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1 johnpye 825 #LyX 1.4.1 created this file. For more info see http://www.lyx.org/
2     \lyxformat 245
3     \begin_document
4     \begin_header
5     \textclass book
6     \language english
7     \inputencoding auto
8     \fontscheme default
9     \graphics default
10     \paperfontsize default
11     \spacing single
12     \papersize a4paper
13     \use_geometry false
14     \use_amsmath 2
15     \cite_engine basic
16     \use_bibtopic false
17     \paperorientation portrait
18     \secnumdepth 3
19     \tocdepth 3
20     \paragraph_separation indent
21     \defskip medskip
22     \quotes_language english
23     \papercolumns 1
24     \papersides 2
25     \paperpagestyle default
26     \tracking_changes false
27     \output_changes true
28     \end_header
29    
30     \begin_body
31    
32     \begin_layout Chapter
33     Vessel Model for Beginners
34     \begin_inset LatexCommand \label{cha:model1}
35    
36     \end_inset
37    
38    
39     \end_layout
40    
41     \begin_layout Standard
42     You read our propaganda about the ASCEND system in which we said it was
43     to help technical people create hard models.
44     We said you can tackle really large models -- 100,000 equations, compiling
45     and solving them in minutes on a PC.
46     We also pointed out that you can readily solve the small problems many
47     currently solve using a spreadsheet, only once posed you can solve them
48     inside out, upside down and backwards.
49    
50     \end_layout
51    
52     \begin_layout Standard
53     This sounded intriguing so you downloaded the system and installed it.
54     Hopefully, this proved quite straight forward.
55     You double-clicked the ASCEND icon on your desktop and started it up for
56     the first time.
57     Four windows opened up.
58     You panicked.
59    
60     \end_layout
61    
62     \begin_layout Standard
63     Who wouldn't?
64     \end_layout
65    
66     \begin_layout Standard
67     To use this system properly requires that you learn how to use it.
68     If you pay the price to do so - and we hope it is not a large price, then
69     we believe you will find the tools we have provided to help you create
70     and debug models will pay you back handsomely.
71    
72     \end_layout
73    
74     \begin_layout Standard
75     This chapter
76     \noun off
77     and the next two chapters (
78     \noun default
79     Chapter
80     \noun off
81    
82     \begin_inset LatexCommand \ref{cha:model2}
83    
84     \end_inset
85    
86     and
87     \noun default
88     Chapter
89     \noun off
90    
91     \begin_inset LatexCommand \ref{cha:model3}
92    
93     \end_inset
94    
95     )
96     \noun default
97    
98     \noun off
99     are meant to be a good first step along the path to learning how to use
100     ASCEND.
101     We
102     \noun default
103     will
104     \noun off
105     lead you through the steps for creating and testing a simple model.
106     You will also learn how to improve this model so it may be more readily
107     shared with others.
108     We will present our reasons for the steps we take.
109     We
110     \noun default
111     will
112     \noun off
113     show you all the buttons you should push as you proceed.
114     \end_layout
115    
116     \begin_layout Standard
117     We strongly suggest you put time aside and go through all three of these
118     early chapters to introduce yourself to ASCEND.
119     It should take you about two to three hours.
120     The second chapter is particularly important if you wish to understand
121     our approach to good modeling practices.
122     \end_layout
123    
124     \begin_layout Standard
125     \begin_inset Marginal
126     status collapsed
127    
128     \begin_layout Standard
129     the problem
130     \end_layout
131    
132     \end_inset
133    
134     Step 1:
135     \emph on
136     We are going to create and test an ASCEND model to compute, the mass of
137     the metal in the sides and ends of the thin-walled cylindrical vessel
138     \emph default
139    
140     \begin_inset LatexCommand \index{vessel}
141    
142     \end_inset
143    
144    
145     \emph on
146     shown in Figure
147     \begin_inset LatexCommand \ref{fig:model1.thinWalledVessel}
148    
149     \end_inset
150    
151     .
152    
153     \end_layout
154    
155     \begin_layout Standard
156     \begin_inset Float figure
157     wide false
158     sideways false
159     status open
160    
161     \begin_layout Standard
162    
163     \noun off
164     \InsetSpace ~
165     \InsetSpace ~
166     \InsetSpace ~
167     \InsetSpace ~
168     \InsetSpace ~
169     \InsetSpace ~
170     \InsetSpace ~
171     \InsetSpace ~
172     \InsetSpace ~
173     \InsetSpace ~
174     \InsetSpace ~
175     \InsetSpace ~
176     \InsetSpace ~
177     \InsetSpace ~
178     \InsetSpace ~
179     \InsetSpace ~
180     \InsetSpace ~
181     \InsetSpace ~
182     \InsetSpace ~
183     \InsetSpace ~
184     \InsetSpace ~
185     \InsetSpace ~
186     \InsetSpace ~
187     \InsetSpace ~
188     \InsetSpace ~
189     \InsetSpace ~
190     \InsetSpace ~
191     \InsetSpace ~
192     \InsetSpace ~
193     \InsetSpace ~
194     \InsetSpace ~
195     \InsetSpace ~
196    
197     \begin_inset Graphics
198     filename howto-model1Fig1.eps
199     BoundingBox 0bp 0bp 280bp 260bp
200    
201     \end_inset
202    
203    
204     \end_layout
205    
206     \begin_layout Caption
207     A thin-walled cylindrical vessel with flat ends
208     \begin_inset LatexCommand \label{fig:model1.thinWalledVessel}
209    
210     \end_inset
211    
212    
213     \end_layout
214    
215     \end_inset
216    
217    
218     \end_layout
219    
220     \begin_layout Standard
221     Step 2:
222     \emph on
223     This model is to become a part of a library of models which others can use
224     in the future.
225     You must document it.
226     You must add methods to it to make it easy for others to make it well-posed.
227     You should probably parameterize it, and finally you must create a script
228     which anyone can easily run that solves an example problem to illustrate
229     its use.
230     \end_layout
231    
232     \begin_layout Standard
233     \begin_inset Marginal
234     status collapsed
235    
236     \begin_layout Standard
237     topics covered
238     \end_layout
239    
240     \end_inset
241    
242     Topics covered in this and the following two chapters are:
243     \end_layout
244    
245     \begin_layout Itemize
246     \begin_inset Marginal
247     status collapsed
248    
249     \begin_layout Standard
250     T
251     \noun off
252     his chapter)
253     \end_layout
254    
255     \end_inset
256    
257     Converting the word description to an ASCEND model.
258     \end_layout
259    
260     \begin_layout Itemize
261     Loading the model into ASCEND, dealing with the error messages.
262     \end_layout
263    
264     \begin_layout Itemize
265     Compiling the model.
266     \end_layout
267    
268     \begin_layout Itemize
269     Browsing the model to see if it looks right
270     \end_layout
271    
272     \begin_layout Itemize
273     Solving the model.
274     \end_layout
275    
276     \begin_layout Itemize
277     Examining the results.
278     \end_layout
279    
280     \begin_layout Itemize
281     More thoroughly testing the model.
282     \end_layout
283    
284     \begin_layout Itemize
285     \begin_inset Marginal
286     status collapsed
287    
288     \begin_layout Standard
289     Chapter\InsetSpace ~
290    
291     \begin_inset LatexCommand \vref{cha:model2}
292    
293     \end_inset
294    
295    
296     \end_layout
297    
298     \end_inset
299    
300     Converting the model to a more reusable form by adding methods to it and
301     by parameterizing it.
302     \end_layout
303    
304     \begin_layout Itemize
305     Creating a script to load and execute an instance of the model.
306     \end_layout
307    
308     \begin_layout Itemize
309     \begin_inset Marginal
310     status collapsed
311    
312     \begin_layout Standard
313     Chapter\InsetSpace ~
314    
315     \begin_inset LatexCommand \vref{cha:model3}
316    
317     \end_inset
318    
319    
320     \end_layout
321    
322     \end_inset
323    
324     Creating an array of models.
325     \end_layout
326    
327     \begin_layout Itemize
328     Using an existing library model for plotting.
329     \end_layout
330    
331     \begin_layout Itemize
332     Creating a case study using the model.
333     \end_layout
334    
335     \begin_layout Standard
336     We shall introduce many of the features of the modeling language as well
337     as the use of the interactive interface you use when compiling, debugging,
338     solving and exploring your model.
339     Language features include units conversion, arrays and sets.
340     \end_layout
341    
342     \begin_layout Section
343     Converting the word description into an ASCEND model
344     \begin_inset LatexCommand \label{sec:model1.converting-the-word}
345    
346     \end_inset
347    
348    
349     \end_layout
350    
351     \begin_layout Standard
352     \begin_inset Marginal
353     status collapsed
354    
355     \begin_layout Standard
356     an ASCEND model is a type
357     \begin_inset LatexCommand \index{type}
358    
359     \end_inset
360    
361     definition
362     \end_layout
363    
364     \end_inset
365    
366     Every ASCEND model is, in fact, a type definition.
367     To "solve a model," we make an instance
368     \begin_inset LatexCommand \index{instance}
369    
370     \end_inset
371    
372     of a type and solve the instance.
373     So we shall start by creating a vessel type definition.
374     We will have to create our type definition as a text file using a text
375     editor.
376     (Some simple text editors
377     \begin_inset LatexCommand \index{text editors}
378    
379     \end_inset
380    
381     include
382     \family typewriter
383     emacs
384     \family default
385    
386     \begin_inset LatexCommand \index{emacs}
387    
388     \end_inset
389    
390     and
391     \family typewriter
392     gedit
393     \begin_inset LatexCommand \index{gedit}
394    
395     \end_inset
396    
397    
398     \family default
399     on Linux, and Notepad
400     \begin_inset LatexCommand \index{Notepad}
401    
402     \end_inset
403    
404     and TextPad
405     \begin_inset LatexCommand \index{TextPad}
406    
407     \end_inset
408    
409     on Windows.
410     We shall discuss editors shortly.)
411     \end_layout
412    
413     \begin_layout Standard
414     We need first to decide the parts to our model.
415     In this case we know that we need the variables
416     \begin_inset LatexCommand \index{variables, vessel}
417    
418     \end_inset
419    
420     listed in Table
421     \begin_inset LatexCommand \ref{tab:model1.variablesVesselModel}
422    
423     \end_inset
424    
425    
426     \noun off
427     .
428     We readily fill in the first three columns in this table.
429     We shall discuss the entry in the last column in a moment.
430     \end_layout
431    
432     \begin_layout Standard
433     \begin_inset Float table
434     wide false
435     sideways false
436     status open
437    
438     \begin_layout Caption
439     Variables required for model
440     \begin_inset LatexCommand \label{tab:model1.variablesVesselModel}
441    
442     \end_inset
443    
444    
445     \end_layout
446    
447     \begin_layout Standard
448     \begin_inset Tabular
449     <lyxtabular version="3" rows="5" columns="4">
450     <features>
451     <column alignment="center" valignment="top" leftline="true" width="0">
452     <column alignment="center" valignment="top" leftline="true" width="0">
453     <column alignment="center" valignment="top" leftline="true" width="0">
454     <column alignment="center" valignment="top" leftline="true" rightline="true" width="1in">
455     <row topline="true" bottomline="true">
456     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
457     \begin_inset Text
458    
459     \begin_layout Standard
460     Symbol
461     \end_layout
462    
463     \end_inset
464     </cell>
465     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
466     \begin_inset Text
467    
468     \begin_layout Standard
469     Meaning
470     \end_layout
471    
472     \end_inset
473     </cell>
474     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
475     \begin_inset Text
476    
477     \begin_layout Standard
478     Typical Units
479     \end_layout
480    
481     \end_inset
482     </cell>
483     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
484     \begin_inset Text
485    
486     \begin_layout Standard
487     ASCEND variable type
488     \end_layout
489    
490     \end_inset
491     </cell>
492     </row>
493     <row topline="true">
494     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
495     \begin_inset Text
496    
497     \begin_layout Standard
498    
499     \family typewriter
500     D
501     \end_layout
502    
503     \end_inset
504     </cell>
505     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
506     \begin_inset Text
507    
508     \begin_layout Standard
509     vessel diameter
510     \end_layout
511    
512     \end_inset
513     </cell>
514     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
515     \begin_inset Text
516    
517     \begin_layout Standard
518     m, ft
519     \end_layout
520    
521     \end_inset
522     </cell>
523     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
524     \begin_inset Text
525    
526     \begin_layout Standard
527    
528     \family typewriter
529     length
530     \end_layout
531    
532     \end_inset
533     </cell>
534     </row>
535     <row topline="true">
536     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
537     \begin_inset Text
538    
539     \begin_layout Standard
540    
541     \family typewriter
542     H
543     \end_layout
544    
545     \end_inset
546     </cell>
547     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
548     \begin_inset Text
549    
550     \begin_layout Standard
551     vessel height
552     \end_layout
553    
554     \end_inset
555     </cell>
556     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
557     \begin_inset Text
558    
559     \begin_layout Standard
560     m, ft
561     \end_layout
562    
563     \end_inset
564     </cell>
565     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
566     \begin_inset Text
567    
568     \begin_layout Standard
569    
570     \family typewriter
571     length
572     \end_layout
573    
574     \end_inset
575     </cell>
576     </row>
577     <row topline="true">
578     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
579     \begin_inset Text
580    
581     \begin_layout Standard
582    
583     \family typewriter
584     wall_thickness
585     \end_layout
586    
587     \end_inset
588     </cell>
589     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
590     \begin_inset Text
591    
592     \begin_layout Standard
593     wall thickness
594     \end_layout
595    
596     \end_inset
597     </cell>
598     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
599     \begin_inset Text
600    
601     \begin_layout Standard
602     mm, in
603     \end_layout
604    
605     \end_inset
606     </cell>
607     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
608     \begin_inset Text
609    
610     \begin_layout Standard
611    
612     \family typewriter
613     length
614     \end_layout
615    
616     \end_inset
617     </cell>
618     </row>
619     <row topline="true" bottomline="true">
620     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
621     \begin_inset Text
622    
623     \begin_layout Standard
624    
625     \family typewriter
626     metal_density
627     \end_layout
628    
629     \end_inset
630     </cell>
631     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
632     \begin_inset Text
633    
634     \begin_layout Standard
635     metal density
636     \end_layout
637    
638     \end_inset
639     </cell>
640     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
641     \begin_inset Text
642    
643     \begin_layout Standard
644     kg/m
645     \begin_inset Formula $^{\textrm{3}}$
646     \end_inset
647    
648     , lbm/ft
649     \begin_inset Formula $^{\textrm{3}}$
650     \end_inset
651    
652    
653     \end_layout
654    
655     \end_inset
656     </cell>
657     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
658     \begin_inset Text
659    
660     \begin_layout Standard
661    
662     \family typewriter
663     mass_density
664     \end_layout
665    
666     \end_inset
667     </cell>
668     </row>
669     </lyxtabular>
670    
671     \end_inset
672    
673    
674     \end_layout
675    
676     \end_inset
677    
678    
679     \end_layout
680    
681     \begin_layout Standard
682     We will be computing the masses for the metal in the side wall and in the
683     ends for this vessel.
684     As this is a thin-walled vessel, we shall compute the volume of metal as
685     the area of the walls times the wall thickness.
686     The following equations allow us to compute the required areas
687     \end_layout
688    
689     \begin_layout Standard
690     \begin_inset Formula \begin{equation}
691     \mathrm{side\, wall\, area}=\pi DH\label{eq:model1.side-wall-area}\end{equation}
692    
693     \end_inset
694    
695    
696     \end_layout
697    
698     \begin_layout Standard
699     \begin_inset Formula \begin{equation}
700     \mathrm{single\, end\, area}=\frac{\pi D^{2}}{4}\label{eq:model1.single-end-area}\end{equation}
701    
702     \end_inset
703    
704    
705     \end_layout
706    
707     \begin_layout Standard
708     We should be interested in the volume of the vessel, which we compute as:
709     \end_layout
710    
711     \begin_layout Standard
712     \begin_inset Formula \begin{equation}
713     \mathrm{vessel\, volume}=\mathrm{single\, end\, area}\times H\label{eq:model1.vessel-volume}\end{equation}
714    
715     \end_inset
716    
717    
718     \end_layout
719    
720     \begin_layout Standard
721     We add the variables in Table
722     \begin_inset LatexCommand \ref{tab:model1.moreVariablesVessel}
723    
724     \end_inset
725    
726    
727     \noun off
728     to our list.
729     \end_layout
730    
731     \begin_layout Standard
732     \begin_inset Float table
733     wide false
734     sideways false
735     status open
736    
737     \begin_layout Caption
738     Some more variables
739     \begin_inset LatexCommand \index{variables, vessel}
740    
741     \end_inset
742    
743     required for vessel model
744     \begin_inset LatexCommand \label{tab:model1.moreVariablesVessel}
745    
746     \end_inset
747    
748    
749     \end_layout
750    
751     \begin_layout Standard
752     \begin_inset Tabular
753     <lyxtabular version="3" rows="6" columns="4">
754     <features>
755     <column alignment="center" valignment="top" leftline="true" width="0">
756     <column alignment="center" valignment="top" leftline="true" width="1.5in">
757     <column alignment="center" valignment="top" leftline="true" width="0">
758     <column alignment="center" valignment="top" leftline="true" rightline="true" width="1in">
759     <row topline="true" bottomline="true">
760     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
761     \begin_inset Text
762    
763     \begin_layout Standard
764     Symbol
765     \end_layout
766    
767     \end_inset
768     </cell>
769     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
770     \begin_inset Text
771    
772     \begin_layout Standard
773     Meaning
774     \end_layout
775    
776     \end_inset
777     </cell>
778     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
779     \begin_inset Text
780    
781     \begin_layout Standard
782     Typical Units
783     \end_layout
784    
785     \end_inset
786     </cell>
787     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
788     \begin_inset Text
789    
790     \begin_layout Standard
791     ASCEND variable type
792     \end_layout
793    
794     \end_inset
795     </cell>
796     </row>
797     <row topline="true">
798     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
799     \begin_inset Text
800    
801     \begin_layout Standard
802    
803     \family typewriter
804     side_area
805     \end_layout
806    
807     \end_inset
808     </cell>
809     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
810     \begin_inset Text
811    
812     \begin_layout Standard
813     area in the sidewall of the vessel
814     \end_layout
815    
816     \end_inset
817     </cell>
818     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
819     \begin_inset Text
820    
821     \begin_layout Standard
822     m
823     \begin_inset Formula $^{\textrm{2}}$
824     \end_inset
825    
826     , ft
827     \begin_inset Formula $^{\textrm{2}}$
828     \end_inset
829    
830    
831     \end_layout
832    
833     \end_inset
834     </cell>
835     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
836     \begin_inset Text
837    
838     \begin_layout Standard
839    
840     \family typewriter
841     area
842     \end_layout
843    
844     \end_inset
845     </cell>
846     </row>
847     <row topline="true">
848     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
849     \begin_inset Text
850    
851     \begin_layout Standard
852    
853     \family typewriter
854     end_area
855     \end_layout
856    
857     \end_inset
858     </cell>
859     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
860     \begin_inset Text
861    
862     \begin_layout Standard
863     total area iin the ends of the vessel
864     \end_layout
865    
866     \end_inset
867     </cell>
868     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
869     \begin_inset Text
870    
871     \begin_layout Standard
872     m
873     \begin_inset Formula $^{\textrm{2}}$
874     \end_inset
875    
876     , ft
877     \begin_inset Formula $^{\textrm{2}}$
878     \end_inset
879    
880    
881     \end_layout
882    
883     \end_inset
884     </cell>
885     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
886     \begin_inset Text
887    
888     \begin_layout Standard
889    
890     \family typewriter
891     area
892     \end_layout
893    
894     \end_inset
895     </cell>
896     </row>
897     <row topline="true">
898     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
899     \begin_inset Text
900    
901     \begin_layout Standard
902    
903     \family typewriter
904     vessel_volume
905     \end_layout
906    
907     \end_inset
908     </cell>
909     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
910     \begin_inset Text
911    
912     \begin_layout Standard
913     volume of the vessel
914     \end_layout
915    
916     \end_inset
917     </cell>
918     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
919     \begin_inset Text
920    
921     \begin_layout Standard
922     m
923     \begin_inset Formula $^{3}$
924     \end_inset
925    
926     , ft
927     \begin_inset Formula $^{\textrm{3}}$
928     \end_inset
929    
930    
931     \end_layout
932    
933     \end_inset
934     </cell>
935     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
936     \begin_inset Text
937    
938     \begin_layout Standard
939    
940     \family typewriter
941     volume
942     \end_layout
943    
944     \end_inset
945     </cell>
946     </row>
947     <row topline="true">
948     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
949     \begin_inset Text
950    
951     \begin_layout Standard
952    
953     \family typewriter
954     metal_volume
955     \end_layout
956    
957     \end_inset
958     </cell>
959     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
960     \begin_inset Text
961    
962     \begin_layout Standard
963     total volume of metal in the walls
964     \end_layout
965    
966     \end_inset
967     </cell>
968     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
969     \begin_inset Text
970    
971     \begin_layout Standard
972     m
973     \begin_inset Formula $^{3}$
974     \end_inset
975    
976     , ft
977     \begin_inset Formula $^{\textrm{3}}$
978     \end_inset
979    
980    
981     \end_layout
982    
983     \end_inset
984     </cell>
985     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
986     \begin_inset Text
987    
988     \begin_layout Standard
989    
990     \family typewriter
991     volume
992     \end_layout
993    
994     \end_inset
995     </cell>
996     </row>
997     <row topline="true" bottomline="true">
998     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
999     \begin_inset Text
1000    
1001     \begin_layout Standard
1002    
1003     \family typewriter
1004     metal_mass
1005     \end_layout
1006    
1007     \end_inset
1008     </cell>
1009     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1010     \begin_inset Text
1011    
1012     \begin_layout Standard
1013     total mass of the metal in the walls of the vessel
1014     \end_layout
1015    
1016     \end_inset
1017     </cell>
1018     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
1019     \begin_inset Text
1020    
1021     \begin_layout Standard
1022     kg, lbm
1023     \end_layout
1024    
1025     \end_inset
1026     </cell>
1027     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
1028     \begin_inset Text
1029    
1030     \begin_layout Standard
1031    
1032     \family typewriter
1033     mass
1034     \end_layout
1035    
1036     \end_inset
1037     </cell>
1038     </row>
1039     </lyxtabular>
1040    
1041     \end_inset
1042    
1043    
1044     \end_layout
1045    
1046     \end_inset
1047    
1048    
1049     \end_layout
1050    
1051     \begin_layout Standard
1052     We believe that no one should create a model of any consequence without
1053     worrying about the units for expressing the variables within it.
1054     We consider that to be a commandment handed down from somewhere on high;
1055     however, we know that others do not believe as we do.
1056     Grant us our beliefs.
1057     We have created in the ASCEND system a library of variable and constant
1058     types called atoms.a4l
1059     \begin_inset LatexCommand \index{atoms.a4l}
1060    
1061     \end_inset
1062    
1063     .
1064     \end_layout
1065    
1066     \begin_layout Standard
1067     The file type "
1068     \family typewriter
1069     .a4l
1070     \begin_inset LatexCommand \index{a4l}
1071    
1072     \end_inset
1073    
1074    
1075     \family default
1076     " designates it to be an ASCEND IV library file
1077     \begin_inset LatexCommand \index{library file}
1078    
1079     \end_inset
1080    
1081     .
1082     Double-click on this link to see the approximately 150 different types
1083     ranging from universal constants
1084     \begin_inset LatexCommand \index{universal constants}
1085    
1086     \end_inset
1087    
1088     such as
1089     \begin_inset Formula $\pi$
1090     \end_inset
1091    
1092     (=3.14159...) and
1093     \begin_inset Formula $e$
1094     \end_inset
1095    
1096     (=2.718...) to
1097     \family typewriter
1098     length
1099     \family default
1100     ,
1101     \family typewriter
1102     mass
1103     \family default
1104     and
1105     \family typewriter
1106     angle
1107     \family default
1108     .
1109     If we have not created one that you need, you can use this library of types
1110     to see how to construct one for yourself and add it to your file of type
1111     definitions.
1112     You will find detailed instructions for how to make your own variable type
1113     library in Chapter\InsetSpace ~
1114    
1115     \begin_inset LatexCommand \vref{cha:atoms}
1116    
1117     \end_inset
1118    
1119     .
1120     \end_layout
1121    
1122     \begin_layout Standard
1123     \begin_inset Marginal
1124     status collapsed
1125    
1126     \begin_layout Standard
1127     type definition library for variables and constants
1128     \end_layout
1129    
1130     \end_inset
1131    
1132     ASCEND considers variable and constant types to be elementary or "atomic"
1133     to the system.
1134     These type definitions can contain only attributes for variables and constants.
1135     They cannot contain equations, for example.
1136     Thus ASCEND calls such a type definition an atom rather than a model.
1137     Figure
1138     \begin_inset LatexCommand \ref{fig:model1.atomVolume}
1139    
1140     \end_inset
1141    
1142    
1143     \noun off
1144     illustrates the definition for the type volume.
1145    
1146     \end_layout
1147    
1148     \begin_layout Standard
1149     \begin_inset Float figure
1150     wide false
1151     sideways false
1152     status open
1153    
1154     \begin_layout LyX-Code
1155     ATOM
1156     \begin_inset LatexCommand \index{ATOM}
1157    
1158     \end_inset
1159    
1160     volume REFINES solver_var
1161     \end_layout
1162    
1163     \begin_layout LyX-Code
1164     DIMENSION L^3
1165     \end_layout
1166    
1167     \begin_layout LyX-Code
1168     DEFAULT 100.0{ft^3};
1169     \end_layout
1170    
1171     \begin_layout LyX-Code
1172     lower_bound := 0.0{ft^3};
1173     \end_layout
1174    
1175     \begin_layout LyX-Code
1176     upper_bound := 1e50{ft^3};
1177     \end_layout
1178    
1179     \begin_layout LyX-Code
1180     nominal := 100.0{ft^3};
1181     \end_layout
1182    
1183     \begin_layout LyX-Code
1184     END volume;
1185     \end_layout
1186    
1187     \begin_layout Caption
1188     A typical type definition, called an atom, used to define variable and constant
1189     types
1190     \begin_inset LatexCommand \label{fig:model1.atomVolume}
1191    
1192     \end_inset
1193    
1194    
1195     \end_layout
1196    
1197     \end_inset
1198    
1199    
1200     \end_layout
1201    
1202     \begin_layout Standard
1203     The definition starts by stating that volume is a specialization of
1204     \begin_inset LatexCommand \index{solver\_var}
1205    
1206     \end_inset
1207    
1208    
1209     \family typewriter
1210     solver_var
1211     \family default
1212     .
1213     The type
1214     \family typewriter
1215     solver_var
1216     \family default
1217     refines a base type in the system known as
1218     \family typewriter
1219     real
1220     \family default
1221    
1222     \begin_inset LatexCommand \index{real}
1223    
1224     \end_inset
1225    
1226     and adds several attributes to it that a nonlinear equation solver may
1227     need, such as a lower and upper bounds, a 'fixed' flag, and so forth.
1228    
1229     \end_layout
1230    
1231     \begin_layout Standard
1232     \begin_inset Marginal
1233     status collapsed
1234    
1235     \begin_layout Standard
1236     dimensions
1237     \begin_inset LatexCommand \index{dimensions}
1238    
1239     \end_inset
1240    
1241     and units
1242     \begin_inset LatexCommand \index{units}
1243    
1244     \end_inset
1245    
1246     in ASCEND.
1247    
1248     \end_layout
1249    
1250     \end_inset
1251    
1252     The type definition for volume states that volume has dimensionality of
1253     length to the power 3 (
1254     \family typewriter
1255     L^3
1256     \family default
1257     ) where L is one of the 10 dimensions supported by ASCEND (see
1258     \noun off
1259     in ASCEND Syntax document for the 10 dimensions defined within the ASCEND
1260     language).
1261     \end_layout
1262    
1263     \begin_layout Standard
1264     One may express the value for a volume using any units which are consistent
1265     with the dimensionality of
1266     \family typewriter
1267     L^3
1268     \family default
1269     , such as
1270     \family typewriter
1271     {ft^3}
1272     \family default
1273     ,
1274     \family typewriter
1275     {m^3}
1276     \family default
1277     ,
1278     \family typewriter
1279     {gal}
1280     \family default
1281     , or even
1282     \family typewriter
1283     {mile^4/mm}
1284     \family default
1285     .
1286     Setting the lower bound to
1287     \family typewriter
1288     0 {ft^3}
1289     \family default
1290     says volume must be a nonnegative number.
1291     ASCEND used the nominal value for scaling a variable of type volume when
1292     solving, here
1293     \begin_inset Formula $100\,{\mathrm{ft}}^{3}$
1294     \end_inset
1295    
1296     .
1297     \end_layout
1298    
1299     \begin_layout Standard
1300     One may change the values for the bounds, default and nominal values at
1301     any time.
1302     \end_layout
1303    
1304     \begin_layout Standard
1305     We now can understand the last column in Table
1306     \begin_inset LatexCommand \ref{tab:model1.variablesVesselModel}
1307    
1308     \end_inset
1309    
1310    
1311     \noun off
1312     and
1313     \noun default
1314     Table
1315     \noun off
1316    
1317     \begin_inset LatexCommand \ref{tab:model1.moreVariablesVessel}
1318    
1319     \end_inset
1320    
1321     .
1322     For each variable or constant in the system, we have identified its type
1323     in the file
1324     \family typewriter
1325     \noun default
1326     atoms.a4l
1327     \family default
1328     \noun off
1329     .
1330     That is, we looked in this file for the type definition that corresponded
1331     to the variable we were defining and listed that type here.
1332     This task is not as onerous as it seems.
1333     As we shall see later, we provide a tool to find for you all atom types
1334     that correspond to a particular set of units, e.g,
1335     \family typewriter
1336     \noun default
1337     ft^3
1338     \family default
1339     \noun off
1340     -- i.e., the computer will do the searching for you.
1341     \end_layout
1342    
1343     \begin_layout Standard
1344     In Figure
1345     \begin_inset LatexCommand \ref{fig:model1.universalConstant}
1346    
1347     \end_inset
1348    
1349    
1350     \noun off
1351     we see the definition of one of the universal constants contained in
1352     \family typewriter
1353     \noun default
1354     atoms.a4l
1355     \family default
1356     \noun off
1357     .
1358     This definition is very short; it gives the name of the type
1359     \family typewriter
1360     \noun default
1361     circle_constant
1362     \family default
1363     \noun off
1364    
1365     \begin_inset LatexCommand \index{circle\_constant}
1366    
1367     \end_inset
1368    
1369     , that it refines
1370     \family typewriter
1371     \noun default
1372     real_constant
1373     \family default
1374     \noun off
1375    
1376     \begin_inset LatexCommand \index{real\_constant}
1377    
1378     \end_inset
1379    
1380     and that it has the value
1381     \family typewriter
1382     \noun default
1383     1 {PI
1384     \begin_inset LatexCommand \index{PI}
1385    
1386     \end_inset
1387    
1388     }
1389     \family default
1390     \noun off
1391    
1392     \begin_inset LatexCommand \index{\{PI\}}
1393    
1394     \end_inset
1395    
1396     where the internal conversion needed for
1397     \family typewriter
1398     \noun default
1399     {PI}
1400     \family default
1401     \noun off
1402     is defined in the file defining the built-in units in ASCEND.
1403     One can add more units if desired at any time to ASCEND by defining one
1404     or more personal units files (
1405     \noun default
1406     Chapter
1407     \noun off
1408    
1409     \begin_inset LatexCommand \vref{cha:units}
1410    
1411     \end_inset
1412    
1413    
1414     \noun default
1415    
1416     \noun off
1417     tells you how to do this).
1418     \end_layout
1419    
1420     \begin_layout Standard
1421     \begin_inset Marginal
1422     status collapsed
1423    
1424     \begin_layout Standard
1425     universal constant
1426     \begin_inset LatexCommand \index{universal constant}
1427    
1428     \end_inset
1429    
1430     definition
1431     \end_layout
1432    
1433     \end_inset
1434    
1435    
1436     \begin_inset Float figure
1437     wide false
1438     sideways false
1439     status open
1440    
1441     \begin_layout LyX-Code
1442     UNIVERSAL CONSTANT circle_constant
1443     \end_layout
1444    
1445     \begin_layout LyX-Code
1446     REFINES real_constant :== 1{PI};
1447     \end_layout
1448    
1449     \begin_layout Caption
1450     \begin_inset LatexCommand \label{fig:model1.universalConstant}
1451    
1452     \end_inset
1453    
1454     Type definition for
1455     \family typewriter
1456     circle_constant;
1457     \family default
1458     has value of
1459     \family typewriter
1460     1 {PI}
1461     \family default
1462     or 3.1415927
1463     \end_layout
1464    
1465     \end_inset
1466    
1467    
1468     \end_layout
1469    
1470     \begin_layout Standard
1471     We shall in fact find this constant useful in our program, and we can either
1472     introduce a constant with this value or simply use the value
1473     \family typewriter
1474     1{PI}
1475     \family default
1476     in our program.
1477     We shall choose to do the latter.
1478     \end_layout
1479    
1480     \begin_layout Standard
1481     It is time to write our first version for the model, which we do in Figure
1482    
1483     \begin_inset LatexCommand \ref{fig:model1.modelVessel}
1484    
1485     \end_inset
1486    
1487    
1488     \noun off
1489     (
1490     \noun default
1491     available as
1492     \begin_inset LatexCommand \index{vesselPlain.a4c}
1493    
1494     \end_inset
1495    
1496    
1497     \family typewriter
1498     vesselPlain.a4c
1499     \family default
1500     in the ASCEND model library).
1501    
1502     \noun off
1503     We first list any other files containing type definitions which this model
1504     will use; here we list
1505     \family typewriter
1506     \noun default
1507     "atoms.a4l"
1508     \family default
1509     \noun off
1510     following the keyword
1511     \family typewriter
1512     \noun default
1513     REQUIRE
1514     \family default
1515     \noun off
1516    
1517     \begin_inset LatexCommand \index{REQUIRE}
1518    
1519     \end_inset
1520    
1521     .
1522     ASCEND is sensitive to case so pay attention to where we use and do not
1523     use capital letters.
1524     Keywords are always capitalized.
1525     Often for clarification we use capital letters in a name we use for a variable
1526     or label (e.g., we use
1527     \family typewriter
1528     \noun default
1529     D
1530     \family default
1531     \noun off
1532     for diameter rather than
1533     \family typewriter
1534     \noun default
1535     d
1536     \family default
1537     \noun off
1538     ).
1539     Note that all ASCEND statements end with a semicolon (i.e., with
1540     \noun default
1541     '
1542     \family typewriter
1543     ;
1544     \family default
1545     '
1546     \noun off
1547     ) and not at the end of a line and that blank lines have no impact.
1548     Comments are between opening and closing parenthesis/asterisk pairs, i.e.,
1549     '
1550     \family typewriter
1551     \noun default
1552     (*
1553     \family default
1554     \noun off
1555     ' and '
1556     \family typewriter
1557     \noun default
1558     *)
1559     \family default
1560     \noun off
1561     '.
1562     \end_layout
1563    
1564     \begin_layout Standard
1565     \begin_inset Marginal
1566     status collapsed
1567    
1568     \begin_layout Standard
1569     the first version of the code for vessel
1570     \end_layout
1571    
1572     \end_inset
1573    
1574    
1575     \begin_inset Float figure
1576     wide false
1577     sideways false
1578     status open
1579    
1580     \begin_layout LyX-Code
1581     REQUIRE "atoms.a4l";
1582     \end_layout
1583    
1584     \begin_layout LyX-Code
1585     MODEL vessel;
1586     \end_layout
1587    
1588     \begin_layout LyX-Code
1589     (* variables *)
1590     \end_layout
1591    
1592     \begin_layout LyX-Code
1593     side_area, end_areaIS_Aarea;
1594     \end_layout
1595    
1596     \begin_layout LyX-Code
1597     vessel_vol, wall_vol IS_Avolume;
1598     \end_layout
1599    
1600     \begin_layout LyX-Code
1601     wall_thickness, H, D IS_Adistance;
1602     \end_layout
1603    
1604     \begin_layout LyX-Code
1605     H_to_D_ratio IS_A factor;
1606     \end_layout
1607    
1608     \begin_layout LyX-Code
1609     metal_density IS_A mass_density;
1610     \end_layout
1611    
1612     \begin_layout LyX-Code
1613     metal_mass IS_A mass;
1614     \end_layout
1615    
1616     \begin_layout LyX-Code
1617    
1618     \end_layout
1619    
1620     \begin_layout LyX-Code
1621     (* equations *)
1622     \end_layout
1623    
1624     \begin_layout LyX-Code
1625     FlatEnds:end_area = 1{PI} * D^2 / 4;
1626     \end_layout
1627    
1628     \begin_layout LyX-Code
1629     Sides:side_area = 1{PI} * D * H;
1630     \end_layout
1631    
1632     \begin_layout LyX-Code
1633     Cylinder:vessel_vol = end_area * H;
1634     \end_layout
1635    
1636     \begin_layout LyX-Code
1637     Metal_volume:(side_area + 2 * end_area) *
1638     \end_layout
1639    
1640     \begin_layout LyX-Code
1641     wall_thickness = wall_vol;
1642     \end_layout
1643    
1644     \begin_layout LyX-Code
1645     HD_definition:D * H_to_D_ratio = H;
1646     \end_layout
1647    
1648     \begin_layout LyX-Code
1649     VesselMass:metal_mass = metal_density * wall_vol;
1650     \end_layout
1651    
1652     \begin_layout LyX-Code
1653     END vessel;
1654     \end_layout
1655    
1656     \begin_layout Caption
1657     \begin_inset LatexCommand \label{fig:model1.modelVessel}
1658    
1659     \end_inset
1660    
1661     First version of the type definition for
1662     \family typewriter
1663     vessel
1664     \family default
1665     .
1666    
1667     \end_layout
1668    
1669     \end_inset
1670    
1671    
1672     \end_layout
1673    
1674     \begin_layout Standard
1675     Our model definition has the following structure for it so far:
1676     \end_layout
1677    
1678     \begin_layout Itemize
1679    
1680     \family typewriter
1681     MODEL
1682     \family default
1683    
1684     \begin_inset LatexCommand \index{MODEL}
1685    
1686     \end_inset
1687    
1688     statement
1689     \end_layout
1690    
1691     \begin_layout Itemize
1692     list of variable we intend to use in the type definition
1693     \end_layout
1694    
1695     \begin_layout Itemize
1696     equations
1697     \end_layout
1698    
1699     \begin_layout Itemize
1700    
1701     \family typewriter
1702     END
1703     \family default
1704    
1705     \begin_inset LatexCommand \index{END}
1706    
1707     \end_inset
1708    
1709     statement
1710     \end_layout
1711    
1712     \begin_layout Standard
1713     While we have put the statements in this order, we could mix up and intermix
1714     the middle two types of statements, even going to the extreme of defining
1715     the variables after we first use them.
1716     The
1717     \family typewriter
1718     MODEL
1719     \family default
1720     and
1721     \family typewriter
1722     END
1723     \family default
1724     statements begin and end the type definition.
1725     \end_layout
1726    
1727     \begin_layout Standard
1728     You should see little that surprises you in the syntax here.
1729     However, you may have noted that we have created a definition that says
1730     absolutely nothing about how to use the variables and equations listed.
1731     There is no solution procedure buried in this type definition.
1732     In ASCEND the idea of solving is separate from saying what we intend to
1733     solve.
1734     Also note that we have not said anything about the values for any of the
1735     variables nor what we intend to calculate and what variables we intend
1736     to treat as fixed input.
1737     \end_layout
1738    
1739     \begin_layout Section
1740     Editing, compiling and browsing an ASCEND model
1741     \end_layout
1742    
1743     \begin_layout Standard
1744     Could we compile an instance of a vessel given this definition? If there
1745     had been some arrays in our definition for which we did not say how many
1746     items were in the arrays, we could not.
1747     However, here we could compile an instance, putting aside storage space
1748     for each of the variables and somehow capturing the equations relating
1749     them.
1750     \end_layout
1751    
1752     \begin_layout Standard
1753     \begin_inset Marginal
1754     status open
1755    
1756     \begin_layout Standard
1757     Do not alter the models subdirectory
1758     \end_layout
1759    
1760     \end_inset
1761    
1762     When we compile new models, we need a place to store them.
1763     One possibility would be to put them into the
1764     \family typewriter
1765     models
1766     \family default
1767    
1768     \begin_inset LatexCommand \index{models}
1769    
1770     \end_inset
1771    
1772     subdirectory of the ASCEND installation
1773     \begin_inset Foot
1774     status collapsed
1775    
1776     \begin_layout Standard
1777     On windows this might be
1778     \family typewriter
1779     c:
1780     \backslash
1781     Program File
1782     \backslash
1783     ASCEND
1784     \backslash
1785     models
1786     \family default
1787     .
1788     On Linux, this might be
1789     \family typewriter
1790     /usr/share/ascend/models
1791     \family default
1792     .
1793     The location can vary depending on how you went about installing ASCEND.
1794     \end_layout
1795    
1796     \end_inset
1797    
1798     .
1799     However, you really should leave the contents of this subdirectory untouched
1800     -- always.
1801     Hopefully the files will be read-only from your user account.
1802     We count on being able to replace the model library totally every time
1803     you install a new version of ASCEND.
1804     Whenever we add new model libraries or corrected versions of previously
1805     existing model libraries, we put them in this subdirectory.
1806     This subdirectory belongs to us (the developers of the system): hands off,
1807     please.
1808     \end_layout
1809    
1810     \begin_layout Standard
1811     \begin_inset Marginal
1812     status open
1813    
1814     \begin_layout Standard
1815     rather put your things into the ascdata
1816     \begin_inset LatexCommand \index{ascdata}
1817    
1818     \end_inset
1819    
1820     subdirectory (you own it)
1821     \end_layout
1822    
1823     \end_inset
1824    
1825     To avoid this problem, ASCEND also creates a subdirectory called
1826     \family typewriter
1827     ascdata
1828     \family default
1829     that it will not touch when you install a new version of ASCEND.
1830     It will look in this subdirectory first when looking for a file to load
1831     when you have not given a full path name for finding that file.
1832     The install process for ASCEND will place
1833     \family typewriter
1834     ascdata
1835     \family default
1836     into your home directory
1837     \begin_inset LatexCommand \ref{id:#id(pgfId-1007944)}
1838    
1839     \end_inset
1840    
1841    
1842     \begin_inset Foot
1843     status collapsed
1844    
1845     \begin_layout Standard
1846     On Windows, your home directory will normally be the My Documents folder.
1847     On Linux, it will normally be
1848     \family typewriter
1849     /home/
1850     \emph on
1851     username
1852     \family default
1853     \emph default
1854     .
1855     Note that in both systems, you can set an
1856     \begin_inset Quotes eld
1857     \end_inset
1858    
1859     environment
1860     \begin_inset Quotes erd
1861     \end_inset
1862    
1863     variable to designate your home directory.
1864     \end_layout
1865    
1866     \end_inset
1867    
1868    
1869     \noun off
1870     .
1871     ASCEND tells you where it has placed this subdirectory when you install
1872     it.
1873     However, if you did not note where that was, then you will have to search
1874     for it (using a tool like "FIND file or folder").
1875     \end_layout
1876    
1877     \begin_layout Standard
1878     It is within the folder
1879     \family typewriter
1880     ascdata
1881     \family default
1882     that you should place any ASCEND models you create.
1883     When running a script (which we shall talk about later), ASCEND first looks
1884     in this subdirectory for files, and then it looks in the models subdirectory.
1885     It stops looking when it finds the first available version of the file.
1886     \end_layout
1887    
1888     \begin_layout Standard
1889     \begin_inset Marginal
1890     status collapsed
1891    
1892     \begin_layout Standard
1893     create a text file containing the model definition
1894     \end_layout
1895    
1896     \end_inset
1897    
1898     Next open an editor
1899     \begin_inset LatexCommand \index{text editors}
1900    
1901     \end_inset
1902    
1903     , such as
1904     \family typewriter
1905     emacs
1906     \family default
1907    
1908     \begin_inset LatexCommand \index{emacs}
1909    
1910     \end_inset
1911    
1912     ,
1913     \family typewriter
1914     gedit
1915     \family default
1916    
1917     \begin_inset LatexCommand \index{gedit}
1918    
1919     \end_inset
1920    
1921     ,
1922     \family typewriter
1923     vi
1924     \family default
1925    
1926     \begin_inset LatexCommand \index{vi}
1927    
1928     \end_inset
1929    
1930     ,
1931     \family typewriter
1932     vim
1933     \family default
1934    
1935     \begin_inset LatexCommand \index{vim}
1936    
1937     \end_inset
1938    
1939     , Notepad
1940     \begin_inset LatexCommand \index{Notepad}
1941    
1942     \end_inset
1943    
1944     or TextPad
1945     \begin_inset LatexCommand \index{TextPad}
1946    
1947     \end_inset
1948    
1949     .
1950     Now type in or, better yet, cut-and-paste the statements in Figure
1951     \begin_inset LatexCommand \ref{fig:model1.modelVessel}
1952    
1953     \end_inset
1954    
1955    
1956     \noun off
1957     .
1958     Be very careful to match the use of capital and small letters.
1959     Do not worry about blanks between symbols but do not embed blanks within
1960     symbols.
1961     In other words, do not put a blank in the middle of the symbol
1962     \family typewriter
1963     \noun default
1964     side_wall
1965     \family default
1966     \noun off
1967     but do not worry about putting zero or more blanks between
1968     \family typewriter
1969     \noun default
1970     side_wall
1971     \family default
1972     \noun off
1973     and
1974     \family typewriter
1975     \noun default
1976     =
1977     \family default
1978     \noun off
1979     in an equation.
1980     \end_layout
1981    
1982     \begin_layout Standard
1983     When you are finished, be sure to save the file as a text file.
1984     Call it
1985     \family typewriter
1986     vesselPlain.a4c
1987     \family default
1988     .
1989     The "
1990     \family typewriter
1991     .a4c
1992     \family default
1993     " stands for "ASCEND 4 Code".
1994     Many Windows editors will append "
1995     \family typewriter
1996     .txt
1997     \family default
1998     " to the file name.
1999     Remove the
2000     \family typewriter
2001     .txt
2002     \family default
2003     ending off the file name -- do not let Microsoft bully you into thinking
2004     you should not -- and change it to "
2005     \family typewriter
2006     .a4c
2007     \begin_inset LatexCommand \index{a4c}
2008    
2009     \end_inset
2010    
2011    
2012     \family default
2013     ".
2014    
2015     \end_layout
2016    
2017     \begin_layout Standard
2018     (This model is also available as
2019     \family typewriter
2020     vesselPlain.a4c
2021     \family default
2022     in the ASCEND models library, but we suggest it would be better for you
2023     to go through the exercise of creating your own version here.
2024     At the least copy the library file to your ASCEND space so you can play
2025     with your own version at this time.)
2026     \end_layout
2027    
2028     \begin_layout Standard
2029     When you are done, you should have a text file called
2030     \family typewriter
2031     vesselPlain.a4c
2032     \family default
2033     stored in your ASCEND/models/vessel subdirectory.
2034     It should contain precisely the statements in Figure
2035     \begin_inset LatexCommand \ref{fig:model1.modelVessel}
2036    
2037     \end_inset
2038    
2039    
2040     \noun off
2041     with care having been taken to match capital and lower case letters as
2042     shown there.
2043     \end_layout
2044    
2045     \begin_layout Standard
2046     \begin_inset Marginal
2047     status collapsed
2048    
2049     \begin_layout Standard
2050     start the ASCEND system.
2051     Move and resize the windows to make yourself comfortable.
2052     \end_layout
2053    
2054     \end_inset
2055    
2056     Start the ASCEND system by double clicking on the ASCEND icon if you are
2057     on Windows or typing
2058     \family typewriter
2059     ascend
2060     \family default
2061     at the command line if you are using a Linux machine
2062     \begin_inset Foot
2063     status collapsed
2064    
2065     \begin_layout Standard
2066     Depending on the Linux version you have installed, you might find that the
2067     command is
2068     \family typewriter
2069     ascend4
2070     \family default
2071     or that you have an ASCEND option in your GNOME 'Applications' menu.
2072     \end_layout
2073    
2074     \end_inset
2075    
2076     .
2077     Four windows will appear, three smaller ones and one larger one that will,
2078     if left unattended, disappear by itself in a few seconds.
2079     Move the three smaller ones around on your screen so they do not overlap
2080     or so they overlap very little.
2081     Resize them if you want to.
2082     You might start by putting the one called Script
2083     \begin_inset LatexCommand \index{Script window}
2084    
2085     \end_inset
2086    
2087     in the upper left, the one called Library
2088     \begin_inset LatexCommand \index{Library window}
2089    
2090     \end_inset
2091    
2092     in the upper right and the one called Console
2093     \begin_inset LatexCommand \index{Console}
2094    
2095     \end_inset
2096    
2097     in the lower right.
2098     We shall assume you have placed them in these positions in the following
2099     so, even if that is not your favorite placement, it might be useful to
2100     use it for now.
2101     \end_layout
2102    
2103     \begin_layout Standard
2104     \begin_inset Marginal
2105     status collapsed
2106    
2107     \begin_layout Standard
2108     note that each window by itself looks pretty nonthreatening
2109     \end_layout
2110    
2111     \end_inset
2112    
2113     As you can see, each window by itself looks like a pretty normal window.
2114     Each has buttons across the top under which one will find different tools
2115     to run.
2116     Each also has one to three sub-windows for displaying things.
2117     Each has a Help button that you can push at any time that you want to read
2118     all kinds of detailed things about the window
2119     \begin_inset Foot
2120     status collapsed
2121    
2122     \begin_layout Standard
2123     assuming you have got the help files installed on your system, which you
2124     may not find you have.
2125     \end_layout
2126    
2127     \end_inset
2128    
2129     .
2130     For the moment we will provide you with the "just-in-time" details here
2131     so you do not need to be sidetracked just yet by pushing these Help buttons.
2132     \end_layout
2133    
2134     \begin_layout Standard
2135     \begin_inset Marginal
2136     status collapsed
2137    
2138     \begin_layout Standard
2139     hey, where did that window go? I want it back NOW!
2140     \end_layout
2141    
2142     \end_inset
2143    
2144     If you ever lose a window, open the Script window and under the Tools
2145     \begin_inset LatexCommand \index{Tools}
2146    
2147     \end_inset
2148    
2149     button, select the window you wish to open.
2150     You cannot lose the Script window unless you shut down ASCEND.
2151     For other windows in ASCEND, you can close them and re-open them as required.
2152     Any window that you closed can usually be restored by going back to the
2153     Script window and selected it from the Tools menu there.
2154     \end_layout
2155    
2156     \begin_layout Standard
2157     \begin_inset Marginal
2158     status collapsed
2159    
2160     \begin_layout Standard
2161     How do I quit
2162     \begin_inset LatexCommand \index{quit ASCEND}
2163    
2164     \end_inset
2165    
2166     ASCEND?
2167     \end_layout
2168    
2169     \end_inset
2170    
2171     To exit
2172     \begin_inset LatexCommand \index{exit ASCEND}
2173    
2174     \end_inset
2175    
2176     ASCEND, close the Script window.
2177     You will be asked to confirm that you want to exit ASCEND.
2178     If you have simulations in memory this will stop you from losing your results.
2179     \end_layout
2180    
2181     \begin_layout Standard
2182     \begin_inset Marginal
2183     status collapsed
2184    
2185     \begin_layout Standard
2186     saving
2187     \begin_inset LatexCommand \index{saving window position}
2188    
2189     \end_inset
2190    
2191     window positions
2192     \begin_inset LatexCommand \index{window position}
2193    
2194     \end_inset
2195    
2196    
2197     \end_layout
2198    
2199     \end_inset
2200    
2201     ASCEND will not remember your window locations automatically.
2202     If you like where you have placed the windows for ASCEND on your display,
2203     go to the Script window and select 'Save all appearances
2204     \begin_inset LatexCommand \index{window locations, save}
2205    
2206     \end_inset
2207    
2208    
2209     \begin_inset LatexCommand \index{appearances, save all}
2210    
2211     \end_inset
2212    
2213     ' under the View
2214     \begin_inset LatexCommand \index{View}
2215    
2216     \end_inset
2217    
2218     menu.
2219     A similar tool exists for each window for saving only its position.
2220     \end_layout
2221    
2222     \begin_layout Standard
2223     \begin_inset Marginal
2224     status collapsed
2225    
2226     \begin_layout Standard
2227     start by loading and compiling using tools in the Library window
2228     \end_layout
2229    
2230     \end_inset
2231    
2232     We shall start with the Library window in the upper right.
2233     This window provides you with the tools to load and compile files containing
2234     type definitions.
2235     You can also display
2236     \begin_inset LatexCommand \index{display}
2237    
2238     \end_inset
2239    
2240     the code for the different types you have loaded.
2241     \end_layout
2242    
2243     \begin_layout Standard
2244     \begin_inset Marginal
2245     status collapsed
2246    
2247     \begin_layout Standard
2248     use the left mouse button unless we tell you otherwise (however, on you
2249     own explore using the right mouse button in any of the windows)
2250     \end_layout
2251    
2252     \end_inset
2253    
2254     Let's load your file.
2255     Under the File button select the 'Read types from File
2256     \begin_inset LatexCommand \index{Read Types from File}
2257    
2258     \end_inset
2259    
2260     ' tool.
2261     You select this tool by clicking on it using the left mouse button - i.e.,
2262     the button you should have expected to use.
2263     A window will appear asking you to find the file you want to read into
2264     ASCEND.
2265     Navigate to where you stored
2266     \family typewriter
2267     vesselPlain.a4c
2268     \family default
2269     (in the subdirectory
2270     \family typewriter
2271     ascdata
2272     \family default
2273     ) and select that file.
2274     If you have the wrong ending on the file (you left
2275     \family typewriter
2276     .txt
2277     \family default
2278     or you forgot to put
2279     \family typewriter
2280     .a4c
2281     \family default
2282     as the ending), tell the system to list all files and pick the one you
2283     want.
2284     The
2285     \family typewriter
2286     .a4c
2287     \family default
2288     is used by the system to list only the files it thinks you might want to
2289     load, but ASCEND isn't fussy.
2290     It will attempt to load any file you pick.
2291     \end_layout
2292    
2293     \begin_layout Standard
2294     Look in the Console window at the lower right, and, if the file loads without
2295     any errors being listed there, you can skip past the next bit to where
2296     you should start to compile an instance.
2297     The next bit has some useful hints on how to debug your models.
2298     If you want some debugging experience, put a known error into your
2299     \family typewriter
2300     vesselPlain.a4c
2301     \family default
2302     file and see what happens.
2303     This move will give you a reason to read the following section.
2304     \end_layout
2305    
2306     \begin_layout Standard
2307     \begin_inset Marginal
2308     status open
2309    
2310     \begin_layout Standard
2311     Do not ignore the diagnostics
2312     \begin_inset LatexCommand \index{diagnostics}
2313    
2314     \end_inset
2315    
2316     that might appear in the Console window
2317     \end_layout
2318    
2319     \end_inset
2320    
2321     If the Console window in the lower right starts filling with several tens
2322     of lines of diagnostics, look to see if you included the
2323     \family typewriter
2324     REQUIRE
2325     \family default
2326    
2327     \begin_inset LatexCommand \index{REQUIRE}
2328    
2329     \end_inset
2330    
2331     statement at the beginning of your model file.
2332     Without that statement, ASCEND is missing all the definitions for the types
2333     of variables in your model, and it will go wild telling you so
2334     \begin_inset Foot
2335     status collapsed
2336    
2337     \begin_layout Standard
2338     It might also be choking on a Word document because you forgot to save
2339     it as a text file.
2340     \end_layout
2341    
2342     \end_inset
2343    
2344     .
2345     \end_layout
2346    
2347     \begin_layout Standard
2348     While loading the files containing these types, ASCEND will look very closely
2349     at the syntax and will give you all kinds of diagnostic messages in the
2350     Console window (lower right) if you have done something wrong.
2351     It will also at times spew out some warning messages
2352     \begin_inset LatexCommand \index{warning messages}
2353    
2354     \end_inset
2355    
2356     if you have done something thought to be poor modeling style.
2357     You must heed the error messages as the file will not load if there are
2358     any.
2359     ASCEND will tell you if it did not load the file.
2360    
2361     \end_layout
2362    
2363     \begin_layout Standard
2364     You should consider heeding the warnings if you get any.
2365     If you ignore them now, they may come back and haunt you later.
2366     However, there are times when we issue a warning but everything will work,
2367     and you will think we were not too clever.
2368     Our response: better modeling style
2369     \begin_inset LatexCommand \index{modeling style}
2370    
2371     \end_inset
2372    
2373     can eliminate these warnings.
2374     (It's been our system so we get to have the last word.)
2375     \end_layout
2376    
2377     \begin_layout Standard
2378     \begin_inset Marginal
2379     status collapsed
2380    
2381     \begin_layout Standard
2382     how do I jump
2383     \begin_inset LatexCommand \index{jump to line}
2384    
2385     \end_inset
2386    
2387    
2388     \begin_inset LatexCommand \index{line numbers}
2389    
2390     \end_inset
2391    
2392     to line 100 of a file when using some of the standard editors?
2393     \end_layout
2394    
2395     \end_inset
2396    
2397     The error and warning messages will contain a line number in the file where
2398     the error has occurred.
2399     This will be the line number as counted by an editor with the first line
2400     being line 1 in the file.
2401     Editors always provide you with a means to get directly to a line number
2402     in a file.
2403     Find out how to do that or you will not be too happy with debugging a large
2404     file.
2405     \end_layout
2406    
2407     \begin_layout Standard
2408     You will be in the debug mode for a new system so do not expect it to be
2409     totally obvious the first few times you make an error.
2410     We have tried to use language that should be meaningful, but we may have
2411     failed or the error may be pretty subtle and not possible for us to anticipate
2412     how to describe it in your terms.
2413     (Send us a bug report if you have any good ideas on language.)
2414     \end_layout
2415    
2416     \begin_layout Standard
2417     \begin_inset Marginal
2418     status collapsed
2419    
2420     \begin_layout Standard
2421     reloading a file
2422     \begin_inset LatexCommand \index{reloading a file}
2423    
2424     \end_inset
2425    
2426    
2427     \begin_inset LatexCommand \index{file, reloading}
2428    
2429     \end_inset
2430    
2431     overwrites the previous version
2432     \end_layout
2433    
2434     \end_inset
2435    
2436     You can reload any file your have corrected using the Read types from file
2437     tool under the File menu.
2438     It will overwrite the previous version of the file only if the file has
2439     changed since it was last loaded (note that we do not reload those big
2440     files unless you make a change even if you tell us to).
2441     \end_layout
2442    
2443     \begin_layout Standard
2444     \begin_inset Marginal
2445     status collapsed
2446    
2447     \begin_layout Standard
2448     displaying the code
2449     \end_layout
2450    
2451     \end_inset
2452    
2453     You can display the code you have written.
2454     Select the model vessel in the right window of the Library.
2455     Then under the Display
2456     \begin_inset LatexCommand \index{Display window}
2457    
2458     \end_inset
2459    
2460     menu at the top, select the tool Code.
2461     The Display window will open displaying the code for this model.
2462     \end_layout
2463    
2464     \begin_layout Standard
2465     \begin_inset Marginal
2466     status collapsed
2467    
2468     \begin_layout Standard
2469     now compile as "
2470     \family typewriter
2471     v
2472     \family default
2473     "
2474     \end_layout
2475    
2476     \end_inset
2477    
2478     Okay, you have your file loaded without getting any diagnostics.
2479     You are ready to compile
2480     \begin_inset LatexCommand \index{compile}
2481    
2482     \end_inset
2483    
2484     .
2485     In the Library window, look in the left window and select the file
2486     \family typewriter
2487     vesselPlain.a4c
2488     \family default
2489     .
2490     It contains the type definition you wish to compile.
2491     You should see the type vessel appear in the right window.
2492     Select vessel.
2493     Under the Edit button, select Create simulation.
2494     A small window opens and asks you to name the simulation.
2495     Call it
2496     \family typewriter
2497     v
2498     \family default
2499     -- yes, just the letter "v", and select "OK".
2500     Short names for instances often seem to be preferable.
2501    
2502     \end_layout
2503    
2504     \begin_layout Standard
2505     Look again in the Console window for diagnostics.
2506     If everything worked without error, you will see some statistics telling
2507     you how many models, relations and so forth you have created during the
2508     compile step.
2509     \end_layout
2510    
2511     \begin_layout Standard
2512     \begin_inset Marginal
2513     status collapsed
2514    
2515     \begin_layout Standard
2516     and pass the instance
2517     \begin_inset LatexCommand \index{instance}
2518    
2519     \end_inset
2520    
2521     to the Browser
2522     \begin_inset LatexCommand \index{Browser}
2523    
2524     \end_inset
2525    
2526    
2527     \end_layout
2528    
2529     \end_inset
2530    
2531     Select
2532     \family typewriter
2533     v IS A vessel
2534     \family default
2535     in the bottom of the Library window.
2536     Then under the Export
2537     \begin_inset LatexCommand \index{Export}
2538    
2539     \end_inset
2540    
2541     button, select 'Simulation to Browser
2542     \begin_inset LatexCommand \index{Export Simulation to Browser}
2543    
2544     \end_inset
2545    
2546     ' to export
2547     \family typewriter
2548     v
2549     \family default
2550     to the Browser tool set.
2551     The Browser window will open and contain
2552     \family typewriter
2553     v
2554     \family default
2555     .
2556     It might be useful to enlarge this window and move it down a bit, placing
2557     it a bit to the right of the center of your screen.
2558     (Remember you can save this positioning and sizing of the Browser window
2559     by going under the View menu and picking 'Save appearance'.)
2560     \end_layout
2561    
2562     \begin_layout Standard
2563     \begin_inset Marginal
2564     status collapsed
2565    
2566     \begin_layout Standard
2567     examine
2568     \family typewriter
2569     v
2570     \family default
2571     by playing with it in the Browser
2572     \end_layout
2573    
2574     \end_inset
2575    
2576     In the left upper window of the Browser, you will find
2577     \family typewriter
2578     v
2579     \family default
2580     to be the current object.
2581     Listed in the right window are all the parts of the current object.
2582     You will see the variables listed here along with an indication of their
2583     type.
2584     For example, you will find
2585     \family typewriter
2586     Cylinder IS A relation
2587     \family default
2588     and
2589     \family typewriter
2590     D IS A distance
2591     \family default
2592     listed, among many others.
2593    
2594     \family typewriter
2595     Cylinder
2596     \family default
2597     is one of the equations you wrote describing the model while
2598     \family typewriter
2599     D
2600     \family default
2601     was the diameter of the vessel.
2602    
2603     \end_layout
2604    
2605     \begin_layout Standard
2606     \begin_inset Marginal
2607     status collapsed
2608    
2609     \begin_layout Standard
2610     included flags
2611     \begin_inset LatexCommand \index{included flags}
2612    
2613     \end_inset
2614    
2615    
2616     \begin_inset LatexCommand \index{flag, included}
2617    
2618     \end_inset
2619    
2620     for relations
2621     \end_layout
2622    
2623     \end_inset
2624    
2625     If you pick any of the parts in the right or bottom windows, it becomes
2626     the current object; its parts then show in the right window.
2627     For example, a relation has a boolean part (a flag that takes the value
2628    
2629     \family typewriter
2630     TRUE
2631     \family default
2632     or
2633     \family typewriter
2634     FALSE
2635     \family default
2636     ) indicating whether or not it is to be included when ASCEND solves the
2637     equations you defined for the model.
2638     \end_layout
2639    
2640     \begin_layout Standard
2641     If you wish to display the current value for this flag, pick 'Display Atom
2642     Values
2643     \begin_inset LatexCommand \index{Display Atom Values}
2644    
2645     \end_inset
2646    
2647     ' under the View menu.
2648     This tool toggles a switch that causes either the value or the type to
2649     show for a variable, a constant or a relation in the upper right window
2650     of the Browser.
2651     Try toggling it back and forth and looking at different things in the Browser.
2652     \end_layout
2653    
2654     \begin_layout Standard
2655     Pick each of the tools under View and note what happens to the displaying
2656     of things in the Browser.
2657     \end_layout
2658    
2659     \begin_layout Standard
2660     Across the bottom of the Browser window note the buttons you can select
2661     labeled
2662     \family typewriter
2663     RV
2664     \family default
2665     ,
2666     \family typewriter
2667     DV
2668     \family default
2669     and so forth.
2670     If you have made the Browser window large enough, you will see to the right
2671     of these buttons the type of objects whose value you want to appear or
2672     not in the lower Browser window as you toggle each button.
2673     Toggle each of these buttons and see if the lower display changes.
2674     If it does not, then this type of part is not in the current object.
2675     \end_layout
2676    
2677     \begin_layout Section
2678     Solving
2679     \begin_inset LatexCommand \index{Solving}
2680    
2681     \end_inset
2682    
2683     an ASCEND instance
2684     \end_layout
2685    
2686     \begin_layout Standard
2687     Well, you have been patient.
2688     While there are lots of interesting tools left to explore in the Browser,
2689     perhaps it is time to try to solve this model.
2690     To solve
2691     \family typewriter
2692     v
2693     \family default
2694     , make it the current object (it alone should be listed in the upper left
2695     window of the Browser).
2696     Then, under the Export
2697     \begin_inset LatexCommand \index{Export to Solver}
2698    
2699     \end_inset
2700    
2701     menu, select 'to Solver'.
2702     The Solver window will open, along with a smaller window labeled Eligible
2703     \begin_inset LatexCommand \index{window, Eligible}
2704    
2705     \end_inset
2706    
2707    
2708     \begin_inset LatexCommand \index{Eligible window}
2709    
2710     \end_inset
2711    
2712     .
2713     Move the Eligible window up a bit so it does not cover any or very little
2714     of the Solver window.
2715     Move the Solver window to the lower left and enlarge it so you can see
2716     all of its contents.
2717    
2718     \end_layout
2719    
2720     \begin_layout Standard
2721     \begin_inset Marginal
2722     status collapsed
2723    
2724     \begin_layout Standard
2725     if ASCEND stops responding
2726     \begin_inset LatexCommand \index{responding, ASCEND stops}
2727    
2728     \end_inset
2729    
2730     , hunt down one of those "nasty" windows with a "yellow lock
2731     \begin_inset LatexCommand \index{yellow lock}
2732    
2733     \end_inset
2734    
2735     " and close it properly
2736     \end_layout
2737    
2738     \end_inset
2739    
2740     This Eligible window is 'modal': if it is open and you do not do something
2741     to make it happy and go away, it will stop you from doing anything else
2742     in the ASCEND system.
2743     Such windows appear with a black lock icon in a yellow field -- we shall
2744     call it a "yellow lock." They demand you attend to them
2745     \emph on
2746     now
2747     \emph default
2748     .
2749     A good solution would be for such a window to stay open and on top of all
2750     the other open windows.
2751     Unfortunately we have not been able under all window managers to stop it
2752     from ducking under another window.
2753     If you ever find ASCEND unwilling to respond, iconify the other windows
2754     to get them out of the way, until you find one of these windows.
2755     On the PC you can go to the icon bar at the bottom of your screen and,
2756     by clicking on the window, bring it to the top.
2757     Then do whatever it takes to make it happy and close properly -- such as
2758     cancel it.
2759     If you are not careful here, for example, this window will hide under the
2760     Solver window before you are through with it.
2761     \end_layout
2762    
2763     \begin_layout Standard
2764     \begin_inset Marginal
2765     status open
2766    
2767     \begin_layout Standard
2768     is our problem well-posed
2769     \begin_inset LatexCommand \index{well-posed}
2770    
2771     \end_inset
2772    
2773     ?
2774     \end_layout
2775    
2776     \end_inset
2777    
2778     The Solver window contains the information we need to see to explain why
2779     the Eligible window opened in the first place.
2780     Examine the information the Solver displays.
2781     It tells you that
2782     \family typewriter
2783     v
2784     \family default
2785     has 6 relations defining it and that all are equalities and included.
2786     It has no inequalities.
2787     On the right side we see there are 10 variables and all are 'free
2788     \begin_inset LatexCommand \index{free variables}
2789    
2790     \end_inset
2791    
2792     .' A free variable is one for which you want the system to compute a value.
2793     Hmm, 6 equations in 10 variables.
2794     Something is wrong here.
2795     For a well-posed problem, you want 6 equations in 6 variables (i.e., square
2796     \begin_inset LatexCommand \index{square}
2797    
2798     \end_inset
2799    
2800     ).
2801     ASCEND reports that the system is underspecified
2802     \begin_inset LatexCommand \index{underspecified}
2803    
2804     \end_inset
2805    
2806     by 4.
2807     This means you need to pick four of the variables and declare them to be
2808     fixed
2809     \begin_inset LatexCommand \index{fixed}
2810    
2811     \end_inset
2812    
2813     .
2814     You will also have to pick values for these fixed variables before you
2815     can solve for the remaining 6.
2816     For such a small problem as this one, this task is not formidable.
2817     For a model with 50,000 equations and 60,000 variables, one would quit
2818     and go home.
2819     We have exposed a need here.
2820     We certainly would like ASCEND to help us here for this small problem.
2821     But we insist that it help us in major ways to make the 50,000 equation,
2822     60,000 variable problem possible.
2823     \end_layout
2824    
2825     \begin_layout Standard
2826     \begin_inset Marginal
2827     status collapsed
2828    
2829     \begin_layout Standard
2830     picking variables we are going to fix
2831     \end_layout
2832    
2833     \end_inset
2834    
2835     Okay, the small help such as needed here is why the Eligible window opened.
2836     Let's return to it.
2837     It lists all the variables of those not yet fixed that are eligible to
2838     be fixed and still leave us a calculation that has a chance to solve.
2839     The algorithm to find eligible variables does an quick analysis of the
2840     structure of the equations.
2841     The variables it lists are those that can be fixed
2842     \emph on
2843     without
2844     \emph default
2845     the system becoming numerically singular.
2846     So any variables that are not shown
2847     \emph on
2848     cannot possibly
2849     \emph default
2850     help you.
2851     \end_layout
2852    
2853     \begin_layout Standard
2854     So look at the list and decide what you would like to fix for your first
2855     calculation with this model.
2856     Diameter (
2857     \family typewriter
2858     v.D
2859     \family default
2860     ) seems a good choice.
2861     Now you can see why we called the instance just plain old
2862     \family typewriter
2863     v
2864     \family default
2865     .
2866     A longer name would get tiring here.
2867     Anyway, pick
2868     \family typewriter
2869     v.D
2870     \family default
2871     .
2872     Immediately the list reappears with
2873     \family typewriter
2874     v.D
2875     \family default
2876     no longer on it.
2877     ASCEND has just repeated the eligibility analysis, and found that more
2878     variables still need to be fixed.
2879     \end_layout
2880    
2881     \begin_layout Standard
2882     We have three more to pick.
2883     On the list are both vessel height,
2884     \family typewriter
2885     v.H
2886     \family default
2887     , and
2888     \family typewriter
2889     v.H_to_D_ratio
2890     \family default
2891     .
2892     We certainly cannot pick both of these.
2893     One implies the other if we know a value for
2894     \family typewriter
2895     v.D
2896     \family default
2897     .
2898     Pick
2899     \family typewriter
2900     v.H_to_D_ratio
2901     \family default
2902     .
2903     Note that
2904     \family typewriter
2905     v.H
2906     \family default
2907     is no longer eligible.
2908     Good.
2909     We would be worried if it were still there.
2910     \end_layout
2911    
2912     \begin_layout Standard
2913     We see
2914     \family typewriter
2915     v.metal_density
2916     \emph on
2917     .
2918    
2919     \family default
2920     \emph default
2921     Pick it.
2922     Strange.
2923     Metal mass and volume stayed eligible.
2924     Why? If we pick metal mass, wall thickness is implied, and the same is
2925     true if we were to pick metal volume.
2926     However, as it seems much more natural to pick
2927     \family typewriter
2928     wall_thickness
2929     \family default
2930     , make that the last variable you choose.
2931     The Solver window now says this problem is square (i.e., it has 6 equations
2932     in the same number of unknowns).
2933     Table
2934     \begin_inset LatexCommand \ref{tab:model1.variableFixed}
2935    
2936     \end_inset
2937    
2938    
2939     \noun off
2940     summarizes the four variables we have elected here to fix.
2941     \end_layout
2942    
2943     \begin_layout Standard
2944     \begin_inset Float table
2945     wide false
2946     sideways false
2947     status open
2948    
2949     \begin_layout Caption
2950     \begin_inset LatexCommand \label{tab:model1.variableFixed}
2951    
2952     \end_inset
2953    
2954     Variables we have fixed
2955     \begin_inset LatexCommand \index{fixed variables}
2956    
2957     \end_inset
2958    
2959    
2960     \end_layout
2961    
2962     \begin_layout Standard
2963     \begin_inset Tabular
2964     <lyxtabular version="3" rows="5" columns="1">
2965     <features>
2966     <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
2967     <row topline="true" bottomline="true">
2968     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2969     \begin_inset Text
2970    
2971     \begin_layout Standard
2972     variable
2973     \end_layout
2974    
2975     \end_inset
2976     </cell>
2977     </row>
2978     <row topline="true">
2979     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2980     \begin_inset Text
2981    
2982     \begin_layout Standard
2983    
2984     \family typewriter
2985     D
2986     \end_layout
2987    
2988     \end_inset
2989     </cell>
2990     </row>
2991     <row topline="true">
2992     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
2993     \begin_inset Text
2994    
2995     \begin_layout Standard
2996    
2997     \family typewriter
2998     H_to_D_ratio
2999     \end_layout
3000    
3001     \end_inset
3002     </cell>
3003     </row>
3004     <row topline="true">
3005     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3006     \begin_inset Text
3007    
3008     \begin_layout Standard
3009    
3010     \family typewriter
3011     meta_density
3012     \end_layout
3013    
3014     \end_inset
3015     </cell>
3016     </row>
3017     <row topline="true" bottomline="true">
3018     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3019     \begin_inset Text
3020    
3021     \begin_layout Standard
3022    
3023     \family typewriter
3024     wall_thickness
3025     \end_layout
3026    
3027     \end_inset
3028     </cell>
3029     </row>
3030     </lyxtabular>
3031    
3032     \end_inset
3033    
3034    
3035     \end_layout
3036    
3037     \end_inset
3038    
3039    
3040     \end_layout
3041    
3042     \begin_layout Standard
3043     \begin_inset Marginal
3044     status collapsed
3045    
3046     \begin_layout Standard
3047     ASCEND partitions the problem into smaller problems for solving
3048     \end_layout
3049    
3050     \end_inset
3051    
3052     Toward the bottom right of the
3053     \series bold
3054     Solver
3055     \series default
3056     window, we see there are 6 "blocks
3057     \begin_inset LatexCommand \index{blocks}
3058    
3059     \end_inset
3060    
3061     ." What are blocks? ASCEND has examined the equations and, in this case,
3062     has discovered that not all the equations have to be solved simultaneously.
3063     There are 6 blocks of equations which it can solve in sequence.
3064     6 blocks and 6 equations means that ASCEND has found a way to solve the
3065     model by solving 6 individual equations in sequence -- i.e., one at a time.
3066     This is a good thing: it usually means that the solver will have less problems
3067     with locating the overall solution.
3068     \end_layout
3069    
3070     \begin_layout Standard
3071     As well as breaking down the system into blocks, ASCEND has the ability
3072     to rearrange some simple algebraic equations so that unknown variables
3073     can be evaluated directly from the known values, with no need for iterative
3074     numerical methods.
3075     This is only possible if there is just one equation in the block.
3076     In fact, this problem, with the 4 variables we selected to be fixed, can
3077     be solved entirely without iteration.
3078     \end_layout
3079    
3080     \begin_layout Standard
3081     \begin_inset Marginal
3082     status open
3083    
3084     \begin_layout Standard
3085     displaying the incidence matrix
3086     \begin_inset LatexCommand \index{incidence matrix}
3087    
3088     \end_inset
3089    
3090    
3091     \end_layout
3092    
3093     \end_inset
3094    
3095     Can we see what ASCEND has just discovered? It turns out we can (we would
3096     not have asked if we could not).
3097     Under the Display menu on the Solver, select the 'Incidence matrix tool
3098     \begin_inset LatexCommand \index{incidence matrix tool}
3099    
3100     \end_inset
3101    
3102     '.
3103     A window pops open showing us the incidence of variables in the equations
3104     and display them in the order that ASCEND has found to solve them, also
3105     known as a sparsity matrix
3106     \begin_inset LatexCommand \index{sparsity matrix}
3107    
3108     \end_inset
3109    
3110     or sparsity pattern
3111     \begin_inset LatexCommand \index{sparsity pattern}
3112    
3113     \end_inset
3114    
3115     .
3116     The dark squares are incidences under the variables for which we are solving;
3117     the lighter looking 'X' symbols to the right side are incidences for the
3118     fixed (known) variables.
3119     Click on the incidence in the upper left corner.
3120     ASCEND immediately identifies it for us as the
3121     \family typewriter
3122     end_area
3123     \family default
3124     .
3125     It identifies the equation as the one we labeled
3126     \family typewriter
3127     FlatEnds
3128     \family default
3129     .
3130     We can go back to our model and find the equation ASCEND will solve first.
3131     The other variable in this equation is in the set we fixed; pick it and
3132     discover it is
3133     \family typewriter
3134     D
3135     \family default
3136     , the vessel diameter.
3137     Of course we can compute the area of the ends given the diameter.
3138     The
3139     \emph on
3140     end_area
3141     \emph default
3142     is
3143     \begin_inset Formula $\pi D^{2}/4$
3144     \end_inset
3145    
3146     .
3147     \end_layout
3148    
3149     \begin_layout Standard
3150     Play with the other incidences here.
3151     See what the other equations are and the order ASCEND will use to solve
3152     them.
3153     \end_layout
3154    
3155     \begin_layout Standard
3156     Okay, we return to our task of solving.
3157     We need next to supply values for the variables we have selected to be
3158     fixed.
3159     Again, the approach we are going to take is acceptable for this small problem,
3160     but we would not want to have to do what we are about to do for a large
3161     problem.
3162     Fortunately, we really have thought about these issues and have some nice
3163     approaches that work even for extremely large problem -- like 100,000 equations.
3164     \end_layout
3165    
3166     \begin_layout Standard
3167     \begin_inset Marginal
3168     status collapsed
3169    
3170     \begin_layout Standard
3171     which variables are currently fixed for this problem?
3172     \end_layout
3173    
3174     \end_inset
3175    
3176     Let's see.
3177     Do you remember the variables we fixed? What if you do not? Well, we go
3178     back to the Browser.
3179     Be sure
3180     \family typewriter
3181     v
3182     \family default
3183     remains the current object (it alone is in the upper left window).
3184     Under the Find menu select 'by Type
3185     \begin_inset LatexCommand \index{Find by Type}
3186    
3187     \end_inset
3188    
3189     .' A small window opens with default information in it saying it will find
3190     for us all objects contained in the current object
3191     \family typewriter
3192     v
3193     \family default
3194     of type
3195     \family typewriter
3196     solver_var
3197     \family default
3198     whose
3199     \family typewriter
3200     fixed
3201     \family default
3202     flags are set to
3203     \family typewriter
3204     TRUE
3205     \family default
3206     .
3207     These are precisely the attributes for the variables we have fixed.
3208     Select OK and a list of the four variables we fixed earlier appears.
3209     \end_layout
3210    
3211     \begin_layout Standard
3212     \begin_inset Marginal
3213     status collapsed
3214    
3215     \begin_layout Standard
3216     specifying values for the fixed variables - this approach is useful for
3217     small problems
3218     \end_layout
3219    
3220     \end_inset
3221    
3222     For each variable on this list, we should supply a value.
3223     Select
3224     \family typewriter
3225     D
3226     \family default
3227     in the lower window of the Browser using the right (the right, not the
3228     left -- make
3229     \family typewriter
3230     v
3231     \family default
3232     the current object and do it again) mouse button.
3233     A window opens in which we input a value for
3234     \family typewriter
3235     D
3236     \family default
3237     .
3238     Put in the value 4 in the left window and ft in the right.
3239     Continue by putting in the values for the variables as listed in Table
3240    
3241     \begin_inset LatexCommand \ref{tab:model1.valuesFixedVars}
3242    
3243     \end_inset
3244    
3245    
3246     \noun off
3247     .
3248     These values immediately appear in the Browser window as you enter them.
3249     If you did not fully appreciate the proper handling of dimension and units
3250     before, you just got a taste of its advantages.
3251    
3252     \noun default
3253     You
3254     \noun off
3255     did not have to worry about specifying these things in consistent preselected
3256     units
3257     \noun default
3258     -- ASCEND did this for you.
3259     \end_layout
3260    
3261     \begin_layout Standard
3262     \begin_inset Float table
3263     wide false
3264     sideways false
3265     status open
3266    
3267     \begin_layout Caption
3268     \begin_inset LatexCommand \label{tab:model1.valuesFixedVars}
3269    
3270     \end_inset
3271    
3272     Values to use for fixed variables
3273     \end_layout
3274    
3275     \begin_layout Standard
3276     \begin_inset Tabular
3277     <lyxtabular version="3" rows="5" columns="3">
3278     <features>
3279     <column alignment="center" valignment="top" leftline="true" width="0">
3280     <column alignment="center" valignment="top" leftline="true" width="0">
3281     <column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
3282     <row topline="true" bottomline="true">
3283     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3284     \begin_inset Text
3285    
3286     \begin_layout Standard
3287     variable
3288     \end_layout
3289    
3290     \end_inset
3291     </cell>
3292     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3293     \begin_inset Text
3294    
3295     \begin_layout Standard
3296     value
3297     \end_layout
3298    
3299     \end_inset
3300     </cell>
3301     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3302     \begin_inset Text
3303    
3304     \begin_layout Standard
3305     units
3306     \end_layout
3307    
3308     \end_inset
3309     </cell>
3310     </row>
3311     <row topline="true">
3312     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3313     \begin_inset Text
3314    
3315     \begin_layout Standard
3316    
3317     \family typewriter
3318     D
3319     \end_layout
3320    
3321     \end_inset
3322     </cell>
3323     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3324     \begin_inset Text
3325    
3326     \begin_layout Standard
3327     4
3328     \end_layout
3329    
3330     \end_inset
3331     </cell>
3332     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3333     \begin_inset Text
3334    
3335     \begin_layout Standard
3336    
3337     \family typewriter
3338     ft
3339     \end_layout
3340    
3341     \end_inset
3342     </cell>
3343     </row>
3344     <row topline="true">
3345     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3346     \begin_inset Text
3347    
3348     \begin_layout Standard
3349    
3350     \family typewriter
3351     H_to_D_ratio
3352     \end_layout
3353    
3354     \end_inset
3355     </cell>
3356     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3357     \begin_inset Text
3358    
3359     \begin_layout Standard
3360     3
3361     \end_layout
3362    
3363     \end_inset
3364     </cell>
3365     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3366     \begin_inset Text
3367    
3368     \begin_layout Standard
3369    
3370     \end_layout
3371    
3372     \end_inset
3373     </cell>
3374     </row>
3375     <row topline="true">
3376     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3377     \begin_inset Text
3378    
3379     \begin_layout Standard
3380    
3381     \family typewriter
3382     meta_density
3383     \end_layout
3384    
3385     \end_inset
3386     </cell>
3387     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3388     \begin_inset Text
3389    
3390     \begin_layout Standard
3391     5000
3392     \end_layout
3393    
3394     \end_inset
3395     </cell>
3396     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3397     \begin_inset Text
3398    
3399     \begin_layout Standard
3400    
3401     \family typewriter
3402     kg/m^3
3403     \end_layout
3404    
3405     \end_inset
3406     </cell>
3407     </row>
3408     <row topline="true" bottomline="true">
3409     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3410     \begin_inset Text
3411    
3412     \begin_layout Standard
3413    
3414     \family typewriter
3415     wall_thickness
3416     \end_layout
3417    
3418     \end_inset
3419     </cell>
3420     <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
3421     \begin_inset Text
3422    
3423     \begin_layout Standard
3424     5
3425     \end_layout
3426    
3427     \end_inset
3428     </cell>
3429     <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
3430     \begin_inset Text
3431    
3432     \begin_layout Standard
3433    
3434     \family typewriter
3435     mm
3436     \end_layout
3437    
3438     \end_inset
3439     </cell>
3440     </row>
3441     </lyxtabular>
3442    
3443     \end_inset
3444    
3445    
3446     \end_layout
3447    
3448     \end_inset
3449    
3450    
3451     \end_layout
3452    
3453     \begin_layout Standard
3454     You can now solve this model.
3455     Go the Solver window and, under the Execute menu, select Solve.
3456     You will get a message telling you the model solved.
3457     Dismiss that message and return to the Browser window to examine the results.
3458     You should see the following results:
3459     \end_layout
3460    
3461     \begin_layout LyX-Code
3462     D = 1.21922 meter
3463     \end_layout
3464    
3465     \begin_layout LyX-Code
3466     H = 3.65765 meter
3467     \end_layout
3468    
3469     \begin_layout LyX-Code
3470     H_to_D_ratio = 3
3471     \end_layout
3472    
3473     \begin_layout LyX-Code
3474     end_area = 1.16748 meter^2
3475     \end_layout
3476    
3477     \begin_layout LyX-Code
3478     metal_density = 5000 kilogram/meter^3
3479     \end_layout
3480    
3481     \begin_layout LyX-Code
3482     metal_mass = 408.62 kilogram
3483     \end_layout
3484    
3485     \begin_layout LyX-Code
3486     side_area = 14.0098 meter^2
3487     \end_layout
3488    
3489     \begin_layout LyX-Code
3490     vessel_vol = 4.27025 meter^3
3491     \end_layout
3492    
3493     \begin_layout LyX-Code
3494     wall_thickness = 0.005 meter
3495     \end_layout
3496    
3497     \begin_layout LyX-Code
3498     wall_vol = 0.0817239 meter^3
3499     \end_layout
3500    
3501     \begin_layout Standard
3502     \begin_inset Note Note
3503     status collapsed
3504    
3505     \begin_layout Standard
3506     Some of this stuff appears to have changed in the PDF....
3507     \end_layout
3508    
3509     \end_inset
3510    
3511    
3512     \end_layout
3513    
3514     \begin_layout Standard
3515     \begin_inset Marginal
3516     status collapsed
3517    
3518     \begin_layout Standard
3519     alter the units used for displaying values
3520     \end_layout
3521    
3522     \end_inset
3523    
3524     You may wish to alter the units used to display these results.
3525     For example, you enter the diameter
3526     \emph on
3527     D
3528     \emph default
3529     in ft.
3530     You may wish to reassure yourself the
3531     \family typewriter
3532     1.21922 meter
3533     \family default
3534     is 4 ft.
3535     Go to the Script window and under the Tools menu select
3536     \emph on
3537     '
3538     \emph default
3539     Measuring units'.
3540     The
3541     \series bold
3542     Units
3543     \series default
3544     window
3545     \begin_inset LatexCommand \index{Units window}
3546    
3547     \end_inset
3548    
3549    
3550     \begin_inset LatexCommand \index{window, Units}
3551    
3552     \end_inset
3553    
3554     will open.
3555     Enlarge it appropriately and then place it to the top and far right of
3556     your display.
3557     \end_layout
3558    
3559     \begin_layout Standard
3560     There are two ways you can reset the units for displaying length.
3561     \end_layout
3562    
3563     \begin_layout Enumerate
3564     Length is a basic dimension in ASCEND so under the
3565     \emph on
3566     Display
3567     \emph default
3568     button select Length.
3569     A side window will open with all the alternate units supported in ASCEND
3570     for length.
3571     Select ft.
3572     \end_layout
3573    
3574     \begin_layout Enumerate
3575     Or, in the lower part of the Units window is a frame labeled 'Set units'.
3576     Clear and then type
3577     \family typewriter
3578     ft
3579     \family default
3580     then hit Enter.
3581     \end_layout
3582    
3583     \begin_layout Standard
3584     In either way, the units for all length variables will switch to ft.
3585     Look at the values in the Browser window.
3586     \end_layout
3587    
3588     \begin_layout Standard
3589     The left upper window of the Units window contains many variable types that
3590     have composite dimensions.
3591     For example, you will find volume there.
3592     Pick it and the right window fills with all the alternative units in which
3593     you can express volume.
3594     \end_layout
3595    
3596     \begin_layout Standard
3597     Play with changing the units for displaying the various variables in the
3598     vessel instance v.
3599    
3600     \end_layout
3601    
3602     \begin_layout Standard
3603     One point - the left window displaying types having composite dimensions
3604     will display only one type for each composite dimension.
3605     If the atom types you have loaded were to include volume_difference as
3606     well as volume, then only one of the two types, volume or volume_difference,
3607     will be listed here.
3608     Changing the units to express either changes the units for both.
3609     \end_layout
3610    
3611     \begin_layout Standard
3612     \begin_inset Marginal
3613     status collapsed
3614    
3615     \begin_layout Standard
3616     returning to a consistent set of units
3617     \end_layout
3618    
3619     \end_inset
3620    
3621     When you are done, you may wish to return to a consistent set, such as SI
3622     \begin_inset LatexCommand \index{SI}
3623    
3624     \end_inset
3625    
3626     .
3627     Under the Display button are different sets; pick
3628     \emph on
3629     SI (MKS) set
3630     \emph default
3631     .
3632     \end_layout
3633    
3634     \begin_layout Standard
3635     \begin_inset Marginal
3636     status collapsed
3637    
3638     \begin_layout Standard
3639     now we can solve the model in other ways
3640     \end_layout
3641    
3642     \end_inset
3643    
3644     We can now resolve our vessel instance in any number of different ways.
3645     For example we can ask what the diameter would be if we had a volume of
3646    
3647     \emph on
3648     250 ft3
3649     \emph default
3650     .
3651     To accomplish this calculation, we need first to make
3652     \emph on
3653     vessel_volume
3654     \emph default
3655     a variable whose value we wish to fix.
3656     When we do this the model will be overspecified.
3657     ASCEND will indicate this problem to us and offer us a list of variables
3658     - including the vessel diameter
3659     \emph on
3660     D
3661     \emph default
3662     , one of which we will have to "unfix
3663     \begin_inset LatexCommand \index{unfix}
3664    
3665     \end_inset
3666    
3667     ." Finally we need to alter the value of
3668     \emph on
3669     vessel_volume
3670     \emph default
3671     to the desired value and solve.
3672     Explicit instructions to accomplish these steps are as follows.
3673     \end_layout
3674    
3675     \begin_layout Itemize
3676     In the
3677     \series bold
3678     Browser
3679     \series default
3680     window, make
3681     \emph on
3682     vessel_volume
3683     \emph default
3684     the current object (select it using the left mouse button).
3685     The right window of the
3686     \series bold
3687     Browser
3688     \series default
3689     display the parts of the
3690     \emph on
3691     vessel_volume
3692     \emph default
3693     , among them is the fixed flag with a value of
3694     \emph on
3695     FALSE
3696     \emph default
3697     .
3698    
3699     \end_layout
3700    
3701     \begin_layout Itemize
3702     (If you do not see the value for fixed but rather its type as a boolean,
3703     under the
3704     \emph on
3705     View
3706     \emph default
3707     button at the top, select
3708     \emph on
3709     Display Atom Values.
3710     \emph default
3711     )
3712     \end_layout
3713    
3714     \begin_layout Itemize
3715     Pick fixed with the right mouse button, and, in the small window that opens,
3716     delete the value
3717     \emph on
3718     FALSE
3719     \emph default
3720     , enter the value
3721     \emph on
3722     TRUE
3723     \emph default
3724     and select
3725     \emph on
3726     OK
3727     \emph default
3728     .
3729     \end_layout
3730    
3731     \begin_layout Itemize
3732     Now make v the current object by picking it in the left window of the
3733     \series bold
3734     Browser
3735     \series default
3736     .
3737     \end_layout
3738    
3739     \begin_layout Itemize
3740     Export v to the Solver again by selecting to Solver under the Export button.
3741     A window entitled Overspecified
3742     \begin_inset LatexCommand \index{Overspecified}
3743    
3744     \end_inset
3745    
3746     will appear listing the variables v.D, v.H_to_D_ratio and v.vessel_volume.
3747     Pick v.D and hit the OK button; ASCEND will reset its fixed flag to FALSE.
3748     \end_layout
3749    
3750     \begin_layout Itemize
3751     Finally, return to the
3752     \series bold
3753     Browser
3754     \series default
3755     window and select
3756     \emph on
3757     vessel_volume
3758     \emph default
3759     with the right mouse button.
3760     In the small window that appears type
3761     \emph on
3762     250
3763     \emph default
3764     in the left window,
3765     \emph on
3766     ft^3
3767     \emph default
3768     in the right, and hit the
3769     \emph on
3770     OK
3771     \emph default
3772     button.
3773     \end_layout
3774    
3775     \begin_layout Itemize
3776     Under the
3777     \emph on
3778     Execute
3779     \emph default
3780     button in the
3781     \series bold
3782     Solver
3783     \series default
3784     window, select
3785     \emph on
3786     Solve
3787     \emph default
3788     .
3789     \end_layout
3790    
3791     \begin_layout Standard
3792     Note the
3793     \series bold
3794     Solver
3795     \series default
3796     reports only 4 blocks for 6 equations.
3797     This time it has to solve some equations simultaneously.
3798     In the
3799     \series bold
3800     Solver
3801     \series default
3802     window, under the
3803     \emph on
3804     Display
3805     \emph default
3806     button, select the
3807     \emph on
3808     Incidence matrix
3809     \emph default
3810     tool.
3811     You will see that the first three equations must be solved together as
3812     a single block of equations.
3813     \end_layout
3814    
3815     \begin_layout Standard
3816     \begin_inset Marginal
3817     status collapsed
3818    
3819     \begin_layout Standard
3820     clearing all the fixed flags
3821     \end_layout
3822    
3823     \end_inset
3824    
3825     For a more complicated model you may wish to start over on the process of
3826     selecting which variables are fixed.
3827     You can set the fixed flags for all the variables in a problem to FALSE
3828     all at once -- without knowing which are currently set to TRUE.
3829     In the Browser window, under the Edit button, select the Run method tool.
3830     A window will open that displays a list of default methods that are automatical
3831     ly attached to every model in ASCEND.
3832     One is called ClearAll.
3833     Pick it and hit OK.
3834     All the fixed flags for the entire model will now be reset to FALSE.
3835     Can you think of a way to check if this is true? (Do you remember how to
3836     check which variables are currently fixed? Repeat that check and you should
3837     find no variables are on the list.)
3838     \end_layout
3839    
3840     \begin_layout Standard
3841     You might now want to play by changing what you calculate and fix.
3842     \end_layout
3843    
3844     \begin_layout Section
3845     Discussion
3846     \end_layout
3847    
3848     \begin_layout Standard
3849     You have just completed the creation and solving of a very small model in
3850     ASCEND.
3851     In doing so, you have been exposed to some interesting issues.
3852     How can we separate the concept of the model from how we intend to solve
3853     it? How do we make a model to be well-posed -- i.e., a model involving n
3854     equations in n unknowns -- so we can solve it? How should one handle the
3855     units for the variables in a modeling system? What we have shown you here
3856     is for a small model.
3857     We still need to show you how one can make a large model well-posed, for
3858     example.
3859     You will start to understand how one can do this in the next chapter.
3860     \end_layout
3861    
3862     \begin_layout Standard
3863     The next chapter is crucial for you to understand if you want to begin to
3864     understand how we approach good modeling practice.
3865     Please do continue with it.
3866     As it uses the vessel model, it would, of course, be best to continue with
3867     that chapter now.
3868     \end_layout
3869    
3870     \end_body
3871     \end_document

john.pye@anu.edu.au
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