Multisolitons-like patterns in a one-dimensional MARCKS protein cyclic model.

In this paper, we study the nonlinear dynamics of the MARCKS protein between cytosol and cytoplasmic membrane through the modulational instability phenomenon. The reaction-diffusion generic model used here is firstly transformed into a cubic complex Ginzburg-Landau equation. Then, modulational instability (MI) is carried out in order to derive the MI criteria.

Pure quartic modulational instability in weakly nonlocal birefringent fibers.

The modulational instability (MI) phenomenon is theoretically investigated in birefringent optical media with pure quartic dispersion and weak Kerr nonlocal nonlinearity. We find from the MI gain that instability regions are more expanded due to nonlocality, which is confirmed via direct numerical simulations showing the emergence of Akhmediev breathers (ABs) in the total energy context. In addition, the balanced competition between nonlocality and other nonlinear and dispersive effects exclusively gives the possibility of generating long-lived structures which deepens our understanding of soliton dynamics in pure-quartic dispersive optical systems and opens new investigation routes in fields related to nonlinear optics and lasers.

Interplay between spin-orbit couplings and residual interatomic interactions in the modulational instability of two-component Bose-Einstein condensates.

The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equations on which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths.

Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity.

The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response.

INDOOR RADON (222RN) MEASUREMENTS AND ESTIMATION OF ANNUAL EFFECTIVE DOSE IN MVANGAN LOCALITY, SOUTH CAMEROON.

The present work was aimed at measuring indoor radon activity concentrations in dwellings in Mvangan locality, South Cameroon, in order to assess the extent of measures that may be necessary for controlling public indoor radon exposure in this area. Measurements were carried out using passive solid-state nuclear track detectors (RADONAVA Inc., RadTrak2, Sweden) following ISO 11665-4 standard.

Amplitude response, Melnikov's criteria, and chaos occurrence in a Duffing's system subjected to an external periodic excitation with a variable shape.

The present study considers the nonlinear dynamics of a Duffing oscillator under a symmetric potential subjected to a pulse-type excitation with a deformable shape. Our attention is focused on the effects of the external excitation shape parameter r and its period. The frequency response of the system is derived by using a semi-analytical approach.

Controlling discharge mode in electrical activities of myocardial cell using mixed frequencies magnetic radiation.

Based on the standard Fitzhugh-Nagumo model for myocardial cell excitations and electrical activities, the effect of electromagnetic induction is considered and through which mixed frequencies magnetic radiation is imposed to detect the mode transition. Indeed, time-varying electromagnetic field can be induced when myocardial cell is exposed or surrounded by electromagnetic field and thus the effect of electromagnetic induction should be considered. From the analyzes of sampled series for membrane potentials, the improved model holds many bifurcation parameters and the mode of excitations and electric activities can be detected and observed in larger parameter zones.

Higher-order dispersion and nonlinear effects of optical fibers under septic self-steepening and self-frequency shift.

We investigate the modulational instability (MI) of a continuous wave (cw) under the combined effects of higher-order dispersions, self steepening and self-frequency shift, cubic, quintic, and septic nonlinearities. Using Maxwell's theory, an extended nonlinear Schrödinger equation is derived. The linear stability analysis of the cw solution is employed to extract an expression for the MI gain, and we point out its sensitivity to both higher-order dispersions and nonlinear terms.

Modulation instability in helicoidal spin-orbit coupled open Bose-Einstein condensates.

We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open Bose-Einstein condensates (BECs), where the addition of dissipative interactions is done through coupled rate equations. Furthermore, the standard linear stability analysis is used to investigate theoretically the stability of continuous-wave (cw) solutions and to obtain an expression for the modulational instability gain spectrum. Using direct simulations of the Fourier space, we numerically investigate the dynamics of the modulational instability in the presence of helicoidal spin-orbit coupling.

Modulation instability in nonlinear metamaterials modeled by a cubic-quintic complex Ginzburg-Landau equation beyond the slowly varying envelope approximation.

Considering the theory of electromagnetic waves from the Maxwell's equations, we introduce a (3+1)-dimensionsal cubic-quintic complex Ginzburg-Landau equation describing the dynamics of dissipative light bullets in nonlinear metamaterials. The model equation, which is derived beyond the slowly varying envelope approximation, includes the effects of diffraction, dispersion, loss, gain, cubic, and quintic nonlinearities, as well as cubic and quintic self-steepening effects. The modulational instability of the plane waves is studied both theoretically, using the linear stability analysis, and numerically, using direct simulations of the Fourier space of the proposed nonlinear wave equation, based on the Drude model.

Chaotic vibration of microtubules and biological information processing.

A new nonlinear phenomenon has been studied theoretically on one of the main cytoskeletal element of eukaryotic cells, namely chaos in microtubules vibrations. The general model of microtubules is used to draw phase portraits and Lyapunov spectra. The examination of numerical results reveals that the velocity of the chaotic wave could be the physical parameter that governs chaos.

Base pairs opening and bubble transport in damped DNA dynamics with transport memory effects.

Transport memory effects on nonlinear wave propagation are addressed in a damped Peyrard-Bishop-Dauxois model of DNA dynamics. Under the continuum and overdamped limits, the multiple-scale expansion method is employed to show that an open-state configuration of the DNA molecule is described by a complex nonlinear Schrödinger equation. For the latter, solutions are proposed as bright solitons, which suitably represent the open-state configuration that takes place along the DNA molecule in the form of bubbles.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion.

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities.

Comment on "Defocusing complex short-pulse equation and its multi-dark-soliton solution".

In their recent paper, Feng et al. [Phys. Rev.

Fractional formalism to DNA chain and impact of the fractional order on breather dynamics.

We have investigated the impact of the fractional order derivative on the dynamics of modulated waves of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We have reformulated the classical Lagrangian of the system by including the coordinates depending on the Riemann-Liouville time derivative of fractional order γ. From the Lagrange equation, we derived the fractional nonlinear equation of motion.

Ultrashort optical waveguide excitations in uniaxial silica fibers: elastic collision scenarios.

In this work, we investigate the dynamics of an uniaxial silica fiber under the viewpoint of propagation of ultimately ultrashort optical waveguide channels. As a result, we unveil the existence of three typical kinds of ultrabroadband excitations whose profiles strongly depend upon their angular momenta. Looking forward to surveying their scattering features, we unearth some underlying head-on scenarios of elastic collisions.

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion.

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime.

Soliton interactions between multivalued localized waveguide channels within ferrites.

In this paper, we investigate both analytically and numerically the localized multivalued waveguide channels-the loop solitons-dynamics within a ferrite slab. In the starting point of the work, we solve in detail the initial value problem of the system while unveiling the existence of multivalued waveguide channels solutions. Paying particular interest to the nonlinear scattering among these excitations, we study extensively the different kinds of interacting features between these localized waves alongside the depiction of their energy densities.

Nonlinear mechanics of DNA doule strand: existence of the compact-envelope bright solitary wave.

We study the nonlinear dynamics of a homogeneous DNA chain which is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schrödinger equation describing the dynamics of modulated wave in DNA model. We obtain envelope bright solitary waves with compact support as a solution.

Dynamics of kink-dark solitons in Bose-Einstein condensates with both two- and three-body interactions.

The matter-wave solutions of Bose-Einstein condensates with three-body interaction are examined through the one-dimensional Gross-Pitaevskii equation. By using a modified lens-type transformation and a further extension of the tanh-function method we obtain the exact analytical solutions which describe the propagation of kink-shaped solitons, anti-kink-shaped solitons, and other families of solitary waves. We realize that the shape of a kink solitary wave depends on both the scattering length and the parameter of atomic exchange with the substrate.

Wave train generation of solitons in systems with higher-order nonlinearities.

Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain.

Generation of pulse trains in nonlinear optical fibers through the generalized complex Ginzburg-Landau equation.

We consider a higher-order complex Ginzburg-Landau equation, with the fourth-order dispersion and cubic-quintic nonlinear terms, which can describe the propagation of an ultrashort subpicosecond or femtosecond optical pulse in an optical fiber system. We investigate the modulational instability (MI) of continuous wave solution of this equation. Several types of modulational instability gains are shown to exist in both the anomalous and normal dispersion regimes.

Discrete instability in the DNA double helix.

Modulational instability (MI) is explored in the framework of the base-rotor model of DNA dynamics. We show, in fact, that the helicoidal coupling introduced in the spin model of DNA reduces the system to a modified discrete sine-Gordon (sG) equation. The MI criterion is thus modified and displays interesting features because of the helicoidal coupling.

Modulational instability of charge transport in the Peyrard-Bishop-Holstein model.

We report on modulational instability (MI) on a DNA charge transfer model known as the Peyrard-Bishop-Holstein (PBH) model. In the continuum approximation, the system reduces to a modified Klein-Gordon-Schrödinger (mKGS) system through which linear stability analysis is performed. This model shows some possibilities for the MI region and the study is carried out for some values of the nearest-neighbor transfer integral.

Discrete Lange-Newell criterion for dissipative systems.

We report on the derivation of the discrete complex Ginzburg-Landau equation with first- and second-neighbor couplings using a nonlinear electrical network. Furthermore, we discuss theoretically and numerically modulational instability of plane carrier waves launched through the line. It is pointed out that the underlying analysis not only spells out the discrete Lange-Newell criterion by the means of the linear stability analysis at which the modulational instability occurs for the generation of a train of ultrashort pulses, but also characterizes the long-time dynamical behavior of the system when the instability grows.