Analytical model of magnetic reconnection in the presence of shock waves attached to a current sheet

We consider a stationary two-dimensional model of magnetic reconnection in plasma. The model includes a current sheet and four MHD shock waves attached to its endpoints. The solution to the problem has been found in an analytical form that admits of efficient numerical implementation. We analyze in detail the structure of the magnetic field in the reconnection region and its variation with model parameters.     

Functional behaviour of pedotransfer functions in soil water flow simulation

Soil hydraulic parameter values for large‐scale modelling cannot be obtained by direct methods. Pedotransfer functions (PTFs) that relate soil hydraulic properties (SHPs) to generally available soil texture data may provide an alternative. A considerable number of PTF models has been developed, the application of three recent PTFs is evaluated. As a first step sets of SHPs derived from the PTFs are compared with measured sets of SHPs for three sites. No good agreement was found statistically between measured and PTF results or between PTF results. As a second step and from a practical point of view results for three hydrologically functional variables were compared and evaluated. The three selected functional variables are saturated hydraulic conductivity, k₀, in relation to infiltration excess runoff, available soil water amounts for evapotranspiration and water table depth for a specified upward flux or capillary rise. Derived k₀ distributions from PTFs show substantially less variance than from the measured data at all three sites. This can have a considerable impact on infiltration excess runoff, depending on the actual rainfall regime. Simulated available soil water amounts for evapotranspiration for some combinations of PTFs and sites are close to those obtained for measured SHPs, however, no consistency in results can be detected. Water table depths for specified upward flux densities using PTF derived SHPs are generally deeper than those based on measured SHPs and means a potentially higher water availability. Overall, differences in capillary rise among the selected PTFs and between measured and PTF based results are again inconsistent and show no clear relationship with soil texture. Finally, as a third step, effective SHPs were calculated by using spatially averaged texture as PTF input representing areal average behaviour. For these effective SHPs the calculated effective values for the three selected functional variables appear to be close to the areally averaged values obtained with step 2. The selected functional variables thus appear to depend linearly on the PTFs over the range for which the data are representative. This suggests that for our specific PTFs areal mean or effective values for the three functional variables can be obtained fairly accurately from a single measurement of a bulk collection of soil samples as input. Copyright © 2003 John Wiley & Sons, Ltd.     

Vulnerability of three spatially variable soil groups for solute leaching

Solute leaching in unsaturated soil is influenced by the variability in hydraulic functions (water retention and conductivity) that govern the flow process. Variability in measured soil hydraulic functions of a coarse-, medium- and fine-textured soil group was quantified with the scaling theory of similar media. Solute leaching in these soils was calculated with Monte Carlo simulation assuming, successively, hydraulic conductivity, K, volumetric water content, 0, and pressure head, h, to be constant. In addition to variability in hydraulic functions, variability in the solute retardation factor was also taken into account. To examine this effect five solutes were considered: a conservative solute (chloride), a non-retarded solute subject to decay (nitrate), a retarded solute that does not decay (cadmium) and two organic solutes which are retarded but have different sorption and decay parameters (the pesticide atrazine and a chlorinated hydrocarbon). The numerical results obtained with Monte Carlo simulation were in a number of instances verified with analytical solutions. The three soil groups distinguished showed considerable differences in vulnerability for leaching of the five solutes, emphasizing the importance of the effect of variability in soil hydraulic functions when studying solute leaching. Numerical and analytical results showed good agreement. Therefore, in relatively simple situations analytical solutions are attractive. However, in complicated situations, analytical solutions are cumbersome and numerical solutions are the only realistic alternative.     

General planetary theory in elliptic functions

It is shown that the first-order general planetary theory, i.e. the theory without secular terms, developed in (Brumberg and Chapront, 1973) may be re-constructed and presented by the series in powers of the eccentricity and inclination variables with the closed form coefficients expressed in terms of elliptic functions. The intermediate solution of the zero degree in eccentricities and inclinations has been given explicitly with the aid of elliptic functions and the Hansen type quadratures with trigonometric function kernels. In determining the first and higher degree terms in eccentricities and inclinations one meets the Hansen type quadratures with elliptic function kernels. The secular evolution is described by the autonomous polynomial differential system.     

Discriminant analysis as a method of predicting mineral occurrence potentials in central Norway

The statistical technique of discriminant analysis is used to define target areas for detailed general exploration given only general geological information and aeromagnetic anomaly blues. In the test area, located in Central Norway, on-going exploration surveys have revealed the presence of mineralization; however, it still has not been determined if any of the sites will beeconomically feasible. The area was divided into 1400 1-km × 1-km cells by superimposing square grid on 1:50,000-scale geological and geophysical maps. Later the area was divided into two subareas based on major differences in each area's geology. A number of geological natures and the aeromagnetic anomaly values were coded systematically in each cell. The cells representing an advanced degree of exploration were chosen as control cells in each of the subareas. The geological and geophysical parameters were transformed, by means of relatively simple transformations, to produce near-normal frequency distributions. A discriminant function was then obtained by discriminant analysis to divide the control data into two groups, cells with presence of mineral occurrence and cells without mineral occurrence. the discriminant function obtained for the control area proved to be relevant both geologically and statistically. Consequently, the discriminant equation was applied to cells outside the control area. The cells were assigned to one of the two groups by entering the geologic factors pleasured from the maps into the discriminant model. The exploration potential of a large number of cells was evaluated by this procedure. To test the results, field work including geochemical sampling was carried out in the cells with highest probability of mineral occurrance The field work results have shown that the application of discriminant analysis to geological information at 1:50,000 scale with 1-km × 1-km cells combined with a careful selection of techniques for transforming the variables is a feasible method for predicting gaeralization, and as such could become a valuable tool for mining exploration.This paper was presented at Symposium 116.3, Quantitative Strategy for Exploration, held as part of the 25th International Geological Congress, Sydney, Australia, August 1976.     

热-流-固耦合建模过程

热-流-固耦合作用是存在高度非线性的复杂耦合作用。有关这三场的耦合作用研究在地石油工程、热资源开发、地下核废料存储安全、采矿工程等很多领域有着非常重要的应用价值。由于研究对象的不同,热流固耦合模型的形式存在差异,建立符合实际问题的三场耦合模型十分困难,文中在国内外学者对三场耦合模型理论研究的进展状况的基础上,通过一个例子,介绍了用adina建立模型的过程。