In this paper, we apply an a posteriori error control theory that we develop in a very recent paper to three families of the discontinuous Galerkin methods for the Reissner-Mindlin plate problem. We derive robust a posteriori error estimators for them and prove their reliability and efficiency.

In this paper, we develop a multi-symplectic wavelet collocation method for three-dimensional (3-D) Maxwell’s equations. For the multi-symplectic formulation of the equations, wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration. Theoretical analysis shows that the proposed method is multi-symplectic, unconditionally stable and energy-preserving under periodic boundary conditions. The numerical dispersion relation is investigated. Combined with splitting scheme, an explicit splitting symplectic wavelet collocation method is also constructed. Numerical experiments illustrate that the proposed methods are efficient, have high spatial accuracy and can preserve energy conservation laws exactly.

The exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

In this paper, we propose several solar cell designs based on metamaterials. Extensive numerical simulations of various designs with different materials are carried out. Our tests show that metamaterial solar cells are quite efficient, and over 80% and 90% absorption rates can be attained for solar spectrum and visible rays, respectively.

Ramp load/unload (L/UL) mechanisms are widely used to rest sliders in hard disk drives (HDDs). Loading/unloading a slider swiftly and smoothly is crucial in a HDD design. A novel, efficient simulation scheme is proposed to investigate the behaviors of a head disk interface (HDI) in ramp unloading processes. A dual scale model is enabled by decoupling the nano-meter scale change of an air bearing and the micro- or milli-meter scale deformation of a suspension. A modified Reynolds equation governing the air bearing was solved numerically. The slider design was characterized with performance functions. Three stages in an unloading process were analyzed with a lumped parameter suspension model. Key parameters for the model were estimated with a comprehensive finite element suspension model. Finally, simulation results are presented for a commercial HDI design.

In studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.

The dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magneto-thermoelastic solid. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave cases. The results for partition of the energy for various values of the angle of incidence are computed numerically under the stress-free and rigidly fixed thermally insulated boundaries. The reflection coefficients are depending on the angle of incidence, magnetic field, phase lags and other material constants. Results show that the sum of energy ratios is unity at the interface. The results are discussed and depicted graphically.

In this paper, we construct a simplified neuronal model that is capable of simulating the instigation of cortical spreading depression (CSD) and propagation of a CSD wave. Our model is a simplification and extension of a single neuron model proposed in the literature for studying the instigation of CSD. Using the simplified neuronal model, we construct a network of these simplified neurons. This network model shows that the propagation of a CSD wave occurs naturally after it is instigated electrically or chemically. Although the model is simple, the speed of the CSD wave predicted by our model is consistent with experimentally observed values. Finally, our model allows us to investigate the effects of specific ion channels on the spread of a CSD wave.

A scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method (HPM). The fractional derivatives are taken in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical results are illustrated through the graph.