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一类具有不连续源的奇摄动半线性微分方程组边值问题 被引量:1
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作者 包立平 《高校应用数学学报(A辑)》 CSCD 北大核心 2017年第4期413-422,共10页
讨论了一类具有不连续源的奇摄动半线性微分方程组边值问题,构造了形式渐近解.利用Hartman-Nagumo不等式证明了奇摄动半线性微分方程组的解的存在性与唯一性,利用Aumann介值定理,得到了该方程组解的光滑性,并且得到了一致有效估计.
关键词 奇摄动 半线性微分方程组 Hartman-Nagumo不等式 不连续源 Aumann介值定理
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一类带不连续源项的二阶半线性奇摄动Robin边值问题 被引量:3
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作者 林红绪 杨李凡 胡雨欣 《应用数学》 CSCD 北大核心 2015年第1期47-56,共10页
本文研究一类带不连续源项的二阶奇摄动方程Robin边值问题.利用边界层函数法和缝接法,分别构造左、右问题的边界层校正函数,得到奇摄动问题在整个区间上解的渐近行为,证明解的存在性,并对余项进行估计.通过一个典型的例子,验证了本文结... 本文研究一类带不连续源项的二阶奇摄动方程Robin边值问题.利用边界层函数法和缝接法,分别构造左、右问题的边界层校正函数,得到奇摄动问题在整个区间上解的渐近行为,证明解的存在性,并对余项进行估计.通过一个典型的例子,验证了本文结果的正确性. 展开更多
关键词 边界层函数法 缝接法 ROBIN边值问题 不连续源 奇摄动
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具有不连续源项的二阶半线性系统边值问题的奇摄动
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作者 李静 谢峰 《应用数学进展》 2019年第8期1341-1351,共11页
本文讨论了一类带有不连续源项的二阶半线性系统边值问题。首先,用边界函数法和缝接法构造出原问题的形式渐近解;然后运用上下解定理证明形式解的一致有效性。最后给出一个例子验证了结果的有效性。
关键词 边界函数法 缝接法 不连续源 奇摄动
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流体动力学中不连续源项大Reynolds数问题的有限体积法 被引量:1
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作者 蔡新 储理才 《福州大学学报(自然科学版)》 CAS CSCD 北大核心 2007年第3期353-360,共8页
讨论不连续源项大Reynolds数问题,引入2种非均匀网格技术,应用有限体积法构造了数值方法:Sh-ishkin型有限体积法和多过渡点型有限体积法.数值实验显示,2种方法都较好地模拟了边界层和内部层的性质,具有一致收敛的计算效果;多过渡点型有... 讨论不连续源项大Reynolds数问题,引入2种非均匀网格技术,应用有限体积法构造了数值方法:Sh-ishkin型有限体积法和多过渡点型有限体积法.数值实验显示,2种方法都较好地模拟了边界层和内部层的性质,具有一致收敛的计算效果;多过渡点型有限体积法明显优于Farrell所提出的Shishkin有限差分法. 展开更多
关键词 流体动力学 大Reynolds数 不连续源 有限体积法
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Some Challenges of Deep Mining 被引量:19
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作者 Charles Fairhurst 《Engineering》 SCIE EI 2017年第4期527-537,共11页
An increased global supply of minerals is essential to meet the needs and expectations of a rapidly rising world population. This implies extraction from greater depths. Autonomous mining systems, developed through su... An increased global supply of minerals is essential to meet the needs and expectations of a rapidly rising world population. This implies extraction from greater depths. Autonomous mining systems, developed through sustained R&D by equipment suppliers, reduce miner exposure to hostile work environments and increase safety. This places increased focus on "ground control" and on rock mechanics to define the depth to which minerals may be extracted economically. Although significant efforts have been made since the end of World War II to apply mechanics to mine design, there have been both technological and organizational obstacles. Rock in situ is a more complex engineering material than is typically encountered in most other engineering disciplines. Mining engineering has relied heavily on empirical procedures in design for thousands of years. These are no longer adequate to address the challenges of the 21st century, as mines venture to increasingly greater depths. The development of the synthetic rock mass (SRM) in 2008 provides researchers with the ability to analyze the deformational behavior of rock masses that are anisotropic and discontinuous-attributes that were described as the defining characteristics of in situ rock by Leopold Mfiller, the president and founder of the International Society for Rock Mechanics (ISRM), in 1966. Recent developments in the numerical modeling of large-scale mining operations (e.g., caving) using the SRM reveal unanticipated deformational behavior of the rock. The application of massive parallelization and cloud computational techniques offers major opportunities: for example, to assess uncertainties in numerical predictions: to establish the mechanics basis for the empirical rules now used in rock engineering and their validity for the prediction of rock mass behavior beyond current experience: and to use the discrete element method (DEM) in the optimization of deep mine design. For the first time, mining-and rock engineering-will have its own mechanics-based Ulaboratory." This promises to be a major tool in future planning for effective mining at depth. The paper concludes with a discussion of an opportunity to demonstrate the application of DEM and SRM procedures as a laboratory, by back-analysis of mining methods used over the 80-year history of the Mount Lvell Copper Mine in Tasmania. 展开更多
关键词 Deep mining Rock discontinuities Synthetic rock mass Mineral resources Rock mechanics
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Detection of the Lehmann discontinuity beneath Tonga with short-period waveform data from Hi-net 被引量:4
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作者 CHEN Jian ZHOU YuanZe WANG HongCai 《Science China Earth Sciences》 SCIE EI CAS 2014年第8期1953-1960,共8页
The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and co... The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and corresponding geodynamic processes. Vertical waveform data from six earthquakes with focal depths between 75 and 150 km and magnitudes Mb 5.0–6.0 since 2004 were collected from the short-period Hi-net array. Selected waveform data were processed for each event network pair using the Nth-root slant stack method to retrieve the SdP conversion phases from the possible 220 km(Lehmann) discontinuity. The conversion points related to the SdP phases show that there is a clear and flat velocity interface around 230 km, suggesting that there is a sinking of the Lehmann discontinuity beneath Tonga with no obvious undulation. The 230 km depth of the Lehmann discontinuity in this location could be explained by an hypothesis of transition in the deformation mechanism from dislocation creep to diffusion creep. 展开更多
关键词 Lehmann discontinuity Nth-root slant stack Hi-net array Tonga region
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Differential patterns of SH and P wave velocity structures in the transition zone beneath northwestern Tibet 被引量:6
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作者 ZHANG RuiQing WU QingJu +1 位作者 LI YongHua ZENG RongSheng 《Science China Earth Sciences》 SCIE EI CAS 2011年第10期1551-1562,共12页
Triplicate waveform modeling is used to resolve SH (Vs) and P (Vp) wave velocity structures in the upper mantle transition zone (TZ) beneath northwestern (NW) Tibet. Focal depth move out stacking is proposed t... Triplicate waveform modeling is used to resolve SH (Vs) and P (Vp) wave velocity structures in the upper mantle transition zone (TZ) beneath northwestern (NW) Tibet. Focal depth move out stacking is proposed to enhance the identification of triplicate phases, and can be used to test consistency of our data. Our results show that the Vs and Vp structures are decorrelated, and that a large Vs jump occurred across the 660-km discontinuity, with a small Vs gradient above it. Conversely, the Vp model is characterized by a relatively small contrast across the discontinuity, accompanied by a high Vp gradient in the TZ. There seem no significant depth anomalies of the 660-kin discontinuity in both models. The seismic structures in TZ beneath NW Tibet are similar to recent studies beneath the central Qiangtang and western Lhasa terrains. Taking the lower TZ structures under India as references, Vs is normal but Vp appears slightly high, and thus a high ratio of Vp/Vs was indicated beneath NW Tibet. Combined results with experiment information from mineral studies, we suggest that the differential anomalies of Vp and Vs can be attributed to a chemical heterogeneity, such as increased A1 content in the lower TZ. Considering the tectonic evolution of Tibet, the chemical heterogeneity may be associated with subduction or detachment of the Tethys oceanic slab. 展开更多
关键词 mantle transition zone seismic velocity northwestern Tibet
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