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The mild slope equation in its linear and non-linear forms is used for the modelling of nearshore wave propagation. The finite difference method is used to descretize the governing elliptic equations and the resulting system of equations is solved using GMRES-based iterative method. The original GMRES solution technique of Saad and Schultz is not directly applicable to the present case owing to the complex coefficient matrix. The simpler GMRES algorithm of Walker and Zhou is used as the core solver, making the upper Hessenberg factorization unneccessary when solving the least squares problem. Several preconditioning-based acceleration strategies are tested and the results show that the GMRES-based iteration scheme performs very well and leads to monotonic convergence for all the test-cases considered. 相似文献
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直立顺层边坡的黏弹性稳定分析 总被引:5,自引:1,他引:4
直立边坡的失稳与岩体的流变性质密切相关,其在一定载荷作用下失稳表现出延迟特性。采用自重作用下的梁柱力学模型,考虑岩石的流变性,给出了不同材料模型下直立边坡的极限坡高及其分析方法。 相似文献
35.
A.R. Kacimov Yu.V. Obnosov 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2002,82(6):363-376
Soil slopes satisfying the condition of a constant exit gradient (constant Darcian velocity) and the seepage face (isobaricity) condition are found by complex analysis. For an empty drainage trench, soil is infinitely deep and the flow domain is bounded by two branches of a phreatic surface and the trench contour. The problem is solved by conformal mapping of the Zhukovskii domain (half‐plane) onto the hodograph domain (lune). The ultimately stable seepage face and the inflow rate are determined as functions of a specified exit gradient. With decreasing of the gradient the trench flattens. If the gradient is 1, the depth‐width aspect ratio of the trench reaches 0.21. Similar conformal mapping of a lune in the hodograph plane on a half‐strip in the complex potential plane is used to solve the problem of a phreatic surface flow from a soil channel, whose equipotential contour satisfies the condition of constant “entrance” gradient. For a dam slope, the flow domain is underlain by an impermeable bottom and the hodograph is a circular triangle with a unit‐gradient circle as the slope image. The Polubarinova‐Kochina method of analytical differential equations is modified to reconstruct the complex coordinate and the complex potential as a function of an auxiliary variable. The resulting slope of unit exit gradient has a depth‐width ratio of 1.22. 相似文献
36.
Crisólogo Dolores-Flores Martha Iris Rivera-López Javier García-García 《International Journal of Mathematical Education in Science & Technology》2019,50(3):369-389
This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration. 相似文献
38.
新疆天山北坡典型研究区融雪期地物光谱特征分析 总被引:1,自引:0,他引:1
地物的波谱特性乃是整个遥感技术的物理基础,更是遥感技术应用尤其是定量遥感的基石。由于融雪期静态地物与冰-雪-水等动态地物交互存在,地物光谱特征更为复杂。选取了新疆天山北坡乌鲁木齐河流域以及军塘湖流域作为典型研究区,采用美国CID公司生产的CI700便携式野外光谱仪,通过2006年到2009年融雪期大量的野外调查和实地测量,获取了新疆天山北坡典型研究区融雪期典型地物包括各种积雪、冰、水以及土壤的光谱曲线及其变化规律,并对其进行了光谱特征分析。结果表明,融雪期虽然地物类型较为单一,但是因为积雪-冰-水-土壤复杂系统的交互式影响,地物的光谱特性及其变化均较为复杂,给融雪期地表参数的定量遥感研究带来了较大的挑战。对于融雪期复杂地物光谱的系列观测及特征分析无论是对于地物光谱特征基础研究还是定量遥感应用研究均具有重要意义。 相似文献
39.
Dispersion compensating fibers (DCFs) are being widely used as dispersion compensation techniques because of its superior characteristics. This work reports the theoretical modelling of a single mode DCF having W-shaped shallow as well as deeply depressed clad profile. The DCFs have been designed and optimized by suitable adjusting different fiber parameters such as, central relative index difference (Δ+), inner core radius (a), depression depth parameter (ρ), normalized end position of the depressed clad (p), etc. at a given spot size . The figure of merit (FOM) characteristics including the bend loss as well as other losses associated with fiber manufacturing technique have been thoroughly investigated. Performances of these DCFs for recent wavelength division multiplexing (WDM) transmission system have also been discussed. By adjusting different fiber parameters, the effective core area (Aeff) of the above DCFs can be controlled to minimize the effect of non-linearities on them. 相似文献
40.
1 Introduction Stressanalystsareofteninterestedinthederivativesofthedisplacementratherthanthedisplacementitself ,becausestrainsandhencestressesarefirst orderderivativesofdisplacement.Thederivativescanbeobtainednumericallyfromthedisplacementdatabutthep… 相似文献