Chapter 13. Introduction to Modeling Species Transport
Chapter13.Introduction to Modeling Species Transportand Reacting Flows FLUENT provides several models for chemical species transport and chemical reactions.This chapter provides an overview of the species transport and reaction models available in FLUENT.Details about the models are provided in Chapters14–18.Models for engine ignition and pollutant formation are described in Chapters19and20,respectively.•Section13.1:Overview of Species and Reaction Modeling•Section13.2:Approaches to Reaction Modeling•Section13.3:Choosing a Reaction Model13.1Overview of Species and Reaction ModelingFLUENT can model species transport with or without chemical reactions.For information about modeling species transport without chemical reactions,see Section14.4:Species Transport Without Reactions.Chemical reactions that can be modeled in FLUENT include the following:•Gas phase reactions that may involve NO x and other pollutant formation,etc.•Spark and autoignition(Chapter19:Engine Ignition Model)that involve volumetricand chemical kinetics of reactingflow.•Surface reactions(e.g.,chemical vapor deposition)in which the reaction occurs ata solid(wall)boundary.•Particle surface reactions(e.g.,coal char combustion)in which the reaction occursat the surface of a discrete-phase particle.Additional information on modeling of droplet/particle reactions is presented in Sec-tion23.3:Heat and Mass Transfer Calculations.Introduction to Modeling Species Transport and Reacting Flows13.2Approaches to Reaction ModelingFLUENT providesfive approaches to modeling gas phase reactingflows:•Generalizedfinite-rate model•Non-premixed combustion model•Premixed combustion model•Partially premixed combustion model•Composition PDF Transport modelA brief overview of each model is provided in Sections13.2.1–13.2.5.See Section13.3:Choosing a Reaction Model for guidelines on choosing a model.13.2.1Generalized Finite-Rate ModelThis approach is based on the solution of transport equations for species mass fractions.The reaction rates that appear as source terms in the species transport equations are com-puted from Arrhenius rate expressions.You can use chemical kinetic mechanisms from the FLUENT database,create one yourself,or import a mechanism in Chemkin format.For turbulentflows,turbulence-chemistry interaction can be ignored using the Laminar Finite-Rate model,or modeled with the Eddy Dissipation[215]or EDC models[214].The Generalized Finite-Rate Model is suitable for a wide range of applications including premixed,partially premixed,non-premixed turbulent combustion,and ignition delay in diesel engines(Section19.2:Autoignition Model).FLUENT provides several options to handle the stiffnumerics of detailed kinetic mechanism.See Chapter14:Modeling Species Transport and Finite-Rate Chemistry for details.13.2.2Non-Premixed Combustion ModelIn this approach individual species transport equations are not solved.Instead,trans-port equations for one or two conserved scalars(the mixture fractions)are solved and individual component concentrations are derived from the predicted mixture fraction distribution.This approach has been specifically developed for the simulation of tur-bulent diffusionflames and offers many benefits over thefinite-rate formulation.In the Non-Premixed Combustion Model,turbulence effects are accounted for with the help of an assumed shape Probability Density Function(PDF).Reaction mechanisms are not required;species and temperature can be modeled as in chemical equilibrium.Alterna-tively,the steady Laminar Flamelet model can include localfinite-rate kinetic effects due to straining by the turbulence.See Chapter15:Modeling Non-Premixed Combustion for details.13.2Approaches to Reaction Modeling13.2.3Premixed Combustion ModelThis model can be applied to turbulent combustion systems that are of the purely pre-mixed type.In these problems perfectly mixed reactants and burned products are sepa-rated by aflame front.The“reaction progress variable”is solved to predict the position of this front.The influence of turbulence is accounted for by means of a turbulentflame speed.See Chapter16:Modeling Premixed Combustion for details.13.2.4Partially Premixed Combustion ModelThe partially premixed combustion model has been developed for turbulent reacting flows that have a combination of non-premixed and premixed combustion.The mix-ture fraction equations and the reaction progress variable are solved to determine the species concentrations and position of theflame front,respectively.The knock model (Section19.2:Autoignition Model)demonstrates the use of the concepts discussed in Chapters16and17.13.2.5Composition PDF Transport Combustion ModelThe composition PDF transport model simulates realisticfinite-rate kinetic effects in turbulentflames.Arbitrary chemical mechanisms can be imported into FLUENT,and kinetic effects such as non-equilibrium species and ignition/extinction can be captured. This model is applicable to premixed,non-premixed,and partially premixedflames.Note that the model is computationally expensive.See Chapter18:The Composition PDF Transport Model for details.Introduction to Modeling Species Transport and Reacting Flows13.3Choosing a Reaction ModelThefirst step in solving any problem involving species transport and reactingflow is to determine which model is appropriate.Consider the following guidelines:•For cases involving the mixing,transport,or reaction of chemical species,or re-actions on the surface of a wall or particle(e.g.,chemical vapor deposition),usethe generalizedfinite-rate model.See Chapter14:Modeling Species Transportand Finite-Rate Chemistry for more information about the generalizedfinite-ratemodel.•For reacting systems involving turbulent diffusionflames that are near chemicalequilibrium where the fuel and oxidizer enter the domain in two or three distinctstreams,use the non-premixed combustion model.See Chapter15:Modeling Non-Premixed Combustion for more information about non-premixed combustion.•For cases with a single,perfectly premixed reactant stream,use the premixed com-bustion model.See Chapter16:Modeling Premixed Combustion for more informa-tion about premixed combustion.•For cases involving premixedflames with varying equivalence ratio in the domain,use the partially premixed combustion model.See Chapter17:Modeling PartiallyPremixed Combustion for more information about partially premixed combustion.•For turbulentflames wherefinite-rate chemistry is important,use the LaminarFlamelet model(see Chapter15:Modeling Non-Premixed Combustion),the Lam-inar Finite-Rate or EDC model(see Chapter14:Modeling Species Transport andFinite-Rate Chemistry),or the composition PDF Transport model(see Chap-ter18:The Composition PDF Transport Model).。
sas enterprise miner操作手册英文版目录
Applied Analytics Using SAS® Enterprise Miner™Course NotesApplied Analytics Using SAS® Enterprise Miner™ Course Notes was developed by Peter Christie, Jim Georges, Jeff Thompson, and Chip Wells. Additional contributions were made by Tom Bohannon, Mike Hardin, Dan Kelly, Bob Lucas, and Sue Walsh. Editing and production support was provided by the Curriculum Development and Support Department.SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are trademarks of their respective companies.Applied Analytics Using SAS® Enterprise Miner™ Course NotesCopyright © 2011 SAS Institute Inc. Cary, NC, USA. All rights reserved. Printed in the United States of America. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc.Book code E2056, course code LWAAEM71/AAEM71, prepared date 18Oct2011. LWAAEM71_001ISBN 978-1-61290-139-8For Your Information iii Table of ContentsCourse Description (x)Prerequisites (xi)Chapter 1 Introduction ......................................................................................... 1-11.1 Introduction to SAS Enterprise Miner ............................................................................. 1-31.2 Solutions ........................................................................................................................ 1-24Solutions to Student Activities (Polls/Quizzes) ...................................................... 1-24 Chapter 2 Accessing and Assaying Prepared Data ........................................... 2-12.1 Introduction ...................................................................................................................... 2-32.2 Creating a SAS Enterprise Miner Project, Library, and Diagram ................................... 2-5Demonstration: C reating a SAS Enterprise Miner Project ....................................... 2-6Demonstration: C reating a SAS Library ................................................................. 2-10Demonstration: C reating a SAS Enterprise Miner Diagram ................................... 2-12Exercises ................................................................................................................. 2-132.3 Defining a Data Source .................................................................................................. 2-14Demonstration: D efining a Data Source ................................................................. 2-18Exercises ................................................................................................................. 2-332.4 Exploring a Data Source ................................................................................................ 2-34Demonstration: E xploring Source Data .................................................................. 2-35Demonstration: C hanging the Explore Window Sampling Defaults ...................... 2-59Exercises ................................................................................................................. 2-61Demonstration: M odifying and Correcting Source Data ........................................ 2-622.5 Chapter Summary .......................................................................................................... 2-742.6 Solutions ........................................................................................................................ 2-75iv For Your InformationSolutions to Exercises ............................................................................................. 2-75Solutions to Student Activities (Polls/Quizzes) ...................................................... 2-76 Chapter 3 Introduction to Predictive Modeling: Decision Trees ....................... 3-1 3.1 Introduction ...................................................................................................................... 3-3Demonstration: C reating Training and Validation Data .......................................... 3-23 3.2 Cultivating Decision Trees ............................................................................................ 3-28Demonstration: C onstructing a Decision Tree Predictive Model ........................... 3-43 3.3 Optimizing the Complexity of Decision Trees .............................................................. 3-61Demonstration: A ssessing a Decision Tree ............................................................. 3-77 3.4 Understanding Additional Diagnostic Tools (Self-Study) ............................................. 3-88Demonstration: U nderstanding Additional Plots and Tables (Optional) ................ 3-89 3.5 Autonomous Tree Growth Options (Self-Study) ........................................................... 3-94Exercises ............................................................................................................... 3-102 3.6 Chapter Summary ........................................................................................................ 3-104 3.7 Solutions ...................................................................................................................... 3-105Solutions to Exercises ........................................................................................... 3-105Solutions to Student Activities (Polls/Quizzes) .................................................... 3-120 Chapter 4 Introduction to Predictive Modeling: Regressions ........................... 4-1 4.1 Introduction ...................................................................................................................... 4-3Demonstration: M anaging Missing Values ............................................................. 4-18Demonstration: R unning the Regression Node ....................................................... 4-24 4.2 Selecting Regression Inputs ........................................................................................... 4-28Demonstration: S electing Inputs ............................................................................. 4-32 4.3 Optimizing Regression Complexity ............................................................................... 4-38Demonstration: O ptimizing Complexity ................................................................. 4-40For Your Information v 4.4 Interpreting Regression Models ..................................................................................... 4-49Demonstration: I nterpreting a Regression Model ................................................... 4-514.5 Transforming Inputs ...................................................................................................... 4-52Demonstration: T ransforming Inputs ...................................................................... 4-564.6 Categorical Inputs .......................................................................................................... 4-66Demonstration: R ecoding Categorical Inputs ......................................................... 4-694.7 Polynomial Regressions (Self-Study) ............................................................................ 4-75Demonstration: A dding Polynomial Regression Terms Selectively ....................... 4-77Demonstration: A dding Polynomial Regression Terms Autonomously(Self-Study) ................................................................................... 4-85 Exercises ................................................................................................................. 4-884.8 Chapter Summary .......................................................................................................... 4-894.9 Solutions ........................................................................................................................ 4-91Solutions to Exercises ............................................................................................. 4-91Solutions to Student Activities (Polls/Quizzes) .................................................... 4-104 Chapter 5 Introduction to Predictive Modeling: Neural Networks andOther Modeling Tools ......................................................................... 5-15.1 Introduction ...................................................................................................................... 5-3Demonstration: T raining a Neural Network ........................................................... 5-125.2 Input Selection ............................................................................................................... 5-20Demonstration: S electing Neural Network Inputs .................................................. 5-215.3 Stopped Training ............................................................................................................ 5-24Demonstration: I ncreasing Network Flexibility ..................................................... 5-35Demonstration: U sing the AutoNeural Tool (Self-Study) ....................................... 5-395.4 Other Modeling Tools (Self-Study) ............................................................................... 5-46Exercises ................................................................................................................. 5-585.5 Chapter Summary .......................................................................................................... 5-59vi For Your Information5.6 Solutions ........................................................................................................................ 5-60Solutions to Exercises ............................................................................................. 5-60Solutions to Student Activities (Polls/Quizzes) ...................................................... 5-63 Chapter 6 Model Assessment .............................................................................. 6-1 6.1 Model Fit Statistics .......................................................................................................... 6-3Demonstration: C omparing Models with Summary Statistics .................................. 6-6 6.2 Statistical Graphics .......................................................................................................... 6-9Demonstration: C omparing Models with ROC Charts ........................................... 6-13Demonstration: C omparing Models with Score Rankings Plots ............................ 6-19Demonstration: A djusting for Separate Sampling .................................................. 6-22 6.3 Adjusting for Separate Sampling ................................................................................... 6-29Demonstration: A djusting for Separate Sampling (Continued) .............................. 6-32Demonstration: C reating a Profit Matrix ................................................................ 6-35 6.4 Profit Matrices ............................................................................................................... 6-44Demonstration: E valuating Model Profit ................................................................ 6-47Demonstration: V iewing Additional Assessments .................................................. 6-49Demonstration: O ptimizing with Profit (Self-Study) .............................................. 6-52Exercises ................................................................................................................. 6-54 6.5 Chapter Summary .......................................................................................................... 6-55 6.6 Solutions ........................................................................................................................ 6-56Solutions to Exercises ............................................................................................. 6-56Solutions to Student Activities (Polls/Quizzes) ...................................................... 6-59 Chapter 7 Model Implementation ........................................................................ 7-1 7.1 Introduction ...................................................................................................................... 7-3 7.2 Internally Scored Data Sets ............................................................................................. 7-5Demonstration: C reating a Score Data Source ......................................................... 7-6For Your Information vii Demonstration: S coring with the Score Tool ............................................................ 7-7Demonstration: E xporting a Scored Table (Self-Study) ......................................... 7-107.3 Score Code Modules ...................................................................................................... 7-16Demonstration: C reating a SAS Score Code Module ............................................. 7-17Demonstration: C reating Other Score Code Modules ............................................ 7-23Exercises ................................................................................................................. 7-257.4 Chapter Summary .......................................................................................................... 7-267.5 Solutions to Exercises .................................................................................................... 7-27 Chapter 8 Introduction to Pattern Discovery ..................................................... 8-18.1 Introduction ...................................................................................................................... 8-38.2 Cluster Analysis ............................................................................................................... 8-8Demonstration: S egmenting Census Data ............................................................... 8-16Demonstration: E xploring and Filtering Analysis Data .......................................... 8-23Demonstration: S etting Cluster Tool Options ......................................................... 8-34Demonstration: C reating Clusters with the Cluster Tool ........................................ 8-38Demonstration: S pecifying the Segment Count ...................................................... 8-41Demonstration: E xploring Segments ...................................................................... 8-43Demonstration: P rofiling Segments ........................................................................ 8-53Exercises ................................................................................................................. 8-578.3 Market Basket Analysis (Self-Study)............................................................................. 8-59Demonstration: M arket Basket Analysis ................................................................. 8-63Demonstration: S equence Analysis ......................................................................... 8-79Exercises ................................................................................................................. 8-828.4 Chapter Summary .......................................................................................................... 8-848.5 Solutions ........................................................................................................................ 8-85Solutions to Exercises ............................................................................................. 8-85Solutions to Student Activities (Polls/Quizzes) ...................................................... 8-96viii For Your InformationChapter 9 Special Topics ..................................................................................... 9-1 9.1 Introduction ...................................................................................................................... 9-3 9.2 Ensemble Models ............................................................................................................. 9-4Demonstration: C reating Ensemble Models ............................................................. 9-5 9.3 Variable Selection ............................................................................................................ 9-9Demonstration: U sing the Variable Selection Node ............................................... 9-10Demonstration: U sing Partial Least Squares for Input Selection ........................... 9-14Demonstration: U sing the Decision Tree Node for Input Selection ....................... 9-19 9.4 Categorical Input Consolidation .................................................................................... 9-23Demonstration: C onsolidating Categorical Inputs .................................................. 9-24 9.5 Surrogate Models ........................................................................................................... 9-32Demonstration: D escribing Decision Segments with Surrogate Models ................ 9-33 9.6 SAS Rapid Predictive Modeler ...................................................................................... 9-39Demonstration: R unning a Basic RPM Model ....................................................... 9-41Demonstration: R unning an Intermediate RPM Model (Self-Study)...................... 9-50Demonstration: O pening an RPM Model in SAS Enterprise Miner ....................... 9-51Demonstration: R egistering an RPM Model ........................................................... 9-53Demonstration: S coring in SAS Enterprise Guide with a Registered Model ......... 9-54 Appendix A Case Studies ...................................................................................... A-1 A.1 Banking Segmentation Case Study ................................................................................. A-3 A.2 Web Site Usage Associations Case Study ..................................................................... A-19 A.3 Credit Risk Case Study ................................................................................................. A-22 A.4 Enrollment Management Case Study ............................................................................ A-40 Appendix B Bibliography ....................................................................................... B-1 B.1 References ....................................................................................................................... B-3For Your Information ix Appendix C Index ................................................................................................... C-1x For Your InformationCourse DescriptionThis course covers the skills required to assemble analysis flow diagrams using the rich tool set of SAS Enterprise Miner for both pattern discovery (segmentation, association, and sequence analyses) and predictive modeling (decision tree, regression, and neural network models).To learn more…For information on other courses in the curriculum, contact the SAS EducationDivision at 1-800-333-7660, or send e-mail to training@. You can alsofind this information on the Web at /training/ as well as in theTraining Course Catalog.For a list of other SAS books that relate to the topics covered in thisCourse Notes, USA customers can contact our SAS Publishing Department at1-800-727-3228 or send e-mail to sasbook@. Customers outside theUSA, please contact your local SAS office.Also, see the Publications Catalog on the Web at /pubs for acomplete list of books and a convenient order form.For Your Information xi PrerequisitesBefore attending this course, you should be acquainted with Microsoft Windows and Windows-based software. In addition, you should have at least an introductory-level familiarity with basic statistics and regression modeling. Previous SAS software experience is helpful but not required.xii For Your Information。
感受数学之美的给孩子看的英文书
感受数学之美的给孩子看的英文书全文共3篇示例，供读者参考篇1Title: Exploring the Beauty of MathematicsIntroductionMathematics is more than just numbers and equations, it is a fascinating and intricate puzzle that challenges our minds and shapes the world around us. In this book, we will delve into the beauty of mathematics and explore its endless possibilities. Through engaging stories, colorful illustrations, and interactive activities, children will discover the magic of numbers and the wonders of geometry, algebra, and more.Chapter 1: The Power of PatternsFrom the mesmerizing spiral of a seashell to the symmetrical petals of a flower, patterns are everywhere in nature. In this chapter, children will learn how to recognize and create patterns using basic shapes and colors. Through hands-on activities such as drawing and coloring, they will develop a keen eye for symmetry and repetition.Chapter 2: The Joy of GeometryGeometry is the study of shapes and their properties, and it is the foundation of many mathematical concepts. In this chapter, children will explore the world of polygons, circles, and angles. They will learn how to measure and calculate areas and perimeters, and discover the beauty of tessellations and fractals.Chapter 3: The Wonder of NumbersNumbers are the building blocks of mathematics, and they hold endless mysteries waiting to be uncovered. In this chapter, children will learn about the history of numbers, from the ancient civilizations to modern mathematicians. They will explore the concepts of prime numbers, fractions, and decimals, and engage in fun games and puzzles to sharpen their numerical skills.Chapter 4: The Magic of AlgebraAlgebra is the language of equations and variables, and it is crucial for solving complex problems. In this chapter, children will embark on a journey through algebraic expressions, equations, and inequalities. They will learn how to simplify expressions, solve equations, and graph functions, giving them the tools to tackle real-world challenges with confidence.Chapter 5: The Beauty of CalculusCalculus is the study of change and motion, and it is a powerful tool for understanding the world around us. In this chapter, children will be introduced to the concepts of derivatives, integrals, and limits. They will explore the connection between calculus and physics, biology, and other sciences, and witness the beauty of mathematical modeling in action.ConclusionMathematics is a treasure trove of beauty and wonder, waiting to be explored by curious minds. By diving into the world of patterns, geometry, numbers, algebra, and calculus, children can unlock the secrets of the universe and unleash their creativity and problem-solving skills. This book is just the beginning of their mathematical journey, and I hope it inspires them to continue exploring the infinite possibilities of this fascinating field.篇2Title: Exploring the Beauty of Mathematics: A Book for ChildrenIntroductionMathematics is a beautiful and fascinating subject that is often misunderstood and feared by many children. However, it isessential to teach children about the beauty and wonders of mathematics from a young age to foster a love and appreciation for the subject. This book aims to introduce children to the beauty of mathematics in a fun and engaging way, helping them see the world through the lens of mathematics.Chapter 1: The Magic of NumbersIn this chapter, children will learn about the magic of numbers and how they are used in everyday life. From counting to discovering patterns and sequences, numbers are all around us. Children will explore the concept of symmetry, prime numbers, and the Fibonacci sequence, opening their minds to the beauty of mathematics.Chapter 2: The Language of ShapesShapes are everywhere, from the geometry of buildings to the symmetry of nature. In this chapter, children will learn about different geometric shapes, such as circles, squares, triangles, and polygons. They will discover the beauty of symmetry and tessellations, as well as the concept of fractals and the golden ratio.Chapter 3: The Art of Problem SolvingMathematics is not just about numbers and shapes but also about problem-solving. In this chapter, children will learn about different problem-solving strategies, such as breaking down a problem, looking for patterns, and using logical reasoning. They will explore puzzles, riddles, and games that challenge their minds and nurture their problem-solving skills.Chapter 4: The Power of PatternsPatterns are an essential part of mathematics, helping us make sense of the world around us. In this chapter, children will learn about different types of patterns, such as number patterns, shape patterns, and symmetry. They will discover how patterns are used in mathematics, art, music, and nature, showing them the interconnectedness of the world.Chapter 5: The Beauty of InfinityThe concept of infinity is both mind-boggling and beautiful. In this chapter, children will learn about different types of infinity, such as countable and uncountable infinity. They will explore the concept of limits, sequences, and series, as well as the infinite nature of fractals and the Mandelbrot set. Children will be amazed by the endless possibilities of infinity and its presence in mathematics and beyond.ConclusionMathematics is a subject full of wonder, beauty, and creativity. By introducing children to the beauty of mathematics at a young age, we can help them develop a love and appreciation for the subject. This book aims to inspire children to see the world through the lens of mathematics, encouraging them to explore, discover, and create with confidence and curiosity. Let's unlock the beauty of mathematics together and open the doors to endless possibilities.篇3Title: Discovering the Beauty of Mathematics: A Children's BookIntroduction:Mathematics is often seen as a difficult and intimidating subject, but in reality, it is a beautiful and fascinating field of study. Through this children's book, we aim to help young readers discover the beauty of mathematics and develop a deeper appreciation for the subject.Chapter 1: Introduction to MathematicsIn this chapter, we introduce the basic concepts of mathematics, such as numbers, shapes, and patterns. We explain how mathematics is all around us, from the natural world to the technology we use every day.Chapter 2: The Beauty of SymmetrySymmetry is a key concept in mathematics and can be found in nature, art, and architecture. In this chapter, we explore different types of symmetry and how they can be used to create beautiful designs.Chapter 3: Exploring PatternsMathematics is all about finding and understanding patterns. In this chapter, we look at different types of patterns, such as geometric patterns, number patterns, and fractals. We show how patterns can be both simple and complex, and how they can be found in nature and art.Chapter 4: The Magic of NumbersNumbers are the building blocks of mathematics, and they have many fascinating properties. In this chapter, we explore the beauty of numbers, from prime numbers to Fibonacci sequences. We also look at how numbers are used in everyday life, from telling time to measuring distances.Chapter 5: The Language of MathematicsMathematics has its own language, with symbols and equations that help us solve problems and communicate ideas. In this chapter, we introduce young readers to some basic mathematical symbols and show how they are used in equations.Chapter 6: The World of ShapesGeometry is a branch of mathematics that studies shapes and their properties. In this chapter, we explore different types of shapes, such as polygons, circles, and solids. We also look at how shapes are used in art and design.Conclusion:By the end of this book, we hope that young readers will have a better understanding of the beauty of mathematics and be inspired to explore the subject further. Mathematics is not just about solving equations - it is a way of thinking and seeing the world in a new light. We encourage children to embrace the beauty of mathematics and enjoy the journey of discovery that it offers.。
Modeling,Simulat...
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:*****************。
北美精算师C考试内容2013-Oct-exam-C
Construction and Evaluation of Actuarial Models ExamThe Construction and Evaluation of Actuarial Models exam is called Exam C by the SOA and Exam 4 by the CAS. This three-and-a-half hour exam consists of 35 multiple-choice questions. The examination is jointly sponsored and administered by the SOA, CAS, and the Canadian Institute of Actuaries (CIA). The examination is also jointly sponsored by the American Academy of Actuaries (AAA) and the Conference of Consulting Actuaries (CCA).The Construction and Evaluation of Actuarial Models Exam is administered as a computer-based test. For additional details, please refer to Exam Rules. The syllabus for this examination provides an introduction to modeling and covers important actuarial methods that are useful in modeling. A thorough knowledge of calculus, probability, and mathematical statistics is assumed.The candidate will be introduced to a variety of useful frequency and severity models. The candidate will be required to understand the steps involved in the modeling process and how to carry out these steps in solving business problems. The candidate should be able to: 1) analyze data from an application in a business context; 2) determine a suitable model including parameter values; and 3) provide measures of confidence for decisions based upon the model. The candidate will be introduced to a variety of tools for the calibration and evaluation of the models.A variety of tables is available below for the candidate and will be provided to the candidate at the examination. These include values for the standard normal distribution, chi-square distribution, and abridged inventories of discrete and continuous probability distributions. Candidates will not be allowed to bring copies of the tables into the examination room. A preview of the CBT layout of the Exam C/4 tables in HTML is available online since the tables have been divided into five sections for viewing purposes.Check the Updates section on this exam's home page for any changes to the exam or syllabus. In the learning outcomes, weights have been provided to indicate the relative emphasis on different sections. The ranges of weights shown are intended to apply to the large majority of exams administered. On occasion, the weights of topics on an individual exam may fall outside the published range. Candidates should also recognize that some questions may cover multiple learning outcomes.Each multiple-choice problem includes five answer choices identified by the letters A, B, C, D, and E, only one of which is correct. Candidates must indicate responses to each question on the computer.As part of the computer-based testing process, a few pilot questions will be randomly placed in the exam (paper and pencil and computer-based forms). These pilot questions are included to judge their effectiveness for future exams, but they will NOT be used in the scoring of this exam.1 All other questions will be considered in the scoring. All unanswered questions are scored incorrect. Therefore, candidates should answer every question on the exam. There is no set requirement for the distribution of correct answers for the SOA/CAS/CIA multiple-choice preliminary examinations. It is possible that a particular answer choice could appear many times on an examination or not at all. Candidates are advised to answer each question to the best of their ability, independently from how they have answered other questions on the examination.Because the CBT exam will be offered over a period of a few days, each candidate will receive a test form composed of questions selected from a pool of questions. Statistical scaling methods are used to ensure within reasonable and practical limits that, during the same testing period of a few days, all forms of the test are comparable in content and passing criteria. The methodology that has been adopted is used by many credentialing programs that give multiple forms of an exam.LEARNING OUTCOMESThe candidate is expected to be familiar with survival, severity, frequency and aggregate models, and use statistical methods to estimate parameters of such models given sample data. The candidate is further expected to identify steps in the modeling process, understand the underlying assumptions implicit in each family of models, recognize which assumptions are applicable in a given business application, and appropriately adjust the models for impact of insurance coverage modifications.Specifically, the candidate is expected to be able to perform the tasks listed below. Items in italic font are additions or replacements with respect to the June 2013 syllabus.Sections A–E have a combined weight of 15-20%.A. Severity Models1. Calculate the basic distributional quantities:a) momentsb) Percentilesc) Generating functions2. Describe how changes in parameters affect the distribution.3. Recognize classes of distributions and their relationships.4. Apply the following techniques for creating new families of distributions:a) Multiplication by a constant1 Beginning with the October 2013 examination there are some revised learning objectives and readings. Items covering them may appear as scored or pilot items in the same manner as items on continuing topics.b) Raising to a powerc) Exponentiation,d) Mixing5. Identify the applications in which each distribution is used and reasons why.6. Apply the distribution to an application, given the parameters.7. Calculate various measures of tail weight and interpret the results to compare the tailweights.8. Identify and describe two extreme value distributions.B. Frequency ModelsFor the Poisson, Mixed Poisson, Binomial, Negative Binomial, Geometric distribution and mixtures thereof:1. Describe how changes in parameters affect the distribution,2. Calculate moments,3. Identify the applications for which each distribution is used and reasons why,4. Apply the distribution to an application given the parameters.5. Apply the zero-truncated or zero-modified distribution to an application given theparametersC. Aggregate Models1. Compute relevant parameters and statistics for collective risk models.2. Evaluate compound models for aggregate claims.3. Compute aggregate claims distributions.D. For severity, frequency and aggregate models1. Evaluate the impacts of coverage modifications:a) Deductiblesb) Limitsc) Coinsurance2. Calculate Loss Elimination Ratios.3. Evaluate effects of inflation on losses.E. Risk Measures1. Calculate VaR, and TVaR and explain their use and limitations.Sections F and G have a combined weight of 20-25%.F. Construction of Empirical Models1. Estimate failure time and loss distributions using:a) Kaplan-Meier estimatorb) Nelson-Åalen estimatorc) Kernel density estimators2. Estimate the variance of estimators and confidence intervals for failure time and lossdistributions.3. Apply the following concepts in estimating failure time and loss distribution:a) Unbiasednessb) Consistencyc) Mean squared errorG. Estimation of decrement probabilities from large samples1. Estimate decrement probabilities using both parametric and nonparametric approachesfor both individual and interval data2. Approximate the variance of the estimatorsH. Construction and Selection of Parametric Models (25-30%)1. Estimate the parameters of failure time and loss distributions using:a) Maximum likelihoodb) Method of momentsc) Percentile matchingd) Bayesian procedures2. Estimate the parameters of failure time and loss distributions with censored and/ortruncated data using maximum likelihood.3. Estimate the variance of estimators and the confidence intervals for the parameters andfunctions of parameters of failure time and loss distributions.4. Apply the following concepts in estimating failure time and loss distributions:a) Unbiasednessb) Asymptotic unbiasednessc) Consistencyd) Mean squared errore) Uniform minimum variance estimator5. Determine the acceptability of a fitted model and/or compare models using:a) Graphical proceduresb) Kolmogorov-Smirnov testc) Anderson-Darling testd) Chi-square goodness-of-fit teste) Likelihood ratio testf) Schwarz Bayesian CriterionI. Credibility (20-25%)1. Apply limited fluctuation (classical) credibility including criteria for both full and partialcredibility.2. Perform Bayesian analysis using both discrete and continuous models.3. Apply Bühlmann and Bühlmann-Straub models and understand the relationship of theseto the Bayesian model.4. Apply conjugate priors in Bayesian analysis and in particular the Poisson-gamma model.5. Apply empirical Bayesian methods in the nonparametric and semiparametric cases. J. Simulation (5-10%)1. Simulate both discrete and continuous random variables using the inversion method.2. Simulate from discrete mixtures, decrement tables, the (a,b,0) class, and the normal andlognormal distributions using methods designed for those distributions3. Estimate the number of simulations needed to obtain an estimate with a given error anda given degree of confidence.4. Use simulation to determine the p-value for a hypothesis test.5. Use the bootstrap method to estimate the mean squared error of an estimator.6. Apply simulation methods within the context of actuarial models.Reading Selections for learning outcomes A through H and J:Text• Loss Models: From Data to Decisions, (Fourth Edition), 2012, by Klugman, S.A., Panjer,H.H. and Willmot, G.E.Chapter 3Chapter 4Chapter 5Chapter 6Chapter 8Chapter 9, Sections 9.1–9.7 (excluding 9.6.1), Sections 9.8.1–9.8.2Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14, Sections 14.1 – 14.4 and 14.6Chapter 15Chapter 16Chapter 20Reading Options for learning outcome I (Credibility) will be:Option ACandidates may prepare for this exam using either the Third or Fourth Editions.• Loss Models: From Data to Decisions, (Fourth Edition), 2012, by Klugman, S.A., Panjer,H.H., and Willmot, G.E.Chapter 17, Sections 17.2 – 17.7Chapter 18Chapter 19Option B•Foundations of Casualty Actuarial Science (Fourth Edition), 2001, Casualty Actuarial SocietyChapter 8, Section 1 (background only) Sections 2–5•Topics in Credibility by Dean, C.G.Option C• Introduction to Credibility Theory (Fourth Edition), 2010, Herzog, T.N.Chapters 1-3 (background only)Chapters 4–8Chapter 9 (background only)Other ResourcesTables for Exam C/Exam 4Preview of the CBT layout of the Exam C/4 tables in HTMLAll released exam papers since 2000, can be found at:Past Exam Questions and SolutionsExam C/4 Sample Questions and Solutions. These documents will be updated to reflect the October 2013 syllabus changes. The cover page of each document will indicate any updates that have been made.。
地下水污染物迁移转化模型及数值解_Parts 3
有限差分与有限元数值解法的 主要差异： 主要差异： （1）网格刨分灵活性方面 （2）质量守恒方面
地下水污染控制与修复——王明玉
地下水模拟建模过程与方法
地下水污染控制与修复——王明玉
Introduction to Modeling Approaches
地下水污染控制与修复——王明玉
地下水污染控制与修复——王明玉
PRIMARY ISSUES OF CONCERN AT LARGE AND COMPLEX SITES
Data availability – How many sampling points are there? For how long? Data spatial distribution – Where are they located relative to the plume / source? Data quality / data management – Where is the data housed? Who uses it? Characterization and conceptualization of Site Conditions - How can they be represented conceptually?
地下水污染控制与修复——王明玉
National Academy of Sciences:
Thus, when models form the basis for decision-making, uncertainty will be an inescapable component of environmental management and regulation. A key consideration in any modeling process is whether the model has undergone sufficient development and testing to address the problem being analyzed in a sufficiently meaningful manner.
SOLIDWORKS 在线试用教程说明书
SOLIDWORKS Product T rialsContentsWelcome to SOLIDWORKS in the Browser (3)Introduction (4)Evaluation Data (5)Video Resolution (6)Basic Tools (7)Exiting SOLIDWORKS (8)Using a Cloud Storage Account with SOLIDWORKS in the Browser (9)Uploading Files (10)Downloading Files (11)Working with SOLIDWORKS (12)FAQ (13)Welcome to SOLIDWORKS in the BrowserWelcome to SOLIDWORKS in the BrowserThank you for trying SOLIDWORKS.The SOLIDWORKS software has intuitive solutions for all aspects of the design process.When you sign up for a trial version with a MySolidWorks account,you get access to SOLIDWORKS in the browser for the duration of your trial.With your MySolidWorksaccount,you can access training videos,blog posts,and other content related to designing products with SOLIDWORKS.We are always working to make our products better and more useful for you.If you have questions,you will likely find the answer in MySolidWorks.We hope you enjoy your new SOLIDWORKS in the browser experience,SOLIDWORKS Sales TeamIntroductionThis SOLIDWORKS trial is streamed in a Web browser instead of installing it on your computer.This means you can run the SOLIDWORKS software from anywhere with an Internet connection.Evaluation Data•SOLIDWORKS in the browser runs inside your Web browser.You will need the latest Google Chrome™,Mozilla®Firefox®,Apple Safari®,or Windows®Internet Explorer11browser to use it.•With this evaluation,you cannot open or save data to your own computer.If you want to experiment with your own data,you can read&write data using DropBox,Box,or Google Drive.•Any files you create will be deleted from the evaluation system after you close the evaluation session.Video ResolutionThe SOLIDWORKS software is maximized(dynamic)to your browser window size.To experiment with video resolution settings to find the best balance ofperformance and clarity:•Click Settings>Change resolution(lower left of the browser window)to find the setting that works best.Most people use Dynamic resolution.You might also need to experiment with your browser’s zoom level.A value less than 100%causes buttons and menus in SOLIDWORKS to shrink.To make them moreaccessible,increase the zoom level through your browser’s settings.Basic ToolsHere are some basic tools for using SOLIDWORKS in a browser .Select running applications,change the resolution,reporta problem,show and hide usage statistics,share yoursession,and soon.Settings Upload files from your local computer to the Uploadsfolder (under Favorites )in thesession.Upload files Connects to your Dropboxaccount.Dropbox Connects to your Google Driveaccount.Google Drive Connects to your Boxaccount.Box Basic ToolsExiting SOLIDWORKSExiting SOLIDWORKSClose the browser window or tab to exit the SOLIDWORKS software.The SOLIDWORKS in the browser session may also end if it times out.Time outs happen if you:•Exceed the maximum duration.The maximum duration of a session is shown in a countdown timer at the bottom of the screen while you run SOLIDWORKS in the browser.•Do not interact with it(by keyboard or mouse)for20minutes.Make sure you save any work to your cloud storage account before leaving the session unattended.SeeUsing a Cloud Storage Account with SOLIDWORKS in the Browser on page9.Using a Cloud Storage Account with SOLIDWORKS in the BrowserUsing a Cloud Storage Account with SOLIDWORKS in the BrowserTo use a cloud storage account with SOLIDWORKS in the browser,you must first have an account with either DropBox,Box,or Google Drive.To use a cloud storage account with SOLIDWORKS in the browser:1.Start SOLIDWORKS in the browser.2.Open the Web page provided to you in the welcome email you received when yousigned up for trial access to SOLIDWORKS in the browser.3.Log in to MySolidWorks.4.Click the appropriate icon for your cloud storage account(lower right of the browserwindow).5.Click Connect.6.Log in using your account credentials.After the connection is made,a new drive is available in your Open and Save dialog boxes.Larger DropBox accounts might take a few minutes to fully populate.Uploading FilesInstead of using Dropbox,you can upload files from your computer to the browser.To upload files:Click Uploadfiles.The uploaded files appear in the Uploads folder(under Favorites). Uploading FilesDownloading FilesInstead of using Dropbox,you can download files from the browser to your computer.To download files:1.ClickSave(Standard toolbar).2.In the dialog box,select Download Now(under Favorites)as the save location.3.Enter a File name and click Save.Downloading FilesWorking with SOLIDWORKSWorking with SOLIDWORKS SOLIDWORKS®3D CAD software delivers powerful design functionality with the intuitive SOLIDWORKS user interface to speed your design process and make you instantlyproductive.If you are new to SOLIDWORKS,we recommend that you start with the Introducing SOLIDWORKS Guide.Below are free training videos from .You can open these videos in a separate Web browser so you can use the training videos along with the SOLIDWORKS in the browser version.•Editing Parts•Bottom up Assembly Modeling•Introduction to Drawings and DetailingYou can access the training files used in the videos.Click File>Open.In the dialog box, browse to Libraries>Documents>SOLIDWORKS Product Trial>Training Files.Tutorials are available in the product to help you learn SOLIDWORKS subjects from basic to advanced.Click Help>SolidWorks Tutorials to navigate to the topics.Finally,a collection of sample files are also included in the SOLIDWORKS Product Trial folder to help you further explore SOLIDWORKS capabilities.FAQ1.Which web browser should I use?•Chrome24.0.1312.52+•Safari v7.0.3+•Internet Explorer11.0.10+•Opera21.0.1432.67+•Firefox18.0+If you experience trouble launching SOLIDWORKS,first try updating your browser.For example,see https:///chrome/answer/95414?hl=en.2.How fast should my internet be?SOLIDWORKS is leveraging the latest technology to deliver you incredible3D software over the internet.With that in mind,we do suggest using this with a broadbandconnection of at least3000/300Kbps(Download/Upload).For best experience,wehave found5000/500Kbps to be ideal for1920x1080resolution.For an acceptableexperience,a minimum of1000/100is as low as a user should go.3.How do I save my work?During your browser-based session,any files created or modifications made to sample files are not saved on disk after the session is closed.The platform allows a direct connection to a cloud storage account.See Using a Cloud Storage Account with SOLIDWORKS in the Browser on page9.You can also download or upload individual files through the virtualization platform.See Uploading Files on page10.4.I’m seeing this error:Connection refused:It looks like you already connected….This can happen if you are kicked out of your session.Refresh(F5)your browser and wait30-60seconds for the previous session to close.5.The buttons and menus are too small in SOLIDWORKS.How do I make them bigger?Increase the zoom level in your browser’s settings to100%.This setting is available in all supported browsers,but its location varies.In Google Chrome,for example,the zoom level is in the Zoom section of the Chrome menu on the browser toolbar.6.If I get disconnected while working,will I lose my work?If for any reason you get disconnected,the platform will preserve your session for10 minutes.After10minutes,you will be given a new instance and any unsaved workwill be lost.Recommendation:Connect your browser session to an online storage account tosave your data periodically.7.What if I have performance trouble or errors during the evaluation?•Check your internet connection quality using .•Switch to an ethernet-wired instead of wireless connection.•Try a different,supported web browser.•Try reconnecting at a later time.8.What if I want to continue using web browser-based SOLIDWORKS after purchase?Today,SOLIDWORKS requires local installation on a Windows PC.See systemrequirements here:https:///sw/support/SystemRequirements.htmlWe do not currently offer any SOLIDWORKS tools through the browser platform-it is limited to free evaluations and trials only.。
英语数学科普书
英语数学科普书Title: Introduction to Mathematics: Unlocking the World of NumbersIntroduction:Mathematics, often regarded as the language of the universe, is a discipline that encompasses the study of numbers, shapes, patterns, and quantities. This introductory book aims to provide readers with a comprehensive understanding of the fundamental concepts and applications of mathematics.Chapter 1: The Beauty of NumbersNumbers are the building blocks of mathematics. This chapter explores the different types of numbers, such as natural numbers, integers, rational numbers, and irrational numbers. Through engaging examples and explanations, readers will discover the significance of numbers in everyday life and their role in solving real-world problems.Chapter 2: The Art of Problem SolvingProblem-solving is at the heart of mathematics. This chapter delves into various problem-solving strategies, including logical reasoning, deduction, and induction. By presenting arange of intriguing puzzles and challenges, readers will learn how to approach problems systematically and develop critical thinking skills.Chapter 3: Unraveling the Mysteries of AlgebraAlgebra is the branch of mathematics that deals with symbols and the rules for manipulating these symbols. This chapter introduces the basic principles of algebra, including variables, equations, and inequalities. Through step-by-step explanations and practical examples, readers will grasp the essence of algebra and its applications in various fields.Chapter 4: Geometry: Exploring the World of Shapes Geometry is the study of shapes, sizes, and properties of figures and spaces. This chapter explores the fundamental concepts of geometry, such as points, lines, angles, and polygons. By examining both two-dimensional and three-dimensional shapes, readers will gain a deeper understanding of spatial relationships and geometric principles.Chapter 5: The Power of Functions and CalculusFunctions and calculus play a crucial role in modeling real-world phenomena and solving complex problems. Thischapter introduces the concept of functions and their properties, as well as the basics of calculus, including limits, derivatives, and integrals. Through clear explanations and practical examples, readers will see how functions and calculus are applied in fields like physics, economics, and engineering.Chapter 6: Statistics and Probability: Making Sense of Data Statistics and probability are essential tools for making sense of data and making informed decisions. This chapter covers the basics of data analysis, including collecting, organizing, and interpreting data. It also explores probability theory, including concepts like probability distributions and hypothesis testing. By understanding statistics and probability, readers will be equipped to critically evaluate information and navigate the world of uncertainty.Conclusion:Mathematics is a fascinating field that provides a framework for understanding the world around us. This introductory book has explored various branches of mathematics, from numbers and algebra to geometry, calculus, and statistics. By delving into these topics, readers will develop a solidfoundation in mathematics and gain the confidence to explore further. So, let's embark on this mathematical journey together and unlock the infinite possibilities that numbers hold!。
英文模特培训课程安排计划
英文模特培训课程安排计划Introduction:Modeling is a profession that requires a combination of talent, discipline, and hard work. It's not just about looking pretty or handsome, but also about having the right attitude, understanding the industry, and knowing how to take care of oneself. That's why at our modeling school, we provide a comprehensive training program that covers all these aspects and more. Our goal is not just to help our students become successful models, but also to prepare them for a long and fulfilling career in the fashion industry.Our training program is designed to provide students with the knowledge and skills they need to succeed in the world of modeling. Our team of experienced instructors will guide students through a series of courses that cover various aspects of modeling, including runway walking, posing, grooming, and more. In addition to practical training, students will also receive valuable insights into the industry, as well as tips on how to build a successful career.Course Structure:Week 1: Introduction to Modeling- Introduction to the modeling industry- Understanding the different types of modeling- Discussion on the qualities and characteristics of a successful model- Q&A session with experienced modelsWeek 2: Runway Techniques- Learning the basics of runway walking- Posture and body language- Tips on how to create a strong and confident presence on the runway- Practice sessions with feedback from instructorsWeek 3: Posing for Photoshoots- Understanding the different types of poses- Working with photographers and stylists- Tips on how to relax and be natural in front of the camera- Practice sessions with feedback from instructorsWeek 4: Grooming and Makeup- Skincare and haircare tips- Understanding different makeup styles- Tips on how to do your own makeup for auditions and castings - Practical sessions with professional makeup artistsWeek 5: Nutrition and Fitness- Importance of a healthy diet for models- Tips on how to maintain a fit and toned physique- Creating a personalized fitness and nutrition plan- Q&A session with a nutritionist and fitness trainerWeek 6: Building Your Portfolio- Understanding the importance of a strong portfolio- Tips on how to select the right photographers and stylists- Practice photoshoot sessions with professional photographers - Review and feedback on portfolio developmentWeek 7: The Business of Modeling- Understanding contracts and agreements- Tips on how to negotiate with clients and agencies- Building a professional network- Q&A session with industry professionalsWeek 8: Industry Insights- Understanding the different roles in the fashion industry- Tips on how to navigate through the industry- Developing a personal brand- Q&A session with successful models and industry professionals Week 9: Building Your Personal Brand- Understanding the importance of personal branding- Tips on how to create and maintain a strong personal brand- Developing a social media strategy- Practical sessions on creating a personal brandWeek 10: Marketing Yourself- Understanding the different marketing channels for models- Creating a strong online presence- Tips on how to get noticed by agencies and clients- Q&A session with successful models and industry professionalsWeek 11: Casting and Audition Techniques- Understanding the casting process- Tips on how to prepare for auditions- Practice auditions with industry professionals- Feedback and tips on improving audition skillsWeek 12: Final Project - Fashion Show- Organizing a fashion show featuring the students- Runway walking, posing, and showcasing personal style- Feedback and evaluation from industry professionals- Graduation ceremony and award presentationConclusion:Our model training course is designed to provide students with a comprehensive understanding of the modeling industry and to equip them with the skills and knowledge they need to succeed. Our goal is to not only help students become successful models, but also to prepare them for a long and fulfilling career in the fashion industry. We believe that with the right training and guidance, anyone can achieve their dreams of becoming a successful model.。
用英语海报介绍名人故事英文作文
用英语海报介绍名人故事英文作文全文共3篇示例，供读者参考篇1Title: Famous Celebrity Stories PosterIntroduction:Welcome to our exhibit featuring famous celebrity stories! This poster showcases the incredible lives and achievements of some of the most iconic figures in history. From actors to musicians, athletes to activists, these individuals have left a lasting impact on the world. Join us as we journey through their inspiring stories and learn more about the people behind the fame.Poster 1: "The King of Rock and Roll"Elvis Presley, known as the King of Rock and Roll, rose to fame in the 1950s with his smooth vocals and charismatic stage presence. Despite his success, Elvis faced personal struggles and challenges throughout his career. Learn more about the man behind the music and discover how he became a cultural icon that continues to influence generations of fans.Poster 2: "The People's Princess"Princess Diana captivated the world with her grace, compassion, and humanitarian efforts. From her fairytale wedding to her charitable work, Diana used her influence to bring attention to important causes and advocate for those in need. Explore her legacy and learn about the impact she had on the royal family and beyond.Poster 3: "The Greatest"Muhammad Ali, also known as "The Greatest," was an iconic figure in the world of boxing and beyond. With his unparalleled skills in the ring and his outspoken activism, Ali broke barriers and inspired others to fight for their beliefs. Discover how his legacy lives on and continues to inspire athletes and activists today.Conclusion:These are just a few of the incredible stories featured in our exhibit. Each poster offers a glimpse into the lives of these famous celebrities and the impact they had on the world. We invite you to explore their stories further and learn more about the people behind the fame. Thank you for joining us on this journey through history and culture.篇2Name: Marilyn MonroeIntroduction:Marilyn Monroe was an iconic American actress, singer, and model who became one of the most popular sex symbols of the 1950s. Born Norma Jeane Mortenson on June 1, 1926, in Los Angeles, California, she overcame a difficult childhood to become one of the biggest stars in Hollywood.Early Life:Marilyn Monroe spent much of her childhood in foster homes and orphanages, struggling with abandonment and abuse. She married at a young age and began modeling, catching the eye of a talent scout who helped her secure a contract with 20th Century Fox.Hollywood Career:Monroe quickly rose to fame with her roles in films like "Gentlemen Prefer Blondes" and "Some Like It Hot." Known for her beauty, charisma, and comedic talent, she became a sought-after leading lady in Hollywood.Personal Life:Despite her success, Marilyn Monroe's personal life was filled with turmoil. She struggled with anxiety, depression, and addiction, leading to multiple marriages and affairs. She tragically passed away at the age of 36 from a drug overdose, leaving behind a legacy that continues to captivate audiences worldwide.Legacy:Marilyn Monroe remains a cultural icon, remembered for her beauty, talent, and tragic end. Her films continue to be celebrated, and her image is still a symbol of glamour and sensuality. She is considered one of the greatest actresses of all time and has inspired countless artists and performers.Visit our exhibition to learn more about the life and legacy of Marilyn Monroe, and discover why she remains one of the most enduring figures in Hollywood history.篇3Introduction to Famous People's Stories through English PostersIntroduction:In today's digital age, visual media plays a crucial role in conveying information and capturing the attention of the audience. One popular form of visual media is the poster, which is used to promote events, products, or convey a message in a concise and appealing way. In this essay, we will explore how English posters can be used to introduce the stories of famous people to a larger audience.Section 1: The Power of PostersPosters are a powerful communication tool that can convey a message effectively through visual elements such as images, colors, typography, and layout. They have the ability to capture the viewer's attention at a glance and communicate the intended message in a memorable way. When it comes to introducing the stories of famous people, posters can be a great medium to highlight their achievements, contributions, and the impact they have had on society.Section 2: Famous People's StoriesThere are countless famous people whose life stories have inspired and influenced millions around the world. From leaders and activists to scientists and artists, each of these individuals has a unique story to tell. By creating English posters that encapsulate the key moments and accomplishments of theseindividuals, their stories can be shared with a wider audience in a visually engaging way.Section 3: Creating Engaging PostersWhen creating posters to introduce the stories of famous people, it is important to consider the target audience and the message you want to convey. The design elements such as colors, fonts, images, and layout should be carefully chosen to capture the essence of the individual's story and evoke emotion in the viewer. Including key milestones, quotes, and relevant information can help to create a compelling narrative that resonates with the audience.Section 4: Examples of Famous People PostersTo illustrate the concept of using English posters to introduce the stories of famous people, let's consider a few examples:- Rosa Parks: A poster featuring an image of Rosa Parks sitting on a bus with the caption "The Mother of the Civil Rights Movement" can help to highlight her role in challenging racial segregation in America.- Albert Einstein: A poster showcasing Einstein's iconic image with his famous equation E=mc^2 and a quote on theimportance of imagination and curiosity can emphasize his contributions to science and innovation.- Malala Yousafzai: A poster depicting Malala's journey as a young education activist with the words "One child, one teacher, one book, one pen can change the world" can inspire others to fight for universal education and gender equality.Conclusion:In conclusion, English posters are a versatile medium that can be used to introduce the stories of famous people in a creative and impactful way. By carefully designing posters that encapsulate the essence of an individual's life, achievements, and legacy, their stories can be shared with a wider audience and inspire future generations. So, let's harness the power of visual storytelling through posters to celebrate the lives and accomplishments of famous people around the world.。
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The FLUENT User's Guide tells you what you need to know to use FLUENT. At the end of the User's Guide, you will find a Reference Guide, a nomenclature list, a bibliography, and an index.!! Under U.S. and international copyright law, Fluent is unable to distribute copies of the papers listed in the bibliography, other than those published internally by Fluent. Please use your library or a document delivery service to obtain copies of copyrighted papers.A brief description of what's in each chapter follows:∙Chapter 1, Getting Started, describes the capabilities of FLUENT and the way in which it interacts with other Fluent Inc. and third-party programs. It also advises you on how to choose the appropriate solverformulation for your application, gives an overview of the problem setup steps, and presents a samplesession that you can work through at your own pace. Finally, this chapter provides information aboutaccessing the FLUENT manuals on CD-ROM or in the installation area.∙Chapter 2, User Interface, describes the mechanics of using the graphical user interface, the text interface, and the on-line help. It also provides instructions for remote and batch execution. (See the separate Text Command List for information about specific text interface commands.)∙Chapter 3, Reading and Writing Files, contains information about the files that FLUENT can read and write, including hardcopy files.∙Chapter 4, Unit Systems, describes how to use the standard and custom unit systems available in FLUENT.∙Chapter 5, Reading and Manipulating Grids, describes the various sources of computational grids and explains how to obtain diagnostic information about the grid and how to modify it by scaling, translating, and other methods. This chapter also contains information about the use of non-conformal grids.∙Chapter 6, Boundary Conditions, explains the different types of boundary conditions available in FLUENT, when to use them, how to define them, and how to define boundary profiles and volumetric sources and fix the value of a variable in a particular region. It also contains information about porousmedia and lumped parameter models.∙Chapter 7, Physical Properties, explains how to define the physical properties of materials and the equations that FLUENT uses to compute the properties from the information that you input.∙Chapter 8, Modeling Basic Fluid Flow, describes the governing equations and physical models used by FLUENT to compute fluid flow (including periodic flow, swirling and rotating flows, compressibleflows, and inviscid flows), as well as the inputs you need to provide to use these models.∙Chapter 9, Modeling Flows in Moving Zones, describes the use of single rotating reference frames, multiple moving reference frames, mixing planes, and sliding meshes in FLUENT.∙Chapter 10, Modeling Turbulence, describes FLUENT's models for turbulent flow and when and how to use them.∙Chapter 11, Modeling Heat Transfer, describes the physical models used by FLUENT to compute heat transfer (including convective and conductive heat transfer, natural convection, radiative heat transfer,and periodic heat transfer), as well as the inputs you need to provide to use these models.∙Chapter 12, Introduction to Modeling Species Transport and Reacting Flows, provides an overview of the models available in FLUENT for species transport and reactions, as well as guidelines for selectingan appropriate model for your application.∙Chapter 13, Modeling Species Transport and Finite-Rate Chemistry, describes the finite-rate chemistry models in FLUENT and how to use them. This chapter also provides information about modeling species transport in non-reacting flows.∙Chapter 14, Modeling Non-Premixed Combustion, describes the non-premixed combustion model and how to use it. This chapter includes details about using prePDF.∙Chapter 15, Modeling Premixed Combustion, describes the premixed combustion model and how to use it.∙Chapter 16, Modeling Partially Premixed Combustion, describes the partially premixed combustion model and how to use it.∙Chapter 17, Modeling Pollutant Formation, describes the models for the formation of NOx and soot and how to use them.∙Chapter 18, Introduction to Modeling Multiphase Flows, provides an overview of the models for multiphase flow (including the discrete phase, VOF, mixture, and Eulerian models), as well as guidelines for selecting an appropriate model for your application.∙Chapter 19, Discrete Phase Models, describes the discrete phase models available in FLUENT and how to use them.∙Chapter 20, General Multiphase Models, describes the general multiphase models available in FLUENT (VOF, mixture, and Eulerian) and how to use them.∙Chapter 21, Modeling Solidification and Melting, describes FLUENT's model for solidification and melting and how to use it.∙Chapter 22, Using the Solver, describes the FLUENT solvers and how to use them.∙Chapter 23, Grid Adaption, explains the solution-adaptive mesh refinement feature in FLUENT and how to use it.∙Chapter 24, Creating Surfaces for Displaying and Reporting Data, explains how to create surfaces in the domain on which you can examine FLUENT solution data.∙Chapter 25, Graphics and Visualization, describes the graphics tools that you can use to examine your FLUENT solution.∙Chapter 26, Alphanumeric Reporting, describes how to obtain reports of fluxes, forces, surface integrals, and other solution data.∙Chapter 27, Field Function Definitions, defines the flow variables that appear in the variable selection drop-down lists in FLUENT panels, and tells you how to create your own custom field functions.∙Chapter 28, Parallel Processing, explains the parallel processing features in FLUENT and how to use them. This chapter also provides information about partitioning your grid for parallel processing.18. Introduction to Modeling Multiphase FlowsA large number of flows encountered in nature and technology are a mixture of phases. Physical phases of matter are gas, liquid, and solid, but the concept of phase in a multiphase flow system is applied in a broader sense. In multiphase flow, a phase can be defined as an identifiable class of material that has a particular inertial response to and interaction with the flow and the potential field in which it is immersed. For example, different-sized solid particles of the same material can be treated as different phases because each collection of particles with the same size will have a similar dynamical response to the flow field.This chapter provides an overview of multiphase modeling in FLUENT, and Chapters 19 and 20 provide details about the multiphase models mentioned here. Chapter 21 provides information about melting and solidification.18.1 Multiphase Flow RegimesMultiphase flow can be classified by the following regimes, grouped into four categories:gas-liquid or liquid-liquid flowsbubbly flow: discrete gaseous or fluid bubbles in a continuous fluiddroplet flow: discrete fluid droplets in a continuous gasslug flow: large bubbles in a continuous fluidstratified/free-surface flow: immiscible fluids separated by a clearly-defined interfacegas-solid flowsparticle-laden flow: discrete solid particles in a continuous gaspneumatic transport: flow pattern depends on factors such as solid loading, Reynolds numbers, and particle properties. Typical patterns are dune flow, slug flow, packed beds, and homogeneous flow.fluidized beds: consist of a vertical cylinder containing particles where gas is introduced through a distributor. The gas rising through the bed suspends the particles. Depending on the gas flow rate, bubbles appear and rise through the bed, intensifying the mixing within the bed.liquid-solid flowsslurry flow: transport of particles in liquids. The fundamental behavior of liquid-solid flows varies with the properties of the solid particles relative to those of the liquid. In slurry flows, the Stokes number (seeEquation 18.4-4) is normally less than 1. When the Stokes number is larger than 1, the characteristic of the flow is liquid-solid fluidization.hydrotransport: densely-distributed solid particles in a continuous liquidsedimentation: a tall column initially containing a uniform dispersed mixture of particles. At the bottom, the particles will slow down and form a sludge layer. At the top, a clear interface will appear, and in the middle a constant settling zone will exist.three-phase flows (combinations of the others listed above)Each of these flow regimes is illustrated in Figure 18.1.1.Figure 18.1.1: Multiphase Flow Regimes18.2 Examples of Multiphase SystemsSpecific examples of each regime described in Section 18.1 are listed below:Bubbly flow examples: absorbers, aeration, air lift pumps, cavitation, evaporators, flotation, scrubbersDroplet flow examples: absorbers, atomizers, combustors, cryogenic pumping, dryers, evaporation, gas cooling, scrubbersSlug flow examples: large bubble motion in pipes or tanksStratified/free-surface flow examples: sloshing in offshore separator devices, boiling and condensation in nuclear reactorsParticle-laden flow examples: cyclone separators, air classifiers, dust collectors, and dust-laden environmental flowsPneumatic transport examples: transport of cement, grains, and metal powdersFluidized bed examples: fluidized bed reactors, circulating fluidized bedsSlurry flow examples: slurry transport, mineral processingHydrotransport examples: mineral processing, biomedical and physiochemical fluid systemsSedimentation examples: mineral processing18.3 Approaches to Multiphase ModelingAdvances in computational fluid mechanics have provided the basis for further insight into the dynamics of multiphase flows. Currently there are two approaches for the numerical calculation of multiphase flows: the Euler-Lagrange approach and the Euler-Euler approach.18.3.1 The Euler-Lagrange ApproachThe Lagrangian discrete phase model in FLUENT (described in Chapter 19) follows the Euler-Lagrange approach. The fluid phase is treated as a continuum by solving the time-averaged Navier-Stokes equations, while the dispersed phase is solved by tracking a large number of particles, bubbles, or droplets through the calculated flow field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase.A fundamental assumption made in this model is that the dispersed second phase occupies a low volume fraction, even though high mass loading ( ) is acceptable. The particle or droplet trajectories are computed individually at specified intervals during the fluid phase calculation. This makes the model appropriate for the modeling of spray dryers, coal and liquid fuel combustion, and some particle-laden flows, but inappropriate for the modeling of liquid-liquid mixtures, fluidized beds, or any application where the volume fraction of the second phase is not negligible.18.3.2 The Euler-Euler ApproachIn the Euler-Euler approach, the different phases are treated mathematically as interpenetrating continua. Since the volume of a phase cannot be occupied by the other phases, the concept of phasic volume fraction is introduced. These volume fractions are assumed to be continuous functions of space and time and their sum is equal to one. Conservation equations for each phase are derived to obtain a set of equations, which have similar structure for all phases. These equations are closed by providing constitutive relations that are obtained from empirical information, or, in the case of granular flows , by application of kinetic theory.In FLUENT, three different Euler-Euler multiphase models are available: the volume of fluid (VOF) model, the mixture model, and the Eulerian model.The VOF ModelThe VOF model (described in Section 20.2) is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. Applications of the VOF model include stratified flows , free-surface flows, filling, sloshing , the motion of large bubbles in a liquid, the motion of liquid after a dam break, the prediction of jet breakup (surface tension), and the steady or transient tracking of any liquid-gas interface.The Mixture ModelThe mixture model (described in Section 20.3) is designed for two or more phases (fluid or particulate). As in the Eulerian model, the phases are treated as interpenetrating continua. The mixture model solves for the mixture momentum equation and prescribes relative velocities to describe the dispersed phases. Applications of the mixture model include particle-laden flows with low loading, bubbly flows, sedimentation , and cyclone separators. The mixture model can also be used without relative velocities for the dispersed phases to model homogeneous multiphase flow.The Eulerian ModelThe Eulerian model (described in Section 20.4) is the most complex of the multiphase models in FLUENT. It solves a set of n momentum and continuity equations for each phase. Coupling is achieved through the pressure and interphase exchange coefficients. The manner in which this coupling is handled depends upon the type of phases involved; granular (fluid-solid) flows are handled differently than non-granular (fluid-fluid) flows. For granular flows , the properties are obtained from application of kinetic theory. Momentum exchange between the phases is also dependent upon the type of mixture being modeled. FLUENT's user-defined functions allow you tocustomize the calculation of the momentum exchange. Applications of the Eulerian multiphase model include bubble columns , risers , particle suspension, and fluidized beds .18.4 Choosing a Multiphase ModelThe first step in solving any multiphase problem is to determine which of the regimes described inSection 18.1 best represents your flow. Section 18.4.1 provides some broad guidelines for determining appropriate models for each regime, and Section 18.4.2 provides details about how to determine the degree of interphase coupling for flows involving bubbles, droplets, or particles, and the appropriate model for different amounts of coupling.18.4.1 General GuidelinesIn general, once you have determined the flow regime that best represents your multiphase system, you can select the appropriate model based on the following guidelines. Additional details and guidelines for selecting the appropriate model for flows involving bubbles, droplets, or particles can be found in Section 18.4.2.For bubbly, droplet, and particle-laden flows in which the dispersed-phase volume fractions are less than or equal to 10%, use the discrete phase model. See Chapter 19 for more information about the discrete phase model.For bubbly, droplet, and particle-laden flows in which the phases mix and/or dispersed-phase volume fractions exceed 10%, use either the mixture model (described in Section 20.3) or the Eulerian model (described in Section 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case.For slug flows, use the VOF model. See Section 20.2 for more information about the VOF model.For stratified/free-surface flows, use the VOF model. See Section 20.2 for more information about the VOF model.For pneumatic transport, use the mixture model for homogeneous flow (described in Section 20.3) or the Eulerian model for granular flow (described in Section 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case.For fluidized beds, use the Eulerian model for granular flow. See Section 20.4 for more information about the Eulerian model.For slurry flows and hydrotransport , use the mixture or Eulerian model (described, respectively, inSections 20.3 and 20.4). See Sections 18.4.2 and 20.1 for details about how to determine which is more appropriate for your case.For sedimentation, use the Eulerian model. See Section 20.4 for more information about the Eulerian model.For general, complex multiphase flows that involve multiple flow regimes, select the aspect of the flow that is of most interest, and choose the model that is most appropriate for that aspect of the flow. Note that the accuracy of results will not be as good as for flows that involve just one flow regime, since the model you use will be valid for only part of the flow you are modeling.18.4.2 Detailed GuidelinesFor stratified and slug flows, the choice of the VOF model, as indicated in Section 18.4.1, is straightforward. Choosing a model for the other types of flows is less straightforward. As a general guide, there are some parameters that help to identify the appropriate multiphase model for these other flows: the particulate loading, , and the Stokes number, St. (Note that the word ``particle'' is used in this discussion to refer to a particle, droplet, or bubble.)The Effect of Particulate LoadingParticulate loading has a major impact on phase interactions. The particulate loading is defined as the mass density ratio of the dispersed phase ( d) to that of the carrier phase ( c):The material density ratiois greater than 1000 for gas-solid flows, about 1 for liquid-solid flows, and less than 0.001 for gas-liquid flows. Using these parameters it is possible to estimate the average distance between the individual particles of the particulate phase. An estimate of this distance has been given by Crowe et al. [ 42]:where . Information about these parameters is important for determining how the dispersed phase shouldbe treated. For example, for a gas-particle flow with aparticulate loading of 1, the interparticle space is about 8; the particle can therefore be treated as isolated (i.e., very low particulate loading).Depending on the particulate loading, the degree of interaction between the phases can be divided into three categories:For very low loading, the coupling between the phases is one-way; i.e., the fluid carrier influences the particles via drag and turbulence, but the particles have no influence on the fluid carrier. The discrete phase, mixture, and Eulerian models can all handle this type of problem correctly. Since the Eulerian model is the most expensive, the discrete phase or mixture model is recommended.For intermediate loading, the coupling is two-way; i.e., the fluid carrier influences the particulate phase via drag and turbulence, but the particles in turn influence the carrier fluid via reduction in mean momentum and turbulence. The discrete phase, mixture, and Eulerian models are all applicable in this case, but you need to take into account other factors in order to decide which model is more appropriate. See below for information about using the Stokes number as a guide.For high loading, there is two-way coupling plus particle pressure and viscous stresses due to particles (four-way coupling). Only the Eulerian model will handle this type of problem correctly.The Significance of the Stokes NumberFor systems with intermediate particulate loading, estimating the value of the Stokes number can help you select the most appropriate model. The Stokes number can be defined as the relation between the particle response time and the system response time:where and t s is based on the characteristic length ( L s) and the characteristic velocity ( V s) of thesystem under investigation: .For , the particle will follow the flow closely and any of the three models (discrete phase, mixture, or Eulerian) is applicable; you can therefore choose the least expensive (the mixture model, in most cases), or themost appropriate considering other factors. For , the particles will move independently of the flowand either the discrete phase model or the Eulerian model is applicable. For , again any of the three models is applicable; you can choose the least expensive or the most appropriate considering other factors. ExamplesFor a coal classifier with a characteristic length of 1 m and a characteristic velocity of 10 m/s, the Stokes number is 0.04 for particles with a diameter of 30 microns, but 4.0 for particles with a diameter of 300 microns. Clearly the mixture model will not be applicable to the latter case.For the case of mineral processing, in a system with a characteristic length of 0.2 m and a characteristic velocity of 2 m/s, the Stokes number is 0.005 for particles with a diameter of 300 microns. In this case, you can choose between the mixture and Eulerian models. (The volume fractions are too high for the discrete phase model, as noted below.)Other ConsiderationsKeep in mind that the use of the discrete phase model is limited to low volume fractions. Also, the discrete phase model is the only multiphase model that allows you to specify the particle distribution or include combustion modeling in your simulation.。