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Zakeri Z, Solaimani M, Lavaei L, Terohid SAA. The exotic behavior of the wave evolution in Lévy crystals within a fractional medium. Sci Rep 2023; 13:20747. [PMID: 38007603 PMCID: PMC10676430 DOI: 10.1038/s41598-023-48110-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2023] [Accepted: 11/22/2023] [Indexed: 11/27/2023] Open
Abstract
We investigate a traveling Gaussian wave packet transport through a rectangular quantum barrier of lévy crystals in fractional quantum mechanics formalism. We study both standard and fractional Schrödinger equations in linear and nonlinear regimes by using a split-step finite difference (SSFD) method. We evaluate the reflection, trapping, and transmission coefficients of the wave packet and the wave packet spreading by using time-dependent inverse participation ratio (IPR) and second moment. By simultaneously adjusting the fractional and nonlinear terms, we create sharp pulses, which is an essential issue in optoelectronic devices. We illustrate that the effects of barrier height and width on the transmission coefficient are strangely different for the standard and fractional Schrödinger equations. We observe fortunately soliton-like localized wave packets in the fractional regime. Thus, we can effectively control the behavior of the wave evolution by adjusting the available parameters, which can excite new ideas in optics.
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Affiliation(s)
- Z Zakeri
- Department of Physics, Hamedan Branch, Islamic Azad University, Hamedan, 1574365181, Iran
| | - M Solaimani
- Department of Physics, Qom University of Technology, Qom, 3718146645, Iran
| | - L Lavaei
- Department of Physics, Qom University of Technology, Qom, 3718146645, Iran.
| | - S A A Terohid
- Department of Physics, Hamedan Branch, Islamic Azad University, Hamedan, 1574365181, Iran
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2
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Gninzanlong CL, Ndjomatchoua FT, Tchawoua C. Forward and backward propagating breathers in a DNA model with dipole-dipole long-range interactions. Phys Rev E 2020; 102:052212. [PMID: 33327195 DOI: 10.1103/physreve.102.052212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 10/29/2020] [Indexed: 06/12/2023]
Abstract
The present study explores the existence and orbital stability of discrete bright breathers through the Joyeux-Buyukdagli DNA model incorporating long-range interactions (LRIs). The nonlinear Schrödinger equation is derived from a semidiscrete approximation and subsequently used to construct the targeted initial condition for numerical computations of the discrete breather. It appears that the interplay between the carrier wave frequency and the LRI induces stationary forward or backward propagating waves. For critical values of the LRI, stationary waves can occur out of the center/edge of the first Brillouin zone. The predicted breathers differ in their robustness and mobility for specific carrier-wave frequency and LRI. In all cases, semianalytical predictions agree with numerical simulations.
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Affiliation(s)
| | - Frank Thomas Ndjomatchoua
- Geospatial Science & Modelling Cluster, Sustainable Impact Platform, International Rice Research Institute (IRRI), DAPO Box 7777-1301, Metro Manila, Philippines
| | - Clément Tchawoua
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Yaoundé, Cameroon
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3
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Nji Nde Aboringong E, M Dikandé A. Exciton dynamics in amide-I [Formula: see text] -helix protein chains with long-range intermolecular interactions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:35. [PMID: 29557510 DOI: 10.1140/epje/i2018-11640-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2017] [Accepted: 02/28/2018] [Indexed: 06/08/2023]
Abstract
The amide-I [Formula: see text] -helix protein is a long molecular chain made up of regularly spaced peptide groups interacting via C=O bonds. According to the current theory the energy released by hydrolyzed adenosine triphosphate is carried across the protein via vibration modes, caused by C=O bond stretchings which, in the presence of anharmonic molecular vibrations, can promote nonlinear localized excitations called excitons. In this work the effects of long-range interactions between amide-I molecules on the modulational instability of small-amplitude excitons, and on characteristic parameters of soliton wavetrain-type excitons, are investigated with emphasis on long-range interactions saturating at finite intermolecular interaction ranges. It is found that long-range interactions strongly affect the dispersion of vibration modes of the protein chain, causing a narrowing of the modulational-instability regions for small-amplitude excitons. Characteristic parameters of the exciton soliton wavetrain, including its velocity, tail and average width (i.e., the exciton width at half tail), are drastically enhanced with respect to their values when only the short-range interaction is considered. The results suggest a sizable increase of the energy carried by excitons along the protein chain above predictions based on short-range considerations.
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Affiliation(s)
- E Nji Nde Aboringong
- Laboratory of Research on Advanced Materials and Nonlinear Sciences (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, Cameroon
| | - Alain M Dikandé
- Laboratory of Research on Advanced Materials and Nonlinear Sciences (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, Cameroon.
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4
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Ndzana FI, Mohamadou A. On the effect of discreteness in the modulation instability for the Salerno model. CHAOS (WOODBURY, N.Y.) 2017; 27:073118. [PMID: 28764394 DOI: 10.1063/1.4995357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A Salerno model with first-and second-neighbor couplings is derived for the nonlinear transmission lines. We revisit the problem of modulation instability in the Salerno model. We derive the expression for the modulation instability gain and use them to explore the role of discreteness. We show that discreteness has an impact on the mechanism by which wave trains of soliton type can be generated in the Salerno model. We also show that second-neighbor couplings have an effect on the signal voltage.
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Affiliation(s)
- Fabien Ii Ndzana
- International Center for Complex Systems, Faculty of Science, University of Yaounde I, P.O. Box. 812, Yaoundé, Cameroon
| | - Alidou Mohamadou
- International Center for Complex Systems, Faculty of Science, University of Yaounde I, P.O. Box. 812, Yaoundé, Cameroon
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5
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Ruggiero MT, Zeitler JA. Resolving the Origins of Crystalline Anharmonicity Using Terahertz Time-Domain Spectroscopy and ab Initio Simulations. J Phys Chem B 2016; 120:11733-11739. [PMID: 27766874 DOI: 10.1021/acs.jpcb.6b10248] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Anharmonicity has been shown to be an important piece of the fundamental framework that dictates numerous observable phenomena. In particular, anharmonicity is the driving force of vibrational relaxation processes, mechanisms that are integral to the proper function of numerous chemical processes. However, elucidating its origins has proven difficult due to experimental and theoretical challenges, specifically related to separating the anharmonic contributions from other unrelated effects. While no one technique is particularly suited for providing a complete picture of anharmonicity, by combining multiple complementary methods such a characterization can be made. In this study the role of individual atomic interactions on the anharmonic properties of crystalline purine, the building block of many DNA and RNA nucleobases, is studied by experimental terahertz time-domain spectroscopy and first-principles density functional theory (DFT) and ab initio molecular dynamics simulations (AIMD). In particular, the detailed vibrational information provided by the DFT calculations is used to interpret the atomic origins of anharmonic-related effects as determined by the AIMD calculations, which are in good agreement with the experimental data. The results highlight that anharmonicity is especially pronounced in the intermolecular interactions, particularly along the amine hydrogen bond coordinate, and yields valuable insight into what is similarly observed complex biosystems and crystalline solids.
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Affiliation(s)
- Michael T Ruggiero
- Department of Chemical Engineering and Biotechnology, University of Cambridge , Philippa Fawcett Drive, Cambridge CB3 0AS, United Kingdom
| | - J Axel Zeitler
- Department of Chemical Engineering and Biotechnology, University of Cambridge , Philippa Fawcett Drive, Cambridge CB3 0AS, United Kingdom
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6
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Zampetaki AV, Stockhofe J, Schmelcher P. Dynamics of nonlinear excitations of helically confined charges. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042905. [PMID: 26565302 DOI: 10.1103/physreve.92.042905] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2015] [Indexed: 06/05/2023]
Abstract
We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behavior of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behavior using an effective discrete nonlinear Schrödinger model, which allows us among others to identify a number of breatherlike excitations.
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Affiliation(s)
- A V Zampetaki
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - J Stockhofe
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - P Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
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7
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Miloshevich G, Nguenang JP, Dauxois T, Khomeriki R, Ruffo S. Instabilities and relaxation to equilibrium in long-range oscillator chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032927. [PMID: 25871192 DOI: 10.1103/physreve.91.032927] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2014] [Indexed: 06/04/2023]
Abstract
We study instabilities and relaxation to equilibrium in a long-range extension of the Fermi-Pasta-Ulam-Tsingou (FPU) oscillator chain by exciting initially the lowest Fourier mode. Localization in mode space is stronger for the long-range FPU model. This allows us to uncover the sporadic nature of instabilities, i.e., by varying initially the excitation amplitude of the lowest mode, which is the control parameter, instabilities occur in narrow amplitude intervals. Only for sufficiently large values of the amplitude, the system enters a permanently unstable regime. These findings also clarify the long-standing problem of the relaxation to equilibrium in the short-range FPU model. Because of the weaker localization in mode space of this latter model, the transfer of energy is retarded and relaxation occurs on a much longer timescale.
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Affiliation(s)
- George Miloshevich
- Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University, 0128 Tbilisi, Georgia
- Department of Physics, The University of Texas at Austin, Austin TX 78712, USA
| | - Jean-Pierre Nguenang
- Fundamental Physics Laboratory: Group of Nonlinear Physics and Complex Systems, Department of Physics, University of Douala, P.O. Box 24157, Douala, Cameroon
- Laboratoire de Physique de l'ENS Lyon, Université de Lyon, CNRS, 46, allée d'Italie, 69007 Lyon, France
| | - Thierry Dauxois
- Laboratoire de Physique de l'ENS Lyon, Université de Lyon, CNRS, 46, allée d'Italie, 69007 Lyon, France
| | - Ramaz Khomeriki
- Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University, 0128 Tbilisi, Georgia
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, CNISM and INFN, via G. Sansone, 1, Sesto Fiorentino, Italy
| | - Stefano Ruffo
- Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, CNISM and INFN, via G. Sansone, 1, Sesto Fiorentino, Italy
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8
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Abstract
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 of A 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.
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Affiliation(s)
- Francesco Piazza
- Ecole Polytechnique Fédérale de Lausanne, Laboratoire de Biophysique Statistique, ITP-SB, BSP-720, CH-1015 Lausanne, Switzerland.
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9
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Dreisow F, Szameit A, Heinrich M, Pertsch T, Nolte S, Tünnermann A. Second-order coupling in femtosecond-laser-written waveguide arrays. OPTICS LETTERS 2008; 33:2689-2691. [PMID: 19015710 DOI: 10.1364/ol.33.002689] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We investigate the influence of second-order coupling in femtosecond-laser-written zigzag waveguide arrays, where the ratio Delta between second- and first-order coupling constants is adjusted from Delta=0.0 to Delta=2.8. Propagation patterns are observed directly via color center fluorescence.
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Affiliation(s)
- Felix Dreisow
- Institute of Applied Physics, Friedrich-Schiller-University Jena, Jena, Germany.
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10
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Brunhuber C, Mertens FG, Gaididei Y. Thermal diffusion of solitons on anharmonic chains with long-range coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036615. [PMID: 17500817 DOI: 10.1103/physreve.75.036615] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2006] [Indexed: 05/15/2023]
Abstract
We extend our studies of thermal diffusion of nontopological solitons to anharmonic Fermi-Pasta-Ulam-type chains with additional long-range couplings. The observed superdiffusive behavior in the case of nearest-neighbor interaction turns out to be the dominating mechanism for the soliton diffusion on chains with long-range interactions. Using a collective variable technique in the framework of a variational analysis for the continuum approximation of the chain, we derive a set of stochastic integrodifferential equations for the collective variables (CVs) soliton position and the inverse soliton width. This set can be reduced to a statistically equivalent set of Langevin-type equations for the CV, which shares the same Fokker-Planck equation. The solution of the Langevin set and the Langevin dynamics simulations of the discrete system agree well and demonstrate that the variance of the soliton increases stronger than linearly with time (superdiffusion). This result for the soliton diffusion on anharmonic chains with long-range interactions reinforces the conjecture that superdiffusion is a generic feature of nontopological solitons.
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Affiliation(s)
- C Brunhuber
- Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany.
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11
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Brunhuber C, Mertens FG, Gaididei Y. Persistent breathers in long-ranged discrete nonlinear Schrödinger models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056610. [PMID: 16803060 DOI: 10.1103/physreve.73.056610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2006] [Indexed: 05/10/2023]
Abstract
The DNLS model including Kac-Baker long-range interactions and nonlinear damping exhibits prominent effects in computer simulations. The combination of long-range forces and damping yields a periodic pattern of stationary breathers from an originally uniformly distributed background. The inverse interaction radius determines the periodicity which can be understood in the quasicontinuum approximation of the system. For the undamped system, we investigate the impact of the long-range interactions on the transition to the persistent-breather phase, which only depends on the energy and the norm of the DNLS. Using Monte Carlo techniques, we can monitor the localization strength as a function of the the long-range radius and the system temperature, which is formally negative in the persistent-breather phase.
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Affiliation(s)
- C Brunhuber
- Physikalisches Institut, Universität Bayreuth, Germany.
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12
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Larsen PV, Christiansen PL, Bang O, Archilla JFR, Gaididei YB. Bubble generation in a twisted and bent DNA-like model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036609. [PMID: 15524658 DOI: 10.1103/physreve.70.036609] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2004] [Revised: 06/14/2004] [Indexed: 05/24/2023]
Abstract
The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed initial conditions to simulate thermal fluctuations, a relationship between bubble generation, twist and curvature is established. An analytical approach supports the numerical results.
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Affiliation(s)
- P V Larsen
- Informatics and Mathematical Modelling and Department of Mathematics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
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13
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Larsen PV, Christiansen PL, Bang O, Archilla JFR, Gaididei YB. Energy funneling in a bent chain of Morse oscillators with long-range coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:026603. [PMID: 14995576 DOI: 10.1103/physreve.69.026603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2003] [Indexed: 05/24/2023]
Abstract
A bent chain of coupled Morse oscillators with long-range dispersive interaction is considered. Moving localized excitations may be trapped in the bending region. Thus chain geometry acts like an impurity. An energy funneling effect is observed in the case of random initial conditions.
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Affiliation(s)
- P V Larsen
- Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
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14
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Sánchez-Rey B, Archilla JFR, Palmero F, Romero FR. Breathers in a system with helicity and dipole interaction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:017601. [PMID: 12241525 DOI: 10.1103/physreve.66.017601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2002] [Indexed: 05/23/2023]
Abstract
Recent papers that have studied variants of the Peyrard-Bishop model for DNA, have taken into account the long range interaction due to the dipole moments of the hydrogen bonds between base pairs. In these models the helicity of the double strand is not considered. In this paper we have performed an analysis of the influence of the helicity on the properties of static and moving breathers in a Klein-Gordon chain with dipole-dipole interaction. It has been found that the helicity enlarges the range of existence and stability of static breathers, although this effect is small for a typical helical structure of DNA. However, the effect of the orientation of the dipole moments is considerably higher with transcendental consequences for the existence of mobile breathers.
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Affiliation(s)
- B Sánchez-Rey
- Departamento de Física Aplicada I, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012-Sevilla, Spain
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Archilla JFR, Christiansen PL, Mingaleev SF, Gaididei YB. Numerical study of breathers in a bent chain of oscillators with long-range interaction. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/33/301] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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16
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Ioannidou T, Pouget J, Aifantis E. Kink dynamics in a lattice model with long-range interactions. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/20/301] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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17
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Gaididei YB, Mingaleev SF, Christiansen PL. Curvature-induced symmetry breaking in nonlinear Schrodinger models. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:R53-R56. [PMID: 11088523 DOI: 10.1103/physreve.62.r53] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2000] [Indexed: 05/23/2023]
Abstract
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states decreases with increasing curvature, i.e., bending is a trap for nonlinear excitations. A violation of the Vakhitov-Kolokolov stability criterion is found in the case where the instability is due to the softening of the Peierls internal mode.
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Affiliation(s)
- YB Gaididei
- Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine
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18
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Mingaleev SF, Gaididei YB, Mertens FG. Solitons in anharmonic chains with ultra-long-range interatomic interactions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:R1044-7. [PMID: 11046534 DOI: 10.1103/physreve.61.r1044] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/1999] [Indexed: 11/07/2022]
Abstract
We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened Coulomb) interactions three different types of pulse solitons coexist in a certain velocity interval: one type is unstable but the two others are stable. The high-energy stable soliton is broad and can be described in the quasicontinuum approximation. But the low-energy stable soliton consists of two components, short-range and long-range ones, and can be considered as a bound state of these components.
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Affiliation(s)
- SF Mingaleev
- Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine
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