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A fractional blood flow model, in the presence of magnetic nanoparticles, is considered in this work. The effects of activation energy and thermal radiation on the blood flowing in the oscillating elastic tube are studied. The nanofluid inside the tube is activated by the rotating effect of the charged particles, a constant external magnetic field, and the activation energy. The blood is assumed to be at a temperature and a concentration that vary with the speed of the particles. The study takes advantage of a model, which includes a fractional-order derivative of Caputo’s type. The shape of nanoparticles and the speed of blood and the distributions of temperature and concentration are assimilated to Brownian motion and thermophoresis. They are calculated numerically using the L1-algorithm method. The results show that the applied magnetic field and the effects of the fractional-order parameter reduce the velocity of the nanofluid and nanoparticles, which considerably affects the temperature and concentration of the fluid. It is also found that the particle shape and fractional derivative parameters significantly influence velocities and heat transfer.

The nonlinear excitation of a dust ion acoustic (DIA) wave packet in a viscous dusty plasma consisting of Boltzmann distributed electrons, trapped ions, and variable charged dust is investigated. The dependence of the damping rate of the waves on the plasma parameters is discussed via the linear stability analysis. The standard reductive perturbation method is employed to derive the modified Korteweg-de Vries-Burgers equation due to an interplay among the nonlinearity, dispersion, and dissipation effects, and, the non-dissipative case gives the modified Korteweg-de Vries equation. Bifurcation analysis is discussed for the non-dissipative and dissipative systems assuming a Boltzmann distribution for electrons and a vortex-like distribution for ions. The effects of plasma parameters, among which the dusty plasma viscosity ν, trapping ion parameter β, and dust charge variation γ1 on solitary waves (SWs) and shock wave solutions, are discussed. It is observed that parameters ν and β significantly influence th...

The dynamics of three coupled α-polypeptide chains of a collagen molecule is investigated with the influence of power-law long-range exciton-exciton interactions. The continuum limit of the discrete equations reveal that the collagen dynamics is governed by a set of three coupled nonlinear Schrodinger equations, whose dispersive coefficient depends on the LRI parameter r. We construct the analytic symmetric and asymmetric (antisymmetric) soliton solutions, which match with the structural features of collagen related with the acupuncture channels. These solutions are used as initial conditions for the numerical simulations of the discrete equations, which reveal a coherent transport of energy in the molecule for r > 3. The results also indicate that the width of the solitons is a decreasing function of r, which help to stabilize the solitons propagating in the molecule. To confirm further the efficiency of energy transport in the molecule, the modulational instability of the system is performed and the numerical simulations show that the energy can flow from one polypeptide chain to another in the form of nonlinear waves.

We focus our attention on the coupled short-pulse equation recently derived by Feng [J. Phys. A: Math. Theor. 45, 085202 (2012)] from a two-dimensional Backlund transformation of the Toda lattice equation. Investigating the prolongation structure of such a system, we unveil the hidden structural symmetry that governs the dynamics of the wave solutions to the system alongside with the corresponding Lax-pairs. As a matter of illustration, following the Wadati-Konno-Ichikawa scheme, we construct some solitary wave solutions to the system and study their interactions.

In this paper, we investigate the phase portraits features of a barothropic relaxing medium under pressure perturbations. In the starting point, we show within a third-order of accuracy that the previous system is modeled by a “dissipative” cubic nonlinear evolution equation. Paying particular attention to high-frequency perturbations of the system, we solve the initial value problem of the system both analytically and numerically while unveiling the existence of localized multivalued waveguide channels. Accordingly, we find that the “dissipative” term with a “dissipative” parameter less than some limit value does not destroy the ambiguous solutions. We address some physical implications of the results obtained previously.

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.

We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.

Charge transport in the twist-opening model of DNA is explored via the modulational instability of a plane wave. The dynamics of charge is shown to be governed, in the adiabatic approximation, by a modified discrete nonlinear Schrödinger equation with next-nearest neighbor interactions. The linear stability analysis is performed on the latter and manifestations of the modulational instability are discussed according to the value of the parameter α, which measures hopping interaction correction. In so doing, increasing α leads to a reduction of the instability domain and, therefore, increases our chances of choosing appropriate values of parameters that could give rise to pattern formation in the twist-opening model. Our analytical predictions are verified numerically, where the generic equations for the radial and torsional dynamics are directly integrated. The impact of charge migration on the above degrees of freedom is discussed for different values of α. Soliton-like and localized structures are observed and thus confirm our analytical predictions. We also find that polaronic structures, as known in DNA charge transport, are generated through modulational instability, and hence reinforces the robustness of polaron in the model we study.

Following the Weiss-Tabor-Carnevale approach [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983)10.1063/1.525721; J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984).]10.1063/1.526009 designed for studying the integrability properties of nonlinear partial differential equations, we investigate the singularity structure of a (2+1)-dimensional wave-equation describing the propagation of polariton solitary waves in a ferromagnetic slab. As a result, we show that, out of any damping instability, the system above is integrable. Looking forward to unveiling its complete integrability, we derive its Backlund transformation and Hirota's bilinearization useful in generating a set of soliton solutions. In the wake of such results, using the arbitrary functions to enter into the Laurent series of solutions to the above system, we discuss some typical class of excitations generated from the previous solutions in account of a classification based upon the different expressions of a gene...

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.