342 results on '"Discrete breathers"'
Search Results
2. Spectral Properties of Exact Polarobreathers in Semiclassical Systems.
- Author
-
Archilla, Juan F. R. and Bajārs, Jānis
- Subjects
- *
BORN-Oppenheimer approximation , *SEMICLASSICAL limits , *PROBLEM solving , *NONLINEAR waves , *ELECTRONS , *ATOMS - Abstract
In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Knowns and unknowns in the Davydov model for energy transfer in proteins.
- Author
-
Cruzeiro, Leonor
- Subjects
- *
ENERGY transfer , *PHASE space , *PROTEINS , *THERMAL stability - Abstract
The Davydov model for amide I propagation in hydrogen-bonded chains of proteins is revisited. The many similarities between the mixed quantum-classical dynamical equations and those that are derived from the full quantum Davydov model while applying the so-called D2 ansatz are highlighted. The transition from a minimum energy localized amide I state to a fully delocalized state is shown to operate in four phases, one of which is abrupt and the last of which is a fast but smooth change from a very broad yet localized state to a completely delocalized one. Exploration of the dynamical phase space at zero temperature includes the well-known soliton propagation as well as double and triple discrete breathers, and dispersion of initially localized states. The uncertainties related to the question of the thermal stability of the Davydov soliton are illustrated. A solution to the seemingly endless problem of the short radiative lifetime of the amide I excitations is proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
4. Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices.
- Author
-
Bajārs, Jānis and Archilla, Juan F. R.
- Subjects
- *
CRYSTAL lattices , *CRYSTAL models , *DISPERSION relations , *LINEAR statistical models , *NUMERICAL analysis , *CHARGE transfer - Abstract
We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
5. Slow energy relaxation in anharmonic chains with and without on-site potentials: Roles of distinct types of discrete breathers.
- Author
-
Xiong, Daxing and Dmitriev, Sergey V.
- Subjects
- *
ANHARMONIC motion , *HIGH temperatures , *NONLINEAR systems - Abstract
Slow energy relaxation has been observed in one-dimensional lattices with and without a nonlinear on-site potential; however, a comprehensive understanding of the detailed relaxation process remains elusive. Here we revisit this issue by introducing damping conditions at the free-end boundary of a thermalized lattice. We reveal that, in the long-cooling-time regime considered, for systems with a nonlinear on-site potential, energy relaxation exhibits a strong temperature-dependent behavior and with the increase of temperature, there is a crossover between decaying and non-decaying behaviors, around a crossover temperature point of T c ≃ 4. 2. This non-decaying behavior at higher temperature is attributed to the presence of standing multi Sievers–Takeno discrete breather (DB) states. Conversely, for systems without on-site potentials, relaxation is nearly independent of temperature but dependent on interparticle potential. Notably, we observe that the cubic anharmonicity can generate moving single Page DB states that contribute to the unusual slow energy relaxation within a specific time regime. Our results provide enhanced insights into the mechanisms governing slow energy relaxation during lattice cooling. • We study temperature-dependence of energy relaxation in systems with on-site potentials and reveal a crossover behavior between decaying and non-decaying energy. • We find in systems without on-site potentials, the cubic anharmonicity can lead to a non-decaying energy relaxation within a specific time regime. • We relate the slow energy relaxation of both systems to the presence of multi standing Sievers-Takeno and single moving Page discrete breather modes, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. Spectral Properties of Exact Polarobreathers in Semiclassical Systems
- Author
-
Juan F. R. Archilla and Jānis Bajārs
- Subjects
nonlinear waves ,discrete breathers ,polarobreathers ,charge transport ,spectra ,Mathematics ,QA1-939 - Abstract
In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable.
- Published
- 2023
- Full Text
- View/download PDF
7. Delocalized nonlinear vibrational modes and discrete breathers in a body centered cubic lattice.
- Author
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Shcherbinin, S.A., Bebikhov, Yu.V., Abdullina, D.U., Kudreyko, A.A., and Dmitriev, S.V.
- Subjects
- *
BODY centered cubic structure , *BODY-centered cubic metals , *LATTICE dynamics , *ANHARMONIC motion - Abstract
Body centered cubic (bcc) lattice with nearest and next-nearest interactions described by the β -FPUT interatomic potential is considered. Exact dynamical solutions in the form of zone-boundary delocalized nonlinear vibrational modes (DNVMs) are analyzed. 31 such solutions are revealed from the analysis of only the symmetry of the bcc lattice. Frequency response of DNVMs for the case of soft- and hard-type anharmonicity is calculated. In the case of hard-type anharmonicity, four DNVMs have frequencies bifurcating from the upper edge of the phonon spectrum and growing with the amplitude. Various quasi-discrete breathers are obtained by superimposing localizing functions upon these DNVMs. Our work demonstrates a practical approach to finding quasi-discrete breathers in higher-dimensional lattices. The obtained spatially localized long-lived vibrational modes inspire the search for various discrete breathers in bcc metals. • Dynamics of bcc beta-Fermi–Pasta–Ulam lattice is investigated. • New discrete breathers are found using the delocalized nonlinear vibrational modes. • The obtained results inspire the search for various discrete breathers in bcc metals. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. Amplitude-dependent edge states and discrete breathers in nonlinear modulated phononic lattices
- Author
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Matheus I N Rosa, Michael J Leamy, and Massimo Ruzzene
- Subjects
topological states ,metamaterials ,non-linear ,discrete breathers ,quasiperiodic lattices ,Science ,Physics ,QC1-999 - Abstract
We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge states localized at the boundaries of finite domains. With cubic nonlinearities, we show that edge states whose eigenvalue branch remains within the gap as amplitude increases remain localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches the bulk bands experience de-localization transitions. These transitions are predicted through continuation studies on the linear eigenmodes as a function of amplitude, and are confirmed by direct time domain simulations on finite lattices. Through our predictions, we also observe a series of amplitude-induced localization transitions as the bulk modes detach from the nonlinear bulk bands and become discrete breathers that are localized in one or more regions of the domain. Remarkably, the predicted transitions are independent of the size of the finite lattice, and exist for both periodic and quasiperiodic lattices. These results highlight the co-existence of topological edge states and discrete breathers in nonlinear modulated lattices. Their interplay may be exploited for amplitude-induced eigenstate transitions, for the assessment of the robustness of localized states, and as a strategy to induce discrete breathers through amplitude tuning.
- Published
- 2023
- Full Text
- View/download PDF
9. Time-periodic solutions of driven-damped trimer granular crystals
- Author
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Kevrekidis, P. [Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)]
- Published
- 2015
- Full Text
- View/download PDF
10. Discrete (Dark) Breathers
- Author
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Chong, Christopher, Kevrekidis, Panayotis G., Ananthanarayan, B., Series Editor, Babaev, Egor, Series Editor, Bremer, Malcolm, Series Editor, Calmet, Xavier, Series Editor, Di Lodovico, Francesca, Series Editor, Esquinazi, Pablo D., Series Editor, Hoogerland, Maarten, Series Editor, Le Ru, Eric, Series Editor, Lewerenz, Hans-Joachim, Series Editor, Overduin, James, Series Editor, Petkov, Vesselin, Series Editor, Wang, Charles H.-T., Series Editor, Whitaker, Andrew, Series Editor, Theisen, Stefan, Series Editor, Chong, Christopher, and Kevrekidis, Panayotis G.
- Published
- 2018
- Full Text
- View/download PDF
11. Introduction and Motivation of Models
- Author
-
Chong, Christopher, Kevrekidis, Panayotis G., Ananthanarayan, B., Series Editor, Babaev, Egor, Series Editor, Bremer, Malcolm, Series Editor, Calmet, Xavier, Series Editor, Di Lodovico, Francesca, Series Editor, Esquinazi, Pablo D., Series Editor, Hoogerland, Maarten, Series Editor, Le Ru, Eric, Series Editor, Lewerenz, Hans-Joachim, Series Editor, Overduin, James, Series Editor, Petkov, Vesselin, Series Editor, Wang, Charles H.-T., Series Editor, Whitaker, Andrew, Series Editor, Theisen, Stefan, Series Editor, Chong, Christopher, and Kevrekidis, Panayotis G.
- Published
- 2018
- Full Text
- View/download PDF
12. Fano Resonances in Flat Band Networks
- Author
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Ramachandran, Ajith, Danieli, Carlo, Flach, Sergej, Adibi, Ali, Series Editor, Asakura, Toshimitsu, Series Editor, Hänsch, Theodor W., Series Editor, Krausz, Ferenc, Series Editor, Masters, Barry R., Series Editor, Monemar, Bo A.J., Series Editor, Venghaus, Herbert, Series Editor, Weber, Horst, Series Editor, Weinfurter, Harald, Series Editor, Midorikawa, Katsumi, Series Editor, Rhodes, William T., Editor-in-Chief, Kamenetskii, Eugene, editor, Sadreev, Almas, editor, and Miroshnichenko, Andrey, editor
- Published
- 2018
- Full Text
- View/download PDF
13. Quantum Breathers in a Two-Dimensional Hexangular Heisenberg Ferromagnet.
- Author
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Feng, Wenhui, Wu, Lanjun, Tang, Bing, and Deng, Ke
- Subjects
- *
FERROMAGNETIC materials , *BOUND states , *QUANTUM states , *SEMICLASSICAL limits , *MAGNONS , *ANISOTROPY - Abstract
We present a theoretical study on quantum breathers in a XXZ Heisenberg ferromagnet with the single-ion uniaxial anisotropy on a two-dimensional hexangular lattice. In our work, the full quantum and the semiclassical cases are considered, respectively. For the full quantum case, we find that some isolated two-magnon bands can exist below the free magnon band. Physically, each isolated two-magnon band correspond to a two-magnon bound state, which is the simplest quantum breather state. For the semiclassical case, the analytical form of the discrete breather solution with a line localized structure is obtained by adopting the Glauber's coherent-state representation. Furthermore, the influence of the anisotropy on the properties of quantum breathers is discussed in detail. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
14. Variation of the Specific Heat in the Fermi–Pasta–Ulam Chain due to Energy Localization
- Author
-
Morkina, A. Yu., Singh, M., Bebikhov, Yu. V., Korznikova, E. A., and Dmitriev, S. V.
- Published
- 2022
- Full Text
- View/download PDF
15. Homoclinic solutions of discrete nonlinear Schrodinger equations with partially sublinear nonlinearities
- Author
-
Genghong Lin, Jianshe Yu, and Zhan Zhou
- Subjects
Discrete nonlinear Schrodinger equation ,discrete breathers ,homoclinic solution ,partially sublinear nonlinearities ,variational method ,Mathematics ,QA1-939 - Abstract
We consider a class of discrete nonlinear Schrodinger (DNLS) equations in m dimensional lattices with partially sublinear nonlinearity f. Combining variational methods and a priori estimate, we give a general sufficient condition on f for type (A), that is, a sequence of nontrivial homoclinic solutions accumulating to zero. By using a compact embedding technique, we overcome the loss of compactness due to the problem being set on the unbounded domain $\mathbb{Z}^m$. Another obstacle caused by the local definition of f is solved by using the cutoff methods to recover the global property of f. To the best of our knowledge, this is the first time to obtain infinitely many homoclinic solutions for the DNLS equations with partially sublinear nonlinearity. Moreover, we prove that if f is not sublinear, the zero solution is isolated from other homoclinic solutions. Our results show that the sublinearity and oddness of f yield type (A). Without the oddness assumption, we still can prove that this problem has at least a nontrivial homoclinic solution if f is local sublinear, which improves some existing results.
- Published
- 2019
16. Nonlinear dynamics determines the thermodynamic instability of condensed matter in vacuo.
- Author
-
Cartwright, Julyan H. E.
- Subjects
- *
CONDENSED matter , *CRYSTAL lattices , *THERMODYNAMICS , *LOW temperatures , *DYNAMICAL systems , *NONLINEAR dynamical systems - Abstract
Condensed matter is thermodynamically unstable in a vacuum. That is what thermodynamics tells us through the relation showing that condensed matter at temperatures above absolute zero always has non-zero vapour pressure. This instability implies that at low temperatures energy must not be distributed equally among atoms in the crystal lattice but must be concentrated. In dynamical systems such concentrations of energy in localized excitations are well known in the form of discrete breathers, solitons and related nonlinear phenomena. It follows that to satisfy thermodynamics such localized excitations must exist in systems of condensed matter at arbitrarily low temperature and as such the nonlinear dynamics of condensed matter is crucial for its thermodynamics. This article is part of the theme issue 'Stokes at 200 (Part 1)'. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
17. Edge states and frequency response in nonlinear forced-damped model of valve spring.
- Author
-
Gzal, Majdi and Gendelman, O. V.
- Abstract
This study explores the nonlinear dynamics of helical compression valve springs. To this end, the spring is mathematically modeled as a finite nonhomogenous one-dimensional mass–spring–damper discrete chain. Periodic displacement, which mimics the actual camshaft profile, is assumed at the upper end of the chain, while the other end is fixed. For the linear dynamics, the amplitudes of the periodic response are determined directly; they decrease toward the fixed end of the spring. Then, in order to meet more realistic conditions, the displacement of the upper mass is assumed to be nonnegative. This condition is realized by introducing an appropriate impact constraint. We assume that the impact is described by Newton impact law with restitution coefficient less than unity. For the case of one impact per period (1IPP) of excitation, exact periodic solutions are derived. The interplay between the nonhomogenous structure, multi-frequency excitation and nonlinearity leads to two qualitatively different states of the periodic responses; we refer to them as propagating states and edge states. The propagating states are characterized by weak localization, and the edge states—by strong localization at the forced edge. The stability of the system is analyzed using Floquet theory. Generic pitchfork and Neimark–Sacker bifurcations are observed. Analytical solutions conform to numerical simulations and experimental tests conducted on real valve springs. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
18. Modulational instability in addition to discrete breathers in 2D quantum ultracold atoms loaded in optical lattices.
- Author
-
Djoufack, Z. I., Fotsa-Ngaffo, F., Tala-Tebue, E., Fendzi-Donfack, E., and Kapche-Tagne, F.
- Abstract
The modulational instability associated with discrete breathers in 2D quantum ultracold atoms is studied by using the Glauber's coherent state combined with a semi-discrete approximation and multiple-scale methods. The linear stability analysis exhibits an intriguing threshold amplitude and instability regions associated with modulational growth rate. In addition, we demonstrate a coexistence of two bright intrinsic localized modes namely, the radial symmetric and bilateral symmetric modes, at the center and at the edges of the Brillouin zone, respectively, by alternating the on-site parameter interaction. Numerical investigations reveal a good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
19. Localized Nonlinear Vibrations
- Author
-
Lupichev, Lev N., Savin, Alexander V., Kadantsev, Vasiliy N., Abarbanel, Henry, Series editor, Braha, Dan, Series editor, Èrdi, Péter, Series editor, Friston, Karl, Series editor, Haken, Hermann, Series editor, Jirsa, Viktor, Series editor, Kacprzyk, Janusz, Series editor, Kaneko, Kunihiko, Series editor, Kelso, Scott, Series editor, Kirkilionis, Markus, Series editor, Kurths, Jürgen, Series editor, Nowak, Andrzej, Series editor, Reichl, Linda, Series editor, Schuster, Peter, Series editor, Schweitzer, Frank, Series editor, Sornette, Didier, Series editor, Thurner, Stefan, Series editor, Lupichev, Lev N., Savin, Alexander V., and Kadantsev, Vasiliy N.
- Published
- 2015
- Full Text
- View/download PDF
20. Energy exchange between discrete breathers in graphane in thermal equilibrium.
- Author
-
Krylova, K.A., Baimova, J.A., Murzaev, R.T., and Mulyukov, R.R.
- Subjects
- *
THERMAL equilibrium , *HYDROGEN atom , *NANOELECTROMECHANICAL systems , *HYDROGEN storage , *ENERGY dissipation - Abstract
Abstract Graphane is a fully hydrogenated graphene which is practically interesting for application in electronics, hydrogen storage and transportation, in nanoscale devices. As it was previously shown, the energy of a discrete breather (nonlinear localized mode) in graphane close to the value of the energy barrier at which the dehydrogenation of graphene occurs. In the present work, molecular dynamics simulation is used to investigate the possibility of energy exchange between discrete breathers in graphane in thermal equilibrium at 400 K and 600 K. In thermally equilibrated graphane, hydrogen atoms are spontaneously excited and can be considered as discrete breathers. Comparison of the kinetic energy per atom as the function of time for the selected hydrogen atoms with their displacements along the z axis showed that there is an energy exchange between the discrete breathers at evaluated temperatures. Hydrogen atom, transmitting its energy to the neighboring atom no longer exists as discrete breather. At high temperatures (600 K) the energy exchange between closely located discrete breathers also take place but strong thermo-oscillations of atoms at high temperatures (above 400 K) considerably affect the process. Highlights • Discrete breathers (DBs) are spontaneously excited in thermally equilibrated graphane. • DBs moves from one excited hydrogen atom to another until the total energy loss. • Thermo-oscillations of atoms at 600 K considerably affect the energy exchange between DBs. • Data on the study of DBs in graphane can be used to hydrogen storage and transportation. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
21. Computer simulation of nonlinear localized vibrational modes of large amplitude in the crystal Pt3Al with bivacancies Pt
- Author
-
Pavel Vasilievich Zakharov, Aleksandr Mikhailovich Eremin, Mikhail Dmitrievich Starostenkov, and Artem Vladimirovich Markidonov
- Subjects
molecular dynamics ,discrete breathers ,localized mode ,Applied mathematics. Quantitative methods ,T57-57.97 ,Mathematics ,QA1-939 - Abstract
By method of molecular dynamics investigated the interaction of nonlinear localized modes with bivacancies Pt crystal Pt3Al. Identified dependences of the lifetime of the nonlinear localized modes from the initial temperature of the crystal model, the initial atom Al deviation from its equilibrium position, as well as the distance to the introduced bivacancy Pt in (111) plane of the crystal.
- Published
- 2015
- Full Text
- View/download PDF
22. Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
- Abstract
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly- decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrödinger, where the linear operator of the Schrödinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.
- Published
- 2022
23. Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
- Abstract
We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal
- Published
- 2022
24. Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
- Abstract
We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal
- Published
- 2022
25. Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
- Abstract
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly- decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrödinger, where the linear operator of the Schrödinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.
- Published
- 2022
26. Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
- Abstract
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly- decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrödinger, where the linear operator of the Schrödinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.
- Published
- 2022
27. Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
- Abstract
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly- decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrödinger, where the linear operator of the Schrödinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.
- Published
- 2022
28. Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
- Abstract
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly- decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrödinger, where the linear operator of the Schrödinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.
- Published
- 2022
29. Collisions of Discrete Breathers in Nonlinear Schrödinger and Klein–Gordon Lattices
- Author
-
Cuevas, J., Álvarez, A., Romero, F. R., Archilla, J. F. R., Machado, J.A. Tenreiro, editor, Luo, Albert C.J., editor, Barbosa, Ramiro S., editor, Silva, Manuel F., editor, and Figueiredo, Lino B., editor
- Published
- 2011
- Full Text
- View/download PDF
30. Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices
- Author
-
Jānis Bajārs and Juan Archilla
- Subjects
semi-classical Hamiltonian dynamics ,splitting methods ,symplectic integrators ,lattice models ,charge transfer ,intrinsic localized modes ,discrete breathers ,General Mathematics ,Computer Science (miscellaneous) ,Engineering (miscellaneous) - Abstract
We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal.
- Published
- 2022
- Full Text
- View/download PDF
31. Localization in Finite Asymmetric Vibro-Impact Chains.
- Author
-
Grinberg, Itay and Gendelman, Oleg V.
- Subjects
- *
LINEAR algebra , *DYNAMICAL systems , *JOSEPHSON junctions , *LINEAR equations , *MONODROMY groups - Abstract
We explore the dynamics of localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model is intended to simulate dynamical responses of crack arrays, motion of rigid elements between obstacles, as well as the behavior of arrays of microscopic vibro-impact oscillators. The explored chain involves a parabolic on-site potential with asymmetric rigid constraints (the displacement domain of each particle is finite and asymmetric with respect to its equilibrium position) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an impact that satisfies the Newton impact law. The restitution coeffcient may be less than unity, and it is the only source of damping in the model. Nonlinearity of the system stems from the impact interactions. We demonstrate that this vibro-impact model allows derivation of exact analytical solutions for the asymmetric discrete breathers, in both conservative and forced-damped settings. The asymmetry makes two types of breathers possible: breathers that impact both constraints or only one constraint. Transition between these two types of breathers occurs through a grazing bifurcation. Special character of the nonlinearity permits explicit derivation of the monodromy matrix. Therefore, the stability of the obtained breather solutions can be studied with the desired accuracy in the framework of simple methods of linear algebra, and with rather moderate computational efforts. All three generic scenarios of loss of stability (pitchfork, Neimark{Sacker, and period doubling bifurcations) are observed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. Moving Breather Collisions in the Peyrard-Bishop DNA Model
- Author
-
Alvarez, A., Romero, F. R., Cuevas, J., Archilla, J. F. R., Akan, Ozgur, Series editor, Bellavista, Paolo, Series editor, Cao, Jiannong, Series editor, Dressler, Falko, Series editor, Ferrari, Domenico, Series editor, Gerla, Mario, Series editor, Kobayashi, Hisashi, Series editor, Palazzo, Sergio, Series editor, Sahni, Sartaj, Series editor, Shen, Xuemin (Sherman), Series editor, Stan, Mircea, Series editor, Xiaohua, Jia, Series editor, Zomaya, Albert, Series editor, Coulson, Geoffrey, Series editor, and Zhou, Jie, editor
- Published
- 2009
- Full Text
- View/download PDF
33. Electrical characterization of defects induced by electron beam exposure in low doped n-GaAs.
- Author
-
Tunhuma, S.M., Auret, F.D., Nel, J.M., Omotoso, E., Danga, H.T., Igumbor, E., and Diale, M.
- Subjects
- *
ELECTRON beam measurement , *GALLIUM arsenide , *DEEP level transient spectroscopy , *ELECTRON traps , *THRESHOLD energy , *CRYSTALLOGRAPHY - Abstract
We have used deep level transient spectroscopy (DLTS) and Laplace DLTS (L-DLTS) to characterize the electrically active point defects introduced in n -type gallium arsenide by electron beam exposure prior to Schottky metallization. The GaAs crystals were exposed to incident electrons at sub-threshold energies which are deemed low and insufficient to form defects through ion solid interactions. DLTS revealed a set of electron traps different from those commonly observed in n -GaAs after particle irradiation. These different signatures from the same radiation type suggest that different mechanisms are responsible for defect formation in the two electron irradiation processes. An analysis of the conditions under which the defects were formed was done to distil a number of possible defect formation mechanisms using the experimental evidence obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
34. Periodic and localized wave patterns for coupled Ablowitz-Ladik systems with negative cross phase modulation.
- Author
-
Chan, H.N. and Chow, K.W.
- Subjects
- *
LOCALIZED waves , *NONLINEAR waves , *PHASE modulation , *WAVEGUIDE modulators , *CONSERVATION laws (Mathematics) - Abstract
A new system of coupled Ablowitz-Ladik equations is introduced where cubic nonlinearities from intensities of both waveguide arrays are included. The Hirota bilinear transform is formulated and is used to derive breathers periodic in space or time. One spatially periodic solution is utilized to verify the lowest order conservation laws. Algebraically localized rogue wave modes with pulsating properties are obtained from breathers in the limit of large wave periods. Incorporating additional modes of cubic nonlinearities, namely, cross phase modulations, in two arrays of oscillators on an integer lattice can further enhance the modeling capability in optical physics. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
35. Aspects of Discrete Breathers and New Directions
- Author
-
Aubry, S., Kopidakis, G., Abdullaev, Fatkhulla, editor, Bang, Ole, editor, and Sørensen, Mads Peter, editor
- Published
- 2001
- Full Text
- View/download PDF
36. Growth and Decay of Weakly Perturbed Discrete Breathers
- Author
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Johansson, M., Abdullaev, Fatkhulla, editor, Bang, Ole, editor, and Sørensen, Mads Peter, editor
- Published
- 2001
- Full Text
- View/download PDF
37. Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
- Author
-
Mario I. Molina, Jesús Cuevas-Maraver, F. Palmero, Panayotis G. Kevrekidis, Universidad de Sevilla. Departamento de Física Aplicada I, and Universidad de Sevilla. FQM280: Física no Lineal
- Subjects
Breather ,Discrete breathers ,Continuous spectrum ,FOS: Physical sciences ,General Physics and Astronomy ,Pattern Formation and Solitons (nlin.PS) ,01 natural sciences ,Instability ,010305 fluids & plasmas ,symbols.namesake ,Normal mode ,0103 physical sciences ,Embedded soliton ,010306 general physics ,Nonlinear Sciences::Pattern Formation and Solitons ,Nonlinear Schrödinger equation ,Mathematical Physics ,Physics ,34C15 ,Embedded mode ,Mathematical Physics (math-ph) ,Nonlinear Sciences - Pattern Formation and Solitons ,Linear map ,Nonlinear system ,Lattice (module) ,Classical mechanics ,symbols ,Nonlinear BIC modes - Abstract
For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrodinger equation, where the linear operator of the Schrodinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice., 9 pages, 16 figures
- Published
- 2022
38. Knowns and unknowns in the Davydov model for energy transfer in proteins
- Author
-
Leonor Cruzeiro
- Subjects
Delocalization transition ,Physics and Astronomy (miscellaneous) ,Energy transfer ,Discrete breathers ,Radiationless decay ,General Physics and Astronomy - Abstract
The Davydov model for amide I propagation in hydrogen-bonded chains of proteins is revisited. The many similarities between the mixed quantum-classical dynamical equations and those that are derived from the full quantum Davydov model while applying the so-called D-2 ansatz are highlighted. The transition from a minimum energy localized amide I state to a fully delocalized state is shown to operate in four phases, one of which is abrupt and the last of which is a fast but smooth change from a very broad yet localized state to a completely delocalized one. Exploration of the dynamical phase space at zero temperature includes the well-known soliton propagation as well as double and triple discrete breathers, and dispersion of initially localized states. The uncertainties related to the question of the thermal stability of the Davydov soliton are illustrated. A solution to the seemingly endless problem of the short radiative lifetime of the amide I excitations is proposed. LA/P/0101/2020 info:eu-repo/semantics/publishedVersion
- Published
- 2022
39. Discrete breathers in graphane in thermal equilibrium.
- Author
-
Baimova, J.A., Murzaev, R.T., and Rudskoy, A.I.
- Subjects
- *
GRAPHENE , *THERMAL equilibrium , *HYDROGENATION , *TEMPERATURE effect , *DEHYDROGENATION - Abstract
Nonlinear dynamics of graphane (hydrogenated graphene) as well as some other properties of this new promising material are of high interest nowadays. One of the main challenges is the explanation of hydrogenation/dehydrogenation process of graphane at finite temperatures and the understanding of the underlying mechanisms. In present work, the hypothesis of discrete breathers working as the activators of the dehydrogenation is presented. Molecular dynamics simulation is conducted to study the discrete breathers in graphane in thermal equilibrium for temperature range 50–600 K. With the temperature increase the possibility of atom separation decreases because of thermal oscillations while the critical amplitude of the atom separation increase. It is shown that nonlinear localized modes or discrete breathers can be found in graphane at thermal equilibrium at temperature range of 400–600 K. The lifetime of discrete breather increases with the increase of its initial amplitude while temperature decrease leads to the increase of lifetime. It is concluded, that discrete breathers can facilitate the process of graphene dehydrogenation, because of their high energy. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
40. A Chain, a Bath, a Sink, and a Wall.
- Author
-
Iubini, Stefano, Lepri, Stefano, Livi, Roberto, Oppo, Gian-Luca, and Politi, Antonio
- Subjects
- *
SCHRODINGER equation , *STATIONARY processes , *NONEQUILIBRIUM thermodynamics , *MOLECULAR dynamics , *BIOMOLECULES - Abstract
We numerically investigate out-of-equilibrium stationary processes emerging in a Discrete Nonlinear Schrödinger chain in contact with a heat reservoir (a bath) at temperature TL and a pure dissipator (a sink) acting on opposite edges. Long-time molecular-dynamics simulations are performed by evolving the equations of motion within a symplectic integration scheme. Mass and energy are steadily transported through the chain from the heat bath to the sink. We observe two different regimes. For small heat-bath temperatures TL and chemical-potentials, temperature profiles across the chain display a non-monotonous shape, remain remarkably smooth and even enter the region of negative absolute temperatures. For larger temperatures TL, the transport of energy is strongly inhibited by the spontaneous emergence of discrete breathers, which act as a thermal wall. A strongly intermittent energy flux is also observed, due to the irregular birth and death of breathers. The corresponding statistics exhibit the typical signature of rare events of processes with large deviations. In particular, the breather lifetime is found to be ruled by a stretched-exponential law. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
41. Discrete breathers and modulational instability in a discrete $$\varvec{\phi ^{4}}$$ nonlinear lattice with next-nearest-neighbor couplings.
- Author
-
Tang, Bing and Deng, Ke
- Abstract
The properties of discrete breathers and modulational instability in a discrete $$\phi ^{4}$$ nonlinear lattice which includes the next-nearest-neighbor coupling interaction are investigated analytically. By using the method of multiple scales combined with a quasi-discreteness approximation, we get a dark-type and a bright-type discrete breather solutions and analyze the existence conditions for such discrete breathers. It is found that the introduction of the next-nearest-neighbor coupling interactions will influence the existence condition for the bright discrete breather. Considering that the existence of bright discrete breather solutions is intimately linked to the modulational instability of plane waves, we will analytically study the regions of discrete modulational instability of plane carrier waves. It is shown that the shape of the region of modulational instability changes significantly when the strength of the next-nearest-neighbor coupling is sufficiently large. In addition, we calculate the instability growth rates of the $$q=\pi $$ plane wave for different values of the strength of the next-nearest-neighbor coupling in order to better understand the appearance of the bright discrete breather. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
42. Breather propagation and arrest in a strongly nonlinear locally resonant lattice.
- Author
-
Bukhari, Mohammad A., Barry, Oumar R., and Vakakis, Alexander F.
- Subjects
- *
NONLINEAR acoustics , *ARREST , *FAMILY travel , *METAMATERIALS , *NONLINEAR systems - Abstract
Locally resonant metamaterials have recently drawn the attention of many researchers due to their capability in controlling low-frequency waves by forming a bandgap resulting from mode hybridization. Although linear acoustics of these metamaterials have been extensively explored, only a little is known about their nonlinear acoustics. This work investigates the nonlinear acoustics of a 1D discrete strongly nonlinear locally resonant metamaterial under impulsive force excitation. The metamaterial is modeled as a chain of linearly grounded masses connected by essential strong nonlinearity (purely cubic nonlinearity), and embedded by linear local resonators. Numerical investigations demonstrate the existence of different families of traveling breathers that depend on the coupling coefficient between the local resonator and its holding cell. One of these families is reported for the first time in the current work due to the existence of multiple fast frequencies in its profile. Although the investigated system is undamped, numerical simulations demonstrate that the breather arrest is controlled by certain parameters of the system. In the limit of small energy levels, the complexification averaging method (CX-A) is utilized with the help of numerical observations to demonstrate some aspects of the nonlinear acoustics of the system. Particularly, analytical analysis is used to determine the nonlinear band structure of the system. The outcome indicates the presence of two energy-dependent nonlinear propagation zones (PZs) (i.e., acoustics and optical) and three complementary attenuation zones (AZs) for the infinite lattice case. In addition, the different families of traveling breathers in the semi-infinite lattice are investigated analytically and compared to their corresponding numerical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Nonlinear bandgap transmission with zero frequency in a cross-stitch lattice.
- Author
-
Togueu Motcheyo, A.B. and Macías-Díaz, J.E.
- Subjects
- *
TRANSMISSION zeros , *CROSS-stitch , *PHONONS , *LINEAR statistical models , *ORBITS (Astronomy) - Abstract
We consider a model for a cross-stitch lattice with onsite nonlinearity. The linear analysis and the determination of the homoclinic threshold for this model are carried out theoretically. In the case of a self-focusing nonlinearity, we show that the traveling bandgap soliton is possible as a result from the periodic excitation of the edge of the chains. Contrary to the usual supratransmission phenomenon, the generation of traveling solitons is possible by driving the lattice with zero frequency and constant amplitude. In the case of defocusing nonlinearities, the heteroclinic orbit is obtained with the frequency within the phonon band. By exciting one component of complex waves, a traveling phonon kink is obtained. Meanwhile, in the case of the driving of two complex waves with zero phonon and nonzero phonon frequencies, respectively, the fly phonon breather is observed. The collision of the waves from the flat band and phonon band gives the traveling bright carry by the traveling kink. These results are obtained through computer simulations. • Nonlinear gap transmission is studied in a cross-stitch lattice for the first time. • The generation of traveling solitons is possible by driving the lattice with zero frequency and constant amplitude. • Fly phonon breather is performed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices.
- Author
-
Rojas-Rojas, Santiago, Naether, Uta, Delgado, Aldo, and Vicencio, Rodrigo A.
- Subjects
- *
BOSE-Einstein condensation , *OPTICAL lattices , *STABILITY (Mechanics) , *NONLINEAR systems , *ATOMIC physics - Abstract
We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
45. Quantum Breathers in Anisotropy Ferromagnetic Chains with Second-Order Coupling.
- Author
-
Tang, Bing
- Subjects
- *
QUANTUM states , *ANISOTROPY , *HARTREE-Fock approximation , *FERROMAGNETISM , *HEISENBERG model - Abstract
Under considering the next-nearest-neighbor interaction, quantum breathers in one-dimensional anisotropy ferromagnetic chains are theortically studied. By introducing the Dyson-Maleev transformation for spin operators, a map to a Heisenberg ferromagnetic spin lattice into an extended Bose-Hubbard model can be established. In the case of a small number of bosons, by means of the numerical diagonalization technique, the energy spectrum of the corresponding extended Bose-Hubbard model containing two bosons is calculated. When the strength of the single-ion anisotropy is enough large, a isolated single band appears. This isolated single band corresponds to two-boson bound state, which is the simplest quantum breather state. It is shown that the introduction of the next-nearest-neighbor interaction will lead to interesting band structures. In the case of a large number of bosons, by applying the time-dependent Hartree approximation, quantum breather states for the system is constructed. In this case, the effect of the next-nearest-neighbor interaction on quantum breathers is also analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
46. High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA.
- Author
-
Yao, Ying-Bo, Wang, Xiao-Yun, and Tang, Bing
- Subjects
- *
DNA models , *BRILLOUIN zones , *SOLITONS , *MULTIPLE scale method , *COLLISIONS (Nuclear physics) , *COMPUTER simulation , *EXACT equations - Abstract
By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
47. Multifrequency and edge breathers in the discrete sine-Gordon system via subharmonic driving: Theory, computation and experiment.
- Author
-
Palmero, F., Han, J., English, L.Q., Alexander, T.J., and Kevrekidis, P.G.
- Subjects
- *
MULTIFREQUENCY antennas , *SINE-Gordon equation , *DISCRETE systems , *SUBHARMONIC functions , *COMPUTER simulation , *PARAMETERS (Statistics) - Abstract
We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu et al. (2014) [21] . In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulations with realistic system parameters (including a Floquet stability analysis), and wherever possible to analytical results (e.g. for the subharmonic response of the single driven–damped pendulum), yields good agreement. Finally, we report the period-1 and multifrequency edge breathers which are localized at the open boundaries of the chain, for which we have again found good agreement between experiments and numerical computations. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
48. Impurity–impurity and impurity–breather interactions combined with energy localization in a quantum 1D Klein–Gordon chain.
- Author
-
Djoufack, Z.I., Ribama, R. Abouem A., and Nguenang, J.P.
- Subjects
- *
MULTIPLE scale method , *NONLINEAR Schrodinger equation , *MODULATIONAL instability , *LONG-Term Evolution (Telecommunications) , *COHERENT states , *PARTIAL sums (Series) - Abstract
This paper investigates an analytical and numerical study on impurity–impurity and impurity–breather interactions associated with energy localization in a quantum 1D Klein–Gordon chain. The nonlinear Schrödinger equation (NLSE) is obtained with the use of Glauber's coherent states in addition to a multiple time scale method. The resonant structures are found via the frequency spectrum around the critical impurity mass. The condition of existence of breather and impure localized mode are acquired. The dynamics of the impurity mode can be significantly controlled by the impurity mass. The accuracy of the analytical approach is validated by an excellent agreement with the finding of numerical simulation. When the breather interacts with two impure modes, several behaviors such as trapping, chaotic trapping, well, excitation in addition to total and partial reflection are found. From the modulational instability (MI) probed, we have found from the direct numerical simulations that long-term evolution of modulated wave exhibits chaotic behavior. Finally, energy localization through MI is conducted and a good agreement between the theoretical analysis and the numerical simulations is observed. • Analytical and numerical study on impurity–impurity and impurity–breather interactions in a quantum 1D Klein Gordon chain. • The dynamics of the impurity mode can be significantly controlled by the impurity mass. • When the breather interacts with two impure modes, several behaviors such as trapping, chaotic trapping, well, excitation are found. • Energy localization through MI is conducted and an agreement between the theoretical analysis and the numerical simulations is observed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Surface discrete breathers in Pt3Al intermetallic alloy
- Author
-
Evgeny Grigorjevich Ekomasov, P. V. Zakharov, Elena A. Korznikova, Kun Zhou, Sergey V. Dmitriev, and School of Mechanical and Aerospace Engineering
- Subjects
Materials science ,Condensed matter physics ,Phonon ,Breather ,Intermetallic ,02 engineering and technology ,Surfaces and Interfaces ,бездефектные кристаллы ,010402 general chemistry ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,Polarization (waves) ,01 natural sciences ,0104 chemical sciences ,Surfaces, Coatings and Films ,Crystal ,интерметаллиды ,Amplitude ,Molecular vibration ,Discrete Breathers ,Mechanical engineering [Engineering] ,Materials Chemistry ,Rectangular potential barrier ,Pt3Al ,0210 nano-technology - Abstract
It is known that defect-free crystals having a wide gap in the phonon spectrum can support gap discrete breathers (DB) being spatially localized large amplitude vibrational modes with frequencies within theband gap. One of examples of such crystal type is the intermetallic alloy Pt3Al with a a gap in the phonon spectrum caused by large difference in the atomic masses of the components. In the present work, the first attempts of the molecular dynamics modelling studiesof the DB close to atomically smooth (100) orientation surface of the crystal is presented. It is shown that properties of the DB depend essentially on the composition of the surface atomic plane, which for the considered crystal can consist of Pt atoms or both of Pt and Al atoms in equal proportions. The results obtained can significantly contribute to the development of surface physics science.
- Published
- 2019
50. A Chain, a Bath, a Sink, and a Wall
- Author
-
Stefano Iubini, Stefano Lepri, Roberto Livi, Gian-Luca Oppo, and Antonio Politi
- Subjects
discrete nonlinear schrödinger ,discrete breathers ,negative temperatures ,open systems ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
We numerically investigate out-of-equilibrium stationary processes emerging in a Discrete Nonlinear Schrödinger chain in contact with a heat reservoir (a bath) at temperature T L and a pure dissipator (a sink) acting on opposite edges. Long-time molecular-dynamics simulations are performed by evolving the equations of motion within a symplectic integration scheme. Mass and energy are steadily transported through the chain from the heat bath to the sink. We observe two different regimes. For small heat-bath temperatures T L and chemical-potentials, temperature profiles across the chain display a non-monotonous shape, remain remarkably smooth and even enter the region of negative absolute temperatures. For larger temperatures T L , the transport of energy is strongly inhibited by the spontaneous emergence of discrete breathers, which act as a thermal wall. A strongly intermittent energy flux is also observed, due to the irregular birth and death of breathers. The corresponding statistics exhibit the typical signature of rare events of processes with large deviations. In particular, the breather lifetime is found to be ruled by a stretched-exponential law.
- Published
- 2017
- Full Text
- View/download PDF
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