Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

Study of the flood control scheduling scheme for the Three Gorges Reservoir in a catastrophic flood

The Three Gorges Project is the world's largest water conservancy project. According to the design standards for the 1,000‐year flood, flood diversion areas in the Jingjiang reach of the Yangtze River must be utilized to ensure the safety of the Jingjiang area and the city of Wuhan. However, once these areas are used, the economic and life loss in these areas may be very great. Therefore, it is vital to reduce this loss by developing a scheme that reduces the use of the flood diversion areas through flood regulation by the Three Gorges Reservoir (TGR), under the premise of ensuring the safety of the Three Gorges Dam. For a 1,000‐year flood on the basis of a highly destructive flood in 1954, this paper evaluates scheduling schemes in which flood diversion areas are or are not used. The schemes are simulated based on 2.5‐m resolution reservoir topography and an optimized model of dynamic capacity flood regulation. The simulation results show the following. (a) In accord with the normal flood‐control regulation discharge, the maximum water level above the dam should be not more than 175 m, which ensures the safety of the dam and reservoir area. However, it is necessary to utilize the flood diversion areas within the Jingjiang area, and flood discharge can reach 2.81 billion m³. (b) In the case of relying on the TGR to impound floodwaters independently rather than using the flood diversion areas, the maximum water level above the dam reaches 177.35 m, which is less than the flood check level of 180.4 m to ensure the safety of the Three Gorges Dam. The average increase of the TGR water level in the Chongqing area is not more than 0.11 m, which indicates no significant effect on the upstream reservoir area. Comparing the various scheduling schemes, when the flood diversion areas are not used, it is believed that the TGR can execute safe flood control for a 1,000‐year flood, thereby greatly reducing flood damage.     

Developing constitutive models from EPR‐based self‐learning finite element analysis

A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self‐learning simulation (SelfSim). Self‐learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self‐learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim‐based finite element analysis. These include a total stress‐strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress‐strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR‐based self‐learning finite element method. The EPR‐based self‐learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.     

A CASE STUDY ON CONCENTRATION AND DECENTRALIZATION：BEHAVIOR AND DYNAMIC MECHANISM OF SPATIAL EVOLUTION IN METROPOLITAN AREA，NANJING，CHINA

In rapid socio-economic development,the process of concentration and dispersal of various elements tends to be more dramatic,tremendously influencing the shaping and transformation of the space in metropolitan area.Survey of spatial concentration and decentralization has thus become a basic method in examining metropolitan spatial evolution.In this research,three elements were selected as the essential indicators of the process:demographic density distribu-tion,employment density distribution and business office location.Performance of these elements in Nanjing City was exam-ined historically.As Nanjing City could be regarded as a representative of metropolitan areas in China,its situation large-ly suggestes the general characteristics in similar areas of China.Hence based on the investigation of Nanjing City,four general implications were highlighted.First ,metropolitan areas in China are in a violent process and shift of spatial concentra-tion and decentralization.Second,from now to at least the near future,concentration will continue to be the central fea-ture.Third,the landscape of metropolitan areas basically exhibits a dual structure character.The gap in environmental and ecological qualities among different districts will continue for a long time.Fourth,Central Business District (CBD) is playing an important role in helping to convert the traditionally single-centered city structure into a polycentric one.     

地壳对海洋潮汐的响应

应用三维动态有限元方法研究了中国北部地区的地壳对邻近的渤海与黄海海平面变化的响应。虽然此应力场过于微弱不足以引发地震，但发现应力集中的位置及应力场变化较大的位置恰好与某些现代地震的震中一致。这一结果表明研究地壳对广泛分布的载荷的响应对研究区域地震构造是有帮助的。     

MATLAB在运用系统建模处理南海气象数据过程中应用

介绍了MATLAB语言特点和系统建模方法的基本理论.根据南海气象数据的实际建模处理过程,给出了建模的详细步骤及其MATLAB实现过程以及MATLABTM的主要实现程序.试验讨论和结果表明利用MATLAB语言可以方便地对南海气象数据用系统建模方法进行建模和处理,MATLAB在运用系统建模法处理南海气象数据方面具有明显的优越性.     

Simulations of multimode bolometric interferometers

We describe a procedure for the numerical modelling of astronomical interferometers, with particular relevance to far-infrared and submillimetre wavelengths. The scheme is based on identifying a set of modes that carry power from the sky to the detector. The procedure is extremely general, and can be used to model scalar or vector fields, in any state of coherence and polarization, the only limitation being that the propagation of a coherent field through the system be described by an integral transform, a constraint that is in practise always met.
We present simulations of ideal, multimode two-dimensional interferometers, and show that the modal theory reproduces the correct behaviour of both Michelson and Fizeau interferometers. We calculate simulated visibility data for a multimode bolometric Michelson interferometer, with a synthesized source, and produce a dirty map, recovering the original source with the usual artefacts associated with interferometers.