A compact finite difference scheme with absorbing boundary condition for forced KdV equation.

Studying the long-time solution behavior of the Korteweg-de Vries (KdV) type equation with a periodic force acting at one end of the long channel is important for simulating the blood flow in artery driven by heart pulses. It is of great interest to develop an accurate numerical method for solving the forced KdV problem. In this article, we present the following methods to obtain an accurate approximation to the solution of KdV problem.

Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

The non-Fourier effects, such as wave-like temperature propagation and boundary temperature jumps, arise in nanosized systems due to the multiple time and space scales nature of out-of-equilibrium heat transport. The relaxation to equilibrium occurs in successive time and space scales due to couplings between different excitations, whose relaxation times have different physical meanings and may differ significantly in magnitude. The out-of-equilibrium temperature evolution is described by a hierarchy of partial differential equations of a higher order, which includes both the diffusive and wave modes of heat transport.

A new 3D mass diffusion-reaction model in the neuromuscular junction.

A three-dimensional model of the reaction-diffusion processes of a neurotransmitter and its ligand receptor in a disk shaped volume is proposed which represents the transmission process of acetylcholine in the synaptic cleft in the neuromuscular junction. The behavior of the reaction-diffusion system is described by a three-dimensional diffusion equation with nonlinear reaction terms due to the rate processes of acetylcholine with the receptor. A new stable and accurate numerical method is used to solve the equations with Neumann boundaries in cylindrical coordinates.

Tri-polar concentric ring electrode development for laplacian electroencephalography.

Brain activity generates electrical potentials that are spatio-temporal in nature. Electroencephalography (EEG) is the least costly and most widely used noninvasive technique for diagnosing many brain problems. It has high temporal resolution, but lacks high spatial resolution.

Use of the z-transform to investigate nanopulse penetration of biological matter.

Short duration, fast rise time electromagnetic ultra-wideband (UWB) pulses ("nanopulses") are generated by numerous electronic devices. Many new technologies involving nanopulses are under development and expected to become widely available soon. Study of nanopulse bioeffects therefore is needed to ensure human safety and to probe the useful range of nanopulses in possible biomedical and biotechnological applications.