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Nelin. Dinam., 2018, Volume 14, Number 2, Pages 195–207 (Mi nd607)  

Stationary Modes and Localized Metastable States in a Triangular Lattice of Active Particles

K. S. Sergeeva, S. V. Dmitrievbc, E. A. Korznikovac, A. P. Chetverikova

a National Research Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia
b National Research Tomsk State University, ul. Lenina 36, Tomsk, 634050 Russia
c Institute for Metals Superplasticity Problems RAS, ul. Khalturina 39, Ufa, 450001 Russia

Abstract: The dynamics of a triangular lattice consisting of active particles is studied. Particles with nonlinear friction interact via nonlinear forces of Morse potential. Nonlinear friction slows down fast particles and accelerates slow ones. Each particle interacts mainly with the nearest neighbors due to the choice of the cut-off radius. Stationary modes (attractors) and metastable states of the lattice are studied by methods of numerical simulation. It is shown that the main attractor of the system under consideration is the so-called translational mode — the state with equal and unidirectional velocities of all particles. For some parameter values translational modes with defects in the form of vacancies and interstitial particles are possible. Metastable localized states are presented by the plane soliton-like waves (M-solitons) with inherent velocity and density maxima. The lifetime of such states depends on the lattice parameters and the wavefront width. All metastable states transform into the translational mode after a transient process.

Keywords: lattices, active particles, solitons, Morse potential

Funding Agency Grant Number
Russian Science Foundation 16-12-10175
This work was supported by the Russian Science Foundation, grant no. 16-12-10175.


DOI: https://doi.org/10.20537/nd180204

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MSC: 90B10, 37K40
Received: 06.04.2018
Accepted:01.06.2018
Language:

Citation: K. S. Sergeev, S. V. Dmitriev, E. A. Korznikova, A. P. Chetverikov, “Stationary Modes and Localized Metastable States in a Triangular Lattice of Active Particles”, Nelin. Dinam., 14:2 (2018), 195–207

Citation in format AMSBIB
\Bibitem{SerDmiKor18}
\by K. S. Sergeev, S. V. Dmitriev, E. A. Korznikova, A. P. Chetverikov
\paper Stationary Modes and Localized Metastable States in a Triangular Lattice of Active Particles
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 2
\pages 195--207
\mathnet{http://mi.mathnet.ru/nd607}
\crossref{https://doi.org/10.20537/nd180204}
\elib{http://elibrary.ru/item.asp?id=35417125}


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