scholarly journals A spatial structural derivative model for ultraslow diffusion

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 121-127 ◽  
Author(s):  
Wei Xu ◽  
Wen Chen ◽  
Ying-Jie Liang ◽  
Jose Weberszpil
Keyword(s):  
Mathematical Modeling ◽  
Analytical Solution ◽  
Diffusion Equation ◽  
Exponential Function ◽  
Equation Model ◽  
Structural Function ◽  
Logarithmic Function ◽  
Mean Squared Displacement ◽  
Physical And Mathematical Modeling

This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function ex is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function ex in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.

Analytical solution for soil water redistribution during evaporation process

2013 ◽  
Vol 68 (12) ◽  
pp. 2545-2551 ◽  
Author(s):  
Jidong Teng ◽  
Noriyuki Yasufuku ◽  
Qiang Liu ◽  
Shiyu Liu
Keyword(s):  
Analytical Solution ◽  
Water Content ◽  
Soil Water ◽  
Exponential Function ◽  
Experimental Result ◽  
Water Evaporation ◽  
Evaporation Process ◽  
Climate Control ◽  
Water Redistribution ◽  
Control Apparatus

Simulating the dynamics of soil water content and modeling soil water evaporation are critical for many environmental and agricultural strategies. The present study aims to develop an analytical solution to simulate soil water redistribution during the evaporation process. This analytical solution was derived utilizing an exponential function to describe the relation of hydraulic conductivity and water content on pressure head. The solution was obtained based on the initial condition of saturation and an exponential function to model the change of surface water content. Also, the evaporation experiments were conducted under a climate control apparatus to validate the theoretical development. Comparisons between the proposed analytical solution and experimental result are presented from the aspects of soil water redistribution, evaporative rate and cumulative evaporation. Their good agreement indicates that this analytical solution provides a reliable way to investigate the interaction of evaporation and soil water profile.

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