Modeling

Geometric ModelingGeometric modeling is a crucial aspect of computer graphics and design, allowing for the creation of realistic and visually appealing 3D models. It involves the representation of geometric shapes and structures in a digital format, which can then be manipulated and rendered on a computer screen. Geometric modeling is used in a wide range of applications, including video games, animation, virtual reality, and industrial design. One of the key benefits of geometric modeling is its ability to accurately represent complex shapes and structures that would be difficult or impossible to create by hand. By using mathematicalequations and algorithms, designers can create detailed and realistic 3D modelsthat can be viewed from any angle and manipulated in real-time. This level of precision and flexibility is essential for many modern design projects, where accuracy and realism are paramount. In addition to its practical applications, geometric modeling also plays a crucial role in the artistic and creative process. Designers and artists can use geometric modeling tools to explore new ideas, experiment with different shapes and forms, and push the boundaries of traditional design aesthetics. By combining mathematical precision with artistic vision, geometric modeling allows for the creation of stunning and innovative visual experiences that captivate and inspire audiences. Furthermore, geometric modeling is an essential tool for collaboration and communication in design and engineering fields. By creating digital models that can be easily shared and manipulated, designers and engineers can work together more effectively, exchanging ideas and feedback in real-time. This collaborative approach not only streamlines the design process but also ensures that all stakeholders are on the same page, reducing the risk of miscommunication and errors. Moreover, geometric modeling has revolutionized the manufacturing industry, allowing for the rapid prototyping and production of complex parts and components. By creating digital models of products and machines, engineers can simulate their behavior under various conditions, identify potential issues, and make necessary adjustments before moving to production. This level of virtual testing and validation not only saves time and money but also improves the overall quality and reliability of the final product. Overall, geometric modeling is a versatile and powerful tool that has transformedthe way we design, create, and communicate. From its practical applications in computer graphics and engineering to its artistic and creative potential, geometric modeling continues to push the boundaries of what is possible in the world of design. By embracing this technology and harnessing its capabilities, designers and engineers can unlock new opportunities for innovation and discovery, shaping the future of design and manufacturing for years to come.。

Book reviewModeling,Simulation,and Control of Flexible Manufacturing Systems ±A Petri Net Approach;Meng Chu Zhou;Kurapati Venkatesh;Yushun Fan;World Scienti®c,Singapore,19991.IntroductionA ¯exible manufacturing system (FMS)is an automated,mid-volume,mid-va-riety,central computer-controlled manufacturing system.It can be used to produce a variety of products with virtually no time lost for changeover from one product to the next.FMS is a capital-investment intensive and complex system.In order to get the best economic bene®ts,the design,implementation and operation of FMS should be carefully made.A lot of researches have been done regarding the modeling,simulation,scheduling and control of FMS [1±6].From time to time,Petri net (PN)method has also been used as a tool by di erent researcher in studying the problems regarding the modeling,simulation,scheduling and control of FMS.A lot of papers and books have been published in this area [7±14].``Modeling,Simulation,and Control of Flexible Manufacturing Systems ±A PN Approach''is a new book written by Zhou and Venkatesh which is focused on studying FMS using PN as a systematic method and integrated tool.The book's contents can be classi®ed into four parts.The four parts are introduction part (Chapter 1to Chapter 4),PNs application part (Chapter 5to Chapter 8),new research results part (Chapter 9to Chapter 13),and future development trend part (Chapter 14).In the introduction part,the background,motivation and objectives of the book are described in Chapter 1.The brief history of manufacturing systems and PNs is also presented in Chapter 1.The basic de®nitions and problems in FMS design and implementation are introduced in Chapter 2.The authors divide FMS related problems into two major areas ±managerial and technical.In Chapter 4,basic de®nitions,properties,and analysis techniques of PNs are presented,Chapter 4can be used as the fundamentals of PNs for those who are not familiar with PN method.In Chapter 3,the authors presented their approach to studying FMS related prob-lems,the approach uses PNs as an integrated tool and methodology in FMS design and implementation.In Chapter 3,various applications in modeling,analysis,sim-ulation,performance evaluation,discrete event control,planning and scheduling of FMS using PNs are presented.Through reading the introduction part,the readers can obtain basic concepts and methods about FMS and PNs.The readers can also get a clear picture about the relationshipbetween FMS and PNs.Mechatronics 11(2001)947±9500957-4158/01/$-see front matter Ó2001Elsevier Science Ltd.All rights reserved.PII:S 0957-4158(00)00057-X948Book review/Mechatronics11(2001)947±950The second part of the book is about PNs applications.In this part,various applications of using PNs in solving FMS related problems are introduced.FMS modeling is the basis for simulation,analysis,planning and scheduling.In Chapter5, after introduction of several kinds of PNs,a general modeling method of FMS using PNs is given.The systematic bottom-up and top-down modeling method is pre-sented.The presented method is demonstrated by modeling a real FMS cell in New Jersey Institute of Technology.The application of PNs in FMS performance analysis is introduced in Chapter 6.The stochastic PNs and the time distributions are introduced in this Chapter. The analysis of a¯exible workstation performance using the PN tool called SPNP developed at Duke University is given in Section6.4.In Chapter7,the procedures and steps involved for discrete event simulation using PNs are discussed.The use of various modeling techniques such as queuing network models,state-transition models,high-level PNs,object-oriented models for simulations are brie¯y explained.A software package that is used to simulate PN models is introduced.Several CASE tools for PNs simulations are brie¯y intro-duced.In Chapter8,PNs application in studying the di erent e ects between push and pull paradigms is shown.The presented application method is useful for the selection of suitable management paradigm for manufacturing systems.A manufacturing system is modeled considering both push and pull paradigms in Section8.3which is used as a practical example.The general procedures for performance evaluation of FMS with pull paradigm are given in Section8.4.The third part of the book is mainly the research results of the authors in the area of PNs applications.In Chapter9,an augmented-timed PN is put forward. The proposed method is used to model the manufacturing systems with break-down handling.It is demonstrated using a¯exible assembly system in Section9.3. In Chapter10,a new class of PNs called Real-time PN is proposed.The pro-posed PN method is used to model and control the discrete event control sys-tems.The comparison of the proposed method and ladder logic diagrams is given in Chapter11.Due to the signi®cant advantages of Object-oriented method,it has been used in PNs to de®ne a new kind of PNs.In Chapter12,the authors propose an Object-oriented design methodology for the development of FMS control software.The OMT and PNs are integrated in order to developreusable, modi®able,and extendible control software.The proposed methodology is used in a FMS.The OMT is used to®nd the static relationshipamong di erent objects.The PN models are formulated to study the performance of the FMS.In Chapter12,the scheduling methods of FMS using PNs are introduced.Some examples are presented for automated manufacturing system and semiconductor test facility.In the last Chapter,the future research directions of PNs are pointed out.The contents include CASE tool environment,scheduling of large production system,su-pervisory control,multi-lifecycle engineering and benchmark studies.Book review/Mechatronics11(2001)947±950949 mentsAs a monograph in PNs and its applications in FMS,the book is abundant in contents.Besides the rich knowledge of PNs,the book covers almost every aspects regarding FMS design and analysis,such as modeling,simulation,performance evaluation,planning and scheduling,break down handling,real-time control,con-trol software development,etc.So,the reader can obtain much knowledge in PN, FMS,discrete event system control,system simulation,scheduling,as well as in software development.The book is a very good book in the combinations of PNs theory and prac-tical applications.Throughout the book,the integrated style is demonstrated.It is very well suited for the graduate students and beginners who are interested in using PN methods in studying their speci®c problems.The book is especially suited for the researchers working in the areas of FMS,CIMS,advanced man-ufacturing technologies.The feedback messages from our graduate students show that compared with other books about PNs,this book is more interested and easy to learn.It is easy to get a clear picture about what is PNs method and how it can be used in the FMS design and analysis.So,the book is a very good textbook for the graduate students whose majors are manufacturing systems, industrial engineering,factory automation,enterprise management,and computer applications.Both PNs and FMS are complex and research intensive areas.Due to the deep understanding for PNs,FMS,and the writing skills of the authors,the book has good advantages in describing complex problems and theories in a very easy read and understandable fashion.The easy understanding and abundant contents enable the book to be a good reference book both for the students and researchers. Through reading the book,the readers can also learn the new research results in PNs and its applications in FMS that do not contained in other books.Because the most new results given in the book are the study achievements of the authors,the readers can better know not only the results,but also the background,history,and research methodology of the related areas.This would helpthe researchers who are going to do the study to know the state-of-art of relevant areas,thus the researchers can begin the study in less preparing time and to get new results more earlier.As compared to other books,the organization of the book is very application oriented.The aims are to present new research results in FMS applications using PNs method,the organization of the book is cohesive to the topics.A lot of live examples have reinforced the presented methods.These advantages make the book to be a very good practical guide for the students and beginners to start their re-search in the related areas.The history and reference of related research given in this book provides the reader a good way to better know PNs methods and its applications in FMS.It is especially suited for the Ph.D.candidates who are determined to choose PNs as their thesis topics.950Book review/Mechatronics11(2001)947±9503.ConclusionsDue to the signi®cant importance of PNs and its applications,PNs have become a common background and basic method for the students and researchers to do re-search in modeling,planning and scheduling,performance analysis,discrete event system control,and shop-¯oor control software development.The book under re-view provides us a good approach to learn as well as to begin the research in PNs and its application in manufacturing systems.The integrated and application oriented style of book enables the book to be a very good book both for graduate students and researchers.The easy understanding and step-by-step deeper introduction of the contents makes it to be a good textbook for the graduate students.It is suited to the graduated students whose majors are manufacturing system,industrial engineering, enterprise management,computer application,and automation.References[1]Talavage J,Hannam RG.Flexible manufacturing systems in practice:application,design,andsimulation.New York:Marcel Dekker Inc.;1988.[2]Tetzla UAW.Optimal design of¯exible manufacturing systems.New York:Springer;1990.[3]Jha NK,editor.Handbook of¯exible manufacturing systems.San Diego:Academic Press,1991.[4]Carrie C.Simulation of manufacturing.New York:John Wiley&Sons;1988.[5]Gupta YP,Goyal S.Flexibility of manufacturing systems:concepts and measurements.EuropeanJournal of Operational Research1989;43:119±35.[6]Carter MF.Designing¯exibility into automated manufacturing systems.In:Stecke KE,Suri R,editors.Proceedings of the Second ORSA/TIMS Conference on FMS:Operations Research Models and Applications.New York:Elsevier;1986.p.107±18.[7]David R,Alla H.Petri nets and grafcet.New York:Prentice Hall;1992.[8]Zhou MC,DiCesare F.Petri net synthesis for discrete event control of manufacturing systems.Norwell,MA:Kluwer Academic Publishers;1993.[9]Desrochers AA,Al-Jaar RY.Applications of petri nets in manufacturing systems.New York:IEEEPress;1995.[10]Zhou MC,editor.Petri nets in¯exible and agile automation.Boston:Kluwer Academic Publishers,1995.[11]Lin C.Stochastic petri nets and system performance evaluations.Beijing:Tsinghua University Press;1999.[12]Peterson JL.Petri net theory and the modeling of systems.Englewood Cli s,NJ:Prentice-Hall;1981.[13]Resig W.Petri nets.New York:Springer;1985.[14]Jensen K.Coloured Petri Nets.Berlin:Springer;1992.Yushun FanDepartment of Automation,Tsinghua UniversityBeijing100084,People's Republic of ChinaE-mail address:*****************。

BIM的全拼是Building Information Modeling，中文翻译最为贴切的、也被大家所认可的名称为：建筑信息模型。

这些建筑模型的数据在建筑信息模型中的存在是以多种数字技术为依托，从而以这个数字信息模型作为各个建筑项目的基础，去进行各个相关工作。

建筑工程与之相关的工作都可以从这个建筑信息模型中拿出各自需要的信息，即可指导相应工作又能将相应工作的信息反馈到模型中。

建筑信息模型不是简单的将数字信息进行集成，它还是一种数字信息的应用，并可以用于设计、建造、管理的数字化方法，这种方法支持建筑工程的集成管理环境，可以使建筑工程在其整个进程中显著提高效率、大量减少风险。

在建筑工程整个生命周期中，建筑信息模型可以实现集成管理，因此这一模型既包括建筑物的信息模型，同时又包括建筑工程管理行为的模型。

将建筑物的信息模型同建筑工程的管理行为模型进行完美的组合。

因此在一定范围内，建筑信息模型可以模拟实际的建筑工程建设行为，例如：建筑物的日照、外部维护结构的传热状态等。

同时BIM可以四维模拟实际施工，以便于在早期设计阶段就发现后期真正施工阶段所会出现的各种问题，来提前处理，为后期活动打下坚固的基础。

在后期施工时能作为施工的实际指导，也能作为可行性指导，以提供合理的施工方案及人员，材料使用的合理配置，从而来最大范围内实现资源合理运用。

当前建筑业已步入计算机辅助技术的引入和普及，例如CAD的引入，解决了计算机辅助绘图的问题。

而且这种引入受到了建筑业业内人士大力欢迎，良好地适应建筑市场的需求，设计人员不再用手工绘图了，同时也解决了手工绘制和修改易出现错误的弊端。

在“对图”时也不再用落后的将各专业的硫酸图纸进行重叠式的对图了。

这些CAD图形可以在各专业中进行相互的利用。

给人们带来便捷的工作方式，减轻劳动强度，所以计算机辅助绘图一直在受到人们的热烈欢迎。

其他方面的特点，在此就不再列举了。

特点那么BIM建筑信息模型也同CAD一样，也只是个设计绘图软件或者出图工具吗？对于这个问题，我们需要真正的认识BIM了。

Geometric ModelingGeometric modeling plays a crucial role in various fields such as computer-aided design (CAD), computer graphics, architecture, and engineering. It involves the creation of digital representations of objects and environments using mathematical and computational techniques. Geometric modeling enables designers, engineers, and artists to visualize, simulate, and analyze complex shapes and structures, leading to innovative solutions and advancements in various industries. One of the key aspects of geometric modeling is its application in CAD software. CAD systems are extensively used in industrial design, mechanical engineering, and architecture for creating precise 2D and 3D models of products and buildings. Geometric modeling techniques such as wireframe, surface, and solid modeling are employed to define the shape, size, and geometric properties of the objects. This enables designers and engineers to iterate through multiple design concepts,analyze the behavior of components, and optimize the overall performance of the products. In the realm of computer graphics and animation, geometric modelingplays a pivotal role in creating realistic visual effects and immersive virtual environments. 3D modeling techniques are used to generate lifelike characters, environments, and special effects in movies, video games, and virtual simulations. By manipulating geometric primitives such as vertices, edges, and polygons,artists and animators can bring imaginary worlds to life, captivating audiencesand evoking emotional responses. Moreover, geometric modeling finds applicationsin the field of computational geometry, where algorithms and data structures are developed to solve geometric problems. From determining the intersection of geometric shapes to optimizing the arrangement of objects in space, computational geometry plays a vital role in areas such as robotics, geographic information systems, and computer-aided manufacturing. The efficiency and accuracy ofgeometric algorithms directly impact the performance and reliability of various technological systems. From a mathematical perspective, geometric modelinginvolves the representation of objects using mathematical equations and transformations. Concepts from linear algebra, calculus, and differential geometry are employed to describe the shape, curvature, and topology of geometric entities. This mathematical foundation not only provides a rigorous framework for modelingand analysis but also fosters interdisciplinary research at the intersection of mathematics, computer science, and engineering. In the realm of industrial design and manufacturing, geometric modeling facilitates the rapid prototyping and production of custom parts and assemblies. By leveraging 3D printing and computer numerical control (CNC) machining, designers can translate digital models into physical objects with high precision and complexity. Geometric modeling enables the seamless transition from virtual designs to tangible products, accelerating innovation and customization in the manufacturing industry. In conclusion, geometric modeling is a multifaceted discipline that permeates various domains, from engineering and computer graphics to mathematics and manufacturing. Its impact is evident in the way we design, visualize, and fabricate objects and environments, shaping the future of technology and creativity. As geometric modeling continues to evolve, driven by advances in computational power and interdisciplinary collaboration, it holds the promise of unlocking new frontiers in design, simulation, and fabrication.。

MathematicalModeling理论建模及实际应用数学建模（Mathematical Modeling）是一种将实际问题转化为数学问题，并通过数学方法对问题进行分析和解决的方法。

它既是数学的一种应用，也是一种研究问题并解决问题的工具。

数学建模在各个领域都有广泛的应用，如物理学、经济学、生物学、环境科学等等。

本文将从理论建模和实际应用两个方面来介绍数学建模的基本概念、方法以及一些实际应用案例。

在数学建模中，理论建模是首要的一步。

理论建模是指对实际问题进行分析和抽象，从中提取出数学模型的基本要素和关系。

对于一个复杂的实际问题，我们需要通过对问题的认识和理解，找出其中的关键因素和变量，并确定它们之间的数学关系。

这些关系可以是线性的、非线性的、离散的或连续的，可以用代数方程、微分方程、差分方程或概率统计等形式来表示。

理论建模需要深入地了解问题的背景和相关领域的知识，同时还需要灵活运用数学方法和工具来描述问题和解决问题。

数学建模的方法主要包括定性分析、定量分析和验证分析。

定性分析是指通过观察和分析问题的特征和特性，对问题进行描述和理解，找出问题的关键因素和变量，并确定它们之间的关系。

定量分析是指通过运用数学方法和工具，对问题进行计算和求解，得出问题的数值结果和解决方案。

验证分析是指对数学模型的有效性和可靠性进行检验和验证，通过与实际数据进行对比和比较，评估模型的拟合程度和预测能力。

这些方法相互补充和支持，共同构建了一个完整的数学建模流程。

数学建模在实际应用中有着广泛的应用。

以物理学为例，物理学中的很多问题都可以通过数学建模来解决。

比如，天体物理学中的行星运动、星系演化等问题可以通过数学建模来描述行星和星系的位置、速度和质量等参数，进而研究它们的运动规律和相互作用。

在经济学中，数学建模可以用来描述和分析经济系统中的供需关系、利润最大化、成本最小化等问题，从而指导经济政策和决策。

在生物学中，数学建模可以用来描述生物种群的增长、遗传变异、物种竞争等问题，为生态保护和资源管理提供科学依据。

Geometric ModelingGeometric modeling is a crucial aspect of computer-aided design (CAD) and computer graphics. It involves the creation of digital representations of physical objects, which can be used for various purposes such as visualization, analysis, and manufacturing. Geometric modeling plays a significant role in industries such as architecture, engineering, and entertainment, where accurate and detailed representations of objects are essential. One of the key challenges in geometric modeling is achieving a balance between accuracy and efficiency. Creating highly detailed geometric models can be computationally expensive and time-consuming, especially when dealing with complex shapes and structures. On the other hand, simplifying the models to improve efficiency may result in loss of important details and accuracy. Finding the right balance between these two factors is crucial for ensuring that geometric models are both visually appealing and practical for their intended use. Another important consideration in geometric modeling is the representation of curved surfaces. While straight lines and simple shapes can be easily represented using basic geometric primitives such as points, lines, and polygons, representing curved surfaces requires more advanced techniques. One common approach is to use parametric curves and surfaces, which are defined by mathematical equations and can accurately represent complex curved shapes. However, working with parametric curves and surfaces can be challenging, requiring a deep understanding of mathematical concepts and computational algorithms. In addition to accuracy and representation of curved surfaces, geometric modeling also involves considerations of interoperability and data exchange. In many real-world applications, geometric models need to be shared and used across different software platforms and systems. Ensuring that geometric models can be accurately imported and exported between different software applications is crucial for seamless collaboration and workflow integration. This often requires adherence to industry standards and the use of common file formats for geometric data exchange. Furthermore, geometric modeling also involves considerations of dimensionality and spatial relationships. In many cases, geometric models need to represent three-dimensional objects and their spatial relationships in a realistic and intuitive manner. This requires the use oftechniques such as 3D modeling, spatial indexing, and spatial reasoning to accurately capture the spatial characteristics of physical objects. Additionally, geometric modeling often involves the manipulation and transformation of geometric objects, such as scaling, rotation, and translation, which further adds to the complexity of the modeling process. Moreover, geometric modeling is not onlyabout creating static representations of objects, but also about simulating dynamic behaviors and interactions. In many applications, such as virtual reality, video games, and simulations, geometric models need to accurately represent the dynamic behavior of objects in response to external forces and interactions. This requires the use of techniques such as physics-based modeling, collision detection, and rigid body dynamics to accurately simulate the behavior of objects in avirtual environment. In conclusion, geometric modeling is a complex and multifaceted field that plays a crucial role in various industries and applications. It involves a wide range of considerations, including accuracy, efficiency, representation of curved surfaces, interoperability, dimensionality, spatial relationships, and dynamic behaviors. Addressing these considerations requires a deep understanding of mathematical concepts, computational algorithms, and industry standards, as well as a creative and intuitive approach to capturing the visual and behavioral characteristics of physical objects. Despite its challenges, geometric modeling continues to advance and evolve, driven by the increasing demand for realistic and interactive digital representations of the physical world.。

Geometric ModelingGeometric modeling is a fundamental aspect of computer-aided design and computer graphics. It involves the creation of digital representations of physical objects and shapes using mathematical equations and algorithms. Geometric modeling plays a crucial role in various industries, including manufacturing, architecture, entertainment, and scientific research. It enables designers and engineers to visualize, analyze, and manipulate complex geometries, ultimately leading to the development of innovative products and solutions. One of the key perspectives to consider when discussing geometric modeling is its significance in the field of engineering. Engineers rely on geometric modeling to design and simulate mechanical components, structures, and systems. By creating accurate 3D models of their designs, engineers can assess factors such as strength, durability, and performance, leading to the development of safer and more efficient products. Geometric modeling also facilitates the process of prototyping and testing, allowing engineers to identify and address potential issues before moving into production. In the realm of architecture and construction, geometric modeling plays a critical role in the design and visualization of buildings and infrastructure. Architects use geometric modeling software to create detailed 3D models of their designs, enabling them to explore different concepts, analyze spatial relationships, and communicate their ideas effectively. This technology also allows for the generation of realistic renderings and virtual walkthroughs, providing clients and stakeholders with a clear understanding of the proposed project. Additionally, geometric modeling supports the integration of building information modeling (BIM), which enhances collaboration and coordination among various disciplines involved in the construction process. Another perspective to consider is the impact of geometric modeling in the entertainment industry, particularly in the creation of digital content for films, video games, andvirtual reality experiences. Artists and animators utilize geometric modelingtools to sculpt and manipulate virtual characters, environments, and special effects. This process involves the use of polygons, curves, and surfaces to define the shape and appearance of digital assets. The level of detail and realism achievable through geometric modeling contributes to the immersive and visuallystunning nature of modern entertainment media. Moreover, geometric modeling is a crucial element in the advancement of scientific research and technological innovation. In fields such as medical imaging, geospatial analysis, and computational fluid dynamics, geometric modeling enables researchers to analyze and interpret complex data, leading to discoveries and breakthroughs in their respective domains. For instance, in medical applications, geometric modeling is used to reconstruct and visualize anatomical structures from imaging data, supporting diagnosis, treatment planning, and medical education. From a personal standpoint, as a designer and enthusiast of computer graphics, I have experienced the transformative power of geometric modeling in my creative endeavors. Theability to sculpt and manipulate digital forms has allowed me to bring my imagination to life, whether it's designing futuristic vehicles, otherworldly landscapes, or intricate mechanical assemblies. The process of working with geometric modeling tools is not just a technical exercise but a deeply immersive and expressive journey, where every vertex and edge contributes to the realization of a unique vision. In conclusion, geometric modeling is a multifaceted and indispensable tool that permeates various industries and creative pursuits. Its impact extends beyond the realms of design and engineering, influencing the way we perceive and interact with the world around us. As technology continues to evolve, geometric modeling will undoubtedly play a central role in shaping the future of innovation, art, and human expression.。

SOLID MODELING实体造型6.1 Application of Solid Models实体模型的应用In mechanical engineering, a solid model is used for the following applications:在机械工程中，一个实体模型被用于以下应用：1、Graphics: generating drawings, surface and solid models图形：生成图纸，表面和实体模型2、Design: Mass property calculation, interference analysis, finite element modeling, kinematics and mechanism analysis, animation, etc.设计：质量计算、干涉分析、有限元建模、运动学及机理分析、动画等。

3 、Manufacturing: Tool path generation and verification, process planning, dimension inspection, tolerance and surface finish.制造业：刀具轨迹的生成和验证，工艺设计，尺寸检验，公差及表面处理。

4 、Component Assembly: Application to robotics and flexible manufacturing: Assembly planning, vision algorithm, kinematics and dynamics driven by solid models.组件组装：应用于机器人和柔性制造：装配规划，视觉算法，运动学和动力学模型的驱动。

6.2 Solid Model Representation实体模型表示There are three different forms in which a solid model can be represented in CAD:有三种不同的形式，其中一个实体模型可以表示在计算机辅助设计：·Wireframe Model线架模型·Surface Model曲面模型·Solid Model实体模型Wireframe Models: Joining points and curves creates wireframe models. These models can be ambiguous and unable to provide mass property calculations, hidden surface removal, or generation of shaded images. Wireframe models are mainly used for a quick verification of design ideas.线框模型：连接点和曲线创建线框模型。

Geometric ModelingGeometric modeling is a fundamental concept in the field of computer graphics and design. It involves creating digital representations of physical objects using mathematical equations and algorithms. Geometric modeling plays a crucial role in various applications such as animation, virtual reality, architectural design, and manufacturing. This technology allows designers and engineers to visualize and manipulate complex shapes and structures with precision and accuracy. One of the key perspectives to consider when discussing geometric modeling is its importance in the field of computer-aided design (CAD). CAD software relies heavily on geometric modeling to create 2D and 3D models of products and buildings. These models serve as the basis for the design and development of various products, ranging from consumer goods to industrial machinery. Geometric modeling enables designers to simulate the behavior of their designs under different conditions, leading to better and more efficient products. Another important perspective to explore is the role of geometric modeling in the entertainment industry. In the realm of animation and visual effects, geometric modeling is used to createlifelike characters, environments, and special effects. Whether it's a blockbuster movie or a video game, geometric modeling allows artists and animators to bring their imagination to life in a virtual space. The level of detail and realism that can be achieved through geometric modeling has revolutionized the entertainment industry and has set new standards for visual storytelling. From a scientific and engineering standpoint, geometric modeling is essential for simulating and analyzing complex systems and phenomena. Whether it's studying the behavior of fluid dynamics, analyzing the structural integrity of a building, or simulating the movement of a robotic arm, geometric modeling provides a powerful tool for understanding and predicting real-world scenarios. By creating accurate digital representations of physical objects and environments, scientists and engineers can conduct experiments and tests in a virtual space, saving time and resources while gaining valuable insights. In addition to its practical applications, geometric modeling also has a profound impact on artistic expression and creativity. Artists and designers use geometric modeling tools to explore new forms, shapes, and textures, pushing the boundaries of what is visually possible. From avant-gardesculptures to futuristic architectural designs, geometric modeling has opened up new avenues for artistic exploration and self-expression. The ability to manipulate and transform geometric shapes in a digital environment has empowered artists to create bold and innovative works that challenge traditional notions of art and design. Moreover, geometric modeling has also played a significant role in the advancement of medical technology. From the development of prosthetic limbs to the design of medical devices, geometric modeling has enabled breakthroughs in the field of healthcare. By creating precise digital models of the human body and its various systems, medical professionals and researchers can better understand and address complex medical conditions. This has led to the development of personalized medical treatments and improved patient care, ultimately saving lives and improving the quality of life for countless individuals. In conclusion, geometric modeling is a versatile and powerful tool that has revolutionized various industries and fields. Its impact can be seen in the way we design products, create entertainment experiences, conduct scientific research, express artistic vision, and improve healthcare. As technology continues to advance, the role of geometric modeling will only become more significant, shaping the way we interact with the world around us and pushing the boundaries of what is possible.。

Geometric ModelingGeometric modeling is a crucial aspect of computer graphics and design, allowing for the creation of three-dimensional representations of objects and scenes. It involves the use of mathematical equations and algorithms to define the shape, size, and position of objects in a virtual space. Geometric modeling isused in a wide range of applications, including animation, video games, architectural design, and engineering. One of the key benefits of geometric modeling is its ability to create realistic and detailed representations of objects. By accurately defining the geometry of an object, designers can create lifelike images that closely resemble the real world. This level of detail is essential for applications such as architectural design, where precise measurements and proportions are crucial. In addition to creating realistic images, geometric modeling also allows for the manipulation and transformation of objects in a virtual space. Designers can easily modify the size, shape, and position of objects, allowing for quick iterations and adjustments during the design process. This flexibility is particularly valuable in fields such as industrial design and engineering, where multiple design iterations are common. Another important aspect of geometric modeling is its ability to simulate physical phenomena and interactions. By accurately modeling the geometry of objects andtheir relationships, designers can simulate how objects will behave in different environments and under various conditions. This is essential for applications such as virtual prototyping and simulation, where designers need to test the performance of a design before it is physically built. Geometric modeling also plays a crucial role in computer-aided design (CAD) and computer-aided manufacturing (CAM) processes. By accurately defining the geometry of objects, designers can create detailed blueprints and specifications that can be used to manufacture physical objects. This level of precision is essential for industries such as aerospace and automotive, where small errors in design can havesignificant consequences. Overall, geometric modeling is a powerful tool that enables designers and engineers to create realistic, detailed, and accurate representations of objects in a virtual space. By leveraging mathematicalequations and algorithms, designers can create lifelike images, manipulate objects,simulate physical interactions, and generate detailed specifications for manufacturing. As technology continues to advance, geometric modeling will continue to play a crucial role in a wide range of industries and applications.。

cfa 实践技能模块financial modeling-概述说明以及解释1.引言1.1 概述概述部分的内容：金融建模是金融领域中一个重要的实践技能模块，它涉及对金融数据的建模和分析，以及使用模型预测和评估金融风险和机会。

在金融行业，金融建模是一项关键的技能，对投资银行家、财务分析师、风险经理和投资专业人士等职业的发展至关重要。

金融建模通过对历史和当前金融数据进行分析和解释，帮助从业人员预测未来的趋势和变化。

这些模型可以用于评估投资组合的风险和回报、估值公司、预测金融市场的行为，以及进行风险管理和决策支持。

因此，金融建模被广泛应用于投资决策、财务规划、企业估值和风险管理等领域。

金融建模涉及使用数学、统计学、计量经济学和计算机科学等知识和技巧，结合金融理论和实践，以及市场数据和公司财务数据来构建模型。

这些模型可以是定量模型，如回归模型、时间序列模型和蒙特卡罗模拟等，也可以是定性模型，如决策树和风险评估模型等。

对于金融从业人员来说，掌握金融建模技能是至关重要的。

它不仅可以提高工作效率和准确性，还可以帮助从业人员更好地理解金融市场和公司的运作，以及预测金融趋势和风险。

此外，金融建模还能够提供有关投资决策和风险管理的量化参考，帮助从业人员做出更明智的金融决策。

本文主要围绕CFA实践技能模块中的金融建模展开探讨。

我们将深入研究金融建模的基本概念、方法和应用，并探讨金融建模在投资决策、风险管理和企业估值等方面的重要性。

通过对金融建模的全面理解和应用，我们将帮助读者更好地掌握这个核心技能，并在金融领域取得更好的业绩和发展。

1.2 文章结构文章结构决定了文章的整体框架和组织方式。

本文按照如下结构展开：第一部分是引言部分，包括概述、文章结构和目的。

引言部分通过概述来引导读者对实践技能模块financial modeling的重要性有基本的认识。

接着，文章介绍了本文的结构，即接下来会分为正文和结论两个部分，旨在全面、系统地探讨该主题。

Geometric ModelingGeometric modeling is a fundamental concept in computer graphics and engineering design. It involves the creation of digital representations of objects and environments using mathematical and computational techniques. Geometric modeling is used in a wide range of applications, including animation, video games, virtual reality, and industrial design. It plays a crucial role in visualizing and simulating complex structures, helping engineers and designers to analyze and optimize their designs. One of the key perspectives on geometric modeling is its importance in the field of computer graphics. In computer graphics, geometric modeling is used to create 3D models of objects and scenes, which are then rendered to produce realistic images and animations. This process involves representing the shape and appearance of objects using geometric primitives suchas points, lines, and polygons. Geometric modeling techniques such as surface and solid modeling are used to create detailed and realistic 3D models, which are then manipulated and transformed to create visually stunning graphics. Another important perspective on geometric modeling is its role in engineering design. In engineering, geometric modeling is used to create digital representations of mechanical parts, structures, and systems. These models are used for visualization, analysis, and simulation, allowing engineers to evaluate the performance and behavior of their designs. Geometric modeling techniques such as parametric modeling and finite element analysis are used to create and analyze complex engineering models, helping engineers to optimize their designs and identify potential problems before they occur. Geometric modeling also plays a crucialrole in virtual reality and simulation. In virtual reality, geometric modeling is used to create immersive and interactive 3D environments, allowing users toexplore and interact with digital worlds. Geometric modeling techniques such as 3D scanning and mesh generation are used to create realistic virtual environments, which can be used for training, education, and entertainment. Similarly, in simulation, geometric modeling is used to create accurate models of physical systems, allowing engineers and scientists to study and predict the behavior of complex phenomena. From an emotional perspective, geometric modeling can be both challenging and rewarding. Creating detailed and realistic 3D models requires acombination of technical skill, creativity, and attention to detail. It can be a time-consuming and labor-intensive process, requiring patience and perseverance to achieve the desired results. However, the ability to bring virtual worlds and complex designs to life can be incredibly satisfying, and the impact of geometric modeling in various fields can be truly inspiring. In conclusion, geometric modeling is a versatile and essential concept in computer graphics, engineering design, virtual reality, and simulation. It enables the creation of digital representations of objects and environments, allowing for visualization, analysis, and simulation of complex structures. From creating stunning visual effects to optimizing engineering designs, geometric modeling plays a crucial role in a wide range of applications. Its significance is not only technical but also emotional, as it requires a combination of skill and creativity to achieve impactful results.。

建模相关专业词汇
建模是一个涉及多个领域的广泛概念，包括计算机科学、数学、物理、工程等。

以下是一些与建模相关的专业词汇：
模型（Model）：是对现实世界或抽象系统的简化表示，用于研究、分析或预测系统的行为。

数学建模（Mathematical Modeling）：使用数学语言、符号和公式来描述和解释现实世界的现象或过程。

物理建模（Physical Modeling）：通过建立物理方程和模拟物理过程来理解和预测实际系统的行为。

计算机建模（Computer Modeling）：使用计算机程序和算法来模拟和预测系统的行为。

统计建模（Statistical Modeling）：利用统计学原理和方法来建立模型，以描述和预测数据的分布和变化。

系统建模（System Modeling）：对系统的结构和行为进行建模，以了解系统的整体性能和稳定性。

仿真（Simulation）：通过模拟实际系统的运行过程，来预测系统的性能和行为。

优化建模（Optimization Modeling）：通过建立优化模型，以寻找系统性能的最优解或近似最优解。

动态建模（Dynamic Modeling）：对系统的动态行为进行建模，以了解系统随时间的变化过程。

静态建模（Static Modeling）：对系统的静态特性进行建模，以了解系统在特定条件下的性能。

以上仅是与建模相关的一些常见专业词汇，实际上建模领域涉及的词汇和概念非常广泛，具体还需根据具体的应用领域和背景进行深入了解。

The research in MAS concentrates on the qualitative, numerical and computational aspects of mathema-tical models arising in a wide range of applications within the Dutch society.Particular attention is gi-ven to models describing continuum processes.As examples we mention freefluid and porous mediaflow,chemical reactions in the atmosphere and cir-cuit analysis.The applications are combined into two extensive programmes or themes,each contai-ning a number of characteristic projects.They are accounted for in detail in the theme descriptions of MAS1and MAS2.New developments include the projects MAS2.1(Computationalfluid dynamics,a collaboration with MARIN)and MAS2.7(Mathe-matics of Finance).Preliminary contacts have been made with TNO-TPD and across the border with GMD in Germany.It is expected that new projects will emerge from these contacts.In the midst of much applied work,MAS conti-nues to contribute significantly to the scientific de-velopment in the areas of qualitative,numerical and computational methods for partial differential equati-ons.The number of papers appeared in international journals is certainly satisfactory,and withfive PhD theses MAS contributes substantially to the scientific output of the CWI.Separately from the themes,the Dynamical Sys-tems Laboratory(DSL)operated as an independent unit.During the past years DSL has played a leading role in the software development for bifurcation of equilibria of systems of ordinary differential equa-tions.An extensive description of their activities is given in the DSL contribution.This year was the last year of DSL,which officially ended when Dr.Yu.A. Kuznetsov left the CWI(November1st,1997). MAS is very pleased to have Professor Piet van der Houwen as a CWI Fellow in its ranks.His high level scientific input,interaction with young re-searchers and involvement with several project is very much appreciated.Dynamical Systems Laboratory–DSL-Yu.A.Kuznetsov-V.V.Levitin -J.A.SandersEnvironmental Modelling and Porous Media Re-search–MAS1-J.G.Verwer-C.J.van Duijn-J.Hulshof-P.J.van der Houwen-J.G.Blom-C.Cuesta-M.I.J.van Dijke-G.Galiano-W.Hundsdorfer-J.Koknserstdrager-M.A.A.van Leeuwen-W.M.Lioen-M.van Loon-J.Molenaar-R.J.Schotting-B.P.Sommeijer-E.J.Spee-J.de Vries-P.M.de ZeeuwIndustrial Processes–MAS2-E.H.van Brummelen-S.Cavallar-M.K.C¸amlıbel-M.Genseberger-T.Hantke-P.W.Hemker-J.Hoogland-P.J.van der Houwen-K.Karamazen-M.Kirkilionis-A.de Koeijer-B.Korennserstdrager-W.M.Lioen-P.L.Montgomery-M.Nool-J.Noordmans-O.Penninga-A.van der Ploeg-H.J.J.te Riele-A.J.van der Schaft-J.M.Schumacher-B.P.Sommeijer-W.J.H.Stortelder-J.B.de Swart-N.M.Temme-W.A.van der Veen-D.T.Winter-P.WesselingSecretary:N.MitrovicJ.A.SandersYu.A.KuznetsovV.V.LevitinDuring1997,two versions of CONTENT,1.3and1.4,were released on ftp.cwi.nl in directorypub/CONTENT.Release1.4–December,1997New features:-new class of dynamical systems is supported: differential-algebraic equations(DAEs)Mx’=f(x,p) with possibly singular matrix M;-numerical integration of stiff ODEs and DAEs using RADAU5code;-three-parameter continuation of all codim2bifur-cations of ODEs(cusp,Bogdanov-Takens,genera-lized Hopf,zero-Hopf,and double Hopf);-two-parameter continuation of Hopf bifurcation using the bordered squared Jacobian matrix;-symbolical calculation of derivatives of the4th or-der using the Maple system.Release1.3–August,1997New features:-one-parameter continuation of limit cycles in ODEs;-detection and branch switching at codim1bifurca-tions of limit cycles;-one-parameter continuation offixed points of ite-rated maps;-detection and normal form analysis of codim1bi-furcations of iterated maps;-3D graphic windows;-Staircase window for scalar iterated maps.At the moment,CONTENT completely supportsone-parameter analysis of equilibria and cycles in ODEs and iterated maps.To complete the support of two-parameter analysis of ODEs,one has to imple-ment the continuation of codim1bifurcations of cy-cles(i.e.,fold,period-doubling,and Neimark-Sacker bifurcations),as well as the homoclinic bifurcati-ons of saddle and saddle-node equilibria,and branch switching between them.CONTENT provides the environment to implement all of these continuations. Also,the computation of the remaining normal form coefficients at codim2bifurcations of equilibria has to be implemented in CONTENT(see below).Yu.A.Kuznetsov derived explicit normal form coefficients for the reduced to the central manifold equations for all codim2equilibrium bifurcation of ODEs.A CWI Report is published.Yu.A.Kuznetsov(together with aerts and B. Sijnave,Gent University)developed new algorithms to continue codim1and2bifurcations of equilibria in2and3parameters,respectively.The algorithms were implemented in CONTENT.Yu.A.Kuznetsov(together with A.Champneys (Bristol)and B.Sandstede(Berlin))implemented the homoclinic continuation into AUTO97,the latest version of the continuation/bifurcation software by E.Doedel(Concordia University,Montreal).Now it is the standard part of AUTO.The text of the second edition of the book by Yu.A. Kuznetsov Elements of Applied Bifurcation The-ory has been sent to the Production Departmentof Springer-Verlag in September1997and will be published in1998.E.Doedel(Concordia University,Montreal,Ca-nada)June15–28.The visit was devoted to discussions of new me-thods to continue codim1bifurcations of limit cy-cles.In particular,a new method to continue the period-doubling bifurcation was proposed that combines orthogonal collocation technique with matrix bordering.O.De Feo(Swiss Federal Institute of Technology, Lausanne,Switzerland)September1–30.During the visit,RADAU5method for the numeri-cal integration of ODEs and DAEs was translated from FORTRAN to C and implemented into CON-TENT.A paper on homoclinic bifurcations in a3D food chain model was practicallyfinished.aerts and B.Sijnave(University of Gent, Belgium)June19–22.Bordering methods to continue codim1and2bi-furcation of equilibria were discussed.A proto-type method to continue the Bogdanov-Takens bi-furcation was implemented during the visit.The continuation of all other codim2bifurcations of equilibria in three parameters was implemented la-ter in1997.A.Shilnikov(Institute of Applied Mathematics and Cybernetics,Nizhnii Novgorod,Russia)May30.A lecture was given at CWI on‘A blue-sky cata-strophe model’,demonstrating a new way of a de-struction of a limit cycle.Yu.A.Kuznetsov gave invited lectures on CON-TENT at the International Workshop‘Numerical analysis of Dynamical Systems’,IMA,Minneapo-lis,USA,September15–19,and at the Workshop ‘Hybrid-methods for Bifurcation and Dynamics of Partial Differential Equations’,University of Mar-burg,June8–11.MAS-R9730.Y U.A.K UZNETSOV.Explicit nor-mal form coefficients for all codim2bifurcations of equilibria in ODEs.E.J.D OEDEL,A.R.C HAMPNEYS,T.F.F AIR-GRIEVE,Y U.A.K UZNETSOV,B.S ANDSTEDE,X.-J.W ANG(1997).AUTO97:Continuation and Bifurcation Software for Ordinary Differential Equa-tions(with HomCont).User’s Guide,Concordia University,Montreal,Canada.W.G OVAERTS,Y U.A.K UZNETSOV,B.S IJNAVE (1997).Implementation of Hopf and double Hopf Continuation Using Bordering Methods,Department of Applied Mathematics and Computer Science,Uni-versity of Ghent,Belgium.W.G OVAERTS,Y U.A.K UZNETSOV,B.S IJNAVE (1997).Computation and Continuation of Codimen-sion2Bifurcations in CONTENT,Department of Ap-plied Mathematics and Computer Science,University of Ghent,Belgium.Y U.A.K UZNETSOV(1997).Centre manifold; Codimension-two bifurcations;Equivalence of dyna-mical systems;Homoclinic bifurcations;Hopf bifur-cation;Saddle-node bifurcation.M.H AZEWINKEL (ed.).Encyclopaedia of Mathematics.Supplement Volume I,Kluwer Academic Publishers,The Nether-lands,179–181,190–101,240,293–294,296–297, 444–445.Dr.J.G.Verwer,researcher,theme leader Prof.dr.ir.C.J.van Duijn,researcher,cluster leaderDr.J.Hulshof,advisorProf.dr.P.J.van der Houwen,researcher,CWI fellowDrs.J.G.Blom,researcherMrs.C.Cuesta,Ph.D.studentDrs.M.I.J.van Dijke,Ph.D.studentDr.G.Galiano,postdocDr.W.Hundsdorfer,researcherDrs.J.Kok,researchernser,Ph.D.studentstdrager,Ph.D.studentDr.M.A.A.van Leeuwen,postdocDrs.W.M.Lioen,programmerDr.M.van Loon,postdocDr.J.Molenaar,postdocIr.R.J.Schotting,researcherDr.B.P.Sommeijer,researcherDrs.E.J.Spee,Ph.D.studentDr.J.de Vries,researcherDrs.P.M.de Zeeuw,programmer,till February1The general purpose of this research theme is to develop,analyze and implement mathematical and numerical models for application to complex pro-blems arising in environmental modelling and porous media research.MAS1is particular concerned with ordinary and partial differential equations,descri-bingfluidflow,transport of pollutants and chemical and bio-chemical processes.These differential equa-tions lie at the heart of simulation models used in atmospheric air quality modelling,in surface wa-ter and groundwater water quality modelling,and in porous media research directed for example at en-hanced oil recovery.The research subthemes cover a wide range of scientific activities,ranging from fun-damental mathematical and numerical analysis of differential equations and development of new com-putational techniques for use on vector/parallel and massively parallel computers and heterogeneous net-works(HPCN),to implementation of fully integrated models and application to real life problems.Exten-sive co-operations and contacts are maintained with researchers from the academic world and from the environmental and porous media applicationfields. Externalfinancing comes from a variety of sources, such as industry,special programs from the Nether-lands Organization for Scientific Research,research programs from the European Union and the national HPCN program funded through the Ministry of Eco-nomic Affairs.In1997research was organized in four subthemes:The research concerns the numerical modelling of the long range transport and chemical exchange of atmospheric air pollutants.Within the Netherlandsco-operation has existed with KEMA,NLR,RIVM, TUD,TNO and UU/IMAU.At the international le-vel,two joint papers with CGRER(Center for Global and Regional Environmental Research,Universityof Iowa),have been published in Atmospheric Envi-ronment(See Sandu et al.).The CWI group is also active within the European network GLOREAM and among others involved in the organization of an In-ternational Conference on Air Pollution in Paris in 1998.January23,1998,Edwin Spee will defend his Ph.D.Thesis Numerical Methods in Global Trans-port Models at the University of Amsterdam.Two new Ph.D.students have recently joined the group, viz.Debby Lanser and Boris Lastdrager.In1997 MAS1worked on the following projects:RIFTOZ–The technique of data-assimilation has been examined for improving results of model simulations by usage of actual measurements.A special implementation of an extended Kalmanfilter has been shown promising,see Report MAS-R9702 for details.The project forms part of an EU project in which CWI has been active through a subcon-tract with TUD.At CWI the project has now been terminated with the departure of Dr.M.van Loonto TNO.The Kalmanfilter will be further tested by TNO for use in their dispersion model LOTOS. LOTOS–Here the objective is to develop a regio-nal,three-dimensional,long term ozone simulation model.This LOTOS model should replace at due time an existing regional forecasting model in use at TNO.The model is developed in co-operation with TNO researchers.At TNO the focus lies on physi-cal,meteorological and chemical aspects.The CWI research focuses on the design of the mathematical model for a so-called hybrid(terrain following and pressure based)coordinate system and,in particular, of tailored numerical algorithms and implementa-tions on super and parallel computers.The project is part of the TASC project‘HPCN for Environ-mental Applications’which is funded by the Dutch HPCN program.At the end of1997the project was halfway.Afirst running operational prototype im-plemented at CWI has recently been transferred to TNO.Research details are found in the reports MAS-N9701,R9717.NCF–This one-year project is linked with the LOTOS project and concerns aspects of massive parallelism,in particular for T3E implementations. Special attention has been given to the question to which extent massive(meteo)I/O can degrade the parallel performance of models used in atmospheric simulations.Results will be reported early1998. Support is provided by the NCF/Cray University Grant program.The project lasts until April next year.Early1997the Report MAS-R9702wasfinish-ed.This publication concerns research in a similar NCF project terminated in February,1997.CIRK–This Ph.D.project has been terminatedat the end of1997with the departure of Drs.Edwin Spee.He will defend his Thesis at the Universityof Amsterdam on January23,1998.The project is similar to the LOTOS project,but here the particu-lar objective was to develop numerical algorithms for use in3D models for the whole of the global troposphere/stratosphere.In this last year we have worked on various aspects of a Rosenbrock method (see Report MAS-R9717),including stiff chemis-try integration and a factorization approach within the Rosenbrock framework.The factorization idea was investigated to provide an alternative for time or operator splitting.A second main activity has been the validation of various advection schemes in a real life radon experiment,using analyzed windfields from the ECMWF(see Report MAS-R9710).Sup-port for this project was obtained from the RIVM and very fruitful scientific co-operation has existed with IMAU/UU.This co-operation will continue in a following project,planned for the next three years. The new project is centered around the existing mo-del TM3.With support from SWON two postdocs will be hired for algorithmic and parallel software research.GOA–This activity concerns a new Ph.D.project on the‘Analysis and Validation of Operator Split-ting in Air Quality Modeling’.This project has been granted by GOA,the Netherlands Geoscien-ces Foundation.It started September1,1997with the employment of Ir.Debby Lanser.Afirst article on the analysis of Strang-splitting for PDEs of the advection-diffusion-reaction type is already in prepa-ration.SWON–A second new project Ph.D.project started December1,1997with the employment of Drs.Boris Lastdrager.This project has been granted by SWON and concerns‘Sparse Grid Methods for Time-Dependent PDEs’.Atmospheric transport-chemistry problems provide a highly useful applica-tion for sparse-grid research.The project is a joint activity between MAS1and MAS2(Dr.ir.B.Ko-ren).The research concentrates on the design of parallel numerical methods for the simulation of water pol-lution(calamitous releases),the marine eco-system,dispersion of river water,sediment transport,etc. Our activities in1997included:HPCN–In1996we started the development of a special purpose3D transport model based onfinite difference space-discretization and unconditionally stable,implicit time-discretization.In1997we ana-lyzed an iterative approach for solving the implicit relations.This iteration process is based on approxi-mate factorization such that only one-dimensionally implicit,linear systems occur in the algorithm.Inco-operation with C.Eichler-Liebenow from the University of Halle,the convergence region of the iteration method and its effect on the overall stabi-lity of the integration method has been analyzed, see Report MAS-R9718.Furthermore,we started the development of tools for domain decomposition with domains of varying grid resolutions.Part of the research was carried out within the research con-sortium TASC,with support from the Dutch HPCN programme.SWEM–The velocityfield needed by transport models either is read from inputfiles or is computed simultaneously with the computation of the pollu-tant concentrations by means of a hydrodynamical model.In view of the complicated data structures in-volved,we decided to focus on the second approach, because the hydrodynamical model can be designed such that it uses the same data structures as the trans-port model.Such an approach is justified,because the underlying partial differential equations are to a large extent identical.By choosing the same type of spatial and temporal discretizations,the same decom-position in domains with the same resolutions,and the same stepsizes in both algorithms,we achieve that the data structures are exactly the same.Since the transport solver is designed and tuned with paral-lel computer systems in mind,the velocityfield sol-ver will also be tuned to parallel computer systems. Moreover,each velocity-field-solver step can be per-formed in parallel with the corresponding transport-solver step.In1997afirst analysis of the underlying numerical model has been performed.This subtheme coordinates a number of research ac-tivities in analysis of nonlinear partial differential equations and in mathematical modelling offlow and transport through porous media.The character of the research ranges from very applied to theoretical.An example of an applied activity is the NAM-project, where software was developed to study the mixingof gases in underground reservoirs.An example of a theoretical activity is the collaboration withH.W.Alt(Universit¨a t Bonn),which involves a de-tailed study of a free boundary problem with a cusp. This project participates in the interaction platform ‘Nonlinear Transport Phenomena in Porous Media’, which brings together researchers from TUD,RUL, LUW,RIVM and CWI,and which is supported by the NWO Priority Programme‘Nonlinear Systems’. There are also numerous international contacts.The scientific output in1997includes two Ph.D.theses: Problems in Degenerate Diffusion by Mark Peletier and Multi-Phase Flow Modeling of Soil Contamina-tion and Soil Remediation by Rink van Dijke.PDE RESEARCH–Nonlinear PDEs arising in models for porous mediaflow form the backbone of this project.Particular attention was given to sys-tems consisting of a convection-diffusion equation coupled with an ordinary differential equation.The general case,in which the ODE is in the time vari-able,is treated in the thesis of M.A.Peletier.A par-ticular case,where the ODE is in a space coordinate, appears in a model for salt uptake by mangroves,see Report MAS-R9728.This leads to non-local con-vection,which is shown to imply non-uniqueness.A second activity involves the collaboration Alt-Van Duijn.In a series of papers they study the behaviour of the interface between fresh and salt groundwater in the presence of wells.The interface appears asa free boundary in an elliptic problem.Depending on the pumping rate of the wells,a singularity de-velops in the free boundary in the form of a cusp.A detailed local analysis of the free boundary near such a cusp is presented in Report MAS-R9703.FTPM–This project deals with density drivenflow in porous media.In1997research concentrated on brine transport problems that are related to high-level radioactive waste disposal in salt domes.High salt concentrations give rise to nonlinear transport phenomena such as enhancedflow due to volume (compressibility)effects and the reduction of hydro-dynamical dispersion due to gravity forces.Mainly (semi)analytical techniques(similarity and V on Mi-ses transformations)were used to study the volume effects,see Report MAS-R9724.Report AM-R9616 (Brine transport in porous media:Self-similar solu-tions)has been accepted for publication in Advances in Water ing experimental data of Dr.H.Moser(Technische Universit¨a t Berlin)we also ve-rified a nonlinear dispersion theory proposed by Dr. S.M.Hassanizadeh(Delft University of Technology), which includes the effect of dispersion reduction due to local high salt concentrations.The nonlinear the-ory is in excellent agreement with the experimentalresults,see Report MAS-R9734.We further consi-dered the interface between fresh and salt groundwa-ter in heterogeneous media.This subject is relatedto salt water intrusion problems in coastal aquifers. The interface approximation can be justified when the width of the mixing zone between thefluids is small compared to the vertical extension of the aqui-fer.We studied the resulting set of interface equa-tions numerically,using a moving mesh Finite Ele-ment Method.Moreover,several simplified Dupuit problems were studied and the results were compa-red with FEM solutions,see Report MAS-R9735. NAM–This project deals with the mathematical modelling of gas injection.The dispersion is studied for gas injection into a reservoir.The aim is to un-derstand and quantify the relevant physical processes that lead to mixing of injected gas with residual gas in old reservoirs.The project is sponsored by the NAM(Nederlandse Aardolie Maatschappij).In co-operation with the Faculty of Mining and Petroleum Engineering of the Delft University of Technology a numerical model is being developed at CWI to study the mixing of the gases in detail.NOBIS–Within this project we study soil reme-diation anic contaminants may be removed from the soil either by pumping methods or by injecting air,which enhances biodegradation and volatilization.The correspondingflow of groundwa-ter,organic contaminant and air is described using multi-phaseflow models.Air injection into ground-water(air sparging)in a horizontally layered medium has been studied in Report MAS-R9729.Accurate numerical simulations of the full transient two-phase flow equations were carried out and an almost ex-plicit solution for the steady state airflow just below a less permeable soil layer was derived.The latter solution showed almost perfect agreement with the numerical results when heterogeneity of the layers was increased.To model pumping of a lens of light organic liquid from an aquifer,multi-phase seepage face conditions were applied at the well boundary (Report MAS-R9725).For two different geome-tries of the lens similarity solutions provided good approximations of the removal rate and the location of the remaining contaminant as a function of time. The above results and other work on behaviour ofa lens of organic contaminant and on air sparging have been gathered in Rink van Dijke’s Ph.D.thesis:‘Multi-phaseflow modeling of soil contamination and soil remediation’,which was defended at Wage-ningen Agricultural University on December5,1997. NWO-NLS–This is the Ph.D.project‘Mathemati-cal Analysis of Dynamic Capillary Pressure Relati-ons in Porous Media Flow’.It started in November 1997,with the employment of C.M.Cuesta.It is supported by the NWO Priority Programme‘Nonli-near Systems’.The aim is to study PDEs with higher order mixed derivatives.Such equations arise in mo-dels for unsaturated groundwaterflow,taking into account dynamic capillary pressure.In1997two different subjects have been studied. Report MAS-R9721contains the results of an inves-tigation to the stability of approximate factorization for-methods.Approximate factorization seems for certain multi-space dimensional PDEs a viable alter-native to time-splitting as a splitting error is avoided. The investigation,however,has revealed limitations of the approximate factorization technique with re-gard to numerical stability.The second subject con-cerns RKC(Runge-Kutta-Chebyshev),an explicit time integrator specifically suitable for multi-space dimensional parabolic PDEs.In RKC the stability limitation inherent in explicit methods is greatly re-duced by the use of a three-step Chebyshev recur-sion.The current study has specifically dealt with the development of a production-grade code for non-experencied users.The work has been carried outin co-operation with Prof.L.Shampine,University of Dallas.Details are given in Report MAS-R9715. This report has been accepted for publication in the Journal of Computational and Applied Mathematics. Mini-symposium on Numerical Analysis,Wage-ningen,April3–anizer:P.M.de Zeeuw. Speakers:W.Hundsdorfer(Stability of the Doug-las Splitting Method),E.J.Spee(Advectieschema’s op een Bol voor Atmosferische Ttransport Model-len).Meeting of the Steering Committee of the ESF-Programme‘Free Boundary Problems,Theory and Applications’,CWI,anizer:C.J.van Duijn.TASC Symposium7,CWI,anizers: J.G.Verwer and J.Kok.Speakers:P.J.H.Builtjes (MEP-TNO)(Atmospheric Transport-chemistry Modelling and HPCN),J.G.Blom(LOTOS,a3D Atmospheric Air Pollution Model),J.Kok(Por-ting Atmospheric Transport-Chemistry Software to the NEC SX–4),K.Dekker(TUD)(Modification of Flow Fields to Recover the Property of Divergence Freedom),G.S.Stelling(WL)(NonhydrostaticPressure in Free Surface Flows)and B.P.Som-meijer(Recent Progress in an Implicit Shallow Water Transport Solver).Colloquium‘Flow and Transport in Porous Me-dia’,CWI,September10.Speakers:G.Dagan (Tel-Aviv)and S.E.A.T.M.van der Zee(LUW). Organizers:R.J.Schotting and C.J.van Duijn. TASC Symposium8(‘HPCN-Platformdag’),CWI, anizers:J.G.Verwer andJ.Kok.Speakers:J.G.Verwer(Het TASC Pro-ject HPCN voor Milieutoepassingen),M.van Loon(MEP-TNO)(Langetermijnsimulatie van Ozon),J.G.Blom(Rekenen aan Ozon),B.P.Som-meijer(Simulatie van Transport in Ondiep Water), E.A.H.V ollebregt(TUD)(Parallelle Software voor Stromings-en Transportmodellen)and G.S.Stel-ling(WL)(Simulatie van Afvalwaterlozingen). Mini-symposium on Partial Differential Equati-ons at SciCADE97–International Conference on Scientific Computation and Differential Equations, Grado,September15–anizer:J.G.Ver-wer.Speakers:K.Dekker(TUD)(Parallel GM-RES and Domain Decomposition),W.Hundsdor-fer(Trapezoidal and Midpoint Splittings for Initial Boundary-value Problems),B.P.Sommeijer(RKC, an Explicit Solver for Parabolic PDEs)and J.M. Hyman(Los Alamos)(Minimizing Numerical Er-rors Introduced by Operator Splitting Methods) Colloquium‘Flow and Transport in Porous Me-dia’,CWI,September24.Speakers:A.de Wit (Brussels)and R.J.Schotting(CWI).Organizers: R.J.Schotting and C.J.van Duijn.Workshop‘Interfaces and Parabolic Regularisa-tion’,Lorentz Center(RUL),November5–7.In-ternational workshop with25speakers anizers:J.Hulshof and C.J.van Duijn.MAS Colloquium,CWI,anizer: C.J.van Duijn.Speakers:C.N.Dawson(UT at Austin)(Dynamic Adaptive Methods for Chemi-cally Reactive Transport in Porous Media),P.Wes-seling(TUD)(Numerical Solution of Hyperbolic Systems with Nonconvex Equation of State)and W.A.Mulder(Shell Rijswijk)(Finite Differences and Finite Elements for Seismic Simulation). TASC Symposium9,CWI,ani-zers:J.G.Verwer and J.Kok.Speakers:A.Peter-sen(IMAU)(More Efficient Advection Schemes for the Global Atmospheric Tracer Model),H.Elbern (EURAD)(A Parallel Implementation of a4D-variational Chemistry Data Similation Scheme), E.J.Spee(Rosenbrock Methods for Atmospheric Dispersion Problems)and M.Krol(IMAU)(The TM3Model:Numerical Aspects of Atmospheric Chemistry Aplications).2nd Annual Meeting MMARIE Concerted Action, Barcelona,January15–17:B.P.Sommeijer(Do-main Decomposition for an Implicit Shallow-water Transport Solver).Meeting of the DFG Panel for the Sonderforsbe-reich1578,M¨u nchen,January16–17:Participa-tion by C.J.van Duijn.Meeting of the Scientific Council of the Weier-strass Institut f¨u r Angewandte Analysis und Sto-chastik,Berlin,January24:C.J.Van Duijn partici-pates and is elected vice-chairman of this council. Guest Lectures at the University of Amsterdam, within the framework of the course‘Parallel Scientific Computing and Simulation’,February21 and26:B.P.Sommeijer(Parallel ODE solvers). Harburger Sommerschulen,TU Hamburg-Harburg, February24–28:J.G.Verwer invited speaker (three lectures on the Method of Lines). Universidad Complutense de Madrid,Madrid, March19–23:C.J.van Duijn visits J.I.Diaz.32e Nederlands Mathematisch Congres,Wage-ningen,April3–4:W.Hundsdorfer(Stability of the Douglas Splitting Method),E.J.Spee(Ad-vectieschema’s op een Bol voor Atmosferische Transport-modellen).Istituto per le Applicazioni del Calcolo‘Mauro Pi-cone’,Rome,April7–11:C.J.van Duijn visits M. Bertsch.1st ERCIM Environmental Modelling Group Workshop on Air Pollution Modelling,GMD FIRST,Berlin,April7–8:J.G.Blom(An Evalua-tion of the Cray T3D Programming Paradigms in Atmospheric Chemistry/transport Problems),J.G. Verwer(A Numerical Study for Atmospheric Che-mistry/transport Problems).Both invited. Measurements and Modelling in Environmen-tal Pollution,Madrid,April22–24:M.van Loon (Data Assimilation for Atmospheric Chemistry Models).22nd General Assembly of the European Geo-physical Society,Vienna,April21–25:B.P.Som-meijer(A Fully Implicit3D Transport-chemistry Solver Combined with Domain Decomposition). NWO Symposium Massaal Parallel Rekenen, Veldhoven,May22:J.G.Verwer invited speaker (High Performance Computing and Environmental Pollutions).。

示范Modeling学会教师示范学生如何知道他们该做什么？通过清楚的教师示范，提供给学生一个明确的有关技能与策略的示范。

教师通过如下几点，提供一个模式对学生进行指导： ∙ 描述技能或策略。

∙ 通过演示这一技能来清楚地描述策略的特征或步骤。

∙ 将技能分解成便于学生学习的几个部分 ∙ 用多种技巧描述/示范要想让学生学习，教师就要充满热情的，循序渐进的提出问题，随时了解学生掌握的情况。

教师一定要先清楚地描述概念，然后示范预期成果，通过展示自己的思维过程，发挥各个感觉器官的功能进行指导。

教师可提供实例或直接告诉学生预期结果，在描述过程中，需要经常性的停顿，以便留出让学生思考或提问的时间。

这种示范的方法能激发高级的师生互动。

在课堂上运用教师示范清楚的教师示范应该运用于所有年级、所有科目中。

为了让示范成功，教师需要仔细设计。

下面的步骤可以帮助你做好示范：1. 保证学生有相关的背景知识和必要的技能来完成任务。

2. 将技能根据学生可接受的情况进行分解。

3. 保证技能之间的联系，水平适当，循序渐进。

4. 调动身体各个器官的功能，讲解重点。

5. 在讲解每一个步骤时，运用思维展示的方式。

6. 在步骤之间设计联系7. 检查学生是否明白，如果有不明白的地方再做示范。

8. 确保学习进度适合学生的学习，不要让学生因感到厌倦，而不能集中注意力。

9. 示范的次数要根据学生是否明白，是否可以自己操作而定。

10. 允许学生提问，然后澄清疑问。

示范一个概念或技能所需的时间有赖于要求学生完成任务的难易度。

示范一些小技巧可能只需几分钟，而复杂的技能可能要花很长的学时。

重要的是教师预先要知道通过示范他想让学生做什么。

因此，当学生开始学习时，对自己所要达到的目标很明确。

在示范之前详细说明需要做的事情，也可以使得评估更具建设性、更具精确性。

教师示范实例思维展示是教师示范综合思维的一种方法。

学习更多 >教学设计集锦: 示范示范教师示范活动思维展示思维展示是一种教学方法，能让学生了解教师的思维过程，教师通过描述思考步骤的方法，示范技巧或方法。

C a m s r M E S解决方案工厂建模m o d e l i n g中文手册Document number【AA80KGB-AA98YT-AAT8CB-2A6UT-A18GG】第一章总体介绍Designer 是camstar提供的用于管理CDO的图形化的程序，如上所叙，你定义和维护你的工厂信息模型的模型对象或者元素。

对对象建模，以NamedDataObject和RevisionedObject代表，在Designer里面是CDO的一个子集。

NDO是用一个用唯一的名字来区分的camstar对象的一个类RO是用一个用唯一的名字和版本来区分的camstar对象的一个类。

数据对象的实例是固定的，关于他们的信息都写进到数据库中。

CDO的实例产生和维护在modleing,而对象本身在Designer被创造(和可以改名)。

例如,一个工厂管理员创建两个新员工的定义：操作员和主管。

要重命名其中一个员工对象为Personnel、管理员必须使用Designer。

对象的名称显示在modleing中，比如ObjectGroup在designer中变成Object Group，这是通过对象的显示名称属性实现的。

在designer里面你可以修改对象域的属性。

比如customer域，对于Product的定义来说是可选项，通过点击域属性中的选择框能被设计成必须的。

对象维护通过WEB APPLICATION 你可以维护你的对象。

你可以定义修改，拷贝，删除实例。

信息模型信息模型包含描述和控制产品生产活动的数据对象。

在camstar Manufacturing 你使用modeling功能来构建制造工厂的独立的模型。

下图展示了信息模型的关键组成部分。

物理的程序模型每一个生产工厂的信息模型由一下部件组成：物理模型制程模型执行模型物理模型物理模型代表制造工厂的物理部件，它包含：企业，工厂，地点，组织，资源实例的其他能被定义的对象是：资源组，装置，文档浏览器，文档，方法，文档集制程模型制程模型代表信息模型的控制部分。

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