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. We find the domains of some parameter space where nonlinear patterns are expected in the model. The analytical results on the MI growth rate predict that phosphorylation and binding rates affect MARCKS dynamics in opposite way: while the phosphorylation rate tends to support highly localized structures of MARCKS, the binding rate in turn tends to slow down such features. On the other hand, self-diffusion process always amplifies the MI phenomenon. These predictions are confirmed by numerical simulations. As a result, the cyclic transport of MARCKS protein from membrane to cytosol may be done by means of multisolitons-like patterns.

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. Direct numerical calculations on the generic model support our analytical predictions and show that the higher-order interspecies interaction and the SO coupling can balance each other suitably for stability to take place. Mainly, it is found that the residual nonlinearity preserves and reinforces the stability of miscible pairs of condensates with SO coupling. Additionally, when a miscible binary mixture of condensates with SO coupling is modulationally unstable, the presence of residual nonlinearity may help soften such instability. Our results finally suggest that MI-induced formation of stable solitons in mixtures of BECs with two-body attraction may be preserved by the residual nonlinearity even though the latter enhances the instability.

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. It is pointed out that the instability spectrum, which tends to be quenched by the high nonlocality parameter, gets amplified under the right choices of the saturation parameters, especially the saturation index. Via direct numerical simulations, confirmations of analytical predictions are given, where competing nonlocal and saturable nonlinearities enable the emergence of trains of patterns as manifestations of MI. The comprehensive parametric analysis carried out throughout the numerical experiment reveals the robustness of the obtained rogue waves of A- and B-type Akhmediev breathers, as the nonlinear signature of MI, providing the saturation index as a suitable tool to manipulate nonlinear waves in nonlocal media.

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. Radon concentration ranged between 36 ± 20 and 150 ± 30 Bq m-3 with arithmetic and geometric means values of 64 ± 25 and 60 ± 1 Bq m-3, respectively. These mean values were greater than worldwide values presented by United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR), which are, respectively, 40 and 30 Bq m-3. 96% of dwellings that have radon concentrations below the World Health Organization (WHO) reference level of 100 Bq m-3, whereas 4% of dwellings have radon concentrations higher than this level but lower than 300 Bq m-3, the International Commission on Radiological Protection (ICRP) reference level. Annual effective doses due to indoor radon ranged between 0.7 and 2.8 mSv y-1 with an arithmetic mean value of 1.2 ± 0.5 mSv y-1. These values were below the lower limit of the ICRP-recommended action level interval 3-10 mSv y-1. It has been observed that annual effective dose received by residents in cement bricks dwellings were not significantly different (P-value = 0.565) than those received by residents in mud dwellings in Mvangan locality. The mean number of persons expected to be diagnosed with or die from cancer (solid cancers and leukemia) were 162 ± 48 (61 ± 25 for males and 101 ± 41 for females) and 82 ± 24 (33 ± 13 for males and 49 ± 20 for females), respectively. The results obtained in this study prove that the populations of Mvangan locality are exposed to a relatively low potential risk of cancer incidence and mortality.

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. It is found that apart from exciting a myocardial cell, the mixed frequencies magnetic radiation can promote mode transition to bursting type behavior as the frequency is increased as well as suppress the electrical activities to quiescent state under high intensities magnetic radiations, which are consistent with biological experiments.

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. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold for amplitude perturbations.

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. The linear theory predicts instability for any amplitude of the primary wave. Also, in the linear stability analysis, self-steepening effects of different orders are confronted and one discusses their effects on the behavior of the gain spectrum under both normal and anomalous group-velocity dispersion regimes. Analytical results are equally confronted to direct numerical simulations and fully agree with the predictions from the gain spectra. Modulational instability is manifested by clusters of solitons and multihump and dromion-like structures, whose emergence and features depend not only on system parameters, such as the cubic and quintic self-steepening coefficients, but also on the propagation distance under a suitable balance between nonlinear and dispersive effects.

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. The energy released after the hydrolysation of guanosine triphosphate is converted to active turbulence leading to chaos. The high values of the Lyapunov exponents give hints that there are strong dissipations yielding in the lessening of the velocity of chaotic wave propagation in the microtubules. Moreover, the role of chaos in information processing has been established in microtubules. The energy coming from hydrolysis of guanosine triphosphate stimulates the tubulin leading it to probe its environment and collect information. The net sum of Lyapunov exponents is found to be positive in this stage of the process. Also, the collected information is compressed with a negative sum of Lyapunov exponents. Eventually, the compressibility rate has been estimated to be η=67.2%, and 1.11 bit is lost.

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. A good agreement between numerical experiments and analytical predictions on the impact of memory effects on the angular frequency, velocity, width, and amplitude of the moving bubble is obtained. It also appears that memory effects can modify qualitatively and quantitatively the nonlinear dynamics of DNA, including the energy brought by enzymes for the initiation of the processes of replication and transcription.

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. Emphasis is placed on the effect of the superdiffusion exponent α, the diffusion ratio d, and the inertial time τ. As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τ_{max}=3.6. As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

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. We obtained the fractional breather as solutions by means of a fractional perturbation technique. The impact of the fractional order is investigated and we showed that depending on the values of γ, there are three types of waves that propagate in DNA. We have static breathers, breathers of small amplitude and high velocity, and breathers of high amplitude and small velocity.

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. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

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. Analytical criteria of existence of this solution are derived. The stability of bright compactons is confirmed by numerical simulations of the exact equations of the lattice. The impact of the finite stacking energy is investigated and we show that some of these compact bright solitary waves are robust, while others decompose very quickly depending on the finite stacking parameters.

Dynamics of modulated waves in electrical lines with dissipative elements.

By a means of a method based on the reductive perturbation method, we show that the amplitude of waves on the nonlinear electrical transmission lines (NLTLs) is described by the cubic-quintic complex Ginzburg-Landau (CGL) equation. Then, we revisit analytically and numerically the processes of modulational instability (MI). The evolution of dissipative modulated waves through the network is also examined, and we show that solitonlike excitations can be induced by MI. Analytical results, illustrating the nature of MI of plane-wave solution, are also found to be in good agreement with numerical findings.

Painlevé-integrability of a (2+1)-dimensional reaction-diffusion equation: exact solutions and their interactions.

We investigate the singularity structure analysis of a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion (NLERD) equation by means of the Painlevé (P) test. Following the Weiss et al.'s formalism [J. Math. Phys. 24, 522 (1983)], we prove the arbitrariness of the expansion coefficients of the observables. Thus, without the use of the Kruskal's simplification, we obtain a Bäcklund transformation of the coupled NLERD equation via a consistent truncation procedure stemming from the Weiss 's methodology [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984)]. In the wake of such results, we unveil a typical spectrum of localized and periodic coherent patterns. We also investigate the scattering properties of such structures and we unearth two peculiar soliton phenomena, namely, the fusion and the fission.

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.

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. Numerical simulations are then performed, which confirm analytical predictions and give rise to localized structure formation. We show how the spreading of charge deeply depends on the value of the charge-lattice-vibrational coupling.

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. In the simulations, we have found that a train of pulses is generated when the lattice is subjected to MI, in agreement with analytical results obtained in a modified discrete sG equation. Also, the competitive effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. In the same way, it is shown that MI can lead to energy localization which becomes high for some values of the helicoidal coupling constant.

Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity.

The study of solitary wave solutions is of prime significance for nonlinear physical systems. The Peyrard-Bishop model for DNA dynamics is generalized specifically to include the difference among bases pairs and viscosity. The small amplitude dynamics of the model is studied analytically and reduced to a discrete complex Ginzburg-Landau (DCGL) equation. Exact solutions of the obtained wave equation are obtained by the mean of the extended Jacobian elliptic function approach. These amplitude solutions are made of bubble solitons. The propagation of a soliton-like excitation in a DNA is then investigated through numerical integration of the motion equations. We show that discreteness can drastically change the soliton shape. The impact of viscosity as well as elasticity on DNA dynamic is also presented. The profile of solitary wave structures as well as the energy which is initially evenly distributed over the lattice are displayed for some fixed parameters.

Instability criteria and pattern formation in the complex Ginzburg-Landau equation with higher-order terms.

We study the modulational instability and spatial pattern formation in extended media, taking the one-dimensional complex Ginzburg-Landau equation with higher-order terms as a perturbation of the nonlinear Schrödinger equation as a model. By stability analysis for the original partial differential equation, we derive its stability condition as well as the threshold for amplitude perturbations and we show how nonlinear higher-order terms qualitatively change the behavior of the system. The analytical results are found to be in agreement with numerical findings. Modulational instability mediates pattern formation through the lattice. The main feature of the traveling plane waves is its disintegration in pulse train during the propagation through the system.