Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

On the analytical solutions of the Hindmarsh-Rose neuronal model

In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.

Numerical and Experimental Analysis of Balanced and Unbalanced Adhesive Single-Lap Joints between Aluminium Adherends

The single-lap joint is the most commonly used, although it endures significant bending due to the non-collinear load path, which negatively affects its load bearing capabilities. The use of material or geometric changes is widely documented in the literature to reduce this handicap, acting by reduction of peel and shear peak stresses or alterations of the failure mechanism emerging from local modifications. In this work, the effect of using different thickness adherends on the tensile strength of single-lap joints, bonded with a ductile and brittle adhesive, was numerically and experimentally evaluated. The joints were tested under tension for different combinations of adherend thickness. The effect of the adherends thickness mismatch on the stress distributions was also investigated by Finite Elements (FE), which explained the experimental results and the strength prediction of the joints. The numerical study was made by FE and Cohesive Zone Modelling (CZM), which allowed characterizing the entire fracture process. For this purpose, a FE analysis was performed in ABAQUS® considering geometric non-linearities. In the end, a detailed comparative evaluation of unbalanced joints, commonly used in engineering applications, is presented to give an understanding on how modifications in the bonded structures thickness can influence the joint performance.