Approaches for modeling longitudinal dispersion in pore-networks

The purpose of this study is to quantify the dispersivity in the longitudinal direction by upscaling pore scale mixing over a network domain and to verify the dispersivity with that obtained through the more rigorous upscaling technique, the Brownian particle tracking model (BPTM). We model a porous medium with a network of pore-units that are comprised of pore bodies and bonds of finite volume. Such a pore-unit is assumed to be a mixing cell with the steady state flow condition for a single fluid. Dispersivity can be obtained by solving the mixing cell model (MCM) for the concentration in each pore-unit and by averaging the concentrations for a large number of pore units (as a function of time and space). A minimal size of network that ascertains an asymptotic value of dispersivity was determined and verified with large size pore networks. This numerically computed dispersivity is compared with the results from the BPTM for the same porous medium and flow conditions. We show that the dispersivity obtained from the MCM is equally reliable for the heterogeneous pore-networks and can be estimated as a function of pore size heterogeneity. For homogeneous networks with the MCM, the iteration time step plays an important role. On the other hand, for networks with the BPTM, the assumption of intra-bond velocity profile affects the results.     

分数布朗运动的小波分析

给出了分数布朗运动的连续和离散小波分析，讨论了有关的性质，并将结果用于分维估值、分数布朗运动小波变换系数的相关性研究等方面．     

北京城市下垫面的非均匀性度量研究

城市下垫面非均匀性度量研究对于改进中尺度数值模式、提高城市气象预报准确率具有重要意义.基于分形布朗运动理论和Landsat-TM卫星遥感图像,估算了2011年北京典型下垫面类型个例和整个空间区域的分数维,由此来度量北京城市下垫面的非均匀性特征.研究结果显示:分数维能有效度量北京城市下垫面的非均匀程度,典型下垫面类型的分数维高低顺序为商业区 >大型居民区 >城市绿地 >农田>林地 >水体;北京六环内区域及郊区城镇地表非均匀特征明显,分数维一般在2.50以上,北京城市中心(二环内)存在一个分数维相对低值区,二环—四环之间区域分数维普遍较高,在2.70以上,五环以外分数维则不断降低,反映出北京城市下垫面非均匀性从中心向外呈低—高—低的空间分布;下垫面类型中建筑用地、绿地、未利用地、农田、林地和水体的平均分数维分别为2.71、2.62、2.55、2.38、2.30和2.28,分数维值的高低反映了城市下垫面类型的非均匀程度大小,对定量描述城市边界层参数的复杂特征具有参考意义.     

Stochastic models for the completeness of stratigraphic sections

Properties of stratigraphic completeness are determined here from a Brownian motion model of sediment accumulation. This avoids flaws inherent in application of a discrete-time random walk to the time span, rather than thickness, of sediment layers. Both discrete and continuous models show that the concept of stratigraphic completeness is meaningful only when the time scale is specified. From the discrete model, not surprisingly, completeness improves with increasing relative frequency and average thickness of depositional increments and the error of completeness estimation should decrease for longer sections. The continuous model shows that two dimensionless products determine the probability that a given time interval will be recorded by some preserved sediment. The first is the ratio of the age of the interval to its time span; the second is the product of the square root of the time span and ratio of the mean to the standard deviation of accumulation rate. Expected completeness is the average of these probabilities for all successive intervals of the given time span. For long sections, completeness may be estimated from the second dimensionless product alone. The two dimensionless products are sufficient to predict the relationship of accumulation rate to time span, the distribution of bed thickness, and the weak association of completeness and section thickness.     

Impact of fractional probability distributions on statistics of hydraulic conductivity,dynamics of groundwater flow and solute transport at a low-permeability site

The fractional Brownian motion (fBm) and fractional Lévy motion (fLm) can easily describe the geometry and the statistical structure of hydraulic conductivity (K) for real-world. However, the fBm and fLm models have not been systematically evaluated when building the K field for a low-permeability site. In this study, both the fBm and fLm are used to simulate the low-K field at NingCheGu (NCG), Tianjin, China. Groundwater flow and solute transport are then computed using MODFLOW and MT3DMS, respectively, and the influence of the fBm/fLm models for K on groundwater flow and solute transport is discussed. Results show that the fLm fits better the statistics of the low-K medium than fBm, and the random logarithmic K (LnK) field generated by fLm is more stable because the resultant LnK field captures more of the measured properties at the field site than that generated by fBm. In contrast, the LnK generated by fBm is more likely to form both high-K channels and low-K barriers. The fBm therefore predicts more extreme behaviours in flow and transport, including the preferential flow, low-concentration blocks and solute retention. The overall groundwater renewal period and solute travel time for the fLm simulation are slightly shorter than those for fBm. The impacts of the fLm and fBm models on the statistics of the resultant LnK fields and the dynamics of groundwater flow and solute transport revealed by this study shed light on the selection and evaluation of the fractional probability distribution models in capturing the K fields for low-K media.     

断层的大地震复发概率研究

本文以布朗过程时间物理模型为基础, 以地震孕育过程为研究主线, 计算了中国大陆地区主要活动断层在不同预测时段内的强震复发概率, 进而对断层的地震危险性进行了研究。 结果表明: 鲜水河断裂带、 阿尔金断裂带、 东昆仑断裂带、 小江断裂带这4条断层的强震复发概率值显著高于其他断裂带, 反映了这些断层所处地区的应力积累水平高于其他地区, 应属于未来可能复发强震的危险地带。     

隐伏金属矿床上升气流微粒特征、形成及迁移

结合地球化学和纳米科学技术的理论和研究方法,研究隐伏金属矿床有关微粒的形成、迁移和特征。对十多个金属矿床的研究表明,隐伏金属矿体地表沉积物中上升气流微粒样品有单个微粒和微粒聚合体,单个微粒形态有球状、近球状、不规则状、规则多边形、长柱状,微粒有晶质、非晶质和部分晶质。聚合体形态一般是不规则状、球状和近球状。它们的矿物成分主要有自然Au、自然Cu、氯化物、氧化物、硫酸盐、氢氧化物等。成矿元素Au、Cu可以自然金属或自然合金形式存在,Cu、Pb、Zn等成矿元素可以氧化物或硫酸盐等形式存在,也可以存在于氧化物、氢氧化物、氯化物、硫酸盐等微粒中作为杂质元素,这些是隐伏金属矿体的指示微粒。成矿期后,与隐伏金属矿体有关微粒主要形成于断层作用、氧化作用和生物作用。在上升气流中,微粒呈“布朗运动”。     

From A to B,randomly: a point-to-point random trajectory generator for animal movement

For applications in animal movement, we propose a random trajectory generator (RTG) algorithm that combines the concepts of random walks, space-time prisms, and the Brownian bridge movement model and is capable of efficiently generating random trajectories between a given origin and a destination point, with the least directional bias possible. Since we provide both a planar and a spherical version of the algorithm, it is suitable for simulating trajectories ranging from the local scale up to the (inter-)continental scale, as exemplified by the movement of migrating birds. The algorithm accounts for physical limitations, including maximum speed and maximum movement time, and provides the user with either single or multiple trajectories as a result. Single trajectories generated by the RTG algorithm can be used as a null model to test hypotheses about movement stimuli, while the multiple trajectories can be used to create a probability density surface akin to Brownian bridges.     

浅析DEM分形特征

以图幅为分析单元,选择立方体覆盖法和分形布朗法对所选区域进行分形计算,并比较了两种分形算法。     

Development of FBMINC model for particle diffusion in fluids

An accurate particle tracking method using FBMINC （new fractional Brownian motion） is outlined. It generates non-Fickian diffusion rather than Fickian diffusion as traditional particle tracking model does. The FBMINC model is based on fractional Brownian motion （fl3m） which is generalization of regular Brownian motion. The two models of fBms （FBM model and FBMINC model） were explored and the differences of the two models are compared from the three aspects： the standard deviation of each step, the small memory and the effect of the number of particles in the cloud. The results show the FBMINC model is a better model as it produces more accurate statistics. The effect of simple shear dispersion for both Brownian and fBm was investigated. The power law scaling of fBm shear dispersion was correctly identified. In addition, a scaling coettieient was found numerically. The FBMINC model is then used for producing both superdiffusive and subdiffusive particle paths, therefore, the non-Fickian diffusion of soil particle clouds can be modelled. The particle clouds represent soil contaminant are released in an idealised coastal bay and the fBm particle tracking method is used for simulation the particle cloud spreading in the bay. There is a noticeable increase in the spreading rate of the cloud. In addition, owning to the spreading rate of the cloud, a noticeable part of it has escaped the bay area and transported downstream. The variation of the Hurst exponent can lead to an area of the flow being affected by a contaminant cloud which is not picked up by the regular Brownian motion models. The purpose of this paper is to bring soil transport engineers a new angle on soil particle transport research in fluids. Using FBM1NC particle tracking model allows more flexibility in simulation of diffusion in soil contaminant spread in coastal bay or ocean surface.