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1 #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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