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Ondoua RY, Belobo Belobo D. Solitary waves dynamic for Davydov α-helical protein model: Effects of localized and periodic inhomogeneities. Phys Rev E 2020; 102:062414. [PMID: 33466101 DOI: 10.1103/physreve.102.062414] [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: 06/29/2020] [Accepted: 11/27/2020] [Indexed: 11/07/2022]
Abstract
We describe the dynamic of excitons through single inhomogeneous α-helical proteins with off-diagonal and diagonal couplings. Inhomogeneities considered are either localized or periodic. Intensive numerical simulations carried show stable structures and allow us to single out important features of excitons dynamic. In the absence of inhomogeneities, the interplay between off-diagonal and diagonal couplings leads to two distinct types of solitary waves. Bright solitary waves correspond to an off-diagonal coupling constant lower than a critical diagonal coupling constant, while dark solitary waves are obtained in the opposite case. Inclusion of inhomogeneities profoundly affects the profiles, amplitudes, and energies transported by the waves. For relatively small strength of inhomogeneities, only the profiles of the waves significantly change, the other properties remaining almost unchanged. Large strength inhomogeneities sensitively twist the profiles and increase amplitudes and energies of the waves. Our study suggests that small strength inhomogeneities allow a coherent transport of energy and the biological functions remain unchanged, but large strengths of inhomogeneities affect the biological functioning of the α-helical protein chains. Hence, large strengths of inhomogeneities may amplify the energy of the molecule and could be used to treat some diseases.
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Affiliation(s)
- R Y Ondoua
- Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
- Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
| | - D Belobo Belobo
- Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
- African Centre for Advanced Studies, P.O. Box 4477, Yaounde, Cameroon
- Department of Mathematics and Physical Sciences, National Advanced School of Engineering of Yaounde, University of Yaounde I, P.O. Box 8390, Yaounde, Cameroon
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2
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Sun ZY, Yu X. Anomalous diffusion of discrete solitons driven by evolving disorder. Phys Rev E 2020; 101:062211. [PMID: 32688546 DOI: 10.1103/physreve.101.062211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
Anomalous diffusion is simulated in this paper by studying the transport of discrete solitons in a lattice with evolving disorder. We find a Richardson-type diffusion for the small solitons and a regime of transient diffusion for larger solitons within the ensemble-averaged description. As a comparison, the time-averaged observables present a ballistic scaling for both cases. However, distribution of these observables changes remarkably with the soliton size. Our results suggest violation of ergodicity for the solitons' diffusive processes, which are expected to shed light on further understanding of the discreteness-disorder-nonlinearity interaction.
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Affiliation(s)
- Zhi-Yuan Sun
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
- International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
| | - Xin Yu
- Institute of Fluid Mechanics, Beihang University, Beijing 100191, China
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Gninzanlong CL, Ndjomatchoua FT, Tchawoua C. Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy. CHAOS (WOODBURY, N.Y.) 2018; 28:043105. [PMID: 31906659 DOI: 10.1063/1.5009147] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.
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Affiliation(s)
| | | | - Clément Tchawoua
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Yaoundé, Cameroon
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Das M, Das D, Barik D, Ray DS. Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052102. [PMID: 26651642 DOI: 10.1103/physreve.92.052102] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 06/05/2023]
Abstract
The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Debojyoti Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Debashis Barik
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Sun ZY, Fishman S, Soffer A. Soliton trapping in a disordered lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012901. [PMID: 26274241 DOI: 10.1103/physreve.92.012901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2015] [Indexed: 06/04/2023]
Abstract
In recent years, the competition between randomness and nonlinearity was extensively explored. In the present paper, the dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In the absence of the random potential, it is an integrable model and the solitons are stable. As a result of the random potential, this stability is destroyed. In a certain regime, for short times, particlelike dynamics with constant mass is found; in another regime, particlelike dynamics with varying mass takes place. In particular, an effective potential is found that predicts correctly changes in the direction of motion of the soliton. This potential is a scaling function of time and strength of the potential, leading to a relation between the first time when the soliton changes direction and the strength of the random potential.
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Affiliation(s)
- Zhi-Yuan Sun
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Shmuel Fishman
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Avy Soffer
- Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854, USA
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Tchinang Tchameu JD, Togueu Motcheyo AB, Tchawoua C. Mobility of discrete multibreathers in the exciton dynamics of the Davydov model with saturable nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:043203. [PMID: 25375614 DOI: 10.1103/physreve.90.043203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2014] [Indexed: 06/04/2023]
Abstract
We show that the state of amide-I excitations in proteins is modeled by the discrete nonlinear Schrödinger equation with saturable nonlinearities. This is done by extending the Davydov model to take into account the competition between local compression and local dilatation of the lattice, thus leading to the interplay between self-focusing and defocusing saturable nonlinearities. Site-centered (sc) mode and/or bond-centered mode like discrete multihump soliton (DMHS) solutions are found numerically and their stability is analyzed. As a result, we obtained the existence and stability diagrams for all observed types of sc DMHS solutions. We also note that the stability of sc DMHS solutions depends not only on the value of the interpeak separation but also on the number of peaks, while their counterpart having at least one intersite soliton is instable. A study of mobility is achieved and it appears that, depending on the higher-order saturable nonlinearity, DMHS-like mechanism for vibrational energy transport along the protein chain is possible.
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Affiliation(s)
- J D Tchinang Tchameu
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University de Yaounde I, P.O. Box 812, Yaounde, Cameroon
| | - A B Togueu Motcheyo
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University de Yaounde I, P.O. Box 812, Yaounde, Cameroon
| | - C Tchawoua
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University de Yaounde I, P.O. Box 812, Yaounde, Cameroon
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Oster M, Johansson M. Phase twisted modes and current reversals in a lattice model of waveguide arrays with nonlinear coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:025601. [PMID: 15783371 DOI: 10.1103/physreve.71.025601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2004] [Indexed: 05/24/2023]
Abstract
We consider a lattice model for waveguide arrays embedded in nonlinear Kerr media. Inclusion of nonlinear coupling results in many phenomena involving complex, phase-twisted, stationary modes. The norm (Poynting power) current of stable plane-wave solutions can be controlled in magnitude and direction, and may be reversed without symmetry-breaking perturbations. Also stable localized phase-twisted modes with zero current exist, which for particular parameter values may be compact and expressed analytically. The model also describes coupled Bose-Einstein condensates.
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Affiliation(s)
- Michael Oster
- Department of Physics and Measurement Technology (IFM), Linköping University, S-581 83 Linköping, Sweden.
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d'Ovidio F, Bohr HG, Lindgård PA. Analytical tools for solitons and periodic waves corresponding to phonons on Lennard-Jones lattices in helical proteins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026606. [PMID: 15783440 DOI: 10.1103/physreve.71.026606] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2004] [Indexed: 05/24/2023]
Abstract
We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jones potential, the solitons can be characterized analytically with a good quantitative agreement using formulas for a Toda potential with parameters fitted to the Lennard-Jones potential. We also discuss and show the robustness of the family of periodic solutions called cnoidal waves, corresponding to phonons. The soliton phenomena described in the simulations of alpha helices may help to explain recent x-ray experiments on long alpha helices in Rhodopsin where a long lifetime of the vibrational modes has been observed.
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Affiliation(s)
- Francesco d'Ovidio
- Mediterranean Institute of Advanced Studies IMEDEA (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
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Gómez-Gardeñes J, Floría LM, Peyrard M, Bishop AR. Nonintegrable Schrodinger discrete breathers. CHAOS (WOODBURY, N.Y.) 2004; 14:1130-1147. [PMID: 15568927 DOI: 10.1063/1.1811991] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrödinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.
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Affiliation(s)
- J Gómez-Gardeñes
- Departamento de Teoría y Simulación de Sistemas Complejos, Instituto de Ciencia de Materiales de Aragón, C.S.I.C.-Universidad de Zaragoza, 50009 Zaragoza, Spain.
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Doktorov EV, Matsuka NP, Rothos VM. Dynamics of the Ablowitz-Ladik soliton train. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056607. [PMID: 15244963 DOI: 10.1103/physreve.69.056607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2004] [Indexed: 05/24/2023]
Abstract
It is shown that dynamics of a train of N weakly interacting Ablowitz-Ladik solitons with (almost) equal velocities and masses is governed by the complex Toda chain model. The integrability of the complex Toda chain model provides the means to describe analytically various dynamical regimes of the N-soliton train and to predict initial soliton parameters responsible for each of the regimes. Numerical simulations corroborate well analytical predictions. A specific feature arising for the discrete soliton train system is the appearance of an additional (with respect to the lattice spacing) spatial scale-intersoliton distance. We comment on interplay between both spatial scales.
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Affiliation(s)
- E V Doktorov
- B. I. Stepanov Institute of Physics, 68 F. Skaryna Avenue, 220072 Minsk, Belarus.
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Doktorov EV, Matsuka NP, Rothos VM. Perturbation-induced radiation by the Ablowitz-Ladik soliton. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 68:066610. [PMID: 14754339 DOI: 10.1103/physreve.68.066610] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2003] [Indexed: 11/07/2022]
Abstract
An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are calculated for linear damping and quintic perturbations.
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Affiliation(s)
- E V Doktorov
- B.I. Stepanov Institute of Physics, 68 F. Skaryna Avenue, 220072 Minsk, Belarus.
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Oster M, Johansson M, Eriksson A. Enhanced mobility of strongly localized modes in waveguide arrays by inversion of stability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:056606. [PMID: 12786295 DOI: 10.1103/physreve.67.056606] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2002] [Indexed: 05/24/2023]
Abstract
A model equation governing the amplitude of the electric field in an array of coupled optical waveguides embedded in a material with Kerr nonlinearities is derived and explored. The equation is an extended discrete nonlinear Schrödinger equation with intersite nonlinearities. Attention is turned towards localized solutions and investigations are made from the viewpoint of the theory of discrete breathers (DBs). Stability analysis reveals an inversion of stability between stationary one-site and symmetric or antisymmetric two-site solutions connected to bifurcations with a pair of asymmetric intermediate DBs. The stability inversion leads to the existence of high-intensity narrow mobile solutions, which can propagate essentially radiationless. The direction and transverse velocity of the mobile solutions can be controlled by appropriate perturbations. Such solutions may have an important application for multiport switching, allowing unambiguous selection of output channel. The derived equation also supports compact DBs, which in some sense yield the best possible solutions for switching purposes.
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Affiliation(s)
- Michael Oster
- Department of Physics and Measurement Technology (IFM), Linköping University, S-581 83 Linköping, Sweden.
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Vakhnenko OO, Velgakis MJ. Multimode soliton dynamics in perturbed ladder lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:016612. [PMID: 11304383 DOI: 10.1103/physreve.63.016612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2000] [Revised: 07/27/2000] [Indexed: 05/23/2023]
Abstract
We investigate the interplay between the longitudinal and lateral solitonic modes in perturbed ladder lattices in regard to the transmission of soliton wave packet. (1) In a longitudinal uniform field the lateral and longitudinal solitonic modes are shown to be independent. However, unlike in the unperturbed case the dynamics of the soliton center of mass becomes confined within a finite spatial domain via the Bloch-Zener mechanism in the longitudinal direction and due to the transverse finiteness of the ladder in the lateral one. (2) The segment of on-site impurities causes the soliton mode-mode mixing. As a result the soliton exhibits rather complex two- or three-dimensional dynamics accompanied by wave radiation which may give rise to soliton trapping. Nevertheless, under some specific conditions the soliton is able to bypass even the strong impurities slaloming between them. In particular, the slalom soliton dynamics is possible on a ladder lattice with a segment of zigzig-distributed on-site impurities. We formulate the conditions favorable to the case and show that their violation gives rise to either soliton trapping on or soliton reflection from the impure segment. (3) Finally, we study the effect of the modified transverse bond on the longitudinal soliton dynamics and reveal that it might act on the soliton as either an attractive or a repulsive potential, depending on the sign of the transverse energy of the ingoing soliton. The effect is essentially a solitonic one and becomes strictly pronounced for heavy solitons, when imperfection-induced radiation effects are exponentially suppressed. We expect that transverse-bond imperfection could serve as a filter selecting the solitons with prescribed properties. A similar function is feasible for zigzag-distributed on-site impurities too.
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Affiliation(s)
- O O Vakhnenko
- Engineering Science Department, University of Patras, Patras 26110, Greece
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