Fractional dynamics of systems with long-range interaction
2006
165 citations recorded by the source corpus.
Abstract We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/∣ n − m ∣ α +1 . Continuous medium equation for this system can be obtained in the so-called 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 motion of the particles into a partial differential equation with the Riesz fractional derivative of order α , when 0 α
Subfields: Computer Networks and Communications, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1bc348bf1ddddc96e865dbfc514f4434291a1dbe
Citations in the corpus
- Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian (2015, unknown): “In recent years, there has been a great deal of interest in using the fractional Laplacian to model diverse physical phenomena, such as anomalous diffusion and quasi-geostrophic flows, turbulence and water waves, molecular dynamics, and relativistic quantum mechanics of stars ( see [5] [6] [13] [27]”
- Review of Some Promising Fractional Physical Models (2013, unknown): “As it was shown [50, 51, 52, 53, 54, 55, 56, 57, 58], the equations with fractional derivatives can be directly connected to chain and lattice models with long-range interactions.”
- Necessary and Sucient Conditions for the Fractional Gagliardo-Nirenberg Inequalities and Applications to Navier-Stokes and Generalized Boson Equations (2011, unknown): “[1, 2, 6, 7, 13, 14, 18, 24, 23, 35, 37, 39, 43, 44, 56].”
- Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, unknown): “While fractional powers of Laplacian in (4) have many applications in mathematical physics and related fields, such as anomalous diffusion and quasi-geostrophic flows, turbulence models and water waves, molecular dynamics and relativistic quantum mechanics of stars [5] [6] [22] [49] [61], as well as”