In this work, one-dimensional approximation of internal erosion taking place in a soil made from sand and clay mixture was considered. The clay phase that is susceptible to experience erosion under water flow discharge was assumed to be small. A new erosion law fixing the initiation threshold of erosion and integrating the effect of soil consolidation on internal erosion was proposed. Conversely, the effect of erosion on elastic soil deformation was also integrated through damage mechanics concepts. Asymptotic expansion of the coupled equations in terms of a perturbation parameter linked to the total amount of internal erosion that is likely to occur has been performed. This has enabled to view the internal erosion phenomenon occurring inside the soil as a perturbation affecting the classical soil consolidation equation, and further to evaluate the critical discharge gradient for which internal erosion starts. Equations at order zero that are provided by the asymptotic expansion were exactly integrated while an adequate finite difference scheme was introduced to solve the equations at order one. A parametric study was conducted after that in order to assess effects of the main factors on internal erosion and soil deformation. 相似文献
Aiming at understanding the regional O3 problem and the impacts of city to rural areas, ambient peroxyacetyl nitrate (PAN) and peroxypropionyl nitrate (PPN) were measured by an on-line instrument at a back garden site (BGS), and a receptor site for urban plume from Guangzhou city. The highest mixing ratios for PAN and PPN were 3.9 and 0.7 ppbv, respectively. PAN and PPN had a similar diurnal pattern as that of O3. As revealed by the slope of the linear regression line between PPN and PAN, anthropogenic volatile organic compounds (AVOCs) dominated photochemical O3 production most of the time. From the correlation between PAN and O3, the regional background level of O3 was derived to be 28 ± 15 ppbv. Two night-time plumes containing elevated PAN and O3 were observed, and the backward-trajectory analysis supported the transport of urban plume from Guangzhou city. Based on the temporal variation of PPN/PAN, two day-time episodes were also selected to discuss the influence from Guangzhou. 相似文献
Nanoscale photonic systems involve a broad variety of light–matter interaction regimes beyond the diffraction limit and have opened the path for a variety of application opportunities in sensing, solid‐state lighting, light harvesting, and optical signal processing. The need for numerical modeling is central for the understanding, control, and design of plasmonic and photonic nanostructures. Recently, the increasing sophistication of nanophotonic systems and processes, ranging from simple plasmonic nanostructures to multiscale and complex photonic devices, has been calling for highly efficient numerical simulation tools. This article reviews the state of the art in numerical methods for nanophotonics and describes which method is the best suited for specific problems. The widespread approaches derived from classical electrodynamics such as finite differences in time domain, finite elements, surface integral, volume integral, and hybrid methods are reviewed and illustrated by application examples. Their potential for efficient simulation of nanophotonic systems, such as those involving light propagation, localization, scattering, or multiphysical systems is assessed. The numerical modeling of complex systems including nonlinearity, nonlocal and quantum effects as well as new materials such as graphene is discussed in the perspective of actual and future challenges for computational nanophotonics.