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A fractional model is proposed to study the effect of heat transfer and magnetic field on the blood flowing inside oscillatory arteries. The flow is due to periodic pressure gradient and the fractional model equations include body acceleration. The proposed velocity and temperature distribution equations are solved using the Laplace and Hankel transforms. The effect of the fluid parameters such as the Reynolds number (Re), the magnetic parameter ( M ) and the radiation parameter ( N ) is studied graphically with changing the fractional-order parameter. It is found that the fractional derivative is a valuable tool to control both the temperature and velocity of blood when flow parameters change under treatment, for example. Besides, this work highlights the fact that in the presence of strong magnetic field, blood velocity and temperature reduce. A reversed effect is observed where the applied thermal radiation increase; the velocity and temperature of blood increase. However, the temperature remains high around the artery centerline, which is appropriate during treatment to avoid tissues damage. [ABSTRACT FROM AUTHOR]

We are motivated by recent studies in medium formed by two tunnel-coupled waveguides. One of the waveguides is manufactured from an ordinary dielectric, while the second has negative refraction. We present an investigation of the gain spectrum permitting modulation instability in the nonlinear optical coupler with a negative-index metamaterial channel whose non-linear response includes third- and fifth-order terms. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective cubic–quintic nonlinearity. We emphasize the influence of higher order nonlinear terms, over the MI phenomena, and the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near-zero dispersion regime where higher order linear dispersive effects emerge. Our results show that the MI gain spectra consist of multiple spectral region which are symmetric to the zero point. Moreover, some spectra have a high cut-off frequency but a narrow spectral width, which is obviously beneficial to the generation of high-repetition-rate pulse trains. [ABSTRACT FROM AUTHOR]

Realistic models of α-helix proteins are composed of three covalently-bonded strands, each of which is made of hydrogen-bonded peptide units. The modulational instability analysis of such complex molecular systems is carried out in this work. We show that the exciton-vibron coupling parameter contributes to the explosion and expansion of instability regions. The right choice of the modulational instability parameters leads to the formation of excitonic modulated pulse-like structures. It is argued that covalent bonds are compressed during the process of energy transport, while hydrogen bond oscillations display regular trains of breather-like objects. We also argue that the probable way of energy transport, from modulational instability, is through hydrogen bonds. [ABSTRACT FROM AUTHOR]

• Flow-driven unstable pattern formation of cyclic adenosine monophosphate is investigated. • A perturbed plane wave breaks up into wave patterns under the modulational instability process. • Quasi-periodic waves, spiral seeds and chaotic patterns are found to control information among D. discoideum cells. • Efficient regulation of communication between an amoebas colony is supported by right choice of system parameters. • Pattern formation process among D. discoideum cells under spontaneous fluid flow is discussed. Flow-driven formation of unstable patterns of cyclic adenosine monophosphate (cAMP) is investigated in the Martiel-Goldbeter (MG) model. This is predicted via a complex Ginzburg-Landau equation, derived from the MG model, under the so-called modulational instability process. Regions of parameters where patterns exist are discussed analytically and verified numerically. Quasi-periodic waves, spiral seeds and chaotic patterns are found to control information driven in a colony of homogeneously distributed Dictyostelium discoideum cells under the change of the extracellular cAMP degradation rate (k e), the production rate of cAMP (σ) and the advection flow velocity (V f). Our results suggest that these quantities play a key role in the efficient regulation of communication within an amoeba colony, and the presence of the flow makes it possible to understand pattern formation process among D. discoideum cells under spontaneous fluid flow in their natural environment. [ABSTRACT FROM AUTHOR]