Supratransmission induced by waves collisions in a discrete electrical lattice

Abstract

We numerically performed a way to produce a supratransmission phenomenon in the Salerno equation describing the dynamics of modulated waves in a discrete nonlinear transmission lattice. For the natural supratransmission phenomenon, there exists a threshold of amplitude for which energy can flow in the line. We show that gap transmission is possible with driven amplitude below the threshold due to the collision of different plane waves coming from both edges of the line. One of the two plane waves has a frequency in the forbidden gap, and another has a frequency in the allowed phonon band. During collision, the wave in the allowed band is considered as a perturbation of the ones in the forbidden gap.

Nonlinear resonances and energy transfer in finite granular chains

“…However, the presence of nonlinearity allows energy to propagate down the chain. This can occur through nonlinear supratransmission in which the energy of a signal in the frequency band gap is transmitted by means of nonlinear modes [9][10][11]. This is shown in a series of papers investigating nonlinear supratransmission in sine-Gordon and Klein-Gordon [12], Josephson ladders [9], and Fermi-Pasta-Ulam chains [10].…”

Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor

“…where Q n denotes the charge in the nonlinear capacitor and allows to determine the type of nonlinearity within the lattice. The nonlinear capacitor can be in the form of Toda lattice [13][14][15][16][17][18][19][20] or its expression can be obtained from the Taylor expansion of an experimentally double exponential form [21]. In that case, the nonlinear capacitance of the diode varactor has an asymmetric quadratic expression as in the low voltages reversebiased diode [22][23][24][25][26][27].…”

Supratransmission-induced travelling breathers in long Josephson junctions

“…Nearly two decades ago, it was shown that a nonlinear system subjected to a sinusoidal drive with frequency laying in the forbidden band gap (FBG) can support energy transmission in the form of solitonic excitations, if the forcing amplitude is high enough. The NST phenomenon, initially discussed in a discrete SG chain by F. Geniet and J. Leon [53,54], appears to be the result of a generic nonlinear instability [55] and it is nowdays reported in different contexts, e.g., Bragg media [56], waveguide arrays [57][58][59], Fermi-Pasta-Ulam model [60][61][62], Klein-Gordon electronic network [63], discrete inductance-capacitance electrical line [64], wave collisions in discrete electrical lattices [65], multicomponent non-integrable nonlinear systems [66,67], stacked Miura-origami metastructure [68], and Josephson devices [69][70][71][72]. In the specific case of the LJJ, linear waves, i.e., plasma oscillations, cannot propagate for frequencies lower than the Josephson plasma frequency, ω p ∼ 1 THz, hence a pulse with frequency of the same order may be selected to unlock the NST regime.…”