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johnpye |
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#LyX 1.4.1 created this file. For more info see http://www.lyx.org/ |
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\language english |
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\quotes_language english |
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\end_header |
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\begin_body |
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\begin_layout Chapter |
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Defining Variables and Scaling Values |
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\begin_inset LatexCommand \label{cha:atoms} |
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\end_inset |
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\end_layout |
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\begin_layout Standard |
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\begin_inset Marginal |
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status collapsed |
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\begin_layout Standard |
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the purpose of this chapter |
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\end_layout |
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\end_inset |
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By now you have probably read Chapter\InsetSpace ~ |
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\begin_inset LatexCommand \vref{cha:model1} |
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\end_inset |
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and seen an example of how to create a model using existing variable types |
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in ASCEND. |
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You found that variables of types area, length, mass, mass_density, and |
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volume were needed and that they could be found in the library |
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\family typewriter |
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atoms.a4l |
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\family default |
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. |
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You want to know how to generalize on that; how to use variables, constants, |
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and scaling values in your own models so that the models will be easier |
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to solve. |
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\end_layout |
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\begin_layout Standard |
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This chapter is meant to explain the following things: |
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\end_layout |
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\begin_layout Itemize |
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The "Big Picture" of how variables, constants, and scaling values relate |
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to the rest of the ASCEND IV language and to equations in particular. |
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We'll keep it simple here. |
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More precise explanations for the language purist can be found in our syntax |
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document **syntax.fm5**. |
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You do not need to read about the "Big Picture" in order to read and use |
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the other parts of this chapter, but you may find it helpful if you are |
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having trouble writing an equation |
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\begin_inset LatexCommand \index{equation, writing} |
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\end_inset |
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so that ASCEND will accept it. |
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\end_layout |
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\begin_layout Itemize |
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How to find the type of variable (or constant) you want. |
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We keep a mess of interesting |
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\family typewriter |
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ATOM |
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\family default |
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and |
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\family typewriter |
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CONSTANT |
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\family default |
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definitions in |
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\family typewriter |
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atoms.a4l |
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\family default |
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. |
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We provide tools to search in already loaded libraries to locate the type |
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you need. |
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\end_layout |
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\begin_layout Itemize |
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How to define a new type of variable when we do not have a predefined |
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\family typewriter |
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ATOM |
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\family default |
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or |
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\family typewriter |
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CONSTANT |
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\family default |
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that suits your needs. |
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It is very easy to define your own variable types by copying code into |
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an atoms library of your own from |
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\family typewriter |
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atoms.a4l |
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\family default |
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and then editing the copied definition. |
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\end_layout |
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\begin_layout Itemize |
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How to define a scaling variable to make your equations much easier to solve. |
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\end_layout |
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\begin_layout Section |
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The Big Picture: a taxonomy |
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\begin_inset LatexCommand \index{taxonomy} |
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\end_inset |
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\end_layout |
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\begin_layout Standard |
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As you read in Chapter\InsetSpace ~ |
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\begin_inset LatexCommand \ref{cha:model1} |
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\end_inset |
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, simulations are built from MODEL and ATOM definitions, and MODEL and ATOM |
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definitions are defined by creating types in an ASCEND language text file |
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that you load into the ASCEND system. |
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Figure |
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\begin_inset LatexCommand \ref{fig:atoms.taxonomy} |
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\end_inset |
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\noun off |
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shows the types of objects that can be defined. |
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You can see there are many more types than simply real variables used for |
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writing equations. |
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Some of these types can also be used in equations. |
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You also see that there are three kinds of equations, not simply real relations. |
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Throughout our documentation we call real relations simply "relations" |
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because that is the kind of equation most people are interested in most |
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of the time. |
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Notice that "scaling values" do not appear in this diagram. |
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We will cover scaling values at the end of this The major features of this |
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diagram are: |
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\end_layout |
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\begin_layout Standard |
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\begin_inset Float figure |
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wide false |
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sideways false |
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status open |
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\begin_layout Standard |
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\noun off |
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\begin_inset Graphics |
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filename howto-atomsFig1.eps |
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scale 90 |
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BoundingBox 20bp 0bp 600bp 320bp |
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clip |
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\end_inset |
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\end_layout |
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\begin_layout Caption |
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\begin_inset LatexCommand \label{fig:atoms.taxonomy} |
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\end_inset |
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The big picture: how to think about variables |
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\end_layout |
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\end_inset |
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\end_layout |
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\begin_layout Paragraph |
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\noun off |
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\begin_inset LatexCommand \index{atom} |
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\end_inset |
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\noun default |
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ATOM |
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\end_layout |
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\begin_layout Itemize |
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Any variable quantity for use in relations, logical relations, or when statement |
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s or other computations. |
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These come in the usual programming language flavors real, boolean, symbol, |
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integer. |
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Not all kinds of atoms can be used in all kinds of equations, as we shall |
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explain when describing relations in a little bit. |
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Atoms may be assigned values many times interactively, with the Script |
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ASSIGN statement, with the METHOD := assignment operator, or by an ASCEND |
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client such as a solver. |
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\end_layout |
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\begin_layout Standard |
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An ATOM may have attributes other than its value, such as .fixed in solver_var, |
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but these attributes are not atoms. |
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They are subatomic particles and cannot be used in equations. |
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These attributes are interpretable by ASCEND clients, and assignable by |
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the user in the same ways that the user assigns atom values. |
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\end_layout |
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\begin_layout Standard |
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Each subatomic particle instance belongs to exactly one atom instance (one |
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variable in your compiled simulation). |
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This contrasts with an atom instance which can be shared among several |
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models by passing the atom instance from one model into another or by creating |
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aliases for it. |
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\end_layout |
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\begin_layout Paragraph |
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\begin_inset LatexCommand \index{constant} |
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\end_inset |
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CONSTANT |
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\end_layout |
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\begin_layout Itemize |
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Constants are "variables" that can be assigned no more than once. |
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By convention, all constant types in atoms.a4l have names that end in _constant |
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so that they are not easily confused with atoms. |
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A constant gets a values from the DEFAULT portion of its type definition, |
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by an interactive assignment, or by an assignment in the a model which |
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uses the :== assignment operator. |
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Constants cannot be assigned in a METHOD, nor can they be assigned with |
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the := operator. |
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\end_layout |
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\begin_layout Standard |
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Integer and symbol constants can appear as members of sets or as subscripts |
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of arrays. |
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Integer, boolean, and symbol constants can be used to control SELECT statements |
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which determine your simulation's structure at compile-time or to control |
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SWITCH and WHEN behavior during problem solving . |
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\end_layout |
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\begin_layout Paragraph |
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\begin_inset LatexCommand \index{set} |
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\end_inset |
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set |
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\end_layout |
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\begin_layout Itemize |
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Sets are unordered lists of either integer or symbol constants. |
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A set is assigned its value exactly once. |
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The user interface always presents a set in sorted order, but this is for |
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convenience only. |
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Sets are useful for defining an array range or for writing indexed relations. |
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More about sets and their use can be found in **syntax.fm5**. |
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\end_layout |
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\begin_layout Paragraph |
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\begin_inset LatexCommand \index{relationship} |
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\end_inset |
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relationships |
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\end_layout |
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\begin_layout Itemize |
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Relations and logical relations allow you to state |
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\begin_inset LatexCommand \index{equalities} |
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\end_inset |
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equalities and |
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\begin_inset LatexCommand \index{inequalitites} |
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\end_inset |
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inequalities among the variables and constants in you models. |
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WHEN statements allow you to state relationships among the models and equations |
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which depend on the values of variables in those models. |
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Sets and symbols are not allowed in real or logical relations except when |
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used as array subscripts. |
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\end_layout |
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\begin_layout Standard |
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Real |
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\begin_inset LatexCommand \index{real} |
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\end_inset |
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\begin_inset LatexCommand \index{relation, real} |
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\end_inset |
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relations relate the values of real atoms, real constants, and integer constants. |
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Real relations cannot contain boolean constants and atoms, nor can they |
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contain integer atoms. |
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\end_layout |
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\begin_layout Standard |
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Logical |
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\begin_inset LatexCommand \index{logical} |
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\end_inset |
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relations |
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\begin_inset LatexCommand \index{logical relation} |
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\end_inset |
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relate the values of boolean atoms and boolean constants. |
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The |
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\family typewriter |
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SATISFIED |
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\family default |
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\begin_inset LatexCommand \index{SATISFIED} |
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\end_inset |
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operator makes it possible to include real relations in a logical relation. |
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Neither integer atoms and constants nor real atoms and constants are allowed |
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in logical relations. |
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If you find yourself trying to write an equation with integer atoms, you |
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are really creating a conditional model for which you should use the WHEN |
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statement instead. |
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See **conditional modeling** to learn about how ASCEND represents this |
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kind of mathematical model. |
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There are also a real variable types, solver_integer and solver_binary, |
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which are used to formulate equations when the solver is expected to initially |
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treat the variable as a real value but drive it to an integer or 0-1 value |
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at the solution. |
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The integer programming features of ASCEND are described **elsewhere**. |
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\end_layout |
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\begin_layout Standard |
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Like atoms, real and logical relations may have attributes, subatomic particles |
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for use by ASCEND clients and users. |
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The name of a relation can be used in writing logical relations and WHEN |
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statements. |
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\end_layout |
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\begin_layout Standard |
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WHEN statements are outside the scope of this chapter; please see **conditional |
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modeling** or **syntax.fm5** for the details. |
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\end_layout |
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\begin_layout Paragraph |
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\begin_inset LatexCommand \index{model} |
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\end_inset |
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\family typewriter |
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MODEL |
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\end_layout |
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\begin_layout Itemize |
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A model is simply a container for a collection of atoms, constants, sets, |
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relations, logical relations, when statements, and arrays of any of these. |
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The container also specifies some of the methods that can be used to manipulate |
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its contents. |
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Compiling a model creates an instance of it-- a simulation |
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\begin_inset LatexCommand \index{simulation} |
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\end_inset |
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. |
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\end_layout |
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\begin_layout Paragraph |
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\family typewriter |
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SOLVER_VAR |
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\end_layout |
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\begin_layout Itemize |
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The real atom type |
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\family typewriter |
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solver_var |
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\family default |
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is the type from which all real variables that you want the system to solve |
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for must spring. |
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If you define a real variable using a type which is not a refinement of |
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\family typewriter |
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solver_var |
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\family default |
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, all solvers will treat that variable as an a scaling value or other given |
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constant rather than as a variable. |
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\end_layout |
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\begin_layout Standard |
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Solver_vars have a number of subatomic attributes ( |
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\family typewriter |
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upper_bound |
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\family default |
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, |
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\family typewriter |
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lower_bound |
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\family default |
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, and so forth) that help solvers find the solution of your model. |
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ATOM definitions specify appropriate default values for these attributes |
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that depend on the expected applications of the atom. |
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These attribute values can (and should) be modified by methods in the final |
438 |
|
|
application model where the most accurate problem information is available. |
439 |
|
|
\end_layout |
440 |
|
|
|
441 |
|
|
\begin_layout Paragraph |
442 |
|
|
Scaling |
443 |
|
|
\begin_inset LatexCommand \index{scaling} |
444 |
|
|
|
445 |
|
|
\end_inset |
446 |
|
|
|
447 |
|
|
value |
448 |
|
|
\end_layout |
449 |
|
|
|
450 |
|
|
\begin_layout Itemize |
451 |
|
|
A real that is not a member of the |
452 |
|
|
\family typewriter |
453 |
|
|
solver_var |
454 |
|
|
\family default |
455 |
|
|
family is ignored by the solver. |
456 |
|
|
Numerical solvers for problems with many equations in many variables work |
457 |
|
|
better if the error computed for each equation (before the system is solved) |
458 |
|
|
is of approximately size 1.0. |
459 |
|
|
This is most critical when you are starting to solve a new problem at values |
460 |
|
|
far, far away from the solution. |
461 |
|
|
When the error of one equation is much larger than the errors in the others, |
462 |
|
|
that error will skew the behavior of most numerical solvers and will cause |
463 |
|
|
poor performance. |
464 |
|
|
|
465 |
|
|
\end_layout |
466 |
|
|
|
467 |
|
|
\begin_layout Standard |
468 |
|
|
This is one of the many reasons that scientists and engineers work with |
469 |
|
|
dimensionless models |
470 |
|
|
\begin_inset LatexCommand \index{dimensionless models} |
471 |
|
|
|
472 |
|
|
\end_inset |
473 |
|
|
|
474 |
|
|
: the process of scaling the equations into dimensionless form has the effect |
475 |
|
|
of making the error of each equation roughly the same size even far away |
476 |
|
|
from the solution. |
477 |
|
|
It is sometimes easiest to obtain a dimensionless equation by writing the |
478 |
|
|
equation in its dimensional form using natural variables and then dividing |
479 |
|
|
both sides by an appropriate scaling value. |
480 |
|
|
We will see how to define an atom for scaling purposes in the last part |
481 |
|
|
of this chapter. |
482 |
|
|
\end_layout |
483 |
|
|
|
484 |
|
|
\begin_layout Section |
485 |
|
|
How to find the right variable type |
486 |
|
|
\begin_inset LatexCommand \index{type, variable} |
487 |
|
|
|
488 |
|
|
\end_inset |
489 |
|
|
|
490 |
|
|
|
491 |
|
|
\end_layout |
492 |
|
|
|
493 |
|
|
\begin_layout Standard |
494 |
|
|
The type of real atom you want to use depends first on the dimensionality |
495 |
|
|
(length, mass/time, etc.) needed and then on the application in which the |
496 |
|
|
atom is going to be used. |
497 |
|
|
For example, if you are modeling a moving car and you want an atom type |
498 |
|
|
to describe the car's speed, then you need to find an atom with dimensionality |
499 |
|
|
length/time or in ASCEND terms L/T. |
500 |
|
|
There may be two or three types with this dimensionality, possibly including |
501 |
|
|
real_constants, a real scaling value, and an atom derived from solver_var. |
502 |
|
|
\end_layout |
503 |
|
|
|
504 |
|
|
\begin_layout Standard |
505 |
|
|
\begin_inset Marginal |
506 |
|
|
status collapsed |
507 |
|
|
|
508 |
|
|
\begin_layout Standard |
509 |
|
|
Load atoms.a4l |
510 |
|
|
\end_layout |
511 |
|
|
|
512 |
|
|
\end_inset |
513 |
|
|
|
514 |
|
|
The first step to finding the variable type needed is to make sure that |
515 |
|
|
atoms.a4l is loaded in your Library window from |
516 |
|
|
\family typewriter |
517 |
|
|
ascend4/models/atoms.a4l |
518 |
|
|
\family default |
519 |
|
|
. |
520 |
|
|
\end_layout |
521 |
|
|
|
522 |
|
|
\begin_layout Standard |
523 |
|
|
\begin_inset Marginal |
524 |
|
|
status collapsed |
525 |
|
|
|
526 |
|
|
\begin_layout Standard |
527 |
|
|
Find an ATOM or CONSTANT by units |
528 |
|
|
\end_layout |
529 |
|
|
|
530 |
|
|
\end_inset |
531 |
|
|
|
532 |
|
|
The next step is to open the "ATOM by units" dialog found in the Library |
533 |
|
|
window's Find menu. |
534 |
|
|
This dialog asks for the units of the real variable type you want. |
535 |
|
|
For our example, speed, you would enter "feet/second," "furlongs/fortnight," |
536 |
|
|
"meter^3/second/ft^2" or any other combination of units that corresponds |
537 |
|
|
to the dimensionality L/T. |
538 |
|
|
|
539 |
|
|
\end_layout |
540 |
|
|
|
541 |
|
|
\begin_layout Standard |
542 |
|
|
If the system is able to deduce the dimensionality of the units you have |
543 |
|
|
entered, it will return a list of all the currently loaded ATOM and CONSTANT |
544 |
|
|
definitions with matching dimensions. |
545 |
|
|
It may fail to understand the units, in which case you should try the correspon |
546 |
|
|
ding SI units. |
547 |
|
|
If it understands the units but there are no matching atoms or constants, |
548 |
|
|
you will be duly informed. |
549 |
|
|
If there is no atom that meets your needs, you should create one as outlined |
550 |
|
|
in **the next section**. |
551 |
|
|
\end_layout |
552 |
|
|
|
553 |
|
|
\begin_layout Standard |
554 |
|
|
\begin_inset Marginal |
555 |
|
|
status collapsed |
556 |
|
|
|
557 |
|
|
\begin_layout Standard |
558 |
|
|
Selecting the right type |
559 |
|
|
\end_layout |
560 |
|
|
|
561 |
|
|
\end_inset |
562 |
|
|
|
563 |
|
|
The resulting list of types includes a Code button which will display the |
564 |
|
|
definition of any of the types listed once you select (highlight) that |
565 |
|
|
type with the mouse. |
566 |
|
|
Usually you will need to examine several of the alternatives to see which |
567 |
|
|
one is most appropriate to the physics and mathematics of your problem. |
568 |
|
|
Compare the default, bounds, and nominal values defined to those you need. |
569 |
|
|
Check whether the type you are looking at is a |
570 |
|
|
\family typewriter |
571 |
|
|
CONSTANT |
572 |
|
|
\family default |
573 |
|
|
or an |
574 |
|
|
\family typewriter |
575 |
|
|
ATOM |
576 |
|
|
\family default |
577 |
|
|
. |
578 |
|
|
|
579 |
|
|
\end_layout |
580 |
|
|
|
581 |
|
|
\begin_layout Standard |
582 |
|
|
You now know the name of the variable type you need, or you know that you |
583 |
|
|
must create a new one to suit your needs. |
584 |
|
|
\end_layout |
585 |
|
|
|
586 |
|
|
\begin_layout Section |
587 |
|
|
How to define a new type of variable |
588 |
|
|
\begin_inset LatexCommand \index{type, variable} |
589 |
|
|
|
590 |
|
|
\end_inset |
591 |
|
|
|
592 |
|
|
|
593 |
|
|
\begin_inset LatexCommand \label{ssec:atoms.newVarType} |
594 |
|
|
|
595 |
|
|
\end_inset |
596 |
|
|
|
597 |
|
|
|
598 |
|
|
\end_layout |
599 |
|
|
|
600 |
|
|
\begin_layout Standard |
601 |
|
|
In this section we will give examples of defining the atom and constant |
602 |
|
|
types as well as outline a few exceptional situations when you should NOT |
603 |
|
|
define a new type. |
604 |
|
|
More examples can be found and copied from |
605 |
|
|
\family typewriter |
606 |
|
|
atoms.a4l |
607 |
|
|
\family default |
608 |
|
|
. |
609 |
|
|
You should define your new atoms in your personal atoms library. |
610 |
|
|
|
611 |
|
|
\end_layout |
612 |
|
|
|
613 |
|
|
\begin_layout Standard |
614 |
|
|
\begin_inset Marginal |
615 |
|
|
status collapsed |
616 |
|
|
|
617 |
|
|
\begin_layout Standard |
618 |
|
|
Saving customized variable types |
619 |
|
|
\end_layout |
620 |
|
|
|
621 |
|
|
\end_inset |
622 |
|
|
|
623 |
|
|
The user data file |
624 |
|
|
\family typewriter |
625 |
|
|
~ |
626 |
|
|
\backslash |
627 |
|
|
ascdata |
628 |
|
|
\backslash |
629 |
|
|
myatoms.a4l |
630 |
|
|
\family default |
631 |
|
|
is the normal location for a personal |
632 |
|
|
\begin_inset LatexCommand \index{library, personal} |
633 |
|
|
|
634 |
|
|
\end_inset |
635 |
|
|
|
636 |
|
|
library. |
637 |
|
|
This file contains the following three lines and then the |
638 |
|
|
\family typewriter |
639 |
|
|
ATOM |
640 |
|
|
\family default |
641 |
|
|
and |
642 |
|
|
\family typewriter |
643 |
|
|
CONSTANT |
644 |
|
|
\family default |
645 |
|
|
definitions you create. |
646 |
|
|
\end_layout |
647 |
|
|
|
648 |
|
|
\begin_layout LyX-Code |
649 |
|
|
REQUIRE "atoms.a4l"; (* loads our atoms first *) |
650 |
|
|
\end_layout |
651 |
|
|
|
652 |
|
|
\begin_layout LyX-Code |
653 |
|
|
PROVIDE "myatoms.a4l"; (* registers your library *) |
654 |
|
|
\end_layout |
655 |
|
|
|
656 |
|
|
\begin_layout LyX-Code |
657 |
|
|
(* Custom atoms created by <insert your name here> *) |
658 |
|
|
\end_layout |
659 |
|
|
|
660 |
|
|
\begin_layout Standard |
661 |
|
|
If you develop an interesting set of atoms for some problem domain outside |
662 |
|
|
chemical engineering thermodynamics, please consider mailing it to us through |
663 |
|
|
our web page. |
664 |
|
|
|
665 |
|
|
\end_layout |
666 |
|
|
|
667 |
|
|
\begin_layout Standard |
668 |
|
|
The user data directory |
669 |
|
|
\family typewriter |
670 |
|
|
~/ |
671 |
|
|
\begin_inset LatexCommand \index{ascdata} |
672 |
|
|
|
673 |
|
|
\end_inset |
674 |
|
|
|
675 |
|
|
ascdata |
676 |
|
|
\family default |
677 |
|
|
may have a different name if you are running under Windows and do not have |
678 |
|
|
the environment variable HOME |
679 |
|
|
\begin_inset LatexCommand \index{HOME} |
680 |
|
|
|
681 |
|
|
\end_inset |
682 |
|
|
|
683 |
|
|
defined. |
684 |
|
|
It may be something like C: |
685 |
|
|
\backslash |
686 |
|
|
ascdata or |
687 |
|
|
\backslash |
688 |
|
|
WINNT |
689 |
|
|
\backslash |
690 |
|
|
Profiles |
691 |
|
|
\backslash |
692 |
|
|
Your Name |
693 |
|
|
\backslash |
694 |
|
|
ascdata. |
695 |
|
|
When ASCEND is started, it prints out the name of this directory. |
696 |
|
|
\end_layout |
697 |
|
|
|
698 |
|
|
\begin_layout Standard |
699 |
|
|
When you write a |
700 |
|
|
\family typewriter |
701 |
|
|
MODEL |
702 |
|
|
\family default |
703 |
|
|
which depends on the definition of your new atoms, do not forget to add |
704 |
|
|
the statement |
705 |
|
|
\end_layout |
706 |
|
|
|
707 |
|
|
\begin_layout LyX-Code |
708 |
|
|
REQUIRE "myatoms.a4l"; |
709 |
|
|
\end_layout |
710 |
|
|
|
711 |
|
|
\begin_layout Standard |
712 |
|
|
at the very top of your model file so that your atoms will be loaded before |
713 |
|
|
your model definitions try to use them. |
714 |
|
|
\end_layout |
715 |
|
|
|
716 |
|
|
\begin_layout Subsection |
717 |
|
|
A new real variable for solver use |
718 |
|
|
\end_layout |
719 |
|
|
|
720 |
|
|
\begin_layout Standard |
721 |
|
|
Suppose you need an atom with units {dollar/ft^2/year} for some equation |
722 |
|
|
relating amortized construction costs to building size. |
723 |
|
|
Maybe this example is a bit far fetched, but it is a safe bet that our |
724 |
|
|
library is not going to have an atom or a constant for these units. |
725 |
|
|
Here is the standard incantation for defining a new variable type based |
726 |
|
|
on |
727 |
|
|
\family typewriter |
728 |
|
|
solver_var |
729 |
|
|
\family default |
730 |
|
|
. |
731 |
|
|
ASCEND allows a few permutations on this incantation, but they are of no |
732 |
|
|
practical value. |
733 |
|
|
The parts of this incantation that are in italics should be changed to |
734 |
|
|
match your needs. |
735 |
|
|
You can skip the comments, but you |
736 |
|
|
\emph on |
737 |
|
|
must |
738 |
|
|
\emph default |
739 |
|
|
include the units of the default on the bounds and nominal. |
740 |
|
|
\end_layout |
741 |
|
|
|
742 |
|
|
\begin_layout LyX-Code |
743 |
|
|
ATOM amortized_area_cost |
744 |
|
|
\end_layout |
745 |
|
|
|
746 |
|
|
\begin_layout LyX-Code |
747 |
|
|
REFINES solver_var DEFAULT 3.0 {dollar/ft^2/year}; |
748 |
|
|
\end_layout |
749 |
|
|
|
750 |
|
|
\begin_layout LyX-Code |
751 |
|
|
lower_bound := 0 {dollar/ft^2/year}; |
752 |
|
|
\end_layout |
753 |
|
|
|
754 |
|
|
\begin_layout LyX-Code |
755 |
|
|
(* minimum value *) |
756 |
|
|
\end_layout |
757 |
|
|
|
758 |
|
|
\begin_layout LyX-Code |
759 |
|
|
upper_bound := 10000 {dollar/ft^2/year}; |
760 |
|
|
\end_layout |
761 |
|
|
|
762 |
|
|
\begin_layout LyX-Code |
763 |
|
|
(* maximum value for any sane application *) |
764 |
|
|
\end_layout |
765 |
|
|
|
766 |
|
|
\begin_layout LyX-Code |
767 |
|
|
nominal := 10 {dollar/ft^2/year}; |
768 |
|
|
\end_layout |
769 |
|
|
|
770 |
|
|
\begin_layout LyX-Code |
771 |
|
|
(* expected size for all reasonable applications*) |
772 |
|
|
\end_layout |
773 |
|
|
|
774 |
|
|
\begin_layout LyX-Code |
775 |
|
|
END amortized_area_cost; |
776 |
|
|
\end_layout |
777 |
|
|
|
778 |
|
|
\begin_layout Standard |
779 |
|
|
In picking the name of your atom, remember that names should be as self-explanat |
780 |
|
|
ory as possible. |
781 |
|
|
Also avoid choosing a name that ends in _constant (as this is conventionally |
782 |
|
|
applied only to CONSTANT |
783 |
|
|
\begin_inset LatexCommand \index{CONSTANT} |
784 |
|
|
|
785 |
|
|
\end_inset |
786 |
|
|
|
787 |
|
|
definitions) or _parameter. |
788 |
|
|
Parameter is an extremely ambiguous and therefore useless word. |
789 |
|
|
Also remember that the role a variable plays in solving a set of equations |
790 |
|
|
depends on how the solver being applied interprets .fixed and other attributes |
791 |
|
|
of the variable. |
792 |
|
|
\end_layout |
793 |
|
|
|
794 |
|
|
\begin_layout Standard |
795 |
|
|
\begin_inset Marginal |
796 |
|
|
status collapsed |
797 |
|
|
|
798 |
|
|
\begin_layout Standard |
799 |
|
|
Exceptions |
800 |
|
|
\end_layout |
801 |
|
|
|
802 |
|
|
\end_inset |
803 |
|
|
|
804 |
|
|
If an atom type matches all but one of the attributes you need for your |
805 |
|
|
problem, say for example the |
806 |
|
|
\family typewriter |
807 |
|
|
upper_bound |
808 |
|
|
\family default |
809 |
|
|
is way too high, use the existing variable type and reassign the bound |
810 |
|
|
to a more sensible value in the |
811 |
|
|
\family typewriter |
812 |
|
|
default_self |
813 |
|
|
\family default |
814 |
|
|
method of the model where the variable is created. |
815 |
|
|
Having a dozen atoms defined for the same units gets confusing in short |
816 |
|
|
order to anyone you might share your models with. |
817 |
|
|
\end_layout |
818 |
|
|
|
819 |
|
|
\begin_layout Standard |
820 |
|
|
The exception to the exception (yes, there always seems to be one of those) |
821 |
|
|
is the case of a |
822 |
|
|
\family typewriter |
823 |
|
|
lower_bound |
824 |
|
|
\family default |
825 |
|
|
set at zero. |
826 |
|
|
Usually a |
827 |
|
|
\family typewriter |
828 |
|
|
lower_bound |
829 |
|
|
\family default |
830 |
|
|
of zero indicates that there is something inherently positive about variables |
831 |
|
|
of that type. |
832 |
|
|
Variables with a bound of this type should not have these physical bounds |
833 |
|
|
expanded in an application. |
834 |
|
|
Another example of this type of bound is the |
835 |
|
|
\family typewriter |
836 |
|
|
upper_bound |
837 |
|
|
\family default |
838 |
|
|
1.0 on the type fraction. |
839 |
|
|
\end_layout |
840 |
|
|
|
841 |
|
|
\begin_layout Standard |
842 |
|
|
For example, negative temperature just is not sensible for most physical |
843 |
|
|
systems. |
844 |
|
|
ASCEND defines a temperature atom for use in equations involving the absolute |
845 |
|
|
temperature. |
846 |
|
|
On the other hand, a temperature difference, delta T, is frequently negative |
847 |
|
|
so a separate atom is defined. |
848 |
|
|
Anyone receiving a model written using the two types of atoms, which both |
849 |
|
|
have units of {Kelvin}, can easily tell which variables might legitimately |
850 |
|
|
take on negative values by noting whether the variable is defined as a |
851 |
|
|
temperature or a delta_temperature. |
852 |
|
|
\end_layout |
853 |
|
|
|
854 |
|
|
\begin_layout Subsection |
855 |
|
|
A new real constant |
856 |
|
|
\begin_inset LatexCommand \index{real constant} |
857 |
|
|
|
858 |
|
|
\end_inset |
859 |
|
|
|
860 |
|
|
|
861 |
|
|
\begin_inset LatexCommand \index{constant, real} |
862 |
|
|
|
863 |
|
|
\end_inset |
864 |
|
|
|
865 |
|
|
type |
866 |
|
|
\end_layout |
867 |
|
|
|
868 |
|
|
\begin_layout Standard |
869 |
|
|
Real constants which do not have a default value are usually needed only |
870 |
|
|
in libraries of reusable models, such as |
871 |
|
|
\family typewriter |
872 |
|
|
components.a4l |
873 |
|
|
\family default |
874 |
|
|
, where the values depend on the end-user's selection from alternatives |
875 |
|
|
in a database. |
876 |
|
|
The standard incantation to define a new real constant type is: |
877 |
|
|
\end_layout |
878 |
|
|
|
879 |
|
|
\begin_layout LyX-Code |
880 |
|
|
CONSTANT |
881 |
|
|
\shape italic |
882 |
|
|
critical_pressure_constant |
883 |
|
|
\end_layout |
884 |
|
|
|
885 |
|
|
\begin_layout LyX-Code |
886 |
|
|
REFINES real_constant DIMENSION |
887 |
|
|
\shape italic |
888 |
|
|
M/L/T^2 |
889 |
|
|
\shape default |
890 |
|
|
; |
891 |
|
|
\end_layout |
892 |
|
|
|
893 |
|
|
\begin_layout Standard |
894 |
|
|
Here again, the italic parts of this incantation should be redefined for |
895 |
|
|
your purpose. |
896 |
|
|
\end_layout |
897 |
|
|
|
898 |
|
|
\begin_layout Standard |
899 |
|
|
\begin_inset Marginal |
900 |
|
|
status collapsed |
901 |
|
|
|
902 |
|
|
\begin_layout Standard |
903 |
|
|
Universal exceptions and unit conversions |
904 |
|
|
\end_layout |
905 |
|
|
|
906 |
|
|
\end_inset |
907 |
|
|
|
908 |
|
|
It is wasteful to define a |
909 |
|
|
\family typewriter |
910 |
|
|
CONSTANT |
911 |
|
|
\family default |
912 |
|
|
type and a compiled object to represent a universal |
913 |
|
|
\begin_inset LatexCommand \index{universal constant} |
914 |
|
|
|
915 |
|
|
\end_inset |
916 |
|
|
|
917 |
|
|
|
918 |
|
|
\begin_inset LatexCommand \index{constant, universal} |
919 |
|
|
|
920 |
|
|
\end_inset |
921 |
|
|
|
922 |
|
|
constant. |
923 |
|
|
For example, the thermodynamic gas constant, R = 8.314... |
924 |
|
|
{J/mole/K}, is frequently needed in modeling chemical systems. |
925 |
|
|
The SI value of R does not vary with its application. |
926 |
|
|
Neither does the value of |
927 |
|
|
\begin_inset LatexCommand \index{pi} |
928 |
|
|
|
929 |
|
|
\end_inset |
930 |
|
|
|
931 |
|
|
|
932 |
|
|
\begin_inset Formula $\pi$ |
933 |
|
|
\end_inset |
934 |
|
|
|
935 |
|
|
. |
936 |
|
|
Numeric constants of this sort are better represented as a numeric coefficient |
937 |
|
|
and an appropriately defined unit conversion. |
938 |
|
|
Consider the |
939 |
|
|
\begin_inset LatexCommand \index{ideal gas law} |
940 |
|
|
|
941 |
|
|
\end_inset |
942 |
|
|
|
943 |
|
|
ideal gas law, PV = NRT and the ASCEND unit conversion {GAS_C} which appears |
944 |
|
|
in the library ascend4/models/measures.a4l. |
945 |
|
|
This equation should be written: |
946 |
|
|
\end_layout |
947 |
|
|
|
948 |
|
|
\begin_layout LyX-Code |
949 |
|
|
P * V = n * 1.0{GAS_C} * T; |
950 |
|
|
\end_layout |
951 |
|
|
|
952 |
|
|
\begin_layout Standard |
953 |
|
|
Similarly, area = pi*r^2 should be written |
954 |
|
|
\end_layout |
955 |
|
|
|
956 |
|
|
\begin_layout LyX-Code |
957 |
|
|
area = 1{PI} * r^2; |
958 |
|
|
\end_layout |
959 |
|
|
|
960 |
|
|
\begin_layout Standard |
961 |
|
|
The coefficient 1 of |
962 |
|
|
\family typewriter |
963 |
|
|
{GAS_C} |
964 |
|
|
\family default |
965 |
|
|
and {PI} in these equations takes of the dimensionality of and is multiplied |
966 |
|
|
by the conversion factor implied by the |
967 |
|
|
\family typewriter |
968 |
|
|
UNITS |
969 |
|
|
\family default |
970 |
|
|
definition for the units. |
971 |
|
|
If we check |
972 |
|
|
\family typewriter |
973 |
|
|
measures.a4l |
974 |
|
|
\family default |
975 |
|
|
, we find the definition of PI is simply {3.14159...} and the definition of |
976 |
|
|
|
977 |
|
|
\family typewriter |
978 |
|
|
GAS_C |
979 |
|
|
\family default |
980 |
|
|
is {8.314... |
981 |
|
|
J/mole/K} as we ought to expect. |
982 |
|
|
\end_layout |
983 |
|
|
|
984 |
|
|
\begin_layout Standard |
985 |
|
|
For historical reasons there are a few universal constant definitions in |
986 |
|
|
|
987 |
|
|
\family typewriter |
988 |
|
|
atoms.a4l |
989 |
|
|
\family default |
990 |
|
|
. |
991 |
|
|
New modelers should not use them; they are only provided to support outdated |
992 |
|
|
models that no one has yet taken the time to update. |
993 |
|
|
\end_layout |
994 |
|
|
|
995 |
|
|
\begin_layout Subsection |
996 |
|
|
New types for integers, symbols, and booleans |
997 |
|
|
\end_layout |
998 |
|
|
|
999 |
|
|
\begin_layout Standard |
1000 |
|
|
The syntax for |
1001 |
|
|
\family typewriter |
1002 |
|
|
ATOM |
1003 |
|
|
\family default |
1004 |
|
|
and |
1005 |
|
|
\family typewriter |
1006 |
|
|
CONSTANT |
1007 |
|
|
\family default |
1008 |
|
|
definitions of the non-real types is the same as for real number types, |
1009 |
|
|
except that units are not involved. |
1010 |
|
|
Take your best guess based on the examples above, and you will get it right. |
1011 |
|
|
If even that is too hard, more details are given in **syntax.fm5**. |
1012 |
|
|
\end_layout |
1013 |
|
|
|
1014 |
|
|
\begin_layout Section |
1015 |
|
|
How to define a |
1016 |
|
|
\begin_inset LatexCommand \index{scaling} |
1017 |
|
|
|
1018 |
|
|
\end_inset |
1019 |
|
|
|
1020 |
|
|
scaling variable |
1021 |
|
|
\end_layout |
1022 |
|
|
|
1023 |
|
|
\begin_layout Standard |
1024 |
|
|
A scaling variable |
1025 |
|
|
\family typewriter |
1026 |
|
|
ATOM |
1027 |
|
|
\family default |
1028 |
|
|
is defined with a name that ends in _scale as follows. |
1029 |
|
|
Note that this |
1030 |
|
|
\family typewriter |
1031 |
|
|
ATOM |
1032 |
|
|
\family default |
1033 |
|
|
does not refine |
1034 |
|
|
\family typewriter |
1035 |
|
|
solver_var |
1036 |
|
|
\family default |
1037 |
|
|
, so solvers will not try to change variables of this type during the solution |
1038 |
|
|
process. |
1039 |
|
|
\end_layout |
1040 |
|
|
|
1041 |
|
|
\begin_layout LyX-Code |
1042 |
|
|
ATOM distance_scale REFINES real DEFAULT 1.0{meter}; |
1043 |
|
|
\end_layout |
1044 |
|
|
|
1045 |
|
|
\begin_layout LyX-Code |
1046 |
|
|
END distance_scale; |
1047 |
|
|
\end_layout |
1048 |
|
|
|
1049 |
|
|
\begin_layout Standard |
1050 |
|
|
\begin_inset Marginal |
1051 |
|
|
status collapsed |
1052 |
|
|
|
1053 |
|
|
\begin_layout Standard |
1054 |
|
|
ASCEND cannot do it all for you |
1055 |
|
|
\end_layout |
1056 |
|
|
|
1057 |
|
|
\end_inset |
1058 |
|
|
|
1059 |
|
|
ASCEND uses a combination of symbolic and numerical techniques to create |
1060 |
|
|
and solve mathematical problems. |
1061 |
|
|
Once you get the problem close to the solution, ASCEND can internally compute |
1062 |
|
|
its own scaling values for relations, known elsewhere as "relation nominals |
1063 |
|
|
\begin_inset LatexCommand \index{nominals} |
1064 |
|
|
|
1065 |
|
|
\end_inset |
1066 |
|
|
|
1067 |
|
|
, |
1068 |
|
|
\begin_inset Quotes erd |
1069 |
|
|
\end_inset |
1070 |
|
|
|
1071 |
|
|
assuming you have set good values for the .nominal attribute of all the |
1072 |
|
|
variables. |
1073 |
|
|
It does this by computing the largest additive term in each equation. |
1074 |
|
|
The absolute value of this term is a very good scaling value. |
1075 |
|
|
\end_layout |
1076 |
|
|
|
1077 |
|
|
\begin_layout Standard |
1078 |
|
|
This internal scaling works quite well, but not when the problem is very |
1079 |
|
|
far away from the solution so that the largest additive terms computed |
1080 |
|
|
are not at all representative of the physical situation being modeled. |
1081 |
|
|
The |
1082 |
|
|
\family typewriter |
1083 |
|
|
scale_self |
1084 |
|
|
\family default |
1085 |
|
|
|
1086 |
|
|
\begin_inset LatexCommand \index{scale\_self} |
1087 |
|
|
|
1088 |
|
|
\end_inset |
1089 |
|
|
|
1090 |
|
|
method, which should be written for every model as described in Section\InsetSpace ~ |
1091 |
|
|
|
1092 |
|
|
\begin_inset LatexCommand \ref{sssec:methods.scaleself} |
1093 |
|
|
|
1094 |
|
|
\end_inset |
1095 |
|
|
|
1096 |
|
|
of Chapter |
1097 |
|
|
\noun off |
1098 |
|
|
\InsetSpace ~ |
1099 |
|
|
|
1100 |
|
|
\begin_inset LatexCommand \vref{cha:methods} |
1101 |
|
|
|
1102 |
|
|
\end_inset |
1103 |
|
|
|
1104 |
|
|
should set the equation scaling values you have defined in a |
1105 |
|
|
\family typewriter |
1106 |
|
|
\noun default |
1107 |
|
|
MODEL |
1108 |
|
|
\family default |
1109 |
|
|
\noun off |
1110 |
|
|
based on the best available information. |
1111 |
|
|
In a chemical engineering flowsheeting problem, for example, information |
1112 |
|
|
about a key process material flow should be propagated throughout the process |
1113 |
|
|
flowsheet to scale all the other flows, material balance equations, and |
1114 |
|
|
energy balance equations. |
1115 |
|
|
\end_layout |
1116 |
|
|
|
1117 |
|
|
\begin_layout Standard |
1118 |
|
|
\begin_inset Marginal |
1119 |
|
|
status collapsed |
1120 |
|
|
|
1121 |
|
|
\begin_layout Standard |
1122 |
|
|
Scaling atom default value |
1123 |
|
|
\end_layout |
1124 |
|
|
|
1125 |
|
|
\end_inset |
1126 |
|
|
|
1127 |
|
|
The |
1128 |
|
|
\begin_inset LatexCommand \index{default value} |
1129 |
|
|
|
1130 |
|
|
\end_inset |
1131 |
|
|
|
1132 |
|
|
default value for any scaling atom should always be 1.0 in appropriate SI |
1133 |
|
|
units, so that the scaling will have no effect until you assign a problem |
1134 |
|
|
specific value. |
1135 |
|
|
Multiplying or dividing both sides of an equation by 1.0 obviously will |
1136 |
|
|
not change the mathematical behavior, but you do not want to change the |
1137 |
|
|
behavior arbitrarily either-- you want to change it based on problem informatio |
1138 |
|
|
n that is not contained in your |
1139 |
|
|
\family typewriter |
1140 |
|
|
myatoms.a4l |
1141 |
|
|
\family default |
1142 |
|
|
file. |
1143 |
|
|
\end_layout |
1144 |
|
|
|
1145 |
|
|
\end_body |
1146 |
|
|
\end_document |