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.

Creep properties and a creep equation of delay outburst coal and its adjacent mudstone

The study of the creep properties of coal and its adjacent mudstone is very important for understanding the mechanism of delay outburst coal. The samples of delay outburst coal and its adjacent mudstone collected from Yongshanqiao mine were used to carry out triaxial creep tests. The influence of confining pressure and axial compression on the creep test was analyzed. An accelerated creep model was constructed in parallel with a nonlinear viscous component and plastic component. It is connected with the traditional Burges creep model in series. A creep model which can describe the nonlinear viscoelastic-plastic creep model of rock was established and the corresponding creep equation was derived.According to the results of the creep test, the related parameters of the equation were fitted. The results show that, under the same confining pressure, instantaneous creep strain, creep strain of deceleration phase and constant rate creep of the coal and its adjacent mudstone are increased with an increase in the deviatoric stress. But at the same axial pressure, all of the above decrease with an increase of confining pressure. The duration time of the deceleration creep phase increases with the increase in the deviatoric stress. The theoretical values of the creep equation are in good agreement with the experimental results. It indicates that the creep properties of the delayed outburst coal and its adjacent mudstone can be well described by the creep model established in this paper.

Fiducial generalized p-values for testing zero-variance components in linear mixed-effects models

Linear mixed-effects models are widely used in analysis of longitudinal data. However, testing for zero-variance components of random effects has not been well-resolved in statistical literature, although some likelihood-based procedures have been proposed and studied. In this article, we propose a generalized p-value based method in coupling with fiducial inference to tackle this problem. The proposed method is also applied to test linearity of the nonparametric functions in additive models. We provide theoretical justifications and develop an implementation algorithm for the proposed method. We evaluate its finite-sample performance and compare it with that of the restricted likelihood ratio test via simulation experiments. We illustrate the proposed approach using an application from a nutritional study.