 1989): 1935–43. http://dx.doi.org/10.1143/jpsj.58.1935.

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10

Alwani, Fairuz, and Franco Vivaldi. "Nonlinear rotations on a lattice." Journal of Difference Equations and Applications 24, no. 7 (April 23, 2018): 1074–104. http://dx.doi.org/10.1080/10236198.2018.1459592.

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11

Kitipornchai, S., and F. G. A. Al-Bermani. "Nonlinear analysis of lattice structures." Journal of Constructional Steel Research 23, no. 1-3 (January 1992): 209–25. http://dx.doi.org/10.1016/0143-974x(92)90044-f.

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12

BRAZHNYI, V. A., and V. V. KONOTOP. "THEORY OF NONLINEAR MATTER WAVES IN OPTICAL LATTICES." Modern Physics Letters B 18, no. 14 (June 10, 2004): 627–51. http://dx.doi.org/10.1142/s0217984904007190.

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We consider several effects of the matter wave dynamics which can be observed in Bose–Einstein condensates embedded into optical lattices. For low-density condensates, we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross–Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models, we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force and lattice defects affect the nonlinear matter waves.

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13

Thomson, S. J., M. Durey, and R. R. Rosales. "Collective vibrations of a hydrodynamic active lattice." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (July 2020): 20200155. http://dx.doi.org/10.1098/rspa.2020.0155.

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Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling. By modelling the droplet lattice as a memory-endowed system with spatially non-local coupling, we herein rationalize the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory–rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.

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14

HUANG, GUOXIANG, SEN-YUE LOU, and MANUEL G. VELARDE. "GAP SOLITONS, RESONANT KINKS, AND INTRINSIC LOCALIZED MODES IN PARAMETRICALLY EXCITED DIATOMIC LATTICES." International Journal of Bifurcation and Chaos 06, no. 10 (October 1996): 1775–87. http://dx.doi.org/10.1142/s0218127496001119.

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The dynamics of localized nonlinear excitations of resonant frequencies ωj (j = 0, 1, 2, 3) and carrier wave frequency frequency ωe≈ωj in a damping and parametrically driven lattice system is considered. The excitations are created in a one-dimensional nonlinearly coupled diatomic pendulum lattice which is subjected to a vertical oscillation of frequency 2ωe. The recent experimental observation of gap solitons, resonant kinks, and intrinsic localized modes in the diatomic pendulum lattice system are explained by using an extended nonlinear Schrödinger theory after neglecting the nonuniformity of the pendulums and the small periodic modulations of the amplitudes of the excitations.

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15

Huang, Guoxiang, Bambi Hu, and Jacob Szeftel. "Three-Wave Parametric Simultons in Nonlinear Lattices." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 4215–21. http://dx.doi.org/10.1142/s0217979203022209.

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A new type of nonlinear excitations, i.e. three simultaneous lattice solitons (simultons), in a nonlinear diatomic lattice is predicted. We show that three-wave resonance condition can be fulfilled in the diatomic lattice. Using a quasi-discrete multi-scale method we derive nonlinear amplitude equations for the three-wave resonance with the dispersion of the system taken into account. We provide several types of exact lattice simultons solutions and show that the lattice simultons can be non propagating and their oscillating frequencies may be within the gap of phonon spectrum bands.

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16

Xiao, Yi, and Wen-Hua Hai. "Dispersionless envelope lattice solitons on a D-dimensional nonlinear lattice." Physics Letters A 244, no. 5 (July 1998): 418–26. http://dx.doi.org/10.1016/s0375-9601(98)00344-2.

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17

Nannelli, Francesca, and Sauro Succi. "The lattice Boltzmann equation on irregular lattices." Journal of Statistical Physics 68, no. 3-4 (August 1992): 401–7. http://dx.doi.org/10.1007/bf01341755.

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18

Han, Aoxue, Colm Dineen, Viktoriia E. Babicheva, and Jerome V. Moloney. "Second harmonic generation in metasurfaces with multipole resonant coupling." Nanophotonics 9, no. 11 (July 5, 2020): 3545–56. http://dx.doi.org/10.1515/nanoph-2020-0193.

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AbstractWe report on the numerical demonstration of enhanced second harmonic generation (SHG) originating from collective resonances in plasmonic nanoparticle arrays. The nonlinear optical response of the metal nanoparticles is modeled by employing a hydrodynamic nonlinear Drude model implemented into Finite-Difference Time-Domain (FDTD) simulations, and effective polarizabilities of nanoparticle multipoles in the lattice are analytically calculated at the fundamental wavelength by using a coupled dipole–quadrupole approximation. Excitation of narrow collective resonances in nanoparticle arrays with electric quadrupole (EQ) and magnetic dipole (MD) resonant coupling leads to strong linear resonance enhancement. In this work, we analyze SHG in the vicinity of the lattice resonance corresponding to different nanoparticle multipoles and explore SHG efficiency by varying the lattice periods. Coupling of electric quadrupole and magnetic dipole in the nanoparticle lattice indicates symmetry breaking and the possibility of enhanced SHG under these conditions. By varying the structure parameters, we can change the strength of electric dipole (ED), EQ, and MD polarizabilities, which can be used to control the linewidth and magnitude of SHG emission in plasmonic lattices. Engineering of lattice resonances and associated magnetic dipole resonant excitations can be used for spectrally narrow nonlinear response as the SHG can be enhanced and controlled by higher multipole excitations and their lattice resonances. We show that both ED and EQ–MD lattice coupling contribute to SHG, but the presence of strong EQ–MD coupling is important for spectrally narrow SHG and, in our structure, excitation of narrow higher-order multipole lattice resonances results in five times enhancement.

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19

LIN, K. Y., and W. J. TZENG. "ON THE ROW-CONVEX POLYGON GENERATING FUNCTION FOR THE CHECKERBOARD LATTICE." International Journal of Modern Physics B 05, no. 20 (December 1991): 3275–85. http://dx.doi.org/10.1142/s0217979291001292.

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Exact solution for the most general four-variable generating function of the number of row-convex polygons on the checkerboard lattice is derived. Previous results for the square lattice, rectangular lattice, and honeycomb latticc are special cases of our solution.

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20

TODA, Morikazu. "Study of one-dimensional nonlinear lattice." Proceedings of the Japan Academy, Series B 80, no. 10 (2004): 445–58. http://dx.doi.org/10.2183/pjab.80.445.

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21

CHEN WEI-ZHONG. "SOLITONS IN ONE-DIMENSIONAL NONLINEAR LATTICE." Acta Physica Sinica 42, no. 10 (1993): 1567. http://dx.doi.org/10.7498/aps.42.1567.

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22

Kivshar, Yuri S. "Nonlinear impurity modes in a lattice." Physical Review B 47, no. 17 (May 1, 1993): 11167–70. http://dx.doi.org/10.1103/physrevb.47.11167.

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23

Astakhova, T. Yu, V. A. Kashin, V. N. Likhachev, and G. A. Vinogradov. "Multipeaked polarons in a nonlinear lattice." Russian Journal of Physical Chemistry B 10, no. 6 (November 2016): 865–75. http://dx.doi.org/10.1134/s1990793116060166.

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24

Okada, Yoshiko, Shinsuke Watanabe, and Hiroshi Tanaca. "Solitary Wave in Periodic Nonlinear Lattice." Journal of the Physical Society of Japan 59, no. 8 (August 15, 1990): 2647–58. http://dx.doi.org/10.1143/jpsj.59.2647.

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25

Dauxois, Thierry, and Stefano Ruffo. "Fermi-Pasta-Ulam nonlinear lattice oscillations." Scholarpedia 3, no. 8 (2008): 5538. http://dx.doi.org/10.4249/scholarpedia.5538.

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26

Wang, W. Z., J. Tinka Gammel, A. R. Bishop, and M. I. Salkola. "Quantum Breathers in a Nonlinear Lattice." Physical Review Letters 76, no. 19 (May 6, 1996): 3598–601. http://dx.doi.org/10.1103/physrevlett.76.3598.

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27

Pappas, P., M. Calamiotou, J. Köhler, A. Bussmann-Holder, and E. Liarokapis. "Nonlinear electrostrictive lattice response of EuTiO3." Applied Physics Letters 111, no. 5 (July 31, 2017): 052902. http://dx.doi.org/10.1063/1.4996494.

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28

Vakhnenko, Oleksiy O. "Nonlinear beating excitations on ladder lattice." Journal of Physics A: Mathematical and General 32, no. 30 (July 20, 1999): 5735–48. http://dx.doi.org/10.1088/0305-4470/32/30/315.

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29

Göksel, İzzet, İlkay Bakırtaş, and Nalan Antar. "Nonlinear Lattice Solitons in Saturable Media." Applied Mathematics & Information Sciences 9, no. 1 (January 1, 2015): 377–85. http://dx.doi.org/10.12785/amis/090144.

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30

Molina, M. I. "Nonlinear impurity in a square lattice." Physical Review B 60, no. 4 (July 15, 1999): 2276–80. http://dx.doi.org/10.1103/physrevb.60.2276.

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31

Binczak, S., J. C. Comte, B. Michaux, P. Marquié, and J. M. Bilbault. "Experimental nonlinear electrical reaction-diffusion lattice." Electronics Letters 34, no. 11 (1998): 1061. http://dx.doi.org/10.1049/el:19980774.

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32

Laptyeva, T. V., M. V. Ivanchenko, and S. Flach. "Nonlinear lattice waves in heterogeneous media." Journal of Physics A: Mathematical and Theoretical 47, no. 49 (November 24, 2014): 493001. http://dx.doi.org/10.1088/1751-8113/47/49/493001.

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33

Antillón, A., E. Forest, B. Hoeneisen, and F. Leyvraz. "Transport matrices for nonlinear lattice functions." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 305, no. 2 (July 1991): 247–56. http://dx.doi.org/10.1016/0168-9002(91)90544-z.

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34

Zhu, K., F. G. A. Al-Bermani, and S. Kitipornchai. "Nonlinear dynamic analysis of lattice structures." Computers & Structures 52, no. 1 (July 1994): 9–15. http://dx.doi.org/10.1016/0045-7949(94)90250-x.

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35

Nath, D., B. Roy, and R. Roychoudhury. "PTsymmetric nonlinear optical lattice: Analytical solutions." Chaos, Solitons & Fractals 81 (December 2015): 91–97. http://dx.doi.org/10.1016/j.chaos.2015.08.025.

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36

Slepyan, L. I., and M. V. Ayzenberg–Stepanenko. "Crack dynamics in a nonlinear lattice." International Journal of Fracture 140, no. 1-4 (July 2006): 235–42. http://dx.doi.org/10.1007/s10704-006-0064-9.

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37

BASNARKOV, LASKO, and VIKTOR URUMOV. "SITE- AND BOND-DIFFUSION ON REGULAR LATTICES." International Journal of Modern Physics B 23, no. 24 (September 30, 2009): 4943–52. http://dx.doi.org/10.1142/s0217979209053217.

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We consider two types of motion, one with particle occupying only the sites on a given regular lattice and another when the bonds between neighboring lattice sites are displaced to the positions of the neighboring bonds. We refer to these models as site- and bond-diffusion. The latter is equivalent to site-diffusion on a lattice constructed from the middle points on each bond of the original lattice. The transition probability is assumed equal to all neighboring positions. The diffusion constant is obtained by periodic orbit theory for all Archimedean lattices, as well as some three-dimensional lattices (cubic, diamond, body centered cubic and face centered cubic lattice). Every single step of bond-motion is expressed through two site-motion steps. Analytic results for the diffusion constant for bond-diffusion for square, triangular and Kagomé lattice are also obtained. Kurtosis is calculated for site-diffusion on square and (4, 82)-lattice, to estimate the deviation of the distribution of displacements from the Gaussian. All theoretical results are verified with numerical simulation.

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38

MOLINA, M. I. "SELFTRAPPING DYNAMICS IN TWO-DIMENSIONAL NONLINEAR LATTICES." Modern Physics Letters B 13, no. 24 (October 20, 1999): 837–47. http://dx.doi.org/10.1142/s0217984999001032.

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We compute numerically the selftrapping dynamics for an electron or excitation initially located on a single site of a two-dimensional nonlinear lattice of arbitrary nonlinear exponent. The time evolution is given by the Discrete Nonlinear Schrödinger (DNLS) equation and we focus on the long-time average probability at the initial site and the mean square displacement in terms of both the exponent and strength of the nonlinearity. For the square and triangular nonlinear lattices, we find selftrapping for nonlinearity parameters greater than an exponent-dependent critical value, whose magnitude increases (decreases) with the nonlinear exponent when this is larger (smaller) than one, approximately.

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39

PELIZZOLA, ALESSANDRO. "EXACT BOUNDARY MAGNETIZATION OF THE LAYERED ISING MODEL ON TRIANGULAR AND HONEYCOMB LATTICES." Modern Physics Letters B 10, no. 03n05 (February 28, 1996): 145–51. http://dx.doi.org/10.1142/s0217984996000171.

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In the present paper we extend a previous exact calculation of the boundary magnetization of the square lattice layered Ising model, based on a transfer-matrix effective-field technique, to the triangular lattice. The result is then further extended to the honeycomb lattice by means of a star-triangle transformation. Finally, the (11) boundary of the square lattice is analyzed as a particular case of the triangular and honeycomb lattices.

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40

Owaidat, M. Q., J. H. Asad, and J. M. Khalifeh. "Resistance calculation of the decorated centered cubic networks: Applications of the Green's function." Modern Physics Letters B 28, no. 32 (December 30, 2014): 1450252. http://dx.doi.org/10.1142/s0217984914502522.

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The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

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41

Song, Daohong, Cibo Lou, Liqin Tang, Zhuoyi Ye, Jingjun Xu, and Zhigang Chen. "Experiments on Linear and Nonlinear Localization of Optical Vortices in Optically Induced Photonic Lattices." International Journal of Optics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/273857.

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We provide a brief overview on our recent experimental work on linear and nonlinear localization of singly charged vortices (SCVs) and doubly charged vortices (DCVs) in two-dimensional optically induced photonic lattices. In the nonlinear case, vortex propagation at the lattice surface as well as inside the uniform square-shaped photonic lattices is considered. It is shown that, apart from the fundamental (semi-infinite gap) discrete vortex solitons demonstrated earlier, the SCVs can self-trap into stable gap vortex solitons under the normal four-site excitation with a self-defocusing nonlinearity, while the DCVs can be stable only under an eight-site excitation inside the photonic lattices. Moreover, the SCVs can also turn into stable surface vortex solitons under the four-site excitation at the surface of a semi-infinite photonics lattice with a self-focusing nonlinearity. In the linear case, bandgap guidance of both SCVs and DCVs in photonic lattices with a tunable negative defect is investigated. It is found that the SCVs can be guided at the negative defect as linear vortex defect modes, while the DCVs tend to turn into quadrupole-like defect modes provided that the defect strength is not too strong.

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42

YANG, YANG, MAI-MAI LIN, and WEN-SHAN DUAN. "THE ANISOTROPIC CHARACTERS IN TWO-DIMENSIONAL LATTICE." International Journal of Modern Physics B 27, no. 07 (March 10, 2013): 1361010. http://dx.doi.org/10.1142/s0217979213610109.

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The anisotropic characters of simple cubic lattice are investigated in this paper. Both the linear and nonlinear wave propagating in this lattice have been studied. The dispersion relation has been studied numerically. It is shown that the dispersion relation strongly depends on the directions of wave propagation. Generally, the direction of waves has the inclination angle α with respect to particle displacement. There are compressional waves α = 0 or transverse waves α = π/2 only for some special cases. The nonlinear waves in this lattice have also been studied. The anisotropic characters of this lattice for the nonlinear waves have also been shown. The compressional and transverse nonlinear solitons have also been studied. The characters of both solitons, such as amplitude and width, have been investigated.

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43

Kia, Behnam, Sarvenaz Kia, John F. Lindner, Sudeshna Sinha, and William L. Ditto. "Coupling Reduces Noise: Applying Dynamical Coupling to Reduce Local White Additive Noise." International Journal of Bifurcation and Chaos 25, no. 03 (March 2015): 1550040. http://dx.doi.org/10.1142/s0218127415500406.

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We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices and assume noise is white and additive. Noise from different lattice nodes can diffuse across the lattice and lower the noise level of individual nodes. We develop a theoretical model that explains this observed noise evolution and show how the coupled dynamics can naturally function as an averaging filter. Our numerical simulations are in excellent agreement with the model predictions.

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44

Vakhnenko, O. O. "Distinctive Features Of The Integrable Nonlinear Schrodinger System On A Ribbon Of Triangular Lattice." Ukrainian Journal of Physics 62, no. 3 (March 2017): 271–82. http://dx.doi.org/10.15407/ujpe62.03.0271.

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45

Bachurina, Olga V., Ramil T. Murzaev, and Dmitry V. Bachurin. "Molecular dynamics study of two-dimensional discrete breather in nickel." Journal of Micromechanics and Molecular Physics 04, no. 02 (June 2019): 1950001. http://dx.doi.org/10.1142/s2424913019500012.

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A discrete breather (DB) is a spatially localized vibrational mode of large amplitude in a defect-free anharmonic lattice. Generally, zero-dimensional DB is considered to be localized in all [Formula: see text] directions of the [Formula: see text]-dimensional lattice. However, the question of existence of DBs localized in [Formula: see text]–[Formula: see text] directions and delocalized in other [Formula: see text] directions remains open. In the present paper, for the first time, the case of [Formula: see text] and [Formula: see text] is considered by constructing a two-dimensional (2D) DB in the fcc nickel lattice using molecular dynamics methods. In order to excite such DB, one of the delocalized vibrational modes of the triangular lattice was used (the (111) plane in fcc crystal is a triangular lattice). All simulations were carried out at zero temperature. The investigated 2D DB demonstrates hard-type nonlinearity, when its oscillation frequency increases with increasing amplitude. The oscillation frequencies of the DB are above the upper edge of the phonon spectrum for nickel, which is 10.3[Formula: see text]THz. The maximum DB lifetime is found to be 9.5[Formula: see text]ps. The obtained results expand our understanding of diversity of nonlinear spatially localized vibrational modes in nonlinear lattices.

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46

Udwadia, Firdaus E., and Harshavardhan Mylapilli. "Energy control of inhomogeneous nonlinear lattices." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2176 (April 2015): 20140694. http://dx.doi.org/10.1098/rspa.2014.0694.

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This paper considers energy control of an n -d.f. inhomogeneous nonlinear lattice with fixed–fixed and fixed–free ends. The lattice consists of dissimilar masses wherein each mass is connected to its nearest neighbour by a nonlinear or linear memoryless spring element. The potential functions of the nonlinear spring elements are assumed to be qualitatively different. Each potential is described by a twice continuously differentiable, strictly convex function, possessing a global minimum at zero displacement, with zero curvature possibly only at zero displacement. The energy control requirement is viewed from an analytical dynamics perspective and is recast as a constraint on the motion of the dynamical system. No linearizations and/or approximations of the nonlinear dynamical system or the controller are made. Given the set of masses at which control is to be applied, explicit closed form expressions for the nonlinear control forces are obtained. Global asymptotic convergence to any desired non-zero energy state is guaranteed provided that the first mass, or the last mass or, alternatively, any two consecutive masses in the lattice are included in the subset of masses that are controlled. Numerical simulations involving a 101-mass nonlinear lattice demonstrate the simplicity and efficacy of the approach.

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47

Mora, Peter. "The lattice Boltzmann phononic lattice solid." Journal of Statistical Physics 68, no. 3-4 (August 1992): 591–609. http://dx.doi.org/10.1007/bf01341765.

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48

Wang, Zheng-Bin, Zhao-Zhi Wu, and Chao Gao. "Nonlinear properties of the lattice network-based nonlinear CRLH transmission lines." Chinese Physics B 24, no. 2 (February 2015): 028503. http://dx.doi.org/10.1088/1674-1056/24/2/028503.

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Sande, Guy Van der, Björn Maes, Peter Bienstman, Jan Danckaert, Roel Baets, and Irina Veretennicoff. "Nonlinear lattice model for spatially guided solitons in nonlinear photonic crystals." Optics Express 13, no. 5 (March 7, 2005): 1544. http://dx.doi.org/10.1364/opex.13.001544.

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Fan, H. L., F. N. Jin, and D. N. Fang. "Nonlinear mechanical properties of lattice truss materials." Materials & Design 30, no. 3 (March 2009): 511–17. http://dx.doi.org/10.1016/j.matdes.2008.05.061.

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