Existence of spatial patterns in reaction–diffusion systems incorporating a prey refuge

In real-world ecosystem, studies on the mechanisms of spatiotemporal pattern formation in a system of interacting populations deserve special attention for its own importance in contemporary theoretical ecology. The present investigation deals with the spatial dynamical system of a two-dimensional continuous diffusive predator–prey model involving the influence of intra-species competition among predators with the incorporation of a constant proportion of prey refuge. The linear stability analysis has been carried out and the appropriate condition of Turing instability around the unique positive interior equilibrium point of the present model system has been determined. Furthermore, the existence of the various spatial patterns through diffusion-driven instability and the Turing space in the spatial domain have been explored thoroughly. The results of numerical simulations reveal the dynamics of population density variation in the formation of isolated groups, following spotted or stripe-like patterns or coexistence of both the patterns. The results of the present investigation also point out that the prey refuge does have significant influence on the pattern formation of the interacting populations of the model under consideration

Hydromagnetic rotating flow of Casson fluid in Darcy-Forchheimer porous medium

Present study investigates three dimensional rotating flow of Casson fluid in the presence of magnetic field over a convectively heated linear stretching sheet. Concept of nonlinear radiative heat transfer is considered. The governing nonlinear partial differential equations are converted into ordinary differential equations with the help of similarity transformation and then solved by using shooting method along with Runge-Kutta-Fehlberg integration technique. The primary and secondary velocities and temperature profiles are plotted and analysed corresponding to various pertinent flow parameters. Also, the skin friction for both directions and rate of heat transfer at the surface are computed and explained

Hydromagnetic rotating flow of Casson fluid in Darcy-Forchheimer porous medium

Present study investigates three dimensional rotating flow of Casson fluid in the presence of magnetic field over a convectively heated linear stretching sheet. Concept of nonlinear radiative heat transfer is considered. The governing nonlinear partial differential equations are converted into ordinary differential equations with the help of similarity transformation and then solved by using shooting method along with Runge-Kutta-Fehlberg integration technique. The primary and secondary velocities and temperature profiles are plotted and analysed corresponding to various pertinent flow parameters. Also, the skin friction for both directions and rate of heat transfer at the surface are computed and explained

Unsteady magnetohydrodynamic blood flow through irregular multi-stenosed arteries

Flow of an electrically conducting fluid characterizing blood through the arteries having irregular shaped multi-stenoses in the environment of a uniform transverse magnetic-field is analysed. The flow is considered to be axisymmetric with an outline of the irregular stenoses obtained from a three-dimensional casting of a mild stenosed artery, so that the physical problem becomes more realistic from the physiological point of view. The marker and cell (MAC) and successive-over-relaxation (SOR) methods are respectively used to solve the governing unsteady magnetohydrodynamic (MHD) equations and pressure-Poisson equation quantitatively and to observe the flow separation. The results obtained show that the flow separates mostly towards the downstream of the multi-stenoses. However, the flow separation region keeps on shrinking with the increasing intensity of the magnetic-field which completely disappears with sufficiently large value of the Hartmann number. The present observations certainly have some clinical implications relating to magnetotherapy which help reducing the complex flow separation zones causing flow disorder leading to the formation and progression of the arterial diseases

Unsteady solute dispersion in the presence of reversible and irreversible reactions

In an unsteady pulsatile non-Newtonian fluid past a tube with a thin wall layer, the dispersion of a narrow uniform slug of injected solute over a cross-section is examined. At the interface between the mobile fluid phase and the immobile wall phase, both irreversible and reversible reactions have been adopted. The Carreau-Yasuda model is used to describe the fluid's rheology. The impacts of fluid rheology and reaction parameters on the concentration profiles in the fluid- and wall-phases and the three transport coefficients, viz, the depletion coefficient (K-0), the convection coefficient (K-1), the dispersion coefficient (K-2) in the fluid phase are predicted numerically. A considerable shift in the behaviour of K-1 and K(2 )with a higher reaction rate may be observed in the transient stage. The axial dispersion of mobile-phase concentration in the unsteady Carreau-Yasuda II fluid model is significantly larger than in Poiseuille and steady Carreau-Yasuda II fluid models, and flow pulsatility on the immobile-phase concentration is prominent upstream at a longer time. In addition, the peak value of the mobile-phase section-mean concentration is consistently lower than in other fluid models. This study could help researchers to understand the drug delivery in blood vessels and pulmonary mechanical ventilation. (C) 2022 The Author(s) Published by the Royal Society. All rights reserved