Interface-selected waves and their influence on wave competition

Abstract

In this paper we study nonlinear oscillatory systems consisting of two media, one supporting forward propagating waves and the other inwardly propagating waves, separated by an interface. We find that the interface can select the type of wave. Under certain well-defined parameter condition, these waves propagate in two different media with the same frequency and same wave number; the interface of the two media is transparent to these waves. The frequency and wave number of these interface-selected waves (ISWs) are predicted explicitly. When parameters are varied from this parameter set, the wave numbers of the two domains become different, and the difference increases from zero continuously as the distance between the given parameters and this parameter set increases from zero. It is found that ISWs can play crucial roles in practical problems of wave competition, e.g., ISWs can suppress spirals and antispirals.

Heterogeneity selected target waves and their competition: Outgoing or ingoing?

“…These theoretical results are in agreement with the statements made in Ref. [29] and further confirmed by numerical simulations shown in Fig. 6.…”

“…The criteria or the frequency condition that either ingoing or outgoing target waves are fulfilled is in agreement with the one obtained numerically in Ref. [29]. However, it is deserve emphasizing that the criteria [i.e., Eqs.…”

Self-entanglement of a single polymer chain confined in a cubic box

“…They found that the probability of knotting increased with the length of the string, but plateaued at a value below 100%. 19 Abadie and Dayantis 20 used a lattice representation of random and self-avoiding walks and found that the conformational properties as a function of reduced box size, L/R ee , where L is the edge length of the cube and R ee is the square-root of the mean-squared end-to-end distance of an unconfined polymer chain, were independent of chain length N. 20 Cui et al 21 also used a lattice model of polymers confined in cubes to study the rotational relaxation time T and the looping time for chain ends to meet. At low to moderate confinements, they found that the scaled dynamics s/s 0 $ (L/R ee ) 2 were also independent of N. Here, s 0 $ N 112v is the timescale for an unconfined polymer to diffuse a distance equal to its size, and v describes the variation of an unconfined polymer with the degree of polymerization N, via R ee $ N v .…”

Circular-interface selected wave patterns in the complex Ginzburg-Landau equation

“…Currently, considerable attention has been paid to a particular kind of nonuniform system that is in the presence of an interface [13][14][15][16]. For instance, it has been reported that negative refraction could occur if chemical waves propagated across the interface in nonlinear oscillatory systems [14].…”

“…What is more, the authors in ref. [15] observed the interface selected traveling waves, which propagated in two different media with the same frequency and same wave number. The role of interface selected waves in wave competition in two-dimensional (2D) systems was discussed, however the studies in ref.…”