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68 \end_header
69
70 \begin_body
71
72 \begin_layout Chapter
73 Defining Variables and Scaling Values
74 \begin_inset CommandInset label
75 LatexCommand label
76 name "cha:atoms"
77
78 \end_inset
79
80
81 \end_layout
82
83 \begin_layout Standard
84 \begin_inset Marginal
85 status collapsed
86
87 \begin_layout Plain Layout
88 the purpose of this chapter
89 \end_layout
90
91 \end_inset
92
93 By now you have probably read Chapter
94 \begin_inset space ~
95 \end_inset
96
97
98 \begin_inset CommandInset ref
99 LatexCommand vref
100 reference "cha:model1"
101
102 \end_inset
103
104 and seen an example of how to create a model using existing variable types
105 in ASCEND.
106 You found that variables of types area, length, mass, mass_density, and
107 volume were needed and that they could be found in the library
108 \family typewriter
109 atoms.a4l
110 \family default
111 .
112 You want to know how to generalize on that; how to use variables, constants,
113 and scaling values in your own models so that the models will be easier
114 to solve.
115 \end_layout
116
117 \begin_layout Standard
118 This chapter is meant to explain the following things:
119 \end_layout
120
121 \begin_layout Itemize
122 The "Big Picture" of how variables, constants, and scaling values relate
123 to the rest of the ASCEND IV language and to equations in particular.
124 We'll keep it simple here.
125 More precise explanations for the language purist can be found in our syntax
126 document **syntax.fm5**.
127 You do not need to read about the "Big Picture" in order to read and use
128 the other parts of this chapter, but you may find it helpful if you are
129 having trouble writing an equation
130 \begin_inset Index idx
131 status collapsed
132
133 \begin_layout Plain Layout
134 equation, writing
135 \end_layout
136
137 \end_inset
138
139 so that ASCEND will accept it.
140 \end_layout
141
142 \begin_layout Itemize
143 How to find the type of variable (or constant) you want.
144 We keep a mess of interesting
145 \family typewriter
146 ATOM
147 \family default
148 and
149 \family typewriter
150 CONSTANT
151 \family default
152 definitions in
153 \family typewriter
154 atoms.a4l
155 \family default
156 .
157 We provide tools to search in already loaded libraries to locate the type
158 you need.
159 \end_layout
160
161 \begin_layout Itemize
162 How to define a new type of variable when we do not have a predefined
163 \family typewriter
164 ATOM
165 \family default
166 or
167 \family typewriter
168 CONSTANT
169 \family default
170 that suits your needs.
171 It is very easy to define your own variable types by copying code into
172 an atoms library of your own from
173 \family typewriter
174 atoms.a4l
175 \family default
176 and then editing the copied definition.
177 \end_layout
178
179 \begin_layout Itemize
180 How to define a scaling variable to make your equations much easier to solve.
181 \end_layout
182
183 \begin_layout Section
184 The Big Picture: a taxonomy
185 \begin_inset Index idx
186 status collapsed
187
188 \begin_layout Plain Layout
189 taxonomy
190 \end_layout
191
192 \end_inset
193
194
195 \end_layout
196
197 \begin_layout Standard
198 As you read in Chapter
199 \begin_inset space ~
200 \end_inset
201
202
203 \begin_inset CommandInset ref
204 LatexCommand ref
205 reference "cha:model1"
206
207 \end_inset
208
209 , simulations are built from MODEL and ATOM definitions, and MODEL and ATOM
210 definitions are defined by creating types in an ASCEND language text file
211 that you load into the ASCEND system.
212 Figure
213 \begin_inset CommandInset ref
214 LatexCommand ref
215 reference "fig:atoms.taxonomy"
216
217 \end_inset
218
219
220 \noun off
221 shows the types of objects that can be defined.
222 You can see there are many more types than simply real variables used for
223 writing equations.
224 Some of these types can also be used in equations.
225 You also see that there are three kinds of equations, not simply real relations.
226 Throughout our documentation we call real relations simply "relations"
227 because that is the kind of equation most people are interested in most
228 of the time.
229 Notice that "scaling values" do not appear in this diagram.
230 We will cover scaling values at the end of this The major features of this
231 diagram are:
232 \end_layout
233
234 \begin_layout Standard
235 \begin_inset Float figure
236 wide false
237 sideways false
238 status open
239
240 \begin_layout Plain Layout
241 \align center
242
243 \noun off
244 \begin_inset Graphics
245 filename howto-atomsFig1.eps
246 scale 90
247
248 \end_inset
249
250
251 \end_layout
252
253 \begin_layout Plain Layout
254 \begin_inset Caption Standard
255
256 \begin_layout Plain Layout
257 \begin_inset CommandInset label
258 LatexCommand label
259 name "fig:atoms.taxonomy"
260
261 \end_inset
262
263 The big picture: how to think about variables
264 \end_layout
265
266 \end_inset
267
268
269 \end_layout
270
271 \end_inset
272
273
274 \end_layout
275
276 \begin_layout Paragraph
277
278 \noun off
279 \begin_inset Index idx
280 status collapsed
281
282 \begin_layout Plain Layout
283 atom
284 \end_layout
285
286 \end_inset
287
288
289 \noun default
290 ATOM
291 \end_layout
292
293 \begin_layout Itemize
294 Any variable quantity for use in relations, logical relations, or when statement
295 s or other computations.
296 These come in the usual programming language flavors real, boolean, symbol,
297 integer.
298 Not all kinds of atoms can be used in all kinds of equations, as we shall
299 explain when describing relations in a little bit.
300 Atoms may be assigned values many times interactively, with the Script
301 ASSIGN statement, with the METHOD := assignment operator, or by an ASCEND
302 client such as a solver.
303 \end_layout
304
305 \begin_layout Standard
306 An ATOM may have attributes other than its value, such as .fixed in solver_var,
307 but these attributes are not atoms.
308 They are subatomic particles and cannot be used in equations.
309 These attributes are interpretable by ASCEND clients, and assignable by
310 the user in the same ways that the user assigns atom values.
311 \end_layout
312
313 \begin_layout Standard
314 Each subatomic particle instance belongs to exactly one atom instance (one
315 variable in your compiled simulation).
316 This contrasts with an atom instance which can be shared among several
317 models by passing the atom instance from one model into another or by creating
318 aliases for it.
319 \end_layout
320
321 \begin_layout Paragraph
322 \begin_inset Index idx
323 status collapsed
324
325 \begin_layout Plain Layout
326 constant
327 \end_layout
328
329 \end_inset
330
331 CONSTANT
332 \end_layout
333
334 \begin_layout Itemize
335 Constants are "variables" that can be assigned no more than once.
336 By convention, all constant types in atoms.a4l have names that end in _constant
337 so that they are not easily confused with atoms.
338 A constant gets a values from the DEFAULT portion of its type definition,
339 by an interactive assignment, or by an assignment in the a model which
340 uses the :== assignment operator.
341 Constants cannot be assigned in a METHOD, nor can they be assigned with
342 the := operator.
343 \end_layout
344
345 \begin_layout Standard
346 Integer and symbol constants can appear as members of sets or as subscripts
347 of arrays.
348 Integer, boolean, and symbol constants can be used to control SELECT statements
349 which determine your simulation's structure at compile-time or to control
350 SWITCH and WHEN behavior during problem solving .
351 \end_layout
352
353 \begin_layout Paragraph
354 \begin_inset Index idx
355 status collapsed
356
357 \begin_layout Plain Layout
358 set
359 \end_layout
360
361 \end_inset
362
363 set
364 \end_layout
365
366 \begin_layout Itemize
367 Sets are unordered lists of either integer or symbol constants.
368 A set is assigned its value exactly once.
369 The user interface always presents a set in sorted order, but this is for
370 convenience only.
371 Sets are useful for defining an array range or for writing indexed relations.
372 More about sets and their use can be found in **syntax.fm5**.
373 \end_layout
374
375 \begin_layout Paragraph
376 \begin_inset Index idx
377 status collapsed
378
379 \begin_layout Plain Layout
380 relationship
381 \end_layout
382
383 \end_inset
384
385 relationships
386 \end_layout
387
388 \begin_layout Itemize
389 Relations and logical relations allow you to state
390 \begin_inset Index idx
391 status collapsed
392
393 \begin_layout Plain Layout
394 equalities
395 \end_layout
396
397 \end_inset
398
399 equalities and
400 \begin_inset Index idx
401 status collapsed
402
403 \begin_layout Plain Layout
404 inequalitites
405 \end_layout
406
407 \end_inset
408
409 inequalities among the variables and constants in you models.
410 WHEN statements allow you to state relationships among the models and equations
411 which depend on the values of variables in those models.
412 Sets and symbols are not allowed in real or logical relations except when
413 used as array subscripts.
414 \end_layout
415
416 \begin_layout Standard
417 Real
418 \begin_inset Index idx
419 status collapsed
420
421 \begin_layout Plain Layout
422 real
423 \end_layout
424
425 \end_inset
426
427
428 \begin_inset Index idx
429 status collapsed
430
431 \begin_layout Plain Layout
432 relation, real
433 \end_layout
434
435 \end_inset
436
437 relations relate the values of real atoms, real constants, and integer constants.
438 Real relations cannot contain boolean constants and atoms, nor can they
439 contain integer atoms.
440
441 \end_layout
442
443 \begin_layout Standard
444 Logical
445 \begin_inset Index idx
446 status collapsed
447
448 \begin_layout Plain Layout
449 logical
450 \end_layout
451
452 \end_inset
453
454 relations
455 \begin_inset Index idx
456 status collapsed
457
458 \begin_layout Plain Layout
459 logical relation
460 \end_layout
461
462 \end_inset
463
464 relate the values of boolean atoms and boolean constants.
465 The
466 \family typewriter
467 SATISFIED
468 \family default
469
470 \begin_inset Index idx
471 status collapsed
472
473 \begin_layout Plain Layout
474 SATISFIED
475 \end_layout
476
477 \end_inset
478
479 operator makes it possible to include real relations in a logical relation.
480 Neither integer atoms and constants nor real atoms and constants are allowed
481 in logical relations.
482 If you find yourself trying to write an equation with integer atoms, you
483 are really creating a conditional model for which you should use the WHEN
484 statement instead.
485 See **conditional modeling** to learn about how ASCEND represents this
486 kind of mathematical model.
487 There are also a real variable types, solver_integer and solver_binary,
488 which are used to formulate equations when the solver is expected to initially
489 treat the variable as a real value but drive it to an integer or 0-1 value
490 at the solution.
491 The integer programming features of ASCEND are described **elsewhere**.
492 \end_layout
493
494 \begin_layout Standard
495 Like atoms, real and logical relations may have attributes, subatomic particles
496 for use by ASCEND clients and users.
497 The name of a relation can be used in writing logical relations and WHEN
498 statements.
499
500 \end_layout
501
502 \begin_layout Standard
503 WHEN statements are outside the scope of this chapter; please see **conditional
504 modeling** or **syntax.fm5** for the details.
505 \end_layout
506
507 \begin_layout Paragraph
508 \begin_inset Index idx
509 status collapsed
510
511 \begin_layout Plain Layout
512 model
513 \end_layout
514
515 \end_inset
516
517
518 \family typewriter
519 MODEL
520 \end_layout
521
522 \begin_layout Itemize
523 A model is simply a container for a collection of atoms, constants, sets,
524 relations, logical relations, when statements, and arrays of any of these.
525 The container also specifies some of the methods that can be used to manipulate
526 its contents.
527 Compiling a model creates an instance of it-- a simulation
528 \begin_inset Index idx
529 status collapsed
530
531 \begin_layout Plain Layout
532 simulation
533 \end_layout
534
535 \end_inset
536
537 .
538 \end_layout
539
540 \begin_layout Paragraph
541
542 \family typewriter
543 SOLVER_VAR
544 \end_layout
545
546 \begin_layout Itemize
547 The real atom type
548 \family typewriter
549 solver_var
550 \family default
551 is the type from which all real variables that you want the system to solve
552 for must spring.
553 If you define a real variable using a type which is not a refinement of
554
555 \family typewriter
556 solver_var
557 \family default
558 , all solvers will treat that variable as an a scaling value or other given
559 constant rather than as a variable.
560
561 \end_layout
562
563 \begin_layout Standard
564 Solver_vars have a number of subatomic attributes (
565 \family typewriter
566 upper_bound
567 \family default
568 ,
569 \family typewriter
570 lower_bound
571 \family default
572 , and so forth) that help solvers find the solution of your model.
573 ATOM definitions specify appropriate default values for these attributes
574 that depend on the expected applications of the atom.
575 These attribute values can (and should) be modified by methods in the final
576 application model where the most accurate problem information is available.
577 \end_layout
578
579 \begin_layout Paragraph
580 Scaling
581 \begin_inset Index idx
582 status collapsed
583
584 \begin_layout Plain Layout
585 scaling
586 \end_layout
587
588 \end_inset
589
590 value
591 \end_layout
592
593 \begin_layout Itemize
594 A real that is not a member of the
595 \family typewriter
596 solver_var
597 \family default
598 family is ignored by the solver.
599 Numerical solvers for problems with many equations in many variables work
600 better if the error computed for each equation (before the system is solved)
601 is of approximately size 1.0.
602 This is most critical when you are starting to solve a new problem at values
603 far, far away from the solution.
604 When the error of one equation is much larger than the errors in the others,
605 that error will skew the behavior of most numerical solvers and will cause
606 poor performance.
607
608 \end_layout
609
610 \begin_layout Standard
611 This is one of the many reasons that scientists and engineers work with
612 dimensionless models
613 \begin_inset Index idx
614 status collapsed
615
616 \begin_layout Plain Layout
617 dimensionless models
618 \end_layout
619
620 \end_inset
621
622 : the process of scaling the equations into dimensionless form has the effect
623 of making the error of each equation roughly the same size even far away
624 from the solution.
625 It is sometimes easiest to obtain a dimensionless equation by writing the
626 equation in its dimensional form using natural variables and then dividing
627 both sides by an appropriate scaling value.
628 We will see how to define an atom for scaling purposes in the last part
629 of this chapter.
630 \end_layout
631
632 \begin_layout Section
633 How to find the right variable type
634 \begin_inset Index idx
635 status collapsed
636
637 \begin_layout Plain Layout
638 type, variable
639 \end_layout
640
641 \end_inset
642
643
644 \end_layout
645
646 \begin_layout Standard
647 The type of real atom you want to use depends first on the dimensionality
648 (length, mass/time, etc.) needed and then on the application in which the
649 atom is going to be used.
650 For example, if you are modeling a moving car and you want an atom type
651 to describe the car's speed, then you need to find an atom with dimensionality
652 length/time or in ASCEND terms L/T.
653 There may be two or three types with this dimensionality, possibly including
654 real_constants, a real scaling value, and an atom derived from solver_var.
655 \end_layout
656
657 \begin_layout Standard
658 \begin_inset Marginal
659 status collapsed
660
661 \begin_layout Plain Layout
662 Load atoms.a4l
663 \end_layout
664
665 \end_inset
666
667 The first step to finding the variable type needed is to make sure that
668 atoms.a4l is loaded in your Library window from
669 \family typewriter
670 ascend4/models/atoms.a4l
671 \family default
672 .
673 \end_layout
674
675 \begin_layout Standard
676 \begin_inset Marginal
677 status collapsed
678
679 \begin_layout Plain Layout
680 Find an ATOM or CONSTANT by units
681 \end_layout
682
683 \end_inset
684
685 The next step is to open the "ATOM by units" dialog found in the Library
686 window's Find menu.
687 This dialog asks for the units of the real variable type you want.
688 For our example, speed, you would enter "feet/second," "furlongs/fortnight,"
689 "meter^3/second/ft^2" or any other combination of units that corresponds
690 to the dimensionality L/T.
691
692 \end_layout
693
694 \begin_layout Standard
695 If the system is able to deduce the dimensionality of the units you have
696 entered, it will return a list of all the currently loaded ATOM and CONSTANT
697 definitions with matching dimensions.
698 It may fail to understand the units, in which case you should try the correspon
699 ding SI units.
700 If it understands the units but there are no matching atoms or constants,
701 you will be duly informed.
702 If there is no atom that meets your needs, you should create one as outlined
703 in **the next section**.
704 \end_layout
705
706 \begin_layout Standard
707 \begin_inset Marginal
708 status collapsed
709
710 \begin_layout Plain Layout
711 Selecting the right type
712 \end_layout
713
714 \end_inset
715
716 The resulting list of types includes a Code button which will display the
717 definition of any of the types listed once you select (highlight) that
718 type with the mouse.
719 Usually you will need to examine several of the alternatives to see which
720 one is most appropriate to the physics and mathematics of your problem.
721 Compare the default, bounds, and nominal values defined to those you need.
722 Check whether the type you are looking at is a
723 \family typewriter
724 CONSTANT
725 \family default
726 or an
727 \family typewriter
728 ATOM
729 \family default
730 .
731
732 \end_layout
733
734 \begin_layout Standard
735 You now know the name of the variable type you need, or you know that you
736 must create a new one to suit your needs.
737 \end_layout
738
739 \begin_layout Section
740 How to define a new type of variable
741 \begin_inset Index idx
742 status collapsed
743
744 \begin_layout Plain Layout
745 type, variable
746 \end_layout
747
748 \end_inset
749
750
751 \begin_inset CommandInset label
752 LatexCommand label
753 name "ssec:atoms.newVarType"
754
755 \end_inset
756
757
758 \end_layout
759
760 \begin_layout Standard
761 In this section we will give examples of defining the atom and constant
762 types as well as outline a few exceptional situations when you should NOT
763 define a new type.
764 More examples can be found and copied from
765 \family typewriter
766 atoms.a4l
767 \family default
768 .
769 You should define your new atoms in your personal atoms library.
770
771 \end_layout
772
773 \begin_layout Standard
774 \begin_inset Marginal
775 status collapsed
776
777 \begin_layout Plain Layout
778 Saving customized variable types
779 \end_layout
780
781 \end_inset
782
783 The user data file
784 \family typewriter
785 ~
786 \backslash
787 ascdata
788 \backslash
789 myatoms.a4l
790 \family default
791 is the normal location for a personal
792 \begin_inset Index idx
793 status collapsed
794
795 \begin_layout Plain Layout
796 library, personal
797 \end_layout
798
799 \end_inset
800
801 library.
802 This file contains the following three lines and then the
803 \family typewriter
804 ATOM
805 \family default
806 and
807 \family typewriter
808 CONSTANT
809 \family default
810 definitions you create.
811 \end_layout
812
813 \begin_layout LyX-Code
814 REQUIRE "atoms.a4l"; (* loads our atoms first *)
815 \end_layout
816
817 \begin_layout LyX-Code
818 PROVIDE "myatoms.a4l"; (* registers your library *)
819 \end_layout
820
821 \begin_layout LyX-Code
822 (* Custom atoms created by <insert your name here> *)
823 \end_layout
824
825 \begin_layout Standard
826 If you develop an interesting set of atoms for some problem domain outside
827 chemical engineering thermodynamics, please consider mailing it to us through
828 our web page.
829
830 \end_layout
831
832 \begin_layout Standard
833 The user data directory
834 \family typewriter
835 ~/
836 \begin_inset Index idx
837 status collapsed
838
839 \begin_layout Plain Layout
840 ascdata
841 \end_layout
842
843 \end_inset
844
845 ascdata
846 \family default
847 may have a different name if you are running under Windows and do not have
848 the environment variable HOME
849 \begin_inset Index idx
850 status collapsed
851
852 \begin_layout Plain Layout
853 HOME
854 \end_layout
855
856 \end_inset
857
858 defined.
859 It may be something like C:
860 \backslash
861 ascdata or
862 \backslash
863 WINNT
864 \backslash
865 Profiles
866 \backslash
867 Your Name
868 \backslash
869 ascdata.
870 When ASCEND is started, it prints out the name of this directory.
871 \end_layout
872
873 \begin_layout Standard
874 When you write a
875 \family typewriter
876 MODEL
877 \family default
878 which depends on the definition of your new atoms, do not forget to add
879 the statement
880 \end_layout
881
882 \begin_layout LyX-Code
883 REQUIRE "myatoms.a4l";
884 \end_layout
885
886 \begin_layout Standard
887 at the very top of your model file so that your atoms will be loaded before
888 your model definitions try to use them.
889 \end_layout
890
891 \begin_layout Subsection
892 A new real variable for solver use
893 \end_layout
894
895 \begin_layout Standard
896 Suppose you need an atom with units {dollar/ft^2/year} for some equation
897 relating amortized construction costs to building size.
898 Maybe this example is a bit far fetched, but it is a safe bet that our
899 library is not going to have an atom or a constant for these units.
900 Here is the standard incantation for defining a new variable type based
901 on
902 \family typewriter
903 solver_var
904 \family default
905 .
906 ASCEND allows a few permutations on this incantation, but they are of no
907 practical value.
908 The parts of this incantation that are in italics should be changed to
909 match your needs.
910 You can skip the comments, but you
911 \emph on
912 must
913 \emph default
914 include the units of the default on the bounds and nominal.
915 \end_layout
916
917 \begin_layout LyX-Code
918 ATOM amortized_area_cost
919 \end_layout
920
921 \begin_layout LyX-Code
922 REFINES solver_var DEFAULT 3.0 {dollar/ft^2/year};
923 \end_layout
924
925 \begin_layout LyX-Code
926 lower_bound := 0 {dollar/ft^2/year};
927 \end_layout
928
929 \begin_layout LyX-Code
930 (* minimum value *)
931 \end_layout
932
933 \begin_layout LyX-Code
934 upper_bound := 10000 {dollar/ft^2/year};
935 \end_layout
936
937 \begin_layout LyX-Code
938 (* maximum value for any sane application *)
939 \end_layout
940
941 \begin_layout LyX-Code
942 nominal := 10 {dollar/ft^2/year};
943 \end_layout
944
945 \begin_layout LyX-Code
946 (* expected size for all reasonable applications*)
947 \end_layout
948
949 \begin_layout LyX-Code
950 END amortized_area_cost;
951 \end_layout
952
953 \begin_layout Standard
954 In picking the name of your atom, remember that names should be as self-explanat
955 ory as possible.
956 Also avoid choosing a name that ends in _constant (as this is conventionally
957 applied only to CONSTANT
958 \begin_inset Index idx
959 status collapsed
960
961 \begin_layout Plain Layout
962 CONSTANT
963 \end_layout
964
965 \end_inset
966
967 definitions) or _parameter.
968 Parameter is an extremely ambiguous and therefore useless word.
969 Also remember that the role a variable plays in solving a set of equations
970 depends on how the solver being applied interprets .fixed and other attributes
971 of the variable.
972 \end_layout
973
974 \begin_layout Standard
975 \begin_inset Marginal
976 status collapsed
977
978 \begin_layout Plain Layout
979 Exceptions
980 \end_layout
981
982 \end_inset
983
984 If an atom type matches all but one of the attributes you need for your
985 problem, say for example the
986 \family typewriter
987 upper_bound
988 \family default
989 is way too high, use the existing variable type and reassign the bound
990 to a more sensible value in the
991 \family typewriter
992 default_self
993 \family default
994 method of the model where the variable is created.
995 Having a dozen atoms defined for the same units gets confusing in short
996 order to anyone you might share your models with.
997 \end_layout
998
999 \begin_layout Standard
1000 The exception to the exception (yes, there always seems to be one of those)
1001 is the case of a
1002 \family typewriter
1003 lower_bound
1004 \family default
1005 set at zero.
1006 Usually a
1007 \family typewriter
1008 lower_bound
1009 \family default
1010 of zero indicates that there is something inherently positive about variables
1011 of that type.
1012 Variables with a bound of this type should not have these physical bounds
1013 expanded in an application.
1014 Another example of this type of bound is the
1015 \family typewriter
1016 upper_bound
1017 \family default
1018 1.0 on the type fraction.
1019 \end_layout
1020
1021 \begin_layout Standard
1022 For example, negative temperature just is not sensible for most physical
1023 systems.
1024 ASCEND defines a temperature atom for use in equations involving the absolute
1025 temperature.
1026 On the other hand, a temperature difference, delta T, is frequently negative
1027 so a separate atom is defined.
1028 Anyone receiving a model written using the two types of atoms, which both
1029 have units of {Kelvin}, can easily tell which variables might legitimately
1030 take on negative values by noting whether the variable is defined as a
1031 temperature or a delta_temperature.
1032 \end_layout
1033
1034 \begin_layout Subsection
1035 A new real constant
1036 \begin_inset Index idx
1037 status collapsed
1038
1039 \begin_layout Plain Layout
1040 real constant
1041 \end_layout
1042
1043 \end_inset
1044
1045
1046 \begin_inset Index idx
1047 status collapsed
1048
1049 \begin_layout Plain Layout
1050 constant, real
1051 \end_layout
1052
1053 \end_inset
1054
1055 type
1056 \end_layout
1057
1058 \begin_layout Standard
1059 Real constants which do not have a default value are usually needed only
1060 in libraries of reusable models, such as
1061 \family typewriter
1062 components.a4l
1063 \family default
1064 , where the values depend on the end-user's selection from alternatives
1065 in a database.
1066 The standard incantation to define a new real constant type is:
1067 \end_layout
1068
1069 \begin_layout LyX-Code
1070 CONSTANT
1071 \shape italic
1072 critical_pressure_constant
1073 \end_layout
1074
1075 \begin_layout LyX-Code
1076 REFINES real_constant DIMENSION
1077 \shape italic
1078 M/L/T^2
1079 \shape default
1080 ;
1081 \end_layout
1082
1083 \begin_layout Standard
1084 Here again, the italic parts of this incantation should be redefined for
1085 your purpose.
1086 \end_layout
1087
1088 \begin_layout Standard
1089 \begin_inset Marginal
1090 status collapsed
1091
1092 \begin_layout Plain Layout
1093 Universal exceptions and unit conversions
1094 \end_layout
1095
1096 \end_inset
1097
1098 It is wasteful to define a
1099 \family typewriter
1100 CONSTANT
1101 \family default
1102 type and a compiled object to represent a universal
1103 \begin_inset Index idx
1104 status collapsed
1105
1106 \begin_layout Plain Layout
1107 universal constant
1108 \end_layout
1109
1110 \end_inset
1111
1112
1113 \begin_inset Index idx
1114 status collapsed
1115
1116 \begin_layout Plain Layout
1117 constant, universal
1118 \end_layout
1119
1120 \end_inset
1121
1122 constant.
1123 For example, the thermodynamic gas constant, R = 8.314...
1124 {J/mole/K}, is frequently needed in modeling chemical systems.
1125 The SI value of R does not vary with its application.
1126 Neither does the value of
1127 \begin_inset Index idx
1128 status collapsed
1129
1130 \begin_layout Plain Layout
1131 pi
1132 \end_layout
1133
1134 \end_inset
1135
1136
1137 \begin_inset Formula $\pi$
1138 \end_inset
1139
1140 .
1141 Numeric constants of this sort are better represented as a numeric coefficient
1142 and an appropriately defined unit conversion.
1143 Consider the
1144 \begin_inset Index idx
1145 status collapsed
1146
1147 \begin_layout Plain Layout
1148 ideal gas law
1149 \end_layout
1150
1151 \end_inset
1152
1153 ideal gas law, PV = NRT and the ASCEND unit conversion {GAS_C} which appears
1154 in the library ascend4/models/measures.a4l.
1155 This equation should be written:
1156 \end_layout
1157
1158 \begin_layout LyX-Code
1159 P * V = n * 1.0{GAS_C} * T;
1160 \end_layout
1161
1162 \begin_layout Standard
1163 Similarly, area = pi*r^2 should be written
1164 \end_layout
1165
1166 \begin_layout LyX-Code
1167 area = 1{PI} * r^2;
1168 \end_layout
1169
1170 \begin_layout Standard
1171 The coefficient 1 of
1172 \family typewriter
1173 {GAS_C}
1174 \family default
1175 and {PI} in these equations takes of the dimensionality of and is multiplied
1176 by the conversion factor implied by the
1177 \family typewriter
1178 UNITS
1179 \family default
1180 definition for the units.
1181 If we check
1182 \family typewriter
1183 measures.a4l
1184 \family default
1185 , we find the definition of PI is simply {3.14159...} and the definition of
1186
1187 \family typewriter
1188 GAS_C
1189 \family default
1190 is {8.314...
1191 J/mole/K} as we ought to expect.
1192 \end_layout
1193
1194 \begin_layout Standard
1195 For historical reasons there are a few universal constant definitions in
1196
1197 \family typewriter
1198 atoms.a4l
1199 \family default
1200 .
1201 New modelers should not use them; they are only provided to support outdated
1202 models that no one has yet taken the time to update.
1203 \end_layout
1204
1205 \begin_layout Subsection
1206 New types for integers, symbols, and booleans
1207 \end_layout
1208
1209 \begin_layout Standard
1210 The syntax for
1211 \family typewriter
1212 ATOM
1213 \family default
1214 and
1215 \family typewriter
1216 CONSTANT
1217 \family default
1218 definitions of the non-real types is the same as for real number types,
1219 except that units are not involved.
1220 Take your best guess based on the examples above, and you will get it right.
1221 If even that is too hard, more details are given in **syntax.fm5**.
1222 \end_layout
1223
1224 \begin_layout Section
1225 How to define a
1226 \begin_inset Index idx
1227 status collapsed
1228
1229 \begin_layout Plain Layout
1230 scaling
1231 \end_layout
1232
1233 \end_inset
1234
1235 scaling variable
1236 \end_layout
1237
1238 \begin_layout Standard
1239 A scaling variable
1240 \family typewriter
1241 ATOM
1242 \family default
1243 is defined with a name that ends in _scale as follows.
1244 Note that this
1245 \family typewriter
1246 ATOM
1247 \family default
1248 does not refine
1249 \family typewriter
1250 solver_var
1251 \family default
1252 , so solvers will not try to change variables of this type during the solution
1253 process.
1254 \end_layout
1255
1256 \begin_layout LyX-Code
1257 ATOM distance_scale REFINES real DEFAULT 1.0{meter};
1258 \end_layout
1259
1260 \begin_layout LyX-Code
1261 END distance_scale;
1262 \end_layout
1263
1264 \begin_layout Standard
1265 \begin_inset Marginal
1266 status collapsed
1267
1268 \begin_layout Plain Layout
1269 ASCEND cannot do it all for you
1270 \end_layout
1271
1272 \end_inset
1273
1274 ASCEND uses a combination of symbolic and numerical techniques to create
1275 and solve mathematical problems.
1276 Once you get the problem close to the solution, ASCEND can internally compute
1277 its own scaling values for relations, known elsewhere as "relation nominals
1278 \begin_inset Index idx
1279 status collapsed
1280
1281 \begin_layout Plain Layout
1282 nominals
1283 \end_layout
1284
1285 \end_inset
1286
1287 ,
1288 \begin_inset Quotes erd
1289 \end_inset
1290
1291 assuming you have set good values for the .nominal attribute of all the
1292 variables.
1293 It does this by computing the largest additive term in each equation.
1294 The absolute value of this term is a very good scaling value.
1295 \end_layout
1296
1297 \begin_layout Standard
1298 This internal scaling works quite well, but not when the problem is very
1299 far away from the solution so that the largest additive terms computed
1300 are not at all representative of the physical situation being modeled.
1301 The
1302 \family typewriter
1303 scale_self
1304 \family default
1305
1306 \begin_inset Index idx
1307 status collapsed
1308
1309 \begin_layout Plain Layout
1310 scale
1311 \begin_inset ERT
1312 status collapsed
1313
1314 \begin_layout Plain Layout
1315
1316
1317 \backslash
1318 _
1319 \end_layout
1320
1321 \end_inset
1322
1323 self
1324 \end_layout
1325
1326 \end_inset
1327
1328 method, which should be written for every model as described in Section
1329 \begin_inset space ~
1330 \end_inset
1331
1332
1333 \begin_inset CommandInset ref
1334 LatexCommand ref
1335 reference "sssec:methods.scaleself"
1336
1337 \end_inset
1338
1339 of Chapter
1340 \noun off
1341
1342 \begin_inset space ~
1343 \end_inset
1344
1345
1346 \begin_inset CommandInset ref
1347 LatexCommand vref
1348 reference "cha:methods"
1349
1350 \end_inset
1351
1352 should set the equation scaling values you have defined in a
1353 \family typewriter
1354 \noun default
1355 MODEL
1356 \family default
1357 \noun off
1358 based on the best available information.
1359 In a chemical engineering flowsheeting problem, for example, information
1360 about a key process material flow should be propagated throughout the process
1361 flowsheet to scale all the other flows, material balance equations, and
1362 energy balance equations.
1363 \end_layout
1364
1365 \begin_layout Standard
1366 \begin_inset Marginal
1367 status collapsed
1368
1369 \begin_layout Plain Layout
1370 Scaling atom default value
1371 \end_layout
1372
1373 \end_inset
1374
1375 The
1376 \begin_inset Index idx
1377 status collapsed
1378
1379 \begin_layout Plain Layout
1380 default value
1381 \end_layout
1382
1383 \end_inset
1384
1385 default value for any scaling atom should always be 1.0 in appropriate SI
1386 units, so that the scaling will have no effect until you assign a problem
1387 specific value.
1388 Multiplying or dividing both sides of an equation by 1.0 obviously will
1389 not change the mathematical behavior, but you do not want to change the
1390 behavior arbitrarily either-- you want to change it based on problem informatio
1391 n that is not contained in your
1392 \family typewriter
1393 myatoms.a4l
1394 \family default
1395 file.
1396 \end_layout
1397
1398 \end_body
1399 \end_document

john.pye@anu.edu.au
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