Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fi...Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fickian second law. The new diffusion flux (NDF) taking it into account shows that we can systematically understand the problems of one-way diffusion, impurity diffusion and self-diffusion as a special case of the interdiffusion. Applying the NDF to the interdiffusion problem between metal plates, it is clarified that the Kirkenkall effect is caused by |J0(t) > and also that the interdiffusion coefficients in alloy can be easily obtained. The interdiffusion problems are reasonably solved regardless of the intrinsic diffusion conception. Thus the NDF to replace the Fickian first law is an essential equation in physics.展开更多
Non-Darcian flow has been well documented for fractured media, while the potential non-Darcian flow and its driven factors in field-scale discrete fracture networks (DFNs) remain obscure. This study conducts Monte Car...Non-Darcian flow has been well documented for fractured media, while the potential non-Darcian flow and its driven factors in field-scale discrete fracture networks (DFNs) remain obscure. This study conducts Monte Carlo simulations of water flow through DFNs to identify non-Darcian flow and non-Fickian pressure propagation in field-scale DFNs, by adjusting fracture density, matrix hydraulic conductivity, and the general hydraulic gradient. Numerical simulations and analyses show that interactions of the fracture architecture with the hydraulic gradient affect non-Darcian flow in DFNs, by generating and adjusting complex pathways for water. The fracture density affects significantly the propagation of hydraulic head/pressure in the DFN, likely due to fracture connectivity and flow channeling. The non-Darcian flow pattern may not be directly correlated to the non-Fickian pressure propagation process in the regional-scale DFNs, because they refer to different states of water flow and their controlling factors may not be the same. Findings of this study improve our understanding of the nature of flow in DFNs.展开更多
A new dynamic model for non-Fickian diffu-sion of calcium spark in cardiac myocytes was developed by introducing time lags on the basis of the microscale mass transport theory. Numerical simulation showed that the siz...A new dynamic model for non-Fickian diffu-sion of calcium spark in cardiac myocytes was developed by introducing time lags on the basis of the microscale mass transport theory. Numerical simulation showed that the size of the calcium spark produced by the new dynamic model was larger than that of Fick diffusion and was in more agreement with experimental results. In addition, the time lags of the calcium spark in cardiac myocytes were about 0.1—0.8 ms. These results can be used to understand the mechanism of calcium spark diffusion in cardiac myocytes.展开更多
文摘Based on the divergence theorem, we reveal that the Fickian first law relevant to the diffusion flux |J(t,x,y,z) > in the time and space is incomplete without an integral constant |J0(t) > for the integral of Fickian second law. The new diffusion flux (NDF) taking it into account shows that we can systematically understand the problems of one-way diffusion, impurity diffusion and self-diffusion as a special case of the interdiffusion. Applying the NDF to the interdiffusion problem between metal plates, it is clarified that the Kirkenkall effect is caused by |J0(t) > and also that the interdiffusion coefficients in alloy can be easily obtained. The interdiffusion problems are reasonably solved regardless of the intrinsic diffusion conception. Thus the NDF to replace the Fickian first law is an essential equation in physics.
文摘Non-Darcian flow has been well documented for fractured media, while the potential non-Darcian flow and its driven factors in field-scale discrete fracture networks (DFNs) remain obscure. This study conducts Monte Carlo simulations of water flow through DFNs to identify non-Darcian flow and non-Fickian pressure propagation in field-scale DFNs, by adjusting fracture density, matrix hydraulic conductivity, and the general hydraulic gradient. Numerical simulations and analyses show that interactions of the fracture architecture with the hydraulic gradient affect non-Darcian flow in DFNs, by generating and adjusting complex pathways for water. The fracture density affects significantly the propagation of hydraulic head/pressure in the DFN, likely due to fracture connectivity and flow channeling. The non-Darcian flow pattern may not be directly correlated to the non-Fickian pressure propagation process in the regional-scale DFNs, because they refer to different states of water flow and their controlling factors may not be the same. Findings of this study improve our understanding of the nature of flow in DFNs.
基金supported by the National Natural Science Foundation of China(Grant No.10372007)Bio-x center of Peking University and Japan Society for the Promotion of Science(PO2325).
文摘A new dynamic model for non-Fickian diffu-sion of calcium spark in cardiac myocytes was developed by introducing time lags on the basis of the microscale mass transport theory. Numerical simulation showed that the size of the calcium spark produced by the new dynamic model was larger than that of Fick diffusion and was in more agreement with experimental results. In addition, the time lags of the calcium spark in cardiac myocytes were about 0.1—0.8 ms. These results can be used to understand the mechanism of calcium spark diffusion in cardiac myocytes.
