数学模型

The main factors affecting the soil-structure interface behaviors were found experimentally and theoretically, including: 1 the thickness of the interface that is five to six times the average grain size of the soil; 2 the aeolotropy of interface, which is responsible for anisotropic response of the stress-strain response of the interface; 3 two physical states, including crashing and compression of the soil near the structure surface, which govern the stress-strain response of the interface strongly; 4 two shear deformation components due to sliding and constraint of the structure surface relative to the soil respectively, which forms the deformation of the interface; 5 the volumetric strain due to dilatancy, which is found to be composed of a reversible dilatancy component and an irreversible dilatancy component. 4. A unified constitutive model of the interface, based on new elasto-plasticity damage theory, was developed. It was confirmed to be effective for the conditions considering monotonic and cyclic shearing, coupling effect of shear and volumetric strains, evolution of physical state, micro-structure aeolotropy of the soil and the resulting aeolotropy of the interface as well as the three normal boundary conditions stated above. 5. 2D and 3D finite element formulations of the present model were derived and incorporated into the FEM codes. They were applied to the evaluation of practical engineering problems with different typical interfaces between soil and structure. The new model was shown to be reasonable and effective.

确定了粗粒土与结构接触面厚度约为5～6倍的平均粒径，首次揭示了接触面的细观结构异向性以及由此所引起的宏观剪切异向性，发现了在单调和往返剪切荷载作用下土颗粒破碎和剪切压密两种物态变化机制共同支配着接触面力学性质的变化，通过细观分析证实了接触面的变形可分解为一般同时发生的土与结构交界面上的滑移变形以及结构面位移约束范围之内土体本身的剪切变形两部分，观测到接触面受剪时表现出明显的相对法向位移，并可分解为可逆性和不可逆性两个分量；(4)建立了第一个能够统一地描述单调与往返剪切特性、剪应变与体应变耦合特性、细观结构和宏观剪切异向性以及土颗粒破碎等物态变化特性的土与结构接触面弹塑性损伤本构数学模型，并采用多种法向边界条件复杂加载路径的试验成果验证了新模型的合理性和有效性；(5)提出了新模型的二、三维有限元格式并结合实际边值问题进行了应用计算分析，比较了不同接触面本构模型对计算结果的影响，证实了新模型及其有限元格式不仅能够合理地描述土与结构接触面的主要力学特性，还能够较好地反映土体与结构物在接触面处的滑移、脱开等不连续现象。

Consequently the diathermancy was strengthened, the effect of heat transfer was improved and the flow and combustion process in the boiler has become much better. First, in this thesis the burn characteristic of the rubbish and the process of combustion in the chain boiler has been studied. A series of mathematic model has been given. This thesis carefully introduced the principle and formula of the turbulent flow model、two-equation model、radiation model、dispersed phase model and standard wall function method. The software FLUENT has been applied to simulate the temperature、pressure、velocity and mass fraction of species in the boiler furnace and stokehole. The analysis and the comparison have been done. The calculation results indicate agreement with the fact and the studies both here and abroad.

首先，本文针对SZL10-1.25-MJ造纸垃圾焚烧锅炉，结合其燃料的特性，对垃圾的燃烧特性以及层燃炉中垃圾的焚烧过程进行分析；给出一套完整的垃圾锅炉炉内传热数学模型，并分别详细阐述了湍流流动模型、双方程模型、辐射传热模型、离散相模型及标准壁面函数的原理及计算公式；借助于Fluent软件平台对炉膛内的温度场、速度场、组分浓度场及炉膛出口的温度分布、速度分布、组分浓度分布等进行数值模拟，分别从定性和定量的角度与实际情况进行了比较，得到了较满意的结果；模拟结果与国内外的很多研究能较好符合。

What this paper finished mainly work as follows: Five-phase hybrid step motor driver system with fixed-chopping frequency and constant total current driving is fully described. Mathematical model of the system, included the current control circuit, power driving circuit and five-phase hybrid stepping motor is established. The steady modeling of the system is established and studied. Based on the steady modeling of the system, dynamic modeling of the system is studied and single step response characteristic is constructed with MATLAB/Simulink. The simulation results, which is certified by the theory analysis, coincide with the theory analysis.

本文主要完成的工作包括几个方面：对五相混合式步进电动机恒频斩波恒总流驱动系统进行了完整的描述；建立了包括电流控制电路、功率驱动电路以及五相混合式步进电动机在内的恒频斩波恒总流驱动系统的完整的数学模型；基于MATLAB/Simulink建立了恒频斩波恒总流驱动系统稳态仿真模型，并进行了仿真；在建立其稳态仿真模型的基础上，对动态模型进行研究，并借助于MATLAB/Simulink工具建立了恒频斩波恒总流驱动系统单步响应特性的仿真模型并对其单步响应特性进行了仿真研究，仿真结果与理论分析相符。

The main problems researched in the dissertation and achievements are as follows: The dissertation explains the science background and the theoretical and actual meaning of the task. The progress and the problems of the flow imaging technique are briefly explained. The advantages of electrical capacitance tomography are discussed. The paper discusses the formation and operating principle of ECT, and builds up the definite mathematical model by detail theoretical analyse, and establishes the Finite Element Model of the system by changing the finite boundary value problem of ECT into equivalence variation problem according to variation principle. On the basis of the FEM of the system, the paper builds the finite element model of the capacitance sensitivity field distribution and programs its finite element simulation software and proves the validity of the FEM of the ECT from different aspects. With the FEM and the qualitative analyse of the effect of each structural parameter of the capacitance transducer on its capability, this paper optimizes the structural parameters of the capacitance transducer, and obviously improves its capability. The compare of the simulated result with the static experimental result shows that the error of them is less than 0.9%.

其主要研究内容包括：阐述课题研究的学术背景及其理论与实际意义，概括总结出流动层析成像技术的发展现状和存在的问题，指出电容层析成像技术的优点；讨论电容层析成像系统的组成及工作原理，进行详尽的理论分析，以变分原理为基础，将ECT的有限元边值问题转换为等价的变分问题，从而建立系统的有限元模型；在系统有限元模型的基础上，建立敏感场的数学模型，编制有限元的仿真软件，并从不同角度证明电容层析成像系统有限元模型的正确性；利用有限元模型，定性地分析电容传感器各结构参数对其性能的影响，并对传感器结构参数进行优化设计，使其性能得到明显的改善。8电极ECT系统的仿真和静态实验结果的比较表明，它们之间的相对误差小于0。

Department of Systems Science and Mathematics Math.

刊载计算机在数值分析、概论率、数论、人工智能等数学研究中的使用，计算机的数学模型，计算机与数学相互应用及其在环境科学、生态学、生物学和城市系统领域的应用方面的原始论文、评论等。

This subject combines the basic principle of the calculus of variation and and reply and change basic theories of the function according to fracture mechanics, use mechanics, mathematics knowledge to set up corresponding mathematical model, derive out a series of mechanics and mathematics theory formula, work out procedure carry on number value calculate, to include edge crackle round stress intensity factor of component go on, ask, solve.

本课题结合变分法的基本原理并根据断裂力学和复变函数的基本理论，运用力学、数学知识建立相应的数学模型，推导出一系列的力学及数学理论公式，编制程序进行数值计算，对含边缘裂纹圆形构件的应力强度因子进行求解。

The way on how to compute the optimal math＇s model is given and the survival condition of optimal root is discussed.

研究了一种特殊的订单生产——准时制下非核心企业的生产，分析了计划范围内的成本，并分别就各种成本给出求解公式，尤其在能力波动费用的求解上，引进了符号函数，解决了在任意单位时间段内能力累计的数学表达以及能力波动费用的数学求解，在以上基础上给出了最佳生产的数学模型，给出了求解方法，讨论了最优解的存在条件，最后，讨论了在APS中的应用前景。

The comparison of results from mathematical model and physical model in vacuum tank for simulation of transient in air cushion surge chamber shows that the similarity laws of various quantities in model test may have influences on the dissimilarity of test results.

本文对比了含气垫式调压室的引水系统，数学模型计算和减压模型试验结果，分析了各种减压模型相似因素对试验结果的影响，认为引水系统管道内含气量、模型的缩尺效应、气室内空气的状态变化以及减压试验条件等的相似性都会造成物理模型试验结果的误差。

A new mathematical model with only three parameters is proposed to describe the whole TEG.

提出了一个新的三参数的数学模型表达血栓弹力图，研究了模型参数变化对模型曲线的影响及模型参数与血栓弹力图临床参数间的对应关系，给出了模型参数确切的生理、病理意义。

Besides, the effects of light and temperature on stomata have not been modelled in any mechanistic model.

在第一章中，通过综述气孔对环境因子响应的数学模型的文献，发现目前对描述和模拟气孔行为的经验模型和机理模型是脱节的，可供选择的气孔模型还不能满足理论分析和实际应用的需要；经验模型没有机理的支持，不能用于理论分析，没有普适性；机理模型都过于复杂，而且其中的一些参数难以确定，所以它们还只能作定性模拟，不能作定量预测，另外，对于光强和温度的影响还未见有人模拟。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐