The self-consistent propagation of electrical impulses and of the accompanying distortions of the electron surface in the framework of a cold plasma model with a sharp boundary has been described with help of a derived system of two equations. The method of ‘shallow water theory’ has been applied for the case of bounded plasma and deriving an equation with which to link the spatial and temporal structures and evolution of the boundary curvature and the surface charge. Under certain conditions, such perturbations can propagate along the boundary without changing their shape for a long distance. An approximate analytical solution has been found, and numerical calculations have been performed. Mutual connections between basic parameters of the considered perturbations (velocity components, electrostatic field, etc.) have been presented.

This paper presents optimization-based dynamic three-dimensional (3D) human running prediction. A predictive dynamics method is used to formulate the running problem, and normal running is formulated as a symmetric and cyclic motion. In addition, a slow jog along curved paths has been formulated. It is a non-symmetric running motion, so a stride formulation has been used. The dynamic effort and impulse are used as the performance measure, and the upper body yawing moment is also included in the performance measure. The joint angle profiles and joint torque profiles are calculated for the full-body human model, and the ground reaction force is determined. The effects of foot location and orientation on the running motion prediction are simulated and studied. Simulation results from this methodology show good correlation with experimental data obtained from human subjects.

In this paper we study impulsive periodic solutions for second-order nonautonomous singular differential equations. Our proof is based on the mountain pass theorem. Some recent results in the literature are extended.

A novel approach of numerical modelling using input-output experimental data pairs is presented for deflection-thickness ratio of circular plates subjected to impulse loading. In this way, singular value decomposition (SVD) method is used in conjunction with dimensionless parameters incorporated in such complex process. The closed-form obtained model shows very good agreement with some testing experimental data pairs which have been unforeseen during the training process. Moreover, two modifications are consequently suggested for some similar models already proposed in previous works. The approach of this paper can generally be applied to model very complex real-world processes using appropriate experimental data.

A class of first-order impulsive functional differential equations with forcing terms is considered. It is shown that, under certain assumptions, there exist positive T-periodic solutions, and under some other assumptions, there exists no positive T-periodic solution. Applications and examples are given to illustrate the main results.