Open Access Original Research Article

Breaking of Spiral Waves Due to Obstacles

Daniel Olmos-Liceaga, Dalicia Leal Soto, Roberto Ávila-Pozos

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2017/36584

A spiral wave, which is a self-sustaining wave, is believed to be the source of certain types of arrhythmias, which can lead to fibrillation. In this paper, we study a generic model for the propagation of electrical impulses in cardiac tissue based on the Fitzhugh-Nagumo (FHN) equations. By numerical simulations we consider the evolution of spiral waves and their interaction with obstacles, such as ischemic or dead tissue from a heart attack or surgery. We describe three possible outcomes (attachment, bouncing and break up) when a spiral wave in the trochoidal regime interacts with an obstacle. The results can be useful to understand the dynamics of the interaction between drifting spiral waves and obstacles and to observe that obstacles might act as a switch from a less to a more dangerous arrhythmic regime.

Open Access Original Research Article

Open Access Original Research Article

Velocity Profiles of Unsteady Blood Flow through an Inclined Circular Tube with Magnetic Field

Vincent Mwanthi, Eustance Mwenda, Kennedy K. Gachoka

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/JAMCS/2017/36620

The present paper is devoted to study the flow of incompressible viscous, electrically conducting fluid (blood) in a rigid inclined circular tube with magnetic field. The blood is considered to be Newtonian fluid and the flow is caused by varying pressure gradient with time. The physics of the problem is described using the usual Magneto hydrodynamic (MHD) principles and equations along with appropriate boundary conditions. The governing equations of the motion in terms of cartesian co-ordinates are reduced to ordinary differential equations. Using dimensionless parameters, the Navier-stokes equation is solved numerically using finite difference method of approximation and the expressions for velocity profile is obtained. The velocity profiles for various values of Hartmann number as well as varying the angle of inclination of the tube have been presented graphically and discussed in depth. The obtained results show that on increasing the inclination angle of the tube and Hartmann number leads to increase and decrease of the axial velocity of the blood respectively.

Open Access Original Research Article

Convergence of Differential Transform Method for Ordinary Differential Equations

A. S. Oke

Journal of Advances in Mathematics and Computer Science, Page 1-17
DOI: 10.9734/JAMCS/2017/36489

Differential transform method (DTM) as a method for approximating solutions to differential equations have many theorems that are often used without recourse to their proofs. In this paper, attempts are made to compile these proofs. This paper also proceeds to establish the convergence of the DTM for ordinary differential equations. This paper establishes that if the solution of an ordinary differential equation can be written as Taylors' expansion, then the solution can be obtained using the DTM. This is also demonstrated with some numerical examples.

Open Access Original Research Article

Magnetic Field in Reentry Flows in 2D: Eleven Species

Edisson Sávio de Góes Maciel

Journal of Advances in Mathematics and Computer Science, Page 1-36
DOI: 10.9734/JAMCS/2017/36904

In this work, a study involving magnetic field actuation over reentry flows in thermochemical non-equilibrium is performed. The Euler and Navier-Stokes equations, on a finite volume and structured contexts, are studied. The Maciel algorithm used to perform the numerical experiments is centered and 2nd-order accurate. The “hot gas” hypersonic flow around a blunt body is simulated. Two time integration methods are tested: Euler Backward, and Middle Point. The reactive simulations involve Earth atmosphere of eleven species. The Dunn and Kang model with thirty-two reactions and the Park model with forty-three reactions are taken into account. The work of Gaitonde is the reference to couple the fluid dynamics and Maxwell equations of electromagnetism. The results have indicated that the Maciel scheme, employing the Dunn and Kang chemical model, using the Mavriplis dissipation model and the Euler Backward to march in time, for the inviscid case, yields the best prediction of the stagnation pressure. Moreover, the drag coefficient and the temperature peak have presented the expected behavior in the simulations.