Band 23, Heft 5

The current research explores the slippage phenomenon in hydromagnetic peristaltic activity of a non-Newtonian fluid with porous media in an asymmetric channel. The analysis is performed under the influence of thermal radiation, Hall current, Joule heating and viscous dissipation. The problem is formulated with the assumption of small Reynolds number and large wavelength. Analytical solutions are achieved through perturbation technique and the impacts of involved influential parameters are examined through graphs. It is observed that the pressure gradient rises with fourth grade fluid parameter and decreases with increasing phase difference. The pressure rise increases in pumping regime and decreases in co-pumping regime for increasing magnetic field parameter, whereas it has opposite effects for hall parameter. It is also noted that the velocity drops in the middle of the channel, while it increases near the boundaries for growing slip parameter and magnetic field parameters and it has the opposite behavior for hall and permeability parameters. The slip parameter increases the temperature of the fluid and decreases the concentration. Also, in trapping phenomena, the bolus size reduces by enlarging Deborah parameter. The present research has profound use in biomedical science, polymer technology and artificial heart polishing.

This article discusses the dissipativity analysis of stochastic generalized neural network (NN) models with Markovian jump parameters and time-varying delays. In practical applications, most of the systems are subject to stochastic perturbations. As such, this study takes a class of stochastic NN models into account. To undertake this problem, we first construct an appropriate Lyapunov–Krasovskii functional with more system information. Then, by employing effective integral inequalities, we derive several dissipativity and stability criteria in the form of linear matrix inequalities that can be checked by the MATLAB LMI toolbox. Finally, we also present numerical examples to validate the usefulness of the results.

In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

We analyse exact solutions to the Riemann problem for a one-dimensional isentropic and perfectly conducting non-ideal dusty gas flow in the presence of a transverse magnetic field. We give the expression of wave curves as well as the behaviors of these wave curves. A new technique is provided to get a complete list of analytical solutions with the corresponding criteria. Moreover, the numerical solutions to the Riemann problem are also given. It is shown that the analytical solutions match well with the corresponding numerical solutions.

In this paper, we consider a biharmonic equation with Navier boundary conditions and we decoupled this fourth order biharmonic equation into a system of second order equations. In numerics, there is an advantage because of this decoupling, i.e., one can use C 0 finite elements to solve the decoupled system instead of C 1 finite elements. For solving this decoupled system of second order equations, we use the weighted extended b -spline (WEB-Spline) based mesh-free finite element method. The WEB-Spline method does not require any mesh generation and eliminates the difficult, time-consuming preprocessing step. Also, by the WEB-Spline method higher order approximations are possible with relatively low dimensional spaces. Numerical results based on the WEB-Spline method are compared with the usual finite element method in order to demonstrate the efficiency of the proposed method.

This article focusses on the implementation of cubic B-spline approach to investigate numerical solutions of inhomogeneous time fractional nonlinear telegraph equation using Caputo derivative. L 1 formula is used to discretize the Caputo derivative, while B-spline basis functions are used to interpolate the spatial derivative. For nonlinear part, the existing linearization formula is applied after generalizing it for all positive integers. The algorithm for the simulation is also presented. The efficiency of the proposed scheme is examined on three test problems with different initial boundary conditions. The influence of parameter α on the solution profile for different values is demonstrated graphically and numerically. Moreover, the convergence of the proposed scheme is analyzed and the scheme is proved to be unconditionally stable by von Neumann Fourier formula. To quantify the accuracy of the proposed scheme, error norms are computed and was found to be effective and efficient for nonlinear fractional partial differential equations (FPDEs).

A reaction–diffusion system governing the prey–predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.

The present work numerically investigates the mass and heat transport flow of micropolar fluid in a channel having permeable walls. The appropriate boundary layer approximations are used to convert the system of flow model equations in ODEs, which are then numerically treated with the quasi-linearization method along with finite difference discretization. This technique creates an efficient way to solve the complex dynamical system of equations. A numerical data comparison is presented which assures the accuracy of our code. The outcomes of various problem parameters are portrayed via the graphs and tables. The concentration and temperature accelerate with the impacts of the Peclet numbers for the diffusion of mass and heat, respectively. It is also found that the porosity of the medium has a substantial effect on the skin friction but low effect on the heat and mass transfer rates. Our results may be beneficial in lubrication, foams and aerogels, micro emulsions, micro machines, polymer blends, alloys, etc.

In this paper, we analyze the 3D structure of vortices developed in a rotating cylinder nonhomogeneously heated from below, when the rotation rate is increased. The analysis has been done by using nonlinear simulations. For a fixed Rayleigh number, the rotation rate is the bifurcation parameter. At low rotation rates, one single vortex is developed. When the rotation on the system is increased, another coexistent vortex appears at mid-levels in the cell. If the rotation is high enough, multiple-vortex structures with three or four vortices are developed at different heights. For larger rotation, complex multiple vortices appear with a chaotic behavior. A force balance analysis permits to study the role of the forces being determinant.

Under investigation is a generalized variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources. Our main job is divided into four parts: (i) lump wave solution, (ii) interaction solutions between lump and solitary wave, (iii) breather wave solution and (iv) interaction solutions between lump and periodic wave. Furthermore, the interaction phenomenon of waves is shown in some 3D- and contour plots.