Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

A two-Dimensional finite volume method for variable density flow and solute transport through saturated-unsaturated media

Extensive groundwater withdrawal has resulted in a severe seawater intrusion problem in the Gooburrum aquifers at Bundaberg, Queensland, Australia. Better management strategies can be implemented by understanding the seawater intrusion processes in those aquifers. To study the seawater intrusion process in the region, a two-dimensional density-dependent, saturated and unsaturated flow and transport computational model is used. The model consists of a coupled system of two non-linear partial differential equations. The first equation describes the flow of a variable-density fluid, and the second equation describes the transport of dissolved salt. A two-dimensional control volume finite element model is developed for simulating the seawater intrusion into the heterogeneous aquifer system at Gooburrum. The simulation results provide a realistic mechanism by which to study the convoluted transport phenomena evolving in this complex heterogeneous coastal aquifer.

Environmental health risk assessment of dioxin exposure through foods in a Dioxin hot spot—Bien Hoa City, Vietnam

This study used the Australian Environmental Health Risk Assessment Framework to assess the human health risk of dioxin exposure through foods for local residents in two wards of Bien Hoa City, Vietnam. These wards are known hot-spots for dioxin and a range of stakeholders from central government to local levels were involved in this process. Publications on dioxin characteristics and toxicity were reviewed and dioxin concentrations in local soil, mud, foods, milk and blood samples were used as data for this risk assessment. A food frequency survey of 400 randomly selected households in these wards was conducted to provide data for exposure assessment. Results showed that local residents who had consumed locally cultivated foods, especially fresh water fish and bottom-feeding fish, free-ranging chicken, duck, and beef were at a very high risk, with their daily dioxin intake far exceeding the tolerable daily intake recommended by the WHO. Based on the results of this assessment, a multifaceted risk management program was developed and has been recognized as the first public health program ever to have been implemented in Vietnam to reduce the risks of dioxin exposure at dioxin hot-spots.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy