Nonlinear dispersive waves in repulsive lattices

Abstract

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of $\alpha$-FPU equation, describing a chain of masses connected by nonlinear quadratic springs. The results can be extrapolated to other systems described by this equation.

10 pages, 6 figures

References in corpus (4)

• Quasi-perfect absorption by sub-wavelength acoustic panels in transmission using accumulation of resonances due to slow sound
• Mesoscopic Spin-Boson Models of Trapped Ions
• Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials
• Equilibration of a one-dimensional Wigner crystal

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• Nonlinear Excitations in Magnetic Lattices with Long-Range Interactions
• Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices
• Wavenumber-space band clipping in nonlinear periodic structures
• Demultiplexing infrasound phonons with tunable magnetic lattices
• Nonlinear harmonic generation in two-dimensional lattices of repulsive magnets
• Dynamics of interacting particle systems: Modeling implications of the repulsive interactions and experiments on magnetic prototypes
• Dirac Solitons and Topological Edge States in the $\beta$-Fermi-Pasta-Ulam-Tsingou dimer lattice
• Breathers in lattices with alternating strain-hardening and strain-softening interactions