trunk/doc/howto-model1.lyx

#LyX 1.4.3 created this file. For more info see http://www.lyx.org/
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     REQUIRE,IMPORT,
     ATOM,MODEL,METHOD,METHODS,
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     CONDITIONAL,SATISFIED,WHEN,CASE,OTHERWISE,TRUE,
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\language english
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\end_header

\begin_body

\begin_layout Chapter
Vessel Model for Beginners
\begin_inset LatexCommand \label{cha:model1}

\end_inset


\end_layout

\begin_layout Standard
You read our propaganda about the ASCEND system in which we said it was
 to help technical people create hard models.
 We said you can tackle really large models -- 100,000 equations, compiling
 and solving them in minutes on a PC.
 We also pointed out that you can readily solve the small problems many
 currently solve using a spreadsheet, only once posed you can solve them
 inside out, upside down and backwards.
 
\end_layout

\begin_layout Standard
This sounded intriguing so you downloaded the system and installed it.
 Hopefully, this proved quite straight forward.
 You double-clicked the ASCEND icon on your desktop and started it up for
 the first time.
 Four windows opened up.
 You panicked.
 
\end_layout

\begin_layout Standard
Who wouldn't? 
\end_layout

\begin_layout Standard
To use this system properly requires that you learn how to use it.
 If you pay the price to do so - and we hope it is not a large price, then
 we believe you will find the tools we have provided to help you create
 and debug models will pay you back handsomely.
 
\end_layout

\begin_layout Standard
This chapter 
\noun off
and the next two chapters (
\noun default
Chapter 
\noun off

\begin_inset LatexCommand \ref{cha:model2}

\end_inset

 and 
\noun default
Chapter 
\noun off

\begin_inset LatexCommand \ref{cha:model3}

\end_inset

)
\noun default
 
\noun off
are meant to be a good first step along the path to learning how to use
 ASCEND.
 We 
\noun default
will
\noun off
 lead you through the steps for creating and testing a simple model.
 You will also learn how to improve this model so it may be more readily
 shared with others.
 We will present our reasons for the steps we take.
 We
\noun default
 will
\noun off
 show you all the buttons you should push as you proceed.
\end_layout

\begin_layout Standard
We strongly suggest you put time aside and go through all three of these
 early chapters to introduce yourself to ASCEND.
 It should take you about two to three hours.
 The second chapter is particularly important if you wish to understand
 our approach to good modeling practices.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
the problem
\end_layout

\end_inset

Step 1: 
\emph on
We are going to create and test an ASCEND model to compute, the mass of
 the metal in the sides and ends of the thin-walled cylindrical vessel
\emph default

\begin_inset LatexCommand \index{vessel}

\end_inset


\emph on
 shown in Figure 
\begin_inset LatexCommand \ref{fig:model1.thinWalledVessel}

\end_inset

.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Standard

\noun off
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\begin_inset Graphics
    filename howto-model1Fig1.eps
    BoundingBox 0bp 0bp 280bp 260bp

\end_inset


\end_layout

\begin_layout Caption
A thin-walled cylindrical vessel with flat ends
\begin_inset LatexCommand \label{fig:model1.thinWalledVessel}

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Step 2: 
\emph on
This model is to become a part of a library of models which others can use
 in the future.
 You must document it.
 You must add methods to it to make it easy for others to make it well-posed.
 You should probably parameterize it, and finally you must create a script
 which anyone can easily run that solves an example problem to illustrate
 its use.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
topics covered
\end_layout

\end_inset

Topics covered in this and the following two chapters are:
\end_layout

\begin_layout Itemize
\begin_inset Marginal
status collapsed

\begin_layout Standard
T
\noun off
his chapter)
\end_layout

\end_inset

Converting the word description to an ASCEND model.
\end_layout

\begin_layout Itemize
Loading the model into ASCEND, dealing with the error messages.
\end_layout

\begin_layout Itemize
Compiling the model.
\end_layout

\begin_layout Itemize
Browsing the model to see if it looks right
\end_layout

\begin_layout Itemize
Solving the model.
\end_layout

\begin_layout Itemize
Examining the results.
\end_layout

\begin_layout Itemize
More thoroughly testing the model.
\end_layout

\begin_layout Itemize
\begin_inset Marginal
status collapsed

\begin_layout Standard
Chapter\InsetSpace ~

\begin_inset LatexCommand \vref{cha:model2}

\end_inset


\end_layout

\end_inset

Converting the model to a more reusable form by adding methods to it and
 by parameterizing it.
\end_layout

\begin_layout Itemize
Creating a script to load and execute an instance of the model.
\end_layout

\begin_layout Itemize
\begin_inset Marginal
status collapsed

\begin_layout Standard
Chapter\InsetSpace ~

\begin_inset LatexCommand \vref{cha:model3}

\end_inset


\end_layout

\end_inset

Creating an array of models.
\end_layout

\begin_layout Itemize
Using an existing library model for plotting.
\end_layout

\begin_layout Itemize
Creating a case study using the model.
\end_layout

\begin_layout Standard
We shall introduce many of the features of the modeling language as well
 as the use of the interactive interface you use when compiling, debugging,
 solving and exploring your model.
 Language features include units conversion, arrays and sets.
\end_layout

\begin_layout Section
Converting the word description into an ASCEND model
\begin_inset LatexCommand \label{sec:model1.converting-the-word}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
an ASCEND model is a type
\begin_inset LatexCommand \index{type}

\end_inset

 definition
\end_layout

\end_inset

Every ASCEND model is, in fact, a type definition.
 To "solve a model," we make an instance
\begin_inset LatexCommand \index{instance}

\end_inset

 of a type and solve the instance.
 So we shall start by creating a vessel type definition.
 We will have to create our type definition as a text file using a text
 editor.
 (Some simple text editors
\begin_inset LatexCommand \index{text editors}

\end_inset

 include 
\family typewriter
emacs
\family default

\begin_inset LatexCommand \index{emacs}

\end_inset

 and 
\family typewriter
gedit
\begin_inset LatexCommand \index{gedit}

\end_inset


\family default
 on Linux, and Notepad
\begin_inset LatexCommand \index{Notepad}

\end_inset

 and TextPad
\begin_inset LatexCommand \index{TextPad}

\end_inset

 on Windows.
 We shall discuss editors shortly.)
\end_layout

\begin_layout Standard
We need first to decide the parts to our model.
 In this case we know that we need the variables
\begin_inset LatexCommand \index{variables, vessel}

\end_inset

 listed in Table 
\begin_inset LatexCommand \ref{tab:model1.variablesVesselModel}

\end_inset


\noun off
.
 We readily fill in the first three columns in this table.
 We shall discuss the entry in the last column in a moment.
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status open

\begin_layout Caption
Variables required for model
\begin_inset LatexCommand \label{tab:model1.variablesVesselModel}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="4">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="1in">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Symbol
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Meaning
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Typical Units
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
ASCEND variable type
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
D
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
vessel diameter
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
m, ft
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
length
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
H
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
vessel height
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
m, ft
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
length
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
wall_thickness
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
wall thickness
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
mm, in
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
length
\end_layout

\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
metal_density
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
metal density
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
kg/m
\begin_inset Formula $^{\textrm{3}}$
\end_inset

, lbm/ft
\begin_inset Formula $^{\textrm{3}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
mass_density
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
We will be computing the masses for the metal in the side wall and in the
 ends for this vessel.
 As this is a thin-walled vessel, we shall compute the volume of metal as
 the area of the walls times the wall thickness.
 The following equations allow us to compute the required areas
\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
\mathrm{side\, wall\, area}=\pi DH\label{eq:model1.side-wall-area}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
\mathrm{single\, end\, area}=\frac{\pi D^{2}}{4}\label{eq:model1.single-end-area}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
We should be interested in the volume of the vessel, which we compute as:
\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
\mathrm{vessel\, volume}=\mathrm{single\, end\, area}\times H\label{eq:model1.vessel-volume}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
We add the variables in Table 
\begin_inset LatexCommand \ref{tab:model1.moreVariablesVessel}

\end_inset

 
\noun off
to our list.
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status open

\begin_layout Caption
Some more variables
\begin_inset LatexCommand \index{variables,  vessel}

\end_inset

 required for vessel model
\begin_inset LatexCommand \label{tab:model1.moreVariablesVessel}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="4">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="1.5in">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="1in">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Symbol
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Meaning
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Typical Units
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
ASCEND variable type
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
side_area
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
area in the sidewall of the vessel
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
m
\begin_inset Formula $^{\textrm{2}}$
\end_inset

, ft
\begin_inset Formula $^{\textrm{2}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
area
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
end_area
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
total area iin the ends of the vessel
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
m
\begin_inset Formula $^{\textrm{2}}$
\end_inset

, ft
\begin_inset Formula $^{\textrm{2}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
area
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
vessel_volume
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
volume of the vessel
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
m
\begin_inset Formula $^{3}$
\end_inset

, ft
\begin_inset Formula $^{\textrm{3}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
volume
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
metal_volume
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
total volume of metal in the walls
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
m
\begin_inset Formula $^{3}$
\end_inset

, ft
\begin_inset Formula $^{\textrm{3}}$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
volume
\end_layout

\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
metal_mass
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
total mass of the metal in the walls of the vessel
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
kg, lbm
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
mass
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
We believe that no one should create a model of any consequence without
 worrying about the units for expressing the variables within it.
 We consider that to be a commandment handed down from somewhere on high;
 however, we know that others do not believe as we do.
 Grant us our beliefs.
 We have created in the ASCEND system a library of variable and constant
 types called atoms.a4l
\begin_inset LatexCommand \index{atoms.a4l}

\end_inset

 .
\end_layout

\begin_layout Standard
The file type "
\family typewriter
.a4l
\begin_inset LatexCommand \index{a4l}

\end_inset


\family default
" designates it to be an ASCEND IV library file
\begin_inset LatexCommand \index{library file}

\end_inset

.
 Double-click on this link to see the approximately 150 different types
 ranging from universal constants
\begin_inset LatexCommand \index{universal constants}

\end_inset

 such as 
\begin_inset Formula $\pi$
\end_inset

 (=3.14159...) and 
\begin_inset Formula $e$
\end_inset

 (=2.718...) to 
\family typewriter
length
\family default
, 
\family typewriter
mass
\family default
 and 
\family typewriter
angle
\family default
.
 If we have not created one that you need, you can use this library of types
 to see how to construct one for yourself and add it to your file of type
 definitions.
 You will find detailed instructions for how to make your own variable type
 library in Chapter\InsetSpace ~

\begin_inset LatexCommand \vref{cha:atoms}

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
type definition library for variables and constants
\end_layout

\end_inset

ASCEND considers variable and constant types to be elementary or "atomic"
 to the system.
 These type definitions can contain only attributes for variables and constants.
 They cannot contain equations, for example.
 Thus ASCEND calls such a type definition an atom rather than a model.
 Figure 
\begin_inset LatexCommand \ref{fig:model1.atomVolume}

\end_inset


\noun off
 illustrates the definition for the type volume.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Standard
\begin_inset LatexCommand \index{ATOM}

\end_inset

 
\begin_inset ERT
status open

\begin_layout Standard


\backslash
lstset{language=ASCEND}
\end_layout

\begin_layout Standard


\backslash
begin{lstlisting}
\end_layout

\begin_layout Standard

ATOM volume REFINES solver_var 
\end_layout

\begin_layout Standard

    DIMENSION L^3 
\end_layout

\begin_layout Standard

    DEFAULT 100.0{ft^3};
\end_layout

\begin_layout Standard

  lower_bound := 0.0{ft^3};
\end_layout

\begin_layout Standard

  upper_bound := 1e50{ft^3};
\end_layout

\begin_layout Standard

  nominal := 100.0{ft^3};
\end_layout

\begin_layout Standard

END volume;
\end_layout

\begin_layout Standard


\backslash
end{lstlisting}
\end_layout

\begin_layout Standard

\end_layout

\end_inset


\end_layout

\begin_layout Caption
A typical type definition, called an atom, used to define variable and constant
 types
\begin_inset LatexCommand \label{fig:model1.atomVolume}

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
The definition starts by stating that volume is a specialization of 
\begin_inset LatexCommand \index{solver\_var}

\end_inset


\family typewriter
solver_var
\family default
.
 The type 
\family typewriter
solver_var
\family default
 refines a base type in the system known as 
\family typewriter
real
\family default

\begin_inset LatexCommand \index{real}

\end_inset

 and adds several attributes to it that a nonlinear equation solver may
 need, such as a lower and upper bounds, a 'fixed' flag, and so forth.
 
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
dimensions
\begin_inset LatexCommand \index{dimensions}

\end_inset

 and units
\begin_inset LatexCommand \index{units}

\end_inset

 in ASCEND.
 
\end_layout

\end_inset

The type definition for volume states that volume has dimensionality of
 length to the power 3 (
\family typewriter
L^3
\family default
) where L is one of the 10 dimensions supported by ASCEND (see 
\noun off
in ASCEND Syntax document for the 10 dimensions defined within the ASCEND
 language).
\end_layout

\begin_layout Standard
One may express the value for a volume using any units which are consistent
 with the dimensionality of 
\family typewriter
L^3
\family default
, such as 
\family typewriter
{ft^3}
\family default
, 
\family typewriter
{m^3}
\family default
, 
\family typewriter
{gal}
\family default
, or even 
\family typewriter
{mile^4/mm}
\family default
.
 Setting the lower bound to 
\family typewriter
0 {ft^3}
\family default
 says volume must be a nonnegative number.
 ASCEND used the nominal value for scaling a variable of type volume when
 solving, here 
\begin_inset Formula $100\,\mathrm{ft}^{3}$
\end_inset

.
\end_layout

\begin_layout Standard
One may change the values for the bounds, default and nominal values at
 any time.
\end_layout

\begin_layout Standard
We now can understand the last column in Table 
\begin_inset LatexCommand \ref{tab:model1.variablesVesselModel}

\end_inset


\noun off
 and
\noun default
 Table
\noun off
 
\begin_inset LatexCommand \ref{tab:model1.moreVariablesVessel}

\end_inset

.
 For each variable or constant in the system, we have identified its type
 in the file 
\family typewriter
\noun default
atoms.a4l
\family default
\noun off
.
 That is, we looked in this file for the type definition that corresponded
 to the variable we were defining and listed that type here.
 This task is not as onerous as it seems.
 As we shall see later, we provide a tool to find for you all atom types
 that correspond to a particular set of units, e.g, 
\family typewriter
\noun default
ft^3
\family default
\noun off
 -- i.e., the computer will do the searching for you.
\end_layout

\begin_layout Standard
In Figure 
\begin_inset LatexCommand \ref{fig:model1.universalConstant}

\end_inset


\noun off
 we see the definition of one of the universal constants contained in 
\family typewriter
\noun default
atoms.a4l
\family default
\noun off
.
 This definition is very short; it gives the name of the type 
\family typewriter
\noun default
circle_constant
\family default
\noun off

\begin_inset LatexCommand \index{circle\_constant}

\end_inset

, that it refines 
\family typewriter
\noun default
real_constant
\family default
\noun off

\begin_inset LatexCommand \index{real\_constant}

\end_inset

 and that it has the value 
\family typewriter
\noun default
1 {PI
\begin_inset LatexCommand \index{PI}

\end_inset

}
\family default
\noun off

\begin_inset LatexCommand \index{\{PI\}}

\end_inset

 where the internal conversion needed for 
\family typewriter
\noun default
{PI}
\family default
\noun off
 is defined in the file defining the built-in units in ASCEND.
 One can add more units if desired at any time to ASCEND by defining one
 or more personal units files (
\noun default
Chapter 
\noun off

\begin_inset LatexCommand \vref{cha:units}

\end_inset


\noun default
 
\noun off
tells you how to do this).
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
universal constant
\begin_inset LatexCommand \index{universal constant}

\end_inset

 definition
\end_layout

\end_inset


\begin_inset Float figure
wide false
sideways false
status open

\begin_layout LyX-Code
\begin_inset ERT
status open

\begin_layout Standard


\backslash
begin{ascend}
\end_layout

\begin_layout Standard

UNIVERSAL CONSTANT circle_constant 
\end_layout

\begin_layout Standard

    REFINES real_constant :== 1{PI};
\end_layout

\begin_layout Standard


\backslash
end{ascend}
\end_layout

\end_inset


\end_layout

\begin_layout Caption
\begin_inset LatexCommand \label{fig:model1.universalConstant}

\end_inset

Type definition for 
\family typewriter
circle_constant;
\family default
 has value of 
\family typewriter
1 {PI}
\family default
 or 3.1415927
\end_layout

\end_inset


\end_layout

\begin_layout Standard
We shall in fact find this constant useful in our program, and we can either
 introduce a constant with this value or simply use the value 
\family typewriter
1{PI}
\family default
 in our program.
 We shall choose to do the latter.
\end_layout

\begin_layout Standard
It is time to write our first version for the model, which we do in Figure
 
\begin_inset LatexCommand \ref{fig:model1.modelVessel}

\end_inset


\noun off
 (
\noun default
available as 
\begin_inset LatexCommand \index{vesselPlain.a4c}

\end_inset


\family typewriter
vesselPlain.a4c
\family default
 in the ASCEND model library).

\noun off
 We first list any other files containing type definitions which this model
 will use; here we list 
\family typewriter
\noun default
"atoms.a4l"
\family default
\noun off
 following the keyword 
\family typewriter
\noun default
REQUIRE
\family default
\noun off

\begin_inset LatexCommand \index{REQUIRE}

\end_inset

.
 ASCEND is sensitive to case so pay attention to where we use and do not
 use capital letters.
 Keywords are always capitalized.
 Often for clarification we use capital letters in a name we use for a variable
 or label (e.g., we use 
\family typewriter
\noun default
D
\family default
\noun off
 for diameter rather than 
\family typewriter
\noun default
d
\family default
\noun off
).
 Note that all ASCEND statements end with a semicolon (i.e., with 
\noun default
'
\family typewriter
;
\family default
'
\noun off
) and not at the end of a line and that blank lines have no impact.
 Comments are between opening and closing parenthesis/asterisk pairs, i.e.,
 '
\family typewriter
\noun default
(*
\family default
\noun off
' and '
\family typewriter
\noun default
*)
\family default
\noun off
'.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
the first version of the code for vessel 
\end_layout

\end_inset


\begin_inset Float figure
wide false
sideways false
status open

\begin_layout LyX-Code
\begin_inset ERT
status open

\begin_layout Standard


\backslash
begin{ascend}
\end_layout

\begin_layout Standard

REQUIRE "atoms.a4l";
\end_layout

\begin_layout Standard

MODEL vessel;
\end_layout

\begin_layout Standard

  (* variables *)
\end_layout

\begin_layout Standard

  side_area, end_area     IS_A area;
\end_layout

\begin_layout Standard

  vessel_vol, wall_vol    IS_A volume;
\end_layout

\begin_layout Standard

  wall_thickness, H, D    IS_A distance;
\end_layout

\begin_layout Standard

  H_to_D_ratio            IS_A factor;
\end_layout

\begin_layout Standard

  metal_density           IS_A mass_density;
\end_layout

\begin_layout Standard

  metal_mass              IS_A mass;
\end_layout

\begin_layout Standard

\end_layout

\begin_layout Standard

  (* equations *)
\end_layout

\begin_layout Standard

  FlatEnds:end_area = 1{PI} * D^2 / 4;
\end_layout

\begin_layout Standard

  Sides:side_area = 1{PI} * D * H;
\end_layout

\begin_layout Standard

  Cylinder:vessel_vol = end_area * H;
\end_layout

\begin_layout Standard

  Metal_volume:(side_area + 2 * end_area) *
\end_layout

\begin_layout Standard

  wall_thickness = wall_vol;
\end_layout

\begin_layout Standard

  HD_definition:D * H_to_D_ratio = H;
\end_layout

\begin_layout Standard

  VesselMass:metal_mass = metal_density * wall_vol;
\end_layout

\begin_layout Standard

END vessel;
\end_layout

\begin_layout Standard


\backslash
end{ascend}
\end_layout

\end_inset


\end_layout

\begin_layout Caption
\begin_inset LatexCommand \label{fig:model1.modelVessel}

\end_inset

First version of the type definition for 
\family typewriter
vessel
\family default
.
 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Our model definition has the following structure for it so far:
\end_layout

\begin_layout Itemize

\family typewriter
MODEL
\family default

\begin_inset LatexCommand \index{MODEL}

\end_inset

 statement
\end_layout

\begin_layout Itemize
list of variable we intend to use in the type definition
\end_layout

\begin_layout Itemize
equations
\end_layout

\begin_layout Itemize

\family typewriter
END
\family default

\begin_inset LatexCommand \index{END}

\end_inset

 statement
\end_layout

\begin_layout Standard
While we have put the statements in this order, we could mix up and intermix
 the middle two types of statements, even going to the extreme of defining
 the variables after we first use them.
 The 
\family typewriter
MODEL
\family default
 and 
\family typewriter
END
\family default
 statements begin and end the type definition.
\end_layout

\begin_layout Standard
You should see little that surprises you in the syntax here.
 However, you may have noted that we have created a definition that says
 absolutely nothing about how to use the variables and equations listed.
 There is no solution procedure buried in this type definition.
 In ASCEND the idea of solving is separate from saying what we intend to
 solve.
 Also note that we have not said anything about the values for any of the
 variables nor what we intend to calculate and what variables we intend
 to treat as fixed input.
\end_layout

\begin_layout Section
Editing, compiling and browsing an ASCEND model
\end_layout

\begin_layout Standard
Could we compile an instance of a vessel given this definition? If there
 had been some arrays in our definition for which we did not say how many
 items were in the arrays, we could not.
 However, here we could compile an instance, putting aside storage space
 for each of the variables and somehow capturing the equations relating
 them.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status open

\begin_layout Standard
Do not alter the models subdirectory
\end_layout

\end_inset

When we compile new models, we need a place to store them.
 One possibility would be to put them into the 
\family typewriter
models
\family default

\begin_inset LatexCommand \index{models}

\end_inset

 subdirectory of the ASCEND installation
\begin_inset Foot
status collapsed

\begin_layout Standard
On windows this might be 
\family typewriter
c:
\backslash
Program File
\backslash
ASCEND
\backslash
models
\family default
.
 On Linux, this might be 
\family typewriter
/usr/share/ascend/models
\family default
.
 The location can vary depending on how you went about installing ASCEND.
\end_layout

\end_inset

.
 However, you really should leave the contents of this subdirectory untouched
 -- always.
 Hopefully the files will be read-only from your user account.
 We count on being able to replace the model library totally every time
 you install a new version of ASCEND.
 Whenever we add new model libraries or corrected versions of previously
 existing model libraries, we put them in this subdirectory.
 This subdirectory belongs to us (the developers of the system): hands off,
 please.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status open

\begin_layout Standard
rather put your things into the ascdata
\begin_inset LatexCommand \index{ascdata}

\end_inset

 subdirectory (you own it)
\end_layout

\end_inset

To avoid this problem, ASCEND also creates a subdirectory called 
\family typewriter
ascdata
\family default
 that it will not touch when you install a new version of ASCEND.
 It will look in this subdirectory first when looking for a file to load
 when you have not given a full path name for finding that file.
 The install process for ASCEND will place 
\family typewriter
ascdata
\family default
 into your home directory
\begin_inset LatexCommand \ref{id:#id(pgfId-1007944)}

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Standard
On Windows, your home directory will normally be the My Documents folder.
 On Linux, it will normally be 
\family typewriter
/home/
\emph on
username
\family default
\emph default
.
 Note that in both systems, you can set an 
\begin_inset Quotes eld
\end_inset

environment
\begin_inset Quotes erd
\end_inset

 variable to designate your home directory.
\end_layout

\end_inset


\noun off
.
 ASCEND tells you where it has placed this subdirectory when you install
 it.
 However, if you did not note where that was, then you will have to search
 for it (using a tool like "FIND file or folder").
\end_layout

\begin_layout Standard
It is within the folder 
\family typewriter
ascdata
\family default
 that you should place any ASCEND models you create.
 When running a script (which we shall talk about later), ASCEND first looks
 in this subdirectory for files, and then it looks in the models subdirectory.
 It stops looking when it finds the first available version of the file.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
create a text file containing the model definition
\end_layout

\end_inset

Next open an editor
\begin_inset LatexCommand \index{text editors}

\end_inset

, such as 
\family typewriter
emacs
\family default

\begin_inset LatexCommand \index{emacs}

\end_inset

, 
\family typewriter
gedit
\family default

\begin_inset LatexCommand \index{gedit}

\end_inset

, 
\family typewriter
vi
\family default

\begin_inset LatexCommand \index{vi}

\end_inset

, 
\family typewriter
vim
\family default

\begin_inset LatexCommand \index{vim}

\end_inset

, Notepad
\begin_inset LatexCommand \index{Notepad}

\end_inset

 or TextPad
\begin_inset LatexCommand \index{TextPad}

\end_inset

.
 Now type in or, better yet, cut-and-paste the statements in Figure 
\begin_inset LatexCommand \ref{fig:model1.modelVessel}

\end_inset


\noun off
.
 Be very careful to match the use of capital and small letters.
 Do not worry about blanks between symbols but do not embed blanks within
 symbols.
 In other words, do not put a blank in the middle of the symbol 
\family typewriter
\noun default
side_wall
\family default
\noun off
 but do not worry about putting zero or more blanks between 
\family typewriter
\noun default
side_wall
\family default
\noun off
 and 
\family typewriter
\noun default
=
\family default
\noun off
 in an equation.
\end_layout

\begin_layout Standard
When you are finished, be sure to save the file as a text file.
 Call it 
\family typewriter
vesselPlain.a4c
\family default
.
 The "
\family typewriter
.a4c
\family default
" stands for "ASCEND 4 Code".
 Many Windows editors will append "
\family typewriter
.txt
\family default
" to the file name.
 Remove the 
\family typewriter
.txt
\family default
 ending off the file name -- do not let Microsoft bully you into thinking
 you should not -- and change it to "
\family typewriter
.a4c
\begin_inset LatexCommand \index{a4c}

\end_inset


\family default
".
 
\end_layout

\begin_layout Standard
(This model is also available as 
\family typewriter
vesselPlain.a4c
\family default
 in the ASCEND models library, but we suggest it would be better for you
 to go through the exercise of creating your own version here.
 At the least copy the library file to your ASCEND space so you can play
 with your own version at this time.)
\end_layout

\begin_layout Standard
When you are done, you should have a text file called 
\family typewriter
vesselPlain.a4c
\family default
 stored in your ASCEND/models/vessel subdirectory.
 It should contain precisely the statements in Figure 
\begin_inset LatexCommand \ref{fig:model1.modelVessel}

\end_inset


\noun off
 with care having been taken to match capital and lower case letters as
 shown there.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
start the ASCEND system.
 Move and resize the windows to make yourself comfortable.
\end_layout

\end_inset

Start the ASCEND system by double clicking on the ASCEND icon if you are
 on Windows or typing 
\family typewriter
ascend
\family default
 at the command line if you are using a Linux machine
\begin_inset Foot
status collapsed

\begin_layout Standard
Depending on the Linux version you have installed, you might find that the
 command is 
\family typewriter
ascend4
\family default
 or that you have an ASCEND option in your GNOME 'Applications' menu.
\end_layout

\end_inset

.
 Four windows will appear, three smaller ones and one larger one that will,
 if left unattended, disappear by itself in a few seconds.
 Move the three smaller ones around on your screen so they do not overlap
 or so they overlap very little.
 Resize them if you want to.
 You might start by putting the one called Script
\begin_inset LatexCommand \index{Script window}

\end_inset

 in the upper left, the one called Library
\begin_inset LatexCommand \index{Library window}

\end_inset

 in the upper right and the one called Console
\begin_inset LatexCommand \index{Console}

\end_inset

 in the lower right.
 We shall assume you have placed them in these positions in the following
 so, even if that is not your favorite placement, it might be useful to
 use it for now.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
note that each window by itself looks pretty nonthreatening
\end_layout

\end_inset

As you can see, each window by itself looks like a pretty normal window.
 Each has buttons across the top under which one will find different tools
 to run.
 Each also has one to three sub-windows for displaying things.
 Each has a Help button that you can push at any time that you want to read
 all kinds of detailed things about the window
\begin_inset Foot
status collapsed

\begin_layout Standard
assuming you have got the help files installed on your system, which you
 may not find you have.
\end_layout

\end_inset

.
 For the moment we will provide you with the "just-in-time" details here
 so you do not need to be sidetracked just yet by pushing these Help buttons.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
hey, where did that window go? I want it back NOW!
\end_layout

\end_inset

If you ever lose a window, open the Script window and under the Tools
\begin_inset LatexCommand \index{Tools}

\end_inset

 button, select the window you wish to open.
 You cannot lose the Script window unless you shut down ASCEND.
 For other windows in ASCEND, you can close them and re-open them as required.
 Any window that you closed can usually be restored by going back to the
 Script window and selected it from the Tools menu there.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
How do I quit
\begin_inset LatexCommand \index{quit ASCEND}

\end_inset

 ASCEND?
\end_layout

\end_inset

To exit
\begin_inset LatexCommand \index{exit ASCEND}

\end_inset

 ASCEND, close the Script window.
 You will be asked to confirm that you want to exit ASCEND.
 If you have simulations in memory this will stop you from losing your results.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
saving
\begin_inset LatexCommand \index{saving window position}

\end_inset

 window positions
\begin_inset LatexCommand \index{window position}

\end_inset


\end_layout

\end_inset

ASCEND will not remember your window locations automatically.
 If you like where you have placed the windows for ASCEND on your display,
 go to the Script window and select 'Save all appearances
\begin_inset LatexCommand \index{window locations, save}

\end_inset


\begin_inset LatexCommand \index{appearances, save all}

\end_inset

' under the View
\begin_inset LatexCommand \index{View}

\end_inset

 menu.
 A similar tool exists for each window for saving only its position.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
start by loading and compiling using tools in the Library window
\end_layout

\end_inset

We shall start with the Library window in the upper right.
 This window provides you with the tools to load and compile files containing
 type definitions.
 You can also display
\begin_inset LatexCommand \index{display}

\end_inset

 the code for the different types you have loaded.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
use the left mouse button unless we tell you otherwise (however, on you
 own explore using the right mouse button in any of the windows)
\end_layout

\end_inset

Let's load your file.
 Under the File button select the 'Read types from File
\begin_inset LatexCommand \index{Read Types from File}

\end_inset

' tool.
 You select this tool by clicking on it using the left mouse button - i.e.,
 the button you should have expected to use.
 A window will appear asking you to find the file you want to read into
 ASCEND.
 Navigate to where you stored 
\family typewriter
vesselPlain.a4c
\family default
 (in the subdirectory 
\family typewriter
ascdata
\family default
) and select that file.
 If you have the wrong ending on the file (you left 
\family typewriter
.txt
\family default
 or you forgot to put 
\family typewriter
.a4c
\family default
 as the ending), tell the system to list all files and pick the one you
 want.
 The 
\family typewriter
.a4c
\family default
 is used by the system to list only the files it thinks you might want to
 load, but ASCEND isn't fussy.
 It will attempt to load any file you pick.
\end_layout

\begin_layout Standard
Look in the Console window at the lower right, and, if the file loads without
 any errors being listed there, you can skip past the next bit to where
 you should start to compile an instance.
 The next bit has some useful hints on how to debug your models.
 If you want some debugging experience, put a known error into your 
\family typewriter
vesselPlain.a4c
\family default
 file and see what happens.
 This move will give you a reason to read the following section.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status open

\begin_layout Standard
Do not ignore the diagnostics
\begin_inset LatexCommand \index{diagnostics}

\end_inset

 that might appear in the Console window
\end_layout

\end_inset

If the Console window in the lower right starts filling with several tens
 of lines of diagnostics, look to see if you included the 
\family typewriter
REQUIRE
\family default

\begin_inset LatexCommand \index{REQUIRE}

\end_inset

 statement at the beginning of your model file.
 Without that statement, ASCEND is missing all the definitions for the types
 of variables in your model, and it will go wild telling you so
\begin_inset Foot
status collapsed

\begin_layout Standard
 It might also be choking on a Word document because you forgot to save
 it as a text file.
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
While loading the files containing these types, ASCEND will look very closely
 at the syntax and will give you all kinds of diagnostic messages in the
 Console window (lower right) if you have done something wrong.
 It will also at times spew out some warning messages
\begin_inset LatexCommand \index{warning messages}

\end_inset

 if you have done something thought to be poor modeling style.
 You must heed the error messages as the file will not load if there are
 any.
 ASCEND will tell you if it did not load the file.
 
\end_layout

\begin_layout Standard
You should consider heeding the warnings if you get any.
 If you ignore them now, they may come back and haunt you later.
 However, there are times when we issue a warning but everything will work,
 and you will think we were not too clever.
 Our response: better modeling style
\begin_inset LatexCommand \index{modeling style}

\end_inset

 can eliminate these warnings.
 (It's been our system so we get to have the last word.)
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
how do I jump
\begin_inset LatexCommand \index{jump to line}

\end_inset


\begin_inset LatexCommand \index{line numbers}

\end_inset

 to line 100 of a file when using some of the standard editors?
\end_layout

\end_inset

The error and warning messages will contain a line number in the file where
 the error has occurred.
 This will be the line number as counted by an editor with the first line
 being line 1 in the file.
 Editors always provide you with a means to get directly to a line number
 in a file.
 Find out how to do that or you will not be too happy with debugging a large
 file.
\end_layout

\begin_layout Standard
You will be in the debug mode for a new system so do not expect it to be
 totally obvious the first few times you make an error.
 We have tried to use language that should be meaningful, but we may have
 failed or the error may be pretty subtle and not possible for us to anticipate
 how to describe it in your terms.
 (Send us a bug report if you have any good ideas on language.)
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
reloading a file
\begin_inset LatexCommand \index{reloading a file}

\end_inset


\begin_inset LatexCommand \index{file, reloading}

\end_inset

 overwrites the previous version
\end_layout

\end_inset

You can reload any file your have corrected using the Read types from file
 tool under the File menu.
 It will overwrite the previous version of the file only if the file has
 changed since it was last loaded (note that we do not reload those big
 files unless you make a change even if you tell us to).
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
displaying the code
\end_layout

\end_inset

You can display the code you have written.
 Select the model vessel in the right window of the Library.
 Then under the Display
\begin_inset LatexCommand \index{Display  window}

\end_inset

 menu at the top, select the tool Code.
 The Display window will open displaying the code for this model.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
now compile as "
\family typewriter
v
\family default
"
\end_layout

\end_inset

Okay, you have your file loaded without getting any diagnostics.
 You are ready to compile
\begin_inset LatexCommand \index{compile}

\end_inset

.
 In the Library window, look in the left window and select the file 
\family typewriter
vesselPlain.a4c
\family default
.
 It contains the type definition you wish to compile.
 You should see the type vessel appear in the right window.
 Select vessel.
 Under the Edit button, select Create simulation.
 A small window opens and asks you to name the simulation.
 Call it 
\family typewriter
v
\family default
 -- yes, just the letter "v", and select "OK".
 Short names for instances often seem to be preferable.
 
\end_layout

\begin_layout Standard
Look again in the Console window for diagnostics.
 If everything worked without error, you will see some statistics telling
 you how many models, relations and so forth you have created during the
 compile step.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
and pass the instance
\begin_inset LatexCommand \index{instance}

\end_inset

 to the Browser
\begin_inset LatexCommand \index{Browser}

\end_inset


\end_layout

\end_inset

Select 
\family typewriter
v IS A vessel
\family default
 in the bottom of the Library window.
 Then under the Export
\begin_inset LatexCommand \index{Export}

\end_inset

 button, select 'Simulation to Browser
\begin_inset LatexCommand \index{Export Simulation to Browser}

\end_inset

' to export 
\family typewriter
v
\family default
 to the Browser tool set.
 The Browser window will open and contain 
\family typewriter
v
\family default
.
 It might be useful to enlarge this window and move it down a bit, placing
 it a bit to the right of the center of your screen.
 (Remember you can save this positioning and sizing of the Browser window
 by going under the View menu and picking 'Save appearance'.)
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
examine 
\family typewriter
v
\family default
 by playing with it in the Browser
\end_layout

\end_inset

In the left upper window of the Browser, you will find 
\family typewriter
v
\family default
 to be the current object.
 Listed in the right window are all the parts of the current object.
 You will see the variables listed here along with an indication of their
 type.
 For example, you will find 
\family typewriter
Cylinder IS A relation
\family default
 and 
\family typewriter
D IS A distance
\family default
 listed, among many others.
 
\family typewriter
Cylinder
\family default
 is one of the equations you wrote describing the model while 
\family typewriter
D
\family default
 was the diameter of the vessel.
 
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
included flags
\begin_inset LatexCommand \index{included flags}

\end_inset


\begin_inset LatexCommand \index{flag, included}

\end_inset

 for relations
\end_layout

\end_inset

If you pick any of the parts in the right or bottom windows, it becomes
 the current object; its parts then show in the right window.
 For example, a relation has a boolean part (a flag that takes the value
 
\family typewriter
TRUE
\family default
 or 
\family typewriter
FALSE
\family default
) indicating whether or not it is to be included when ASCEND solves the
 equations you defined for the model.
\end_layout

\begin_layout Standard
If you wish to display the current value for this flag, pick 'Display Atom
 Values
\begin_inset LatexCommand \index{Display Atom Values}

\end_inset

' under the View menu.
 This tool toggles a switch that causes either the value or the type to
 show for a variable, a constant or a relation in the upper right window
 of the Browser.
 Try toggling it back and forth and looking at different things in the Browser.
\end_layout

\begin_layout Standard
Pick each of the tools under View and note what happens to the displaying
 of things in the Browser.
\end_layout

\begin_layout Standard
Across the bottom of the Browser window note the buttons you can select
 labeled 
\family typewriter
RV
\family default
, 
\family typewriter
DV
\family default
 and so forth.
 If you have made the Browser window large enough, you will see to the right
 of these buttons the type of objects whose value you want to appear or
 not in the lower Browser window as you toggle each button.
 Toggle each of these buttons and see if the lower display changes.
 If it does not, then this type of part is not in the current object.
\end_layout

\begin_layout Section
Solving
\begin_inset LatexCommand \index{Solving}

\end_inset

 an ASCEND instance
\end_layout

\begin_layout Standard
Well, you have been patient.
 While there are lots of interesting tools left to explore in the Browser,
 perhaps it is time to try to solve this model.
 To solve 
\family typewriter
v
\family default
, make it the current object (it alone should be listed in the upper left
 window of the Browser).
 Then, under the Export
\begin_inset LatexCommand \index{Export to Solver}

\end_inset

 menu, select 'to Solver'.
 The Solver window will open, along with a smaller window labeled Eligible
\begin_inset LatexCommand \index{window, Eligible}

\end_inset


\begin_inset LatexCommand \index{Eligible window}

\end_inset

.
 Move the Eligible window up a bit so it does not cover any or very little
 of the Solver window.
 Move the Solver window to the lower left and enlarge it so you can see
 all of its contents.
 
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
if ASCEND stops responding
\begin_inset LatexCommand \index{responding, ASCEND stops}

\end_inset

, hunt down one of those "nasty" windows with a "yellow lock
\begin_inset LatexCommand \index{yellow lock}

\end_inset

" and close it properly
\end_layout

\end_inset

This Eligible window is 'modal': if it is open and you do not do something
 to make it happy and go away, it will stop you from doing anything else
 in the ASCEND system.
 Such windows appear with a black lock icon in a yellow field -- we shall
 call it a "yellow lock." They demand you attend to them 
\emph on
now
\emph default
.
 A good solution would be for such a window to stay open and on top of all
 the other open windows.
 Unfortunately we have not been able under all window managers to stop it
 from ducking under another window.
 If you ever find ASCEND unwilling to respond, iconify the other windows
 to get them out of the way, until you find one of these windows.
 On the PC you can go to the icon bar at the bottom of your screen and,
 by clicking on the window, bring it to the top.
 Then do whatever it takes to make it happy and close properly -- such as
 cancel it.
 If you are not careful here, for example, this window will hide under the
 Solver window before you are through with it.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status open

\begin_layout Standard
is our problem well-posed
\begin_inset LatexCommand \index{well-posed}

\end_inset

?
\end_layout

\end_inset

The Solver window contains the information we need to see to explain why
 the Eligible window opened in the first place.
 Examine the information the Solver displays.
 It tells you that 
\family typewriter
v
\family default
 has 6 relations defining it and that all are equalities and included.
 It has no inequalities.
 On the right side we see there are 10 variables and all are 'free
\begin_inset LatexCommand \index{free variables}

\end_inset

.' A free variable is one for which you want the system to compute a value.
 Hmm, 6 equations in 10 variables.
 Something is wrong here.
 For a well-posed problem, you want 6 equations in 6 variables (i.e., square
\begin_inset LatexCommand \index{square}

\end_inset

).
 ASCEND reports that the system is underspecified
\begin_inset LatexCommand \index{underspecified}

\end_inset

 by 4.
 This means you need to pick four of the variables and declare them to be
 fixed
\begin_inset LatexCommand \index{fixed}

\end_inset

.
 You will also have to pick values for these fixed variables before you
 can solve for the remaining 6.
 For such a small problem as this one, this task is not formidable.
 For a model with 50,000 equations and 60,000 variables, one would quit
 and go home.
 We have exposed a need here.
 We certainly would like ASCEND to help us here for this small problem.
 But we insist that it help us in major ways to make the 50,000 equation,
 60,000 variable problem possible.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
picking variables we are going to fix
\end_layout

\end_inset

Okay, the small help such as needed here is why the Eligible window opened.
 Let's return to it.
 It lists all the variables of those not yet fixed that are eligible to
 be fixed and still leave us a calculation that has a chance to solve.
 The algorithm to find eligible variables does an quick analysis of the
 structure of the equations.
 The variables it lists are those that can be fixed 
\emph on
without 
\emph default
the system becoming numerically singular.
 So any variables that are not shown 
\emph on
cannot possibly
\emph default
 help you.
\end_layout

\begin_layout Standard
So look at the list and decide what you would like to fix for your first
 calculation with this model.
 Diameter (
\family typewriter
v.D
\family default
) seems a good choice.
 Now you can see why we called the instance just plain old 
\family typewriter
v
\family default
.
 A longer name would get tiring here.
 Anyway, pick 
\family typewriter
v.D
\family default
.
 Immediately the list reappears with 
\family typewriter
v.D
\family default
 no longer on it.
 ASCEND has just repeated the eligibility analysis, and found that more
 variables still need to be fixed.
\end_layout

\begin_layout Standard
We have three more to pick.
 On the list are both vessel height, 
\family typewriter
v.H
\family default
, and 
\family typewriter
v.H_to_D_ratio
\family default
.
 We certainly cannot pick both of these.
 One implies the other if we know a value for 
\family typewriter
v.D
\family default
.
 Pick 
\family typewriter
v.H_to_D_ratio
\family default
.
 Note that 
\family typewriter
v.H
\family default
 is no longer eligible.
 Good.
 We would be worried if it were still there.
\end_layout

\begin_layout Standard
We see 
\family typewriter
v.metal_density
\emph on
.

\family default
\emph default
 Pick it.
 Strange.
 Metal mass and volume stayed eligible.
 Why? If we pick metal mass, wall thickness is implied, and the same is
 true if we were to pick metal volume.
 However, as it seems much more natural to pick 
\family typewriter
wall_thickness
\family default
, make that the last variable you choose.
 The Solver window now says this problem is square (i.e., it has 6 equations
 in the same number of unknowns).
 Table 
\begin_inset LatexCommand \ref{tab:model1.variableFixed}

\end_inset


\noun off
 summarizes the four variables we have elected here to fix.
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status open

\begin_layout Caption
\begin_inset LatexCommand \label{tab:model1.variableFixed}

\end_inset

Variables we have fixed
\begin_inset LatexCommand \index{fixed variables}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="1">
<features>
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
variable
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
D
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
H_to_D_ratio
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
meta_density
\end_layout

\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
wall_thickness
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
ASCEND partitions the problem into smaller problems for solving
\end_layout

\end_inset

Toward the bottom right of the 
\series bold
Solver
\series default
 window, we see there are 6 "blocks
\begin_inset LatexCommand \index{blocks}

\end_inset

." What are blocks? ASCEND has examined the equations and, in this case,
 has discovered that not all the equations have to be solved simultaneously.
 There are 6 blocks of equations which it can solve in sequence.
 6 blocks and 6 equations means that ASCEND has found a way to solve the
 model by solving 6 individual equations in sequence -- i.e., one at a time.
 This is a good thing: it usually means that the solver will have less problems
 with locating the overall solution.
\end_layout

\begin_layout Standard
As well as breaking down the system into blocks, ASCEND has the ability
 to rearrange some simple algebraic equations so that unknown variables
 can be evaluated directly from the known values, with no need for iterative
 numerical methods.
 This is only possible if there is just one equation in the block.
 In fact, this problem, with the 4 variables we selected to be fixed, can
 be solved entirely without iteration.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status open

\begin_layout Standard
displaying the incidence matrix
\begin_inset LatexCommand \index{incidence matrix}

\end_inset


\end_layout

\end_inset

Can we see what ASCEND has just discovered? It turns out we can (we would
 not have asked if we could not).
 Under the Display menu on the Solver, select the 'Incidence matrix tool
\begin_inset LatexCommand \index{incidence matrix tool}

\end_inset

'.
 A window pops open showing us the incidence of variables in the equations
 and display them in the order that ASCEND has found to solve them, also
 known as a sparsity matrix
\begin_inset LatexCommand \index{sparsity matrix}

\end_inset

 or sparsity pattern
\begin_inset LatexCommand \index{sparsity pattern}

\end_inset

.
 The dark squares are incidences under the variables for which we are solving;
 the lighter looking 'X' symbols to the right side are incidences for the
 fixed (known) variables.
 Click on the incidence in the upper left corner.
 ASCEND immediately identifies it for us as the 
\family typewriter
end_area
\family default
.
 It identifies the equation as the one we labeled 
\family typewriter
FlatEnds
\family default
.
 We can go back to our model and find the equation ASCEND will solve first.
 The other variable in this equation is in the set we fixed; pick it and
 discover it is 
\family typewriter
D
\family default
, the vessel diameter.
 Of course we can compute the area of the ends given the diameter.
 The 
\emph on
end_area
\emph default
 is 
\begin_inset Formula $\pi D^{2}/4$
\end_inset

.
\end_layout

\begin_layout Standard
Play with the other incidences here.
 See what the other equations are and the order ASCEND will use to solve
 them.
\end_layout

\begin_layout Standard
Okay, we return to our task of solving.
 We need next to supply values for the variables we have selected to be
 fixed.
 Again, the approach we are going to take is acceptable for this small problem,
 but we would not want to have to do what we are about to do for a large
 problem.
 Fortunately, we really have thought about these issues and have some nice
 approaches that work even for extremely large problem -- like 100,000 equations.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
which variables are currently fixed for this problem?
\end_layout

\end_inset

Let's see.
 Do you remember the variables we fixed? What if you do not? Well, we go
 back to the Browser.
 Be sure 
\family typewriter
v
\family default
 remains the current object (it alone is in the upper left window).
 Under the Find menu select 'by Type
\begin_inset LatexCommand \index{Find by Type}

\end_inset

.' A small window opens with default information in it saying it will find
 for us all objects contained in the current object 
\family typewriter
v
\family default
 of type 
\family typewriter
solver_var
\family default
 whose 
\family typewriter
fixed
\family default
 flags are set to 
\family typewriter
TRUE
\family default
.
 These are precisely the attributes for the variables we have fixed.
 Select OK and a list of the four variables we fixed earlier appears.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
specifying values for the fixed variables - this approach is useful for
 small problems
\end_layout

\end_inset

For each variable on this list, we should supply a value.
 Select 
\family typewriter
D
\family default
 in the lower window of the Browser using the right (the right, not the
 left -- make 
\family typewriter
v
\family default
 the current object and do it again) mouse button.
 A window opens in which we input a value for 
\family typewriter
D
\family default
.
 Put in the value 4 in the left window and ft in the right.
 Continue by putting in the values for the variables as listed in Table
 
\begin_inset LatexCommand \ref{tab:model1.valuesFixedVars}

\end_inset


\noun off
.
 These values immediately appear in the Browser window as you enter them.
 If you did not fully appreciate the proper handling of dimension and units
 before, you just got a taste of its advantages.
 
\noun default
You
\noun off
 did not have to worry about specifying these things in consistent preselected
 units
\noun default
 -- ASCEND did this for you.
\end_layout

\begin_layout Standard
\begin_inset Float table
wide false
sideways false
status open

\begin_layout Caption
\begin_inset LatexCommand \label{tab:model1.valuesFixedVars}

\end_inset

Values to use for fixed variables
\end_layout

\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="3">
<features>
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
variable
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
value
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
units
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
D
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
4
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
ft
\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
H_to_D_ratio
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
3
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\end_layout

\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
meta_density
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
5000
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
kg/m^3
\end_layout

\end_inset
</cell>
</row>
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
wall_thickness
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
5
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\family typewriter
mm
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
You can now solve this model.
 Go the Solver window and, under the Execute menu, select Solve.
 You will get a message telling you the model solved.
 Dismiss that message and return to the Browser window to examine the results.
 You should see the following results:
\end_layout

\begin_layout LyX-Code
\begin_inset ERT
status open

\begin_layout Standard


\backslash
begin{ascend}
\end_layout

\begin_layout Standard

D = 1.21922 meter
\end_layout

\begin_layout Standard

H = 3.65765 meter
\end_layout

\begin_layout Standard

H_to_D_ratio = 3
\end_layout

\begin_layout Standard

end_area = 1.16748 meter^2
\end_layout

\begin_layout Standard

metal_density = 5000 kilogram/meter^3
\end_layout

\begin_layout Standard

metal_mass = 408.62 kilogram
\end_layout

\begin_layout Standard

side_area = 14.0098 meter^2
\end_layout

\begin_layout Standard

vessel_vol = 4.27025 meter^3
\end_layout

\begin_layout Standard

wall_thickness = 0.005 meter
\end_layout

\begin_layout Standard

wall_vol = 0.0817239 meter^3
\end_layout

\begin_layout Standard


\backslash
end{ascend}
\end_layout

\end_inset


\end_layout

\begin_layout LyX-Code

\end_layout

\begin_layout Standard
\begin_inset Note Note
status collapsed

\begin_layout Standard
Some of this stuff appears to have changed in the PDF....
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
alter the units used for displaying values
\end_layout

\end_inset

You may wish to alter the units used to display these results.
 For example, you enter the diameter 
\emph on
D
\emph default
 in ft.
 You may wish to reassure yourself the 
\family typewriter
1.21922 meter
\family default
 is 4 ft.
 Go to the Script window and under the Tools menu select 
\emph on
'
\emph default
Measuring units'.
 The 
\series bold
Units
\series default
 window
\begin_inset LatexCommand \index{Units window}

\end_inset


\begin_inset LatexCommand \index{window, Units}

\end_inset

 will open.
 Enlarge it appropriately and then place it to the top and far right of
 your display.
\end_layout

\begin_layout Standard
There are two ways you can reset the units for displaying length.
\end_layout

\begin_layout Enumerate
Length is a basic dimension in ASCEND so under the 
\emph on
Display
\emph default
 button select Length.
 A side window will open with all the alternate units supported in ASCEND
 for length.
 Select ft.
\end_layout

\begin_layout Enumerate
Or, in the lower part of the Units window is a frame labeled 'Set units'.
 Clear and then type 
\family typewriter
ft
\family default
 then hit Enter.
\end_layout

\begin_layout Standard
In either way, the units for all length variables will switch to ft.
 Look at the values in the Browser window.
\end_layout

\begin_layout Standard
The left upper window of the Units window contains many variable types that
 have composite dimensions.
 For example, you will find volume there.
 Pick it and the right window fills with all the alternative units in which
 you can express volume.
\end_layout

\begin_layout Standard
Play with changing the units for displaying the various variables in the
 vessel instance v.
 
\end_layout

\begin_layout Standard
One point - the left window displaying types having composite dimensions
 will display only one type for each composite dimension.
 If the atom types you have loaded were to include volume_difference as
 well as volume, then only one of the two types, volume or volume_difference,
 will be listed here.
 Changing the units to express either changes the units for both.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
returning to a consistent set of units
\end_layout

\end_inset

When you are done, you may wish to return to a consistent set, such as SI
\begin_inset LatexCommand \index{SI}

\end_inset

.
 Under the Display button are different sets; pick 
\emph on
SI (MKS) set
\emph default
.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
now we can solve the model in other ways
\end_layout

\end_inset

We can now resolve our vessel instance in any number of different ways.
 For example we can ask what the diameter would be if we had a volume of
 
\emph on
250 ft3
\emph default
.
 To accomplish this calculation, we need first to make 
\emph on
vessel_volume
\emph default
 a variable whose value we wish to fix.
 When we do this the model will be overspecified.
 ASCEND will indicate this problem to us and offer us a list of variables
 - including the vessel diameter 
\emph on
D
\emph default
, one of which we will have to "unfix
\begin_inset LatexCommand \index{unfix}

\end_inset

." Finally we need to alter the value of 
\emph on
vessel_volume
\emph default
 to the desired value and solve.
 Explicit instructions to accomplish these steps are as follows.
\end_layout

\begin_layout Itemize
In the 
\series bold
Browser
\series default
 window, make 
\emph on
vessel_volume
\emph default
 the current object (select it using the left mouse button).
 The right window of the 
\series bold
Browser
\series default
 display the parts of the 
\emph on
vessel_volume
\emph default
, among them is the fixed flag with a value of 
\emph on
FALSE
\emph default
.
 
\end_layout

\begin_layout Itemize
(If you do not see the value for fixed but rather its type as a boolean,
 under the 
\emph on
View
\emph default
 button at the top, select 
\emph on
Display Atom Values.
\emph default
) 
\end_layout

\begin_layout Itemize
Pick fixed with the right mouse button, and, in the small window that opens,
 delete the value 
\emph on
FALSE
\emph default
, enter the value 
\emph on
TRUE
\emph default
 and select 
\emph on
OK
\emph default
.
\end_layout

\begin_layout Itemize
Now make v the current object by picking it in the left window of the 
\series bold
Browser
\series default
.
\end_layout

\begin_layout Itemize
Export v to the Solver again by selecting to Solver under the Export button.
 A window entitled Overspecified
\begin_inset LatexCommand \index{Overspecified}

\end_inset

 will appear listing the variables v.D, v.H_to_D_ratio and v.vessel_volume.
 Pick v.D and hit the OK button; ASCEND will reset its fixed flag to FALSE.
\end_layout

\begin_layout Itemize
Finally, return to the 
\series bold
Browser
\series default
 window and select 
\emph on
vessel_volume
\emph default
 with the right mouse button.
 In the small window that appears type 
\emph on
250
\emph default
 in the left window, 
\emph on
ft^3
\emph default
 in the right, and hit the 
\emph on
OK
\emph default
 button.
\end_layout

\begin_layout Itemize
Under the 
\emph on
Execute
\emph default
 button in the 
\series bold
Solver
\series default
 window, select 
\emph on
Solve
\emph default
.
\end_layout

\begin_layout Standard
Note the 
\series bold
Solver
\series default
 reports only 4 blocks for 6 equations.
 This time it has to solve some equations simultaneously.
 In the 
\series bold
Solver
\series default
 window, under the 
\emph on
Display
\emph default
 button, select the 
\emph on
Incidence matrix
\emph default
 tool.
 You will see that the first three equations must be solved together as
 a single block of equations.
\end_layout

\begin_layout Standard
\begin_inset Marginal
status collapsed

\begin_layout Standard
clearing all the fixed flags
\end_layout

\end_inset

For a more complicated model you may wish to start over on the process of
 selecting which variables are fixed.
 You can set the fixed flags for all the variables in a problem to FALSE
 all at once -- without knowing which are currently set to TRUE.
 In the Browser window, under the Edit button, select the Run method tool.
 A window will open that displays a list of default methods that are automatical
ly attached to every model in ASCEND.
 One is called ClearAll.
 Pick it and hit OK.
 All the fixed flags for the entire model will now be reset to FALSE.
 Can you think of a way to check if this is true? (Do you remember how to
 check which variables are currently fixed? Repeat that check and you should
 find no variables are on the list.)
\end_layout

\begin_layout Standard
You might now want to play by changing what you calculate and fix.
\end_layout

\begin_layout Section
Discussion
\end_layout

\begin_layout Standard
You have just completed the creation and solving of a very small model in
 ASCEND.
 In doing so, you have been exposed to some interesting issues.
 How can we separate the concept of the model from how we intend to solve
 it? How do we make a model to be well-posed -- i.e., a model involving n
 equations in n unknowns -- so we can solve it? How should one handle the
 units for the variables in a modeling system? What we have shown you here
 is for a small model.
 We still need to show you how one can make a large model well-posed, for
 example.
 You will start to understand how one can do this in the next chapter.
\end_layout

\begin_layout Standard
The next chapter is crucial for you to understand if you want to begin to
 understand how we approach good modeling practice.
 Please do continue with it.
 As it uses the vessel model, it would, of course, be best to continue with
 that chapter now.
\end_layout

\end_body
\end_document