Fractional Reaction-Diffusion Equations     

R. K. Saxena  A. M. Mathai  H. J. Haubold 《Astrophysics and Space Science》2006,305(3):289-296

In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen et al. (1999) for anomalous diffusion and del-Castillo-Negrete et al. (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.  相似文献   

Interpretation of tensor gravity data using an adaptive tilt angle method     

Ahmed Salem  Sheona Masterton  Simon Campbell  J. Derek Fairhead  Jade Dickinson  Colm Murphy 《Geophysical Prospecting》2013,61(5):1065-1076

Full Tensor Gravity Gradiometry (FTG) data are routinely used in exploration programmes to evaluate and explore geological complexities hosting hydrocarbon and mineral resources. FTG data are typically used to map a host structure and locate target responses of interest using a myriad of imaging techniques. Identified anomalies of interest are then examined using 2D and 3D forward and inverse modelling methods for depth estimation. However, such methods tend to be time consuming and reliant on an independent constraint for clarification. This paper presents a semi‐automatic method to interpret FTG data using an adaptive tilt angle approach. The present method uses only the three vertical tensor components of the FTG data (T_zx, T_zy and T_zz) with a scale value that is related to the nature of the source (point anomaly or linear anomaly). With this adaptation, it is possible to estimate the location and depth of simple buried gravity sources such as point masses, line masses and vertical and horizontal thin sheets, provided that these sources exist in isolation and that the FTG data have been sufficiently filtered to minimize the influence of noise. Computation times are fast, producing plausible results of single solution depth estimates t hat relate directly to anomalies. For thick sheets, the method can resolve the thickness of these layers assuming the depth to the top is known from drilling or other independent geophysical data. We demonstrate the practical utility of the method using examples of FTG data acquired over the Vinton Salt Dome, Louisiana, USA and basalt flows in the Faeroe‐Shetland Basin, UK. A major benefit of the method is the ability to quickly construct depth maps. Such results are used to produce best estimate initial depth to source maps that can act as initial models for any detailed quantitative modelling exercises using 2D/3D forward/inverse modelling techniques.  相似文献   

Elastic analysis of laterally loaded pile in multi-layered soil     

《Geomechanics and Geoengineering》2013,8(3):183-196

An analysis is developed to determine the response of laterally loaded piles in layered elastic media. The differential equations governing pile deflections in different layers due to a concentrated static force and/or moment acting at the pile head are obtained using the principle of minimum potential energy and calculus of variations. The differential equations are solved analytically using the method of initial parameters. Pile deflection, slope of the deformed axis of the pile, bending moment and shear force can be reliably obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. It is observed that soil layering has a definite impact on pile response and must be taken into account for proper analysis and design. The analysis forms the basis for future formulations that can consider stress–strain nonlinearity.  相似文献   

Hyperspectral image noise reduction based on rank-1 tensor decomposition     

《ISPRS Journal of Photogrammetry and Remote Sensing》2013

In this study, a novel noise reduction algorithm for hyperspectral imagery (HSI) is proposed based on high-order rank-1 tensor decomposition. The hyperspectral data cube is considered as a three-order tensor that is able to jointly treat both the spatial and spectral modes. Subsequently, the rank-1 tensor decomposition (R1TD) algorithm is applied to the tensor data, which takes into account both the spatial and spectral information of the hyperspectral data cube. A noise-reduced hyperspectral image is then obtained by combining the rank-1 tensors using an eigenvalue intensity sorting and reconstruction technique. Compared with the existing noise reduction methods such as the conventional channel-by-channel approaches and the recently developed multidimensional filter, the spatial–spectral adaptive total variation filter, experiments with both synthetic noisy data and real HSI data reveal that the proposed R1TD algorithm significantly improves the HSI data quality in terms of both visual inspection and image quality indices. The subsequent image classification results further validate the effectiveness of the proposed HSI noise reduction algorithm.  相似文献   

一种新的岩石非线性黏弹塑性流变模型     

宋勇军  雷胜友  韩铁林 《岩土力学》2012,33(7):2076-2080

借鉴经典元件组合模型的建模思路,将含分数阶微积分的软体元件与弹簧元件串联,结合一个幂函数黏塑性体,提出一种新的四元件非线性黏弹塑性流变模型,并给出该模型的本构方程和蠕变方程,得到在不同应力条件下的蠕变曲线。可以发现,岩石稳定蠕变阶段的非线性渐变过程和加速蠕变阶段蠕变速率的快慢程度可通过调整蠕变参数进行有效地模拟。在较低应力水平时,模型能够有效地刻画岩石的初始蠕变和稳定蠕变;当应力水平超过岩石的长期强度时,能够反映加速蠕变特性。利用该模型对试验数据拟合的结果表明,含有软体元件和幂函数黏塑性体的非线性流变模型能够有效地描述岩石的蠕变特性,减少组合模型中的元件个数和参数数量。  相似文献   

岩石分数阶体积变形模型及其试验研究     

何明明  李宁  朱才辉  陈蕴生 《岩土力学》2016,37(11):3137-3144

为了可以合理地描述岩石的体积变形行为,从分数阶微积分出发,基于分数阶常黏性和变黏性系数Abel黏壶元件,提出了环向-轴向应变分数阶黏壶,构建了岩石在单三轴压缩,松弛及蠕变条件下的分数阶体积应变-轴向应变关系,得到了模型的解析解,新模型可为求解岩石的体积应变提供一种新方法。在完整砂岩、泥岩试样及单裂隙砂岩试样的单三轴压缩、松弛及裂隙花岗岩蠕变试验数据的基础上,通过拟合分析确定了分数阶导数体积-轴向应变关系模型的参数,并进行了参数敏感性分析,揭示了围压、单裂隙倾角、微分阶数及模型参数对体积应变的影响规律。结果表明,利用该黏壶构建的体积-轴向应变关系模型,不仅可以更好地描述岩石体积变形的剪缩、剪胀特性,还能够反映岩石的松弛及蠕变变形特性。  相似文献   

磁偶极子梯度张量的几何不变量及其应用   总被引：4，自引：1，他引：3       下载免费PDF全文

尹刚  张英堂  李志宁  张光  范红波 《地球物理学报》2016,59(2):749-756

磁梯度张量系统姿态的变化将影响梯度场测量和数据解释的精度,使得具有坐标变换不变性特点的张量不变量成为磁梯度张量数据解释的研究热点.本文在对磁偶极子产生的磁梯度张量进行特征值分析的基础上得到了:测量点与磁偶极子位置形成的位置矢量、磁偶极子磁矩矢量与绝对值最小的特征值对应的特征向量垂直;位置矢量和磁矩矢量与最大及最小特征值对应的特征向量共面,且两矢量间的夹角可由磁梯度张量矩阵的特征值表示.最后,将本文所得磁偶极子梯度张量的几何不变量用于磁性目标的跟踪中,取得了较好的实时跟踪效果.  相似文献   

CSAMT的多偶极子源特征与张量测量   总被引：3，自引：3，他引：0       下载免费PDF全文

王显祥  底青云  许诚 《地球物理学报》2014,57(2):651-661

传统的可控源音频大地电磁法电偶源多为单偶极子源,这种源明显缺点是各分量存在明显的弱区,E_x、H_y强的区域,E_y、H_x弱,很难进行360°张角范围内测量和矢量测量.为了克服传统场源布极方式的缺点,本文介绍了由两个偶极子组成的“L”型源,推导了“L”型源各个分量的表达式,并通过一个简单均匀半空间的模型验证了表达式的正确性.通过对“L”型源与偶极子源的辐射花样图和电流矢量图详细对比可知,在CSAMT测量区内多偶极子源遵从矢量合成原则.在此基础上,设计了一种新的信号发射模式,在这种模式下可实现 360°张角范围内各分量不再存在明显弱区.在新的信号发射模式下,可解决矢量测量时信噪比不对等问题,并可减少张量测量时偶极源的布设次数.在“L”型源的基础上,还进行了张量测量的研究,在一个事例中,计算了倾子、二维判别指数、坐标系的旋转等,结果表明张量测量明显优于标量测量,标量测量一般只适用于一维情况,当地质结构呈现二维或三维性时,标量测量结果很有可能给反演结果带来误差.  相似文献   

天体运行的介质层壳与离散轨道引论   总被引：3，自引：3，他引：0  

阎坤 《地球物理学进展》2004,19(4):984-995

采用介质层壳弯曲的唯象方法,在规整三维空间中给出了能量曲率方程及物体间的能量引力形式表述,其引力方程的二个条件解分别与Newton引力理论及Einstein引力理论的有关结果相近．讨论了目前分维微积分在函数方面的局限性,给出了相似扩展方程,随后通过讨论天体运行轨道的基线扩展特征,给出了天体运行的离散轨道方程,并以太阳系行星及部分卫星为例,给出了这些天体运行离散轨道方程的具体表述形式。  相似文献   

采用分数阶导数描述软黏土蠕变的模型   总被引：5，自引：0，他引：5  

何利军  孔令伟  吴文军  张先伟  蔡羽 《岩土力学》2011,32(Z2):239-243

按遗传流变理论来推导软黏土的蠕变模型,提出了一种新的蠕变核函数形式的选取方法,即用修正Burgers模型的导数形式作为蠕变核函数,随着参数取值的不同,该经验模型能模拟蠕变发展到不同阶段的蠕变曲线,探讨了该模型能精确描述软黏土的蠕变变形的原因,模型具有参数少、物理意义明确,适用性强的特点,能有效地描述湛江软黏土的蠕变特性。该研究内容也是对分数阶微积分进行应用研究的一种新的尝试。  相似文献