Numerical simulation based on two-directional freeze and thaw algorithm for thermal diffusion model

Freeze-thaw processes significantly modulate hydraulic and thermal char- acteristics of soil. The changes in the frost and thaw fronts （FTFs） affect the water and energy cycles between the land surface and the atmosphere. Thus, the frozen soil com- prising permafrost and seasonally frozen soil has important effects on the land surface hydrology in cold regions. In this study, a two-directional freeze and thaw algorithm is incorporated into a thermal diffusion equation for simulating FTFs. A local adaptive variable-grid method is used to discretize the model. Sensitivity tests demonstrate that the method is stable and FTFs can be tracked continuously. The FTFs and soil tempera- ture at the Qinghai-Tibet Plateau D66 site are simulated hourly from September 1, 1997 to September 22, 1998. The results show that the incorporated model performs much better in the soil temperature simulation than the original thermal diffusion equation, showing potential applications of the method in land-surface process modeling.

A computational model of the human glucose-insulin regulatory system

Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.