A numerical method for the fractional Fitzhugh–Nagumo monodomain model

A fractional FitzHugh–Nagumo monodomain model with zero Dirichlet boundary conditions is presented, generalising the standard monodomain model that describes the propagation of the electrical potential in heterogeneous cardiac tissue. The model consists of a coupled fractional Riesz space nonlinear reaction-diffusion model and a system of ordinary differential equations, describing the ionic fluxes as a function of the membrane potential. We solve this model by decoupling the space-fractional partial differential equation and the system of ordinary differential equations at each time step. Thus, this means treating the fractional Riesz space nonlinear reaction-diffusion model as if the nonlinear source term is only locally Lipschitz. The fractional Riesz space nonlinear reaction-diffusion model is solved using an implicit numerical method with the shifted Grunwald–Letnikov approximation, and the stability and convergence are discussed in detail in the context of the local Lipschitz property. Some numerical examples are given to show the consistency of our computational approach.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

Photo-ionization and residual electron effects in guided streamers

Complementary experiments and numerical modeling reveal the important role of photo-ionization in the guided streamer propagation in helium-air gas mixtures. It is shown that the minimum electron concentration ∼108 cm−3 is required for the regular, repeated propagation of the plasma bullets, while the streamers propagate in the stochastic mode below this threshold. The stochastic-to-regular mode transition is related to the higher background electron density in front of the propagating streamers. These findings help improving control of guided streamer propagation in applications from health care to nanotechnology and improve understanding of generic pre-breakdown phenomena.

Automatic wildfire detection and simulation using optical information from unmanned aerial systems

In many parts of the world, uncontrolled fires in sparsely populated areas are a major concern as they can quickly grow into large and destructive conflagrations in short time spans. Detecting these fires has traditionally been a job for trained humans on the ground, or in the air. In many cases, these manned solutions are simply not able to survey the amount of area necessary to maintain sufficient vigilance and coverage. This paper investigates the use of unmanned aerial systems (UAS) for automated wildfire detection. The proposed system uses low-cost, consumer-grade electronics and sensors combined with various airframes to create a system suitable for automatic detection of wildfires. The system employs automatic image processing techniques to analyze captured images and autonomously detect fire-related features such as fire lines, burnt regions, and flammable material. This image recognition algorithm is designed to cope with environmental occlusions such as shadows, smoke and obstructions. Once the fire is identified and classified, it is used to initialize a spatial/temporal fire simulation. This simulation is based on occupancy maps whose fidelity can be varied to include stochastic elements, various types of vegetation, weather conditions, and unique terrain. The simulations can be used to predict the effects of optimized firefighting methods to prevent the future propagation of the fires and greatly reduce time to detection of wildfires, thereby greatly minimizing the ensuing damage. This paper also documents experimental flight tests using a SenseFly Swinglet UAS conducted in Brisbane, Australia as well as modifications for custom UAS.