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Asymmetric Perfect Absorption and Lasing of Nonlinear Waves by a Complex δ-Potential. Symmetry (Basel) 2020. [DOI: 10.3390/sym12101675] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Spectral singularities and coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic behavior of perfectly absorbed waves suggests considering possible generalizations of these phenomena for nonlinear waves. Here, we address the perfect absorption of nonlinear waves by an idealized infinitely narrow dissipative potential modeled by a Dirac δ-function with an imaginary amplitude. Our main result is the existence of perfectly absorbed flows whose spatial amplitude distributions are asymmetric with respect to the position of the absorber. These asymmetric states do not have a linear counterpart. Their linear stability is verified numerically. The nonlinear waveguide also supports symmetric and constant-amplitude perfectly absorbed flows. The stability of solutions of the latter type can be confirmed analytically.
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2
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Gaididei YB, Archilla JFR, Sánchez-Morcillo VJ, Gorria C. Energy localization and shape transformations in semiflexible polymer rings. Phys Rev E 2016; 93:062227. [PMID: 27415273 DOI: 10.1103/physreve.93.062227] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2015] [Indexed: 11/07/2022]
Abstract
Shape transformations in driven and damped molecular chains are considered. Closed chains of weakly coupled molecular subunits under the action of spatially homogeneous time-periodic external field are studied. The coupling between the internal excitations and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape. When the energy pumped into the system exceeds some critical value the chain undergoes a nonequilibrium phase transition: The circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy distribution becomes spatially nonuniform: It localizes in such places where the chain is more flat. The weak interaction of the chain with a flat surface restricts the dynamics to a flat manifold.
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Affiliation(s)
- Yu B Gaididei
- Bogolyubov Institute for Theoretical Physics, Metrologichna Street 14 B, 03143 Kiev, Ukraine
| | - J F R Archilla
- Grupo de Física No Lineal, Universidad de Sevilla, ETSI Informática, A. Reina Mercedes s/n, E-41012 Sevilla, Spain
| | - V J Sánchez-Morcillo
- Instituto de Investigación para la Gestión Integrada de las Zonas Costeras, Universidad Politécnica de Valencia, Paranimf 1, E-46730 Grao de Gandia, Spain
| | - C Gorria
- Department of Applied Mathematics and Statistics, University of the Basque Country, E-48080 Bilbao, Spain
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3
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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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4
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Gaididei Y, Kravchuk VP, Sheka DD. Curvature effects in thin magnetic shells. PHYSICAL REVIEW LETTERS 2014; 112:257203. [PMID: 25014827 DOI: 10.1103/physrevlett.112.257203] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2013] [Indexed: 05/16/2023]
Abstract
A magnetic energy functional is derived for an arbitrary curved thin shell on the assumption that the magnetostatic effects can be reduced to an effective easy-surface anisotropy; it can be used for solving both static and dynamic problems. General static solutions are obtained in the limit of a strong anisotropy of both signs (easy-surface and easy-normal cases). It is shown that the effect of the curvature can be treated as the appearance of an effective magnetic field, which is aligned along the surface normal for the case of easy-surface anisotropy and is tangential to the surface for the case of easy-normal anisotropy. In general, the existence of such a field excludes the solutions that are strictly tangential or strictly normal to the surface. As an example, we consider static equilibrium solutions for a cone surface magnetization.
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Affiliation(s)
- Yuri Gaididei
- Bogolyubov Institute for Theoretical Physics, Kiev 03143, Ukraine
| | | | - Denis D Sheka
- Taras Shevchenko National University of Kiev, Kiev 01601, Ukraine
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5
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Gaididei YB, Gorria C, Christiansen PL. Langevin dynamics of conformational transformations induced by the charge-curvature interaction. J Biol Phys 2009; 35:103-13. [PMID: 19669572 DOI: 10.1007/s10867-009-9140-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2008] [Accepted: 01/23/2009] [Indexed: 11/30/2022] Open
Abstract
The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular chains may undergo transformation to polygonal shape.
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Affiliation(s)
- Yu B Gaididei
- Bogolyubov Institute for Theoretical Physics, 01413, Kiev, Ukraine
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6
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Gaididei YB, Christiansen PL, Zakrzewski WJ. Conformational transformations induced by the charge-curvature interaction: Mean-field approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:021914. [PMID: 17025479 DOI: 10.1103/physreve.74.021914] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2005] [Indexed: 05/12/2023]
Abstract
A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom of closed molecular aggregates may act as drivers giving impetus to conformational dynamics of biopolymers. It is demonstrated that initially circular aggregates may undergo transformation to polygonal shapes and possible application to aggregates of bacteriochlorophyl a molecules is considered.
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Affiliation(s)
- Yu B Gaididei
- Bogolyubov Institute for Theoretical Physics, Metrologichna Street 14 B, 01413, Kiev, Ukraine
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7
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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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Kevrekidis PG, Dmitriev SV, Takeno S, Bishop AR, Aifantis EC. Rich example of geometrically induced nonlinearity: from rotobreathers and kinks to moving localized modes and resonant energy transfer. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066627. [PMID: 15697546 DOI: 10.1103/physreve.70.066627] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2004] [Revised: 10/04/2004] [Indexed: 05/24/2023]
Abstract
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are analyzed. Selective "static" features of the model are examined in the context of nonlinear waves including rotobreathers and kinklike solitary waves. We also explore "dynamic" features of the model concerning the resonant transfer of energy and the role of moving intrinsic localized modes in the process.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003-4515, USA
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Kevrekidis PG, Konotop VV, Malomed BA, Bishop AR. Nonlinearity from geometric interactions: a case example. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:047602. [PMID: 15600568 DOI: 10.1103/physreve.70.047602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2003] [Revised: 01/16/2004] [Indexed: 05/24/2023]
Abstract
We propose a ladder model wherein dynamical nonlinearity arises from geometry. It includes two strings of particles which are set along rigid rails of a "railroad" and coupled by linear springs. Physical realizations of the model include dust-particle strings in plasma sheaths and chains of microparticles trapped in a strong optical lattice. The transverse couplings between the strings, along with the motion constraint imposed by the rails, generate nonlinearity. It gives rise to robust solitary waves, which are found analytically in the long-wavelength limit, and are obtained in simulations of the full system.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, Lederle Graduate Research Tower, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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10
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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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11
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Cuevas J, Kevrekidis PG. Breather statics and dynamics in Klein-Gordon chains with a bend. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056609. [PMID: 15244965 DOI: 10.1103/physreve.69.056609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2003] [Indexed: 05/24/2023]
Abstract
In this paper, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the bifurcation and stability analysis of the modes that emerge as a function of the strength of the bend angle, but we also examine dynamical effects including the scattering of mobile localized modes (discrete breathers) off of such a geometric structure. The potential outcomes of such numerical experiments (including transmission, trapping within the bend as well as reflection) are highlighted and qualitatively explained. Such models are of interest both theoretically in understanding the interplay of breathers with curvature, but also practically in simple models of photonic crystals or of bent chains of DNA.
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Affiliation(s)
- J Cuevas
- Grupo de Física No Lineal, Departamento de Física Aplicada I, ETSI Informática, Universidad de Sevilla, Avenida Reina Mercedes, s/n, 41012-Seville, Spain.
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12
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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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13
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Kevrekidis PG, Williams FL, Bishop AR, Kevrekidis IG, Malomed BA. Coupling fields and underlying space curvature: an augmented Lagrangian approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:047602. [PMID: 12786538 DOI: 10.1103/physreve.67.047602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2002] [Indexed: 05/24/2023]
Abstract
We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space's metric tensor to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent (which gives rise to an ordinary differential equation for its temporal evolution), and the other with spatiotemporal dependence (wherein the metric's evolution is governed by a partial differential equation). Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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14
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Archilla JFR, Gaididei YB, Christiansen PL, Cuevas J. Stationary and moving breathers in a simplified model of curved alpha--helix proteins. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/42/301] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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15
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Kevrekidis PG, Malomed BA, Bishop AR. Discrete nonlinear model with substrate feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:046621. [PMID: 12443363 DOI: 10.1103/physreve.66.046621] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2002] [Indexed: 05/24/2023]
Abstract
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a model and examine its simplest one-dimensional Hamiltonian form, which turns out to be a modified Frenkel-Kontorova model coupled to an extra linear equation. We find static kink solutions and study their stability, and then examine moving kinks (the continuum limit of the model is studied too). We observe how the substrate effectively renormalizes properties of the kinks. In particular, a nontrivial finding is that branches of stable and unstable kink solutions may be extended beyond a critical point at which an effective intersite coupling vanishes; passing this critical point does not destabilize the kink. Kink-antikink collisions are also studied, demonstrating alternation between merger and transmission cases.
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Affiliation(s)
- P G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst 01003-4515, USA
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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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Ibañes M, Sancho JM, Tsironis GP. Dynamical properties of discrete breathers in curved chains with first and second neighbor interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:041902. [PMID: 12005868 DOI: 10.1103/physreve.65.041902] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2000] [Revised: 10/02/2001] [Indexed: 05/23/2023]
Abstract
We present the study of discrete breather dynamics in curved polymerlike chains consisting of masses connected via nonlinear springs. The polymer chains are one dimensional but not rectilinear and their motion takes place on a plane. After constructing breathers following numerically accurate procedures, we launch them in the chains and investigate properties of their propagation dynamics. We find that breather motion is strongly affected by the presence of curved regions of polymers, while the breathers themselves show a very strong resilience and remarkable stability in the presence of geometrical changes. For chains with strong angular rigidity we find that breathers either pass through bent regions or get reflected while retaining their frequency. Their motion is practically lossless and seems to be determined through local energy conservation. For less rigid chains modeled via second neighbor interactions, we find similarly that chain geometry typically does not destroy the localized breather states but, contrary to the angularly rigid chains, it induces some small but constant energy loss. Furthermore, we find that a curved segment acts as an active gate reflecting or refracting the incident breather and transforming its velocity to a value that depends on the discrete breathers frequency. We analyze the physical reasoning behind these seemingly general breather properties.
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Affiliation(s)
- M Ibañes
- Department d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
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Archilla JFR, Christiansen PL, Gaididei YB. Interplay of nonlinearity and geometry in a DNA-related, Klein-Gordon model with long-range dipole-dipole interaction. PHYSICAL REVIEW E 2002; 65:016609. [PMID: 11800813 DOI: 10.1103/physreve.65.016609] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2001] [Indexed: 11/07/2022]
Abstract
Most of the studies on mathematical models of DNA are limited to next neighbor interaction. However, the coupling between base pairs is thought to be caused by dipole interaction, and, when the DNA strand is bent, the distances between base pairs become shorter, therefore the interactions with distant base pairs have to be taken into account. In this paper we analyze the existence and stability of breathers, i.e., localized oscillations in a simple model of bent DNA with long-range dipole interaction. Breathers have been suggested as precursors of the denaturation bubble.
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Affiliation(s)
- J F R Archilla
- Department of Applied Physics I, University of Sevilla, Avenida Reina Mercedes s/n, 41012-Sevilla, Spain
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Reigada R, Sancho JM, Ibañes M, Tsironis GP. Resonant motion of discrete breathers in curved nonlinear chains. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/41/305] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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20
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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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