Computer simulation of intrinsic localized modes in one-dimensional and two-dimensional anharmonic lattices

Burlakov, V. M.; Kiselev, S. A.; Pyrkov, V. N.

doi:10.1103/physrevb.42.4921

Cited by 142 publications

(63 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The latter, also known as intrinsic localized modes (ILMs), are spatially localized, time-periodic vibrations found generically in many-body systems as a combined effect of nonlinearity and spatial discreteness [23,24]. Their existence and stability properties have been widely explored in translationally invariant systems [25] at T = 0, and much effort has also been devoted to understanding the role of thermal noise on DBs [26][27][28][29]. However, little is known on how DBs are affected by the interplay of spatial heterogeneity and nonlinearity [11,30,31], a fortiori in the context of atomic fluctuations in biological macro-molecules.…”

Section: Introductionmentioning

confidence: 99%

Long-range energy transfer in proteins

Piazza

Sanejouand

2009

Phys. Biol.

View full text Add to dashboard Cite

Proteins are large and complex molecular machines. In order to perform their function, most of them need energy, e.g. either in the form of a photon, as in the case of the visual pigment rhodopsin, or through the breaking of a chemical bond, as in the presence of adenosine triphosphate (ATP). Such energy, in turn, has to be transmitted to specific locations, often several tens ofÅ away from where it is initially released. Here we show, within the framework of a coarse-grained nonlinear network model, that energy in a protein can jump from site to site with high yields, covering in many instances remarkably large distances. Following single-site excitations, few specific sites are targeted, systematically within the stiffest regions. Such energy transfers mark the spontaneous formation of a localized mode of nonlinear origin at the destination site, which acts as an efficient energy-accumulating center. Interestingly, yields are found to be optimum for excitation energies in the range of biologically relevant ones.

show abstract

Section: Introductionmentioning

confidence: 99%

Long-range energy transfer in proteins

Piazza

Sanejouand

2009

Phys. Biol.

View full text Add to dashboard Cite

show abstract

“…Whereas a breather of initial amplitude Aϭ0.5 created at the center of a 31-site chain has barely decayed over 3 million time units, a breather of the same initial amplitude in a 21-site chain has disintegrated completely well before that. With Aϭ0.5 and ␥ϭ1 for the centered breather we find ϭ2.8ϫ10 9 for N ϭ31 ͑as reported earlier͒, ϭ3.2ϫ10 12 for Nϭ41, and ϭ3.6ϫ10 15 for Nϭ51.…”

Section: Mixed Arraysmentioning

confidence: 99%

“…7 Discrete nonlinear arrays in thermal equilibrium can support a variety of stationary excitations; away from equilibrium stationarity may turn into finite longevity, and additional excitations may arise. The possible excitations include phonons associated with linear portions of the potential, solitons 8,9 ͑long-wavelength excitations that persist from the continuum limit upon discretization͒, periodic breathers 1,2,9-13 ͑spatially localized time periodic excitations that persist from the anticontinuous limit upon coupling͒, and so-called chaotic breathers 11 ͑localized excitations that evolve chaotically͒. Nonlinear excitations have been observed to arise ͑spontaneously or by design͒ and survive for a long time in numerical experiments, and they clearly play an important role in determining the global macroscopic properties of nonlinear extended systems.…”

Section: Introductionmentioning

confidence: 99%

Breathers and thermal relaxation in Fermi–Pasta–Ulam arrays

Reigada

Sarmiento

Lindenberg

2003

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1537090͔Breathers are highly localized oscillatory excitations in discrete nonlinear lattices that have been invoked as a possible way to store and transport vibrational energy in a large variety of physical and biophysical contexts. A particular scenario where the robustness and longevity of breathers has been a matter of considerable debate involves nonlinear arrays subject to thermal relaxation via the connection of surface sites to a cold environment. The important questions are these: Can breathers "created spontaneously or by design… survive for a long time in such a relaxing environment? If they can survive, can they move? We detail answers to these questions, one of which is rather unequivocal: Breathers that move do not live very long. So is another: Breathers are quite robust when they do not move. The more complicated question then deals with the conditions that allow breathers to remain stationary and undisturbed for a long time in a relaxing environment. We detail some conditions that lead to this outcome, and others that definitely do not.

show abstract

“…For instance, it was already known that Toda-like solitons in a two-dimensional sheet spread rapidly sideways, failing to propagate more than about a hundred atomic spacings [15]. As for discrete breathers, they had been found to be mobile in many 1D models [10,5], but not in higher-dimensional cases [2] (the solutions in Ref. [26] seem too extended to qualify as discrete breathers).…”

Section: Numerical and Analogue Studiesmentioning

confidence: 99%

2-D Breathers and Applications

Marín¹,

Eilbeck²,

Russell³

Nonlinear Science at the Dawn of the 21st Century

View full text Add to dashboard Cite

In this chapter we show how a new type of nonlinear lattice excitation is helping to understand the long-standing puzzle of unexplained dark lines in crystals of muscovite mica. In fact, it was the conjecture that some kind of quasi-one-dimensional lattice soliton was responsible for those lines which led to the discovery of this new family of lattice excitations: mobile localized breathers of longitudinal type. We explore several properties of these moving breathers, both by numerical methods and by experimenting with analogue models. The results suggest a much broader application than just the mica problem.

show abstract

Computer simulation of intrinsic localized modes in one-dimensional and two-dimensional anharmonic lattices

Cited by 142 publications

References 5 publications

Long-range energy transfer in proteins

Long-range energy transfer in proteins

Breathers and thermal relaxation in Fermi–Pasta–Ulam arrays

2-D Breathers and Applications

Contact Info

Product

Resources

About