We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boun...We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method （HAM） to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.展开更多
The spatial distribution of soil physical properties is essential for modeling and understanding hydrological processes. In this study, the different spatial information (the conventional soil types map-based spatial ...The spatial distribution of soil physical properties is essential for modeling and understanding hydrological processes. In this study, the different spatial information (the conventional soil types map-based spatial information (STMB) versus refined spatial information map (RSIM)) of soil physical properties, including field capacity, soil porosity and saturated hydraulic conductivity are used respectively as input data for Water Flow Model for Lake Catchment (WATLAC) to determine their effectiveness in simulating hydrological processes and to expound the effects on model performance in terms of estimating groundwater recharge, soil evaporation, runoff generation as well as partitioning of surface and subsurface water flow. The results show that: 1) the simulated stream flow hydrographs based on the STMB and RSIM soil data reproduce the observed hydrographs well. There is no significant increase in model accuracy as more precise soil physical properties information being used, but WATLAC model using the RSIM soil data could predict more runoff volume and reduce the relative runoff depth errors; 2) the groundwater recharges have a consistent trend for both cases, while the STMB soil data tend to produce higher groundwater recharges than the RSIM soil data. In addition, the spatial distribution of annual groundwater recharge is significantly affected by the spatial distribution of soil physical properties; 3) the soil evaporation simulated using the STMB and RSIM soil data are similar to each other, and the spatial distribution patterns are also insensitive to the spatial information of soil physical properties; and 4) although the different spatial information of soil physical properties does not cause apparent difference in overall stream flow, the partitioning of surface and subsurface water flow is distinct. The implications of this study are that the refined spatial information of soil physical properties does not necessarily contribute to a more accurate prediction of stream flow, and the selection of appropriate soil physical property data needs to consider the scale of watersheds and the level of accuracy required.展开更多
A discontinuous Galerkin finite element method is used to approximate solutions to a classical traffic flow PDE. This PDE is used to model the biological process of transcription; the process of transferring genetic i...A discontinuous Galerkin finite element method is used to approximate solutions to a classical traffic flow PDE. This PDE is used to model the biological process of transcription; the process of transferring genetic information from DNA either to mRNA or to rRNA. The transcription process is punctuated by short, frequent RNAP pauses which are incorporated into the model as traffic lights. These pauses cause a delay in the average transcription process. The DG solution of the nonlinear model is used to calculate the delay and to determine the effect of the pauses on the average transcription time. Numerical error measurements between the DG solution and the true solution （derived by the method of characteristics） are given for a simple model problem. It shows an excellent agreement in a neighborhood away from the shocks as well as C9（Ax） convergence for the delay calculation. Preliminary parameter studies indicate that in a system with multiple pauses both the location and time duration of the pauses can significantly affect the average delay experienced by an RNAP.展开更多
In this article, the fmite element solution of quasi-three-dimensional （quasi-3-D） groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model ...In this article, the fmite element solution of quasi-three-dimensional （quasi-3-D） groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model （FEM） is the results choosing the small time step △t or the large element size L and using the non-diagonal storage matrix. The mechanism for this phenomenon is explained by the negative weighting factor of implicit part in the discretized equations. To avoid spurious oscillation solution, the criteria on the selection of △t and L for quasi-3-D groundwater flow simulations were identified. An application example of quasi-3-D groundwater flow simulation was presented to verify the criteria. The results indicate that temporal discretization scale has significant impact on the spurious oscillations in the finite-element solutions, and the spurious oscillations can be avoided in solving practical quasi-3-D groundwater flow problems if the criteria are satisfied.展开更多
基金supported in part by the Australian Research Council through a Discovery Early Career Researcher Award to Qiang SUN
文摘We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method （HAM） to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.
基金Under the auspices of Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (No. IWHR-SKL-201111)National Natural Science Foundation of China (No. 41101024)
文摘The spatial distribution of soil physical properties is essential for modeling and understanding hydrological processes. In this study, the different spatial information (the conventional soil types map-based spatial information (STMB) versus refined spatial information map (RSIM)) of soil physical properties, including field capacity, soil porosity and saturated hydraulic conductivity are used respectively as input data for Water Flow Model for Lake Catchment (WATLAC) to determine their effectiveness in simulating hydrological processes and to expound the effects on model performance in terms of estimating groundwater recharge, soil evaporation, runoff generation as well as partitioning of surface and subsurface water flow. The results show that: 1) the simulated stream flow hydrographs based on the STMB and RSIM soil data reproduce the observed hydrographs well. There is no significant increase in model accuracy as more precise soil physical properties information being used, but WATLAC model using the RSIM soil data could predict more runoff volume and reduce the relative runoff depth errors; 2) the groundwater recharges have a consistent trend for both cases, while the STMB soil data tend to produce higher groundwater recharges than the RSIM soil data. In addition, the spatial distribution of annual groundwater recharge is significantly affected by the spatial distribution of soil physical properties; 3) the soil evaporation simulated using the STMB and RSIM soil data are similar to each other, and the spatial distribution patterns are also insensitive to the spatial information of soil physical properties; and 4) although the different spatial information of soil physical properties does not cause apparent difference in overall stream flow, the partitioning of surface and subsurface water flow is distinct. The implications of this study are that the refined spatial information of soil physical properties does not necessarily contribute to a more accurate prediction of stream flow, and the selection of appropriate soil physical property data needs to consider the scale of watersheds and the level of accuracy required.
文摘A discontinuous Galerkin finite element method is used to approximate solutions to a classical traffic flow PDE. This PDE is used to model the biological process of transcription; the process of transferring genetic information from DNA either to mRNA or to rRNA. The transcription process is punctuated by short, frequent RNAP pauses which are incorporated into the model as traffic lights. These pauses cause a delay in the average transcription process. The DG solution of the nonlinear model is used to calculate the delay and to determine the effect of the pauses on the average transcription time. Numerical error measurements between the DG solution and the true solution （derived by the method of characteristics） are given for a simple model problem. It shows an excellent agreement in a neighborhood away from the shocks as well as C9（Ax） convergence for the delay calculation. Preliminary parameter studies indicate that in a system with multiple pauses both the location and time duration of the pauses can significantly affect the average delay experienced by an RNAP.
文摘In this article, the fmite element solution of quasi-three-dimensional （quasi-3-D） groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model （FEM） is the results choosing the small time step △t or the large element size L and using the non-diagonal storage matrix. The mechanism for this phenomenon is explained by the negative weighting factor of implicit part in the discretized equations. To avoid spurious oscillation solution, the criteria on the selection of △t and L for quasi-3-D groundwater flow simulations were identified. An application example of quasi-3-D groundwater flow simulation was presented to verify the criteria. The results indicate that temporal discretization scale has significant impact on the spurious oscillations in the finite-element solutions, and the spurious oscillations can be avoided in solving practical quasi-3-D groundwater flow problems if the criteria are satisfied.
