Modulated pressure waves in large elastic tubes

Abstract

Modulational instability is the direct way for the emergence of wave patterns and localized structures in nonlinear systems. We show in this work that it can be explored in the framework of blood flow models. The whole modified Navier-Stokes equations are reduced to a difference-differential amplitude equation. The modulational instability criterion is therefore derived from the latter, and unstable patterns occurrence is discussed on the basis of the nonlinear parameter model of the vessel. It is found that the critical amplitude is an increasing function of α, whereas the region of instability expands. The subsequent modulated pressure waves are obtained through numerical simulations, in agreement with our analytical expectations. Different classes of modulated pressure waves are obtained, and their close relationship with Mayer waves is discussed.

Discrete charge patterns in a Holstein‐SSH DNA lattice

“…[21,22] The plane wave solution to Eq. (9) can therefore be written as w n ðtÞ5w 0 e ihnðtÞ ; with h n ðtÞ5qn2xt;…”

“…For this purpose, motivated by our previous results on the PBH [21] and the B-DNA [19] models, we use the modulational instability (MI) technique, which has been shown to be the direct way solitonic and polaronic structures may be activated in various physical systems under the concomitant effects of nonlinearity and dispersion. [22][23][24] The rest of the article is therefore organized as follows: in Section Model and Linear Stability Analysis, we present the HSSH model and we derive the dynamical equations for charge dynamics and lattice distorsions. We also apply the adiabatic approximation and we show that the whole system can be described by a modified discrete nonlinear Schr€ odinger (MDNLS) equation.…”

Energy patterns in twist-opening models of DNA with solvent interactions

“…As many other systems, these equations can be reduced to more manipulable expressions without losing their characteristics. Among the methods generally used to handle such problems, we have the multiple scale expansion [18,21,22], the semi-discrete approximation [22,23], and the method proposed by Johansson et al [24], just to cite a few. These methods generally lead to nonlinear Schrödinger equations, in the continuum or discrete approximation.…”

“…For system (21) to have non-trivial solutions, its determinant should be null, which satisfies the nonlinear dispersion relation…”

Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

“…Thus, comes out the importance of discrete solitons in explaining local openings of the hydrogen bonds and formation of denaturation bubbles. Discrete solitons in nonlinear lattices have been the focus of considerable attention in diverse branches of science [16][17][18] and they are possible in several physical settings, such as biological systems [19][20][21][22][23], atomic chains [24,25], solid state physics [26], electrical lattices [27] and BoseEinstein condensates [28]. In DNA, such waves have been shown to carry the energy necessary for the initiation of the complex and key phenomena of replication and transcription [11][12][13][14].…”