Lattice with long-range interaction of power-law type for fractional non-local elasticity
نویسندگان
چکیده
منابع مشابه
Nonlinear Fractional Dynamics of Lattice with Long-Range Interaction
A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. Classical case is treated in the framework of the well-known FrenkelKontorova chain model. Qunatum dynamics is considered follow to Davydov’s approach to molecular excitons. In the continuum limit the problem is reduced to dynamical equations with fractional deri...
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A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel-Kontorova chain model for the non-nearest interactions. Quantum dynamics is considered following Davydov’s approach for molecular excitons. In the continuum limit the pro...
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We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0<alpha<2. We consider a few mode...
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We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/jn mj. Continuous medium equation for this system can be obtained in the socalled infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of mot...
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We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long-range power law interaction on a one-dimensional lattice. We have identified the critical value of the power law exponent α(c) across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the ...
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ژورنال
عنوان ژورنال: International Journal of Solids and Structures
سال: 2014
ISSN: 0020-7683
DOI: 10.1016/j.ijsolstr.2014.04.014