Ionic models are used to describe the evolution of the electrical potential across the cardiac cell membranes. The Mitchell-Schaeffer model is a simple two variables nonlinear ionic model with a limited set of parameters. This model can still capture the main features of the cardiac action potential, namely the action potential duration (APD), the conduction velocity (CV), depolarisation time (DT), recovery time (RT), etc. In this paper we have developed an optimization method to recover the specific characteristics ADP, DT and RT by identifying the values that the four parameters τ = [τ in , τ out , τ open , τ close , σ] of the Mitchell-Schaeffer must take. By using the fonction ode in Scilab, Mitchell-Schaeffer model solutions have been oabtained numerically.

This paper proposes an asymptotic approach for describing silting of rivers. The proposed approach is based on the hypothesis that rivers silting can be explained by an asymptotic behavior near shock curves of the governing equations of sediment deposits. The computation of the leading term of the asymptotic expansion is then performed and an example which illustrated the proposed approach is presented.

No abstract

The phenomenon of extinction is an important property of solutions for many evolutionary equations. In this paper, a numerical simulation for computing the extinction time of nonnegative solutions for some nonlinear parabolic equations on general domains is presented. The solution algorithm utilizes the Donor-cell scheme in space and Euler's method in time. Finally, we will give some numerical experiments to illustrate our algorithm.

The river silting process is complex and represents one of the greatest challenges faced in the future. In this paper, we propose an asymptotic approach for describing silting of rivers to study asymptotic solutions governing a coupled (hydro-sedimentary) model. We focus our paper on the inner and outer asymptotic expansions of solutions. The proposed approach is based on the hypothesis that rivers silting can be explain by an asymptotic behavior near shock curves of the governing equations of sediment deposits. We look for an inner and outer asymptotic expansion which gives us expressions of the solution in the neighborhood of the shock zone. Once both asymptotic expansions found , we give matching property of both expansions.