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复杂科学与工程问题仿真的隐式微积分建模 被引量:5
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作者 陈文 《计算机辅助工程》 2014年第5期1-6,共6页
针对现代科学与工程仿真遇到愈来愈多难以用经典微积分建模方法描述的复杂问题,在理论研究和工程实践中提出各种含有多个经验参数的唯象偏微分方程模型,或直接采用统计模型来描述.这些模型的物理意义不是很清楚且参数多,其中部分人为参... 针对现代科学与工程仿真遇到愈来愈多难以用经典微积分建模方法描述的复杂问题,在理论研究和工程实践中提出各种含有多个经验参数的唯象偏微分方程模型,或直接采用统计模型来描述.这些模型的物理意义不是很清楚且参数多,其中部分人为参数缺乏物理意义.因此,利用描述问题的基本解或统计分布构造隐式微积分控制方程.这里"隐式"是指可以不需要或难以推导出该控制方程的显式微积分表达式.该方法仅需微积分控制方程的基本解和相应的边界条件就可以进行数值仿真计算.称该方法为隐式微积分方程建模.考虑多相软物质热传导的幂律行为,采用分数阶里斯(Riesz)势核函数为基本解构造稳态问题的隐式分数阶微积分方程模型并进行数值验证.此外,以列维(Lévy)稳态统计分布的概率密度函数为基本解,构造反常扩散现象的隐式分数阶微积分方程模型.该研究的主要数值计算技术基于径向基函数的配点方法. 展开更多
关键词 隐式微积分方程 唯象 统计 基本解 经验参数
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工程高校《微积分与数学建模》课程改革实践记
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作者 贾晓峰 《煤炭高教研究》 1997年第2期11-13,39,共4页
近年来,随着电子计算机及有关技术的飞速进步和广泛普及,它在社会各行业中的作用越来越重要。由于电子计算机用于解决问题的核心技术——软件技术本质上不过是数学原理的“程式化”,而且近年来数学用于解决实际问题的手段也在不断发... 近年来,随着电子计算机及有关技术的飞速进步和广泛普及,它在社会各行业中的作用越来越重要。由于电子计算机用于解决问题的核心技术——软件技术本质上不过是数学原理的“程式化”,而且近年来数学用于解决实际问题的手段也在不断发展和进步,已逐渐改变了以往在工程、经济等实用领域只扮演辅助的、潜在的、从属的角色的地位,而在解决许多有关问题的过程中提任重要角色甚至主角,这就使数学作为“技术”的特征越来越明显了。 展开更多
关键词 工程高校 《微积分与数学 课程改革 教学内容 教学方法
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分形微积分算子的定义及其应用
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作者 陈文 王发杰 杨旭 《计算机辅助工程》 2016年第3期1-4,12,共5页
基于隐式微积分建模方法,提出分形维空间基本解的概念,从而定义分形维上的微积分算子,用以描述分形材料的各种力学行为.分形微积分算子极大地推广经典的连续介质力学微积分建模方法的使用范围,是分形导数概念的进一步发展.运用奇异边界... 基于隐式微积分建模方法,提出分形维空间基本解的概念,从而定义分形维上的微积分算子,用以描述分形材料的各种力学行为.分形微积分算子极大地推广经典的连续介质力学微积分建模方法的使用范围,是分形导数概念的进一步发展.运用奇异边界法成功地数值模拟分形维拉普拉斯算子方程唯象描述的分形材料势问题. 展开更多
关键词 分形微积分算子 隐式微积分方程 唯象 基本解 分形导数
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雷诺方程中湍流涡黏性的Richardson势算子本构模型
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作者 陈文 《计算机辅助工程》 2016年第4期4-6,共3页
证明三维湍流Richardson扩散方程中的变系数拉普拉斯算子是基本解为r-7/3的一个势算子,并称其为Richardson势算子,其中,r是空间中两点的欧几里得距离.基于Kolmogorov标度律和湍流快扩散(super-diffusion)理论,运用隐式微积分方程建模方... 证明三维湍流Richardson扩散方程中的变系数拉普拉斯算子是基本解为r-7/3的一个势算子,并称其为Richardson势算子,其中,r是空间中两点的欧几里得距离.基于Kolmogorov标度律和湍流快扩散(super-diffusion)理论,运用隐式微积分方程建模方法提出雷诺方程中的Richardson势算子湍流涡黏性本构方程. 展开更多
关键词 瑞流 涡黏性本构 Richardson扩散方程 基本解 Richardson势算子 隐式微积分方程
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近场动力学理论在区域地面沉降建模中的应用研究 被引量:1
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作者 张可 宫辉力 +8 位作者 李小娟 朱琳 王彻 陈蓓蓓 和继军 郭琳 吕明苑 闫倩蒙 李江涛 《地球信息科学学报》 CSCD 北大核心 2023年第1期49-62,共14页
地面沉降是由自然和人类活动共同作用导致的缓变性地质灾害,是区域可持续发展的重要影响因素。以往地面沉降在建模时需要地裂缝等不连续结构的位置、走向、深度等信息,在构建微分方程模拟时需假设模型连续,这对开展地面沉降-地裂缝-地... 地面沉降是由自然和人类活动共同作用导致的缓变性地质灾害,是区域可持续发展的重要影响因素。以往地面沉降在建模时需要地裂缝等不连续结构的位置、走向、深度等信息,在构建微分方程模拟时需假设模型连续,这对开展地面沉降-地裂缝-地面塌陷一体化模拟带来一定的局限性。于2000年出现的近场动力学理论提出以积分形式描述材料受力过程,方法具有无需先验知识与连续性假设的优点,在材料的疲劳、损伤、断裂等模拟研究中展现出良好的应用前景。本文综述了其在岩石水力压裂、滑坡、饱水岩土材料等领域的研究进展;提出了应用近场动力学进行区域地面沉降建模求解的一般方法;结合InSAR技术获取的沉降信息、三维地震频谱谐振勘探技术获取的地下结构与密度信息等,提出了模型的反演调参与优化方法。以北京东部梨园-台湖镇-张家湾镇区域为实验区,建立了其4 km×6 km范围、0.2 km深度的近场动力学地面沉降模型,以实验区地下水位月均下降速率为边界条件,对2007—2010年地面沉降过程进行模拟。模拟结果与实测值的平均绝对误差为18 mm,表明近场动力学在地面沉降建模中有较好的适用性。 展开更多
关键词 近场动力学 地面沉降 地裂缝 积分建模 INSAR技术 三维地震频谱谐振勘探技术
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Combined migration velocity model-building and its application in tunnel seismic prediction 被引量:1
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作者 巩向博 韩立国 +3 位作者 牛建军 张晓培 王德利 杜立志 《Applied Geophysics》 SCIE CSCD 2010年第3期265-271,293,294,共9页
We propose a combined migration velocity analysis and imaging method based on Kirchhoff integral migration and reverse time migration,using the residual curvature analysis and layer stripping strategy to build the vel... We propose a combined migration velocity analysis and imaging method based on Kirchhoff integral migration and reverse time migration,using the residual curvature analysis and layer stripping strategy to build the velocity model.This method improves the image resolution of Kirchhoff integral migration and reduces the computations of the reverse time migration.It combines the advantages of efficiency and accuracy of the two migration methods.Its application in tunnel seismic prediction shows good results.Numerical experiments show that the imaging results of reverse time migration are better than the imaging results of Kirchhoff integral migration in many aspects of tunnel prediction.Field data show that this method has efficient computations and can establish a reasonable velocity model and a high quality imaging section.Combination with geological information can make an accurate prediction of the front of the tunnel geological structure. 展开更多
关键词 Tunnel prediction migration velocity analysis Kirchhoff integral migration reverse time migration velocity model-building
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Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors
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作者 王鼎 吴瑛 《Journal of Central South University》 SCIE EI CAS 2013年第11期3116-3130,共15页
Compared to the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE employing fourth-order cumulants (referred to as FOC-RARE) is capable of dealing with more sources and... Compared to the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE employing fourth-order cumulants (referred to as FOC-RARE) is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en'ors than that of the SOS-RARE from the resolution point of view. 展开更多
关键词 performance analysis rank reduction estimator (RARE) fourth-order cumulants (FOC) spatial spectrum angle resolution probability unexpected modeling errors
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Spatiotemporal distribution model for zinc electrowinning process and its parameter estimation 被引量:1
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作者 邓仕钧 阳春华 +2 位作者 李勇刚 朱红求 伍铁斌 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第9期1968-1976,共9页
This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Con... This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Considering the inverse diffusion of such ions in the electrolyte,the dynamic distribution of ions is described by the axial dispersion model.A parameter estimation strategy based on orthogonal approximation has been proposed to estimate the unknown parameters in the process model.Different industrial data sets are used to test the effectiveness of the spatiotemporal distribution model and the proposed parameter estimation approach.The results demonstrate that the analytical model can effectively capture the trends of the electrolysis reaction in time and thus has the potential to implement further optimization and control in the ZEWP. 展开更多
关键词 zinc electrowirming spatiotemporal distribution model parameter estimation orthogonal approximation
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Modeling and Simulation of the Hydrodynamic Behavior in a High-Density Downer Reactor
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作者 Parinya Khongprom Sunun Limtrakul Terdthai Vatanatham 《Journal of Chemistry and Chemical Engineering》 2012年第10期930-935,共6页
The hydrodynamic behavior in a high-density downer reactor was studied. A two-fluid model based on the kinetic theory of granular flow with a k-ε turbulent model was developed to simulate the flow behavior in the sys... The hydrodynamic behavior in a high-density downer reactor was studied. A two-fluid model based on the kinetic theory of granular flow with a k-ε turbulent model was developed to simulate the flow behavior in the system. This simulation achieved an averaged solid fraction in the bed as high as 18% in this operating regime. The flow development in high-density downer consists of 3 regions, which are first acceleration, second acceleration, and fully developed regions. In the fully developed region, the lateral distribution of the solid volume fraction is low and almost uniform in the center region with a high density peak near the wall region. Gas and solid velocities gradually increase toward the wall and form a peak near the wall region. In addition, the solid volume fraction, gas and solid velocities increase with solid circulation rate. 展开更多
关键词 High-density downer reactor HYDRODYNAMIC SIMULATION two-fluid model kinetic theory of granular flow.
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Modelling and Hazard Analysis for Contaminated Sediments Using STAMP Model and STPA Tool 被引量:1
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作者 Karim Hardy Franck Guarnieri 《Journal of Energy and Power Engineering》 2013年第3期496-500,共5页
The goal of this article is dual: first, introducing a new model of accident named STAMP (systems-theoretic accident modeling and processes); then applying the model to an innovative process for the treatment of co... The goal of this article is dual: first, introducing a new model of accident named STAMP (systems-theoretic accident modeling and processes); then applying the model to an innovative process for the treatment of contaminated substances and the re-use of treated substances. This article is a demonstration for a need of a new tool to take into account hazards and safety within socio-technical systems. 展开更多
关键词 Model of accident safety engineering ENVIRONMENT contaminated substances re-use.
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局部结构导数及其应用 被引量:1
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作者 陈文 梁英杰 黑鑫东 《固体力学学报》 CAS CSCD 北大核心 2016年第5期456-460,共5页
经典的导数建模方法刻画了特定物理量对时间或空间的变化率,较少直接考虑复杂系统介观时间-空间结构对其物理力学行为的重要影响.论文通过引入结构函数,提出了一种局部结构导数建模方法,以克服传统方法的不足.结构函数刻画了系统的时间... 经典的导数建模方法刻画了特定物理量对时间或空间的变化率,较少直接考虑复杂系统介观时间-空间结构对其物理力学行为的重要影响.论文通过引入结构函数,提出了一种局部结构导数建模方法,以克服传统方法的不足.结构函数刻画了系统的时间-空间特征,实际上是一个时空变换,基于其上的结构导数能够描述复杂问题介观时空结构与特定物理量的因果关系,减少模型参数,降低计算成本.我们可通过问题的广义基本解或已知统计分布的概率密度函数,推导出其系统的结构函数.两类应用实例表明,基于对数结构函数的结构导数方法可以描述软物质中的特慢扩散现象,也可用来建立以Weibull分布的概率密度函数为结构函数的可靠性结构导数扩散方程. 展开更多
关键词 结构导数 隐式微积分建模 分数阶微积分 分形导数 Weibull概率密度函数
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Global modeling 2^(nd)-order ionospheric delay and its effects on GNSS precise positioning 被引量:5
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作者 ZHANG HongPing LV HaiXia +1 位作者 LI Min SHI Chuang 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2011年第6期1059-1067,共9页
Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurem... Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurements can only eliminate the first-order term of ionospheric delay,while the effect of the second-order term on GNSS observations may be several centimeters.In this paper,two models,the International Reference Ionosphere (IRI) 2007 and International Geomagnetic Reference Field (IGRF) 11 are used to estimate the second-order term through the integral calculation method.Besides,the simplified single layer ionosphere model in a dipole moment approximation for the earth magnetic field is used.Since the traditional integral calculation method requires large calculation load and takes much time,it is not convenient for practical use.Additionally,although the simplified single layer ionosphere model is simple to implement,it results in larger errors.In this study,second-order term ionospheric correction formula proposed by Hoque (2007) is improved for estimating the second-order term at a global scale.Thus,it is more practicable to estimate the second-order term.More importantly,its results have a higher precision of the sub-millimeter level for a global scale in normal conditions.Compared with Hoque's original regional correction model,which calculates coefficients through polynomial fitting of elevation and latitudes,this study proposes a piece-wise look-up table and interpolation technique to modify Hoque model.Through utilizing a table file,the modified Hoque model can be conveniently implemented in an engineering software package,like as PANDA in this study.Through applying the proposed scheme for the second-order ionospheric correction into GNSS precise positioning in both PPP daily and epoch solutions,the results have shown south-shift characteristics in daily solution at a global scale and periodic change with VTEC daily variation in epoch positioning solution. 展开更多
关键词 ionospheric delay second-order ionospheric correction GNSS precise positioning
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Computation of kinetic isotope effects for enzymatic reactions
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作者 GAO JiaLi 《Science China Chemistry》 SCIE EI CAS 2011年第12期1841-1850,共10页
We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy... We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy surface is represented by a combined quantum mechanical and molecular mechanical(QM/MM) potential in which the bond forming and breaking processes are modeled by electronic structure theory,and(2) a free energy perturbation method in path integral simulation is used to determine both kinetic isotope effects(KIEs).In this approach,which is called the PI-FEP/UM method,a light(heavy) isotope is mutated into a heavy(light) counterpart in centroid path integral simulations.The method is illustrated in the study of primary and secondary KIEs in two enzyme systems.In the case of nitroalkane oxidase,the enzymatic reaction exhibits enhanced quantum tunneling over that of the uncatalyzed process in water.In the dopa delarboxylase reaction,there appears to be distinguishable primary carbon-13 and secondary deuterium KIEs when the internal proton tautomerism is in the N-protonated or in the O-protonated positions.These examples show that the incorporation of quantum mechanical effects in enzyme kinetics modeling offers an opportunity to accurately and reliably model the mechanisms and free energies of enzymatic reactions. 展开更多
关键词 combined QM/MM path integral simulations PI-FEP/UM kinetic isotope effects and enzyme kinetics
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