177:"Many important discoveries have been made when scientists commenced their work as if their theoretically postulated models of atoms, viruses, vitamins, hormones, and genes had actual, real world substantial existence. They proceeded as though each imaginary concept actually existed in precisely the form their theoretical speculation outlined; and, discarding any pretence of analogy, they proceeded with the view that the substantial, real world was exactly as they had theoretically described it. ... Consider the analogue model advanced to assist understanding of the behaviour of gases which suggests possible relationships between some theoretical activities of gas particles and some observable activities of billiard-balls. Achinstein (1964, p.332) reminds us that, despite thinking about gases in this useful way, "the physicist obviously supposes that molecules, not billiard balls, comprise gases" — Yeates (2004, pp.71, 73)
1290:, there is the question of how the physical/biological laws of the target system relate to the analogical models created by humans to represent the target system. We seem to assume that the process of constructing analogical models gives us access to the fundamental laws governing the target system. However strictly speaking we only have empirical knowledge of the laws that hold true for the analogical system, and if the time constant for the target system is larger than the life cycle of human being (as in the case of the geobiosphere) it is therefore very difficult for any single human to empirically verify the validity of the extension of the laws of their model to the target system in their lifetime.
164:
45:
1410:…). Similarity is implicated in this process because a successful, useful analogy depends upon there being some sort of similarity between the source domain and the target domain and because the perception of similarity is likely to play a major role in some of the key processes associated with analogical reasoning" (Vosniadou and Ortony, 1989, pp.6-7).
1169:, introduced by Henry M. Paynter in 1960. It is usual to use the force-voltage analogy (impedance analogy) with bond graphs, but it is not a requirement to do so. Likewise Trent used a different representation (linear graphs) and his representation has become associated with the force-current analogy (mobility analogy), but again this is not mandatory.
120:
Analogical models, also called "analog" or "analogue" models, seek the analogous systems that share properties with the target system as a means of representing the world. It is often practicable to construct source systems that are smaller and/or faster than the target system so that one can deduce
1073:
Maxwell's analogy was initially used merely to help explain electrical phenomena in more familiar mechanical terms. The work of
Firestone, Trent and others moved the field well beyond this, looking to represent systems of multiple energy domains as a single system. In particular, designers started
1273:
Examples are Vogel and Ewel who published 'An
Electrical Analog of a Trophic Pyramid' (1972, Chpt 11, pp. 105–121), Elmore and Sands (1949) who published circuits devised for research in nuclear physics and the study of fast electrical transients done under the Manhattan Project (however no
1164:
Many applications of dynamical models convert all energy domains in the system into an electrical circuit and then proceed to analyse the complete system in the electrical domain. There are, however, more generalised methods of representation. One such representation is through the use of
433:. In this analogy electrical impedance is made analogous to mechanical mobility (the inverse of mechanical impedance). Firestone's idea was to make analogous variables that are measured across an element, and make analogous variables that flow through an element. For instance, the
1437:"An analogue model describes specific relationships between selected components of the "original" by creating analogies with the relationships that are displayed by components in some other "secondary domain" of a totally different medium." (Yeates, 2004, p.72).
1261:
Electronic circuits were used to model and simulate engineering systems such as aeroplanes and nuclear power plants before digital computers became widely available with fast enough turn over times to be practically useful. Electronic circuit instruments called
356:
Dynamical analogies establish analogies between systems in different energy domains by means of comparison of the system dynamic equations. There are many ways such analogies can be built, but one of the most useful methods is to form analogies between pairs of
187:
used the flow of water to model economic systems (the target system); electronic circuits can be used to represent both physiological and ecological systems. When a model is run on either an analog or digital computer this is known as the process of
1172:
Some authors discourage the use of domain specific terminology for the sake of generalisation. For instance, because much of the theory of dynamical analogies arose from electrical theory the power conjugate variables are sometimes called
441:
variable current is the analogy of force. Firestone's analogy has the advantage of preserving the topology of element connections when converting between domains. A modified form of the through and across analogy was proposed in 1955 by
150:
these smaller/bigger, slower/faster systems are scaled up or down so that they match the functioning of the target system, and are therefore called analogs of the target system. Once the calibration has taken place, modellers speak of a
428:
Specifying power conjugate variables still does not result in a unique analogy, there are multiple ways the conjugates and analogies can be specified. A new analogy was proposed by Floyd A. Firestone in 1933 now known as the
408:
is the ratio of force and velocity. The concept of impedance can be extended to other domains, for instance in acoustics and fluid flow it is the ratio of pressure to rate of flow. In general, impedance is the ratio of an
225:
but does not preserve the network topology. The mobility analogy preserves the network topology but does not preserve the analogy between impedances. Both preserve the correct energy and power relationships by making
1147:
A widely used analogy in the thermal domain maps temperature difference as the effort variable and thermal power as the flow variable. Again, these are not power conjugate variables, and the ratio, known as
1097:
in electrical engineering and apply it to mechanical systems. The quality of filters required for radio applications could not be achieved with electrical components. Much better quality resonators (higher
1152:, is not really an analogy of either impedance or electrical resistance as far as energy flows are concerned. A compatible analogy could take temperature difference as the effort variable and
1245:
of an electric circuit attempts to explain circuitry intuitively in terms of plumbing, where water is analogous to the mobile sea of charge within metals, pressure difference is analogous to
1765:
825:
130:
of target system behaviour. Analog devices are therefore those in which may differ in substance or structure but share properties of dynamic behaviour (Truit and Rogers, p. 1-3).
365:. Doing so preserves the correct energy flow between domains, a useful feature when modelling a system as an integrated whole. Examples of systems that require unified modelling are
990:
875:
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1060:
1030:
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1136:, does not measure the rate of dissipation of energy so is not a true impedance. Where a compatible analogy is required, mmf can be used as the effort variable and
71:
are a method of representing a phenomenon of the world, often called the "target system" by another, more understandable or analysable system. They are also called
1723:
Colyvan, Mark and
Ginzburg, Lev R. (2010) "Analogical Thinking in Ecology: Looking Beyond Disciplinary Boundaries", The Quarterly Review of Biology, 85(2): 171–82.
1102:) could be made with mechanical parts but there was no equivalent filter theory in mechanical engineering. It was also necessary to have the mechanical parts, the
1976:
1225:) are entities (models, representations, etc.) that can be replaced, to fulfill the same function. When the entities in question are formally represented by
1074:
converting the mechanical parts of an electromechanical system to the electrical domain so that the whole system could be analyzed as an electrical circuit.
1181:
according to whether they are analogs of voltage or current respectively in the electrical domain. Likewise, the
Hamiltonian variables are sometimes called
1132:(φ) to electric current. However, mmf and φ are not power conjugate variables. The product of these is not in units of power and the ratio, known as
995:
There is a corresponding relationship for other analogies and sets of variables. The
Hamiltonian variables are also called the energy variables. The
1962:
1402:"There is general agreement that analogical reasoning involves the transfer of relational information from a domain that already exists in memory (…
134:
dynamical analogies establish the analogies between electrical, mechanical, acoustical, magnetic and electronic systems: Olson (1958), p. 2.
206:
Any number of systems could be used for mapping electrical phenomena to mechanical phenomena, but two principle systems are commonly used: the
2028:
1773:
1756:
1203:
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are equal to the power conjugate variables. The
Hamiltonian variables are so called because they are the variables which usually appear in
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227:
201:
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1106:, and the electrical components of the circuit analyzed as a complete system in order to predict the overall response of the filter.
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might then represent the arithmetic operations (addition, subtraction, multiplication, and division). Through the process of
1278:(1994) who published circuits devised to analogically model ecological-economic systems at many scales of the geobiosphere.
163:
828:
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between the primary system and its analog. Thus the behaviour of two systems can be determined by experimenting with one.
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79:
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A mechanical device can be used to represent mathematical calculations. For instance, the
Phillips Hydraulic Computer
2021:
1953:
1725:
304:
can be described by analogous equations on a geometrical basis, almost without regard to the physical details about
2106:
1760:, National Nuclear Energy Series, Manhattan Project Technical Section, Division V, Vol. 1, New York: McGraw-Hill.
123:
117:
system), in order "to illustrate some particular aspect (or clarify selected attributes) of the primary domain".
2017:
1945:
1694:
Technology for
Modelling: Electrical Analogies, Engineering Practice, and the Development of Analogue Computing
787:
454:
Comparison of various power conjugate analogies for electrical, mechanical, rotational, and fluid flow domains
38:
1211:
1779:
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is related to "same behavior": they take the same output sequence when submitted to the same input sequence.
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of a power conjugate variable with respect to a
Hamiltonian variable is a measure of energy. For instance,
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1082:, and a coherent presentation of this method was presented in a 1925 paper by Clifford A. Nickle.
214:. The impedance analogy maps force to voltage whereas the mobility analogy maps force to current.
2111:
1994:
1732:
1149:
757:
The
Hamiltonian variables, also called the energy variables, are those variables which when time-
316:
57:
49:
1035:
1005:
1388:"Mechanisms of Analogical Learning", pp.199-241, in Stella Vosniadou and Andrew Ortony (eds.),
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1949:
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helped popularise the use of dynamical analogies in the audio electronics field with his book
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1931:, Graduate Diploma in Arts (By Research) Dissertation, University of New South Wales, 2004.
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according to whether they are analogs of momentum or displacement in the mechanical domain.
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211:
1961:. G - Reference, Information and Interdisciplinary Subjects Series (illustrated ed.).
1955:
Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics
388:. This analogy became so widespread that sources of voltage are still today referred to as
2086:
2060:
2006:
1729:
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circuits having application to weapon technology were included for security reasons), and
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766:
443:
362:
291:
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variable that results. For this reason, the Maxwell analogy is often referred to as the
1927:
Yeates, Lindsay B. (2004), "Comparative Cognitive Processes", pp.40-76 in L.B. Yeates,
1850:
1840:
1275:
1140:(rate of change of magnetic flux) will then be the flow variable. This is known as the
1109:
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1383:
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265:
261:
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The process of analogical modelling has philosophical difficulties. As noted in the
1210:
containing resistances only, with voltage and current sources, can be replaced to a
1950:"Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics"
1780:"Lumped equivalent circuits of magnetic components: the gyrator-capacitor approach"
1320:
1266:
were used to speed up circuit construction time. However analog computers like the
1202:
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366:
171:
Many different instruments and systems can be used to create an analogical model.
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In the translational mechanical domain, the Hamiltonian variables are distance
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1093:, widely used these analogies in order to take the well -developed theory of
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332:
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1883:
Smith, Malcolm C. (2002) "Synthesis of mechanical networks: the inerter]",
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is the process of representing information about a particular subject (the
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A simple type of analogy is one that is based on shared properties; and
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139:
102:
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421:, although the concept of impedance was not conceived until 1886 by
1845:
Ecological and General Systems: and introduction to systems ecology
1743:
1642:
1201:
381:
305:
2075:
Stanford Encyclopedia of Philosophy entry on Models in Science
1078:
was a pioneer of this kind of modelling in his development of
60:
with an equivalent structure and behaviour (bottom), then, an
1921:
A Model Menagerie: Laboratory Studies about Living Systems
765:. The Hamiltonian variables in the electrical domain are
647:
Table of equivalents under the through and across system
1766:
Ecological Orbits: How Planets Move and Populations Grow
1270:
could also consist of gears and pulleys in calculation.
138:
For example, in analog electronic circuits, one can use
27:
Relation of types of systems with corresponding dynamics
335:
requires a similarity within a situation; for example,
1887:, vol. 47, iss. 10, pp. 1648–1662, October 2002.
1038:
1008:
952:
905:
837:
790:
437:
variable voltage is the analogy of velocity, and the
1446:
Ginzburg and Colyvan 2004; Colyvan and Ginzburg 2010
404:
is the ratio of voltage and current, so by analogy,
217:
The impedance analogy preserves the analogy between
1054:
1024:
984:
934:
869:
819:
396:which, in the Maxwell analogy, maps to mechanical
361:. That is, a pair of variables whose product is
132:
86:representations (see illustration) if they are
1681:, Springer Science & Business Media, 1999
1929:Thought Experimentation: A Cognitive Approach
8:
1825:Martinsen, Orjan G.; Grimnes, Sverre (2011)
1637:, Vol.31, No.4, (October 1964), pp.328-350.
247:might perform the mathematical operation of
1916:, John F. Rider Publishing, Inc., New York.
1801:A gravitational and electromagnetic analogy
1633:(1964), "Models, Analogies, and Theories",
1124:A common analogy of magnetic circuits maps
113:system) by another particular subject (the
323:arise that are the same as those found in
2036:
2022:"Introduction to Series-Parallel Duality"
1963:Rowman & Littlefield Publishers, Inc.
1045:
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1007:
953:
951:
906:
904:
838:
836:
820:{\displaystyle {\frac {d\lambda }{dt}}=v}
791:
789:
1392:, Cambridge: Cambridge University Press.
1249:, and water's flow rate is analogous to
1085:From the 1950s onward, manufacturers of
645:
452:
327:, albeit with different interpretations.
296:For example, the inverse-square laws of
162:
43:
1897:Taylor, John T.; Huang, Qiuting (1997)
1764:Ginzburg, Lev and Colyvan, Mark (2004)
1679:Electromechanical Sensors and Actuators
1367:
347:by using the concept of myriad myriads.
2080:Interdisciplinary Electrical Analogies
2002:
1992:
1885:IEEE Transactions on Automatic Control
1827:Bioimpedance and Bioelectricity Basics
1812:Signal And Image Processing Sourcebook
1784:IEEE Transactions on Power Electronics
153:one-to-one correspondence in behaviour
2029:University of California at Riverside
142:to represent an arithmetic quantity;
7:
1768:, Oxford University Press, New York.
1758:Electronics: Experimental Techniques
1374:Stanford Encyclopedia of Philosophy.
392:. The power conjugate of voltage is
380:who, in 1873, associated mechanical
376:The earliest such analogy is due to
167:The Mechanism of the Analogue Model.
1786:, vol. 8, iss. 2, pp. 97–103.
1406:…) to the domain to be explained (…
1390:Similarity and Analogical Reasoning
1288:Stanford Encyclopedia of Philosophy
985:{\displaystyle {\frac {dx}{dt}}=u.}
870:{\displaystyle {\frac {dq}{dt}}=i.}
467:Through and across analogy (Trent)
446:and is the modern understanding of
425:, some time after Maxwell's death.
345:number of grains of sand on a beach
1899:CRC Handbook of Electrical Filters
935:{\displaystyle {\frac {dp}{dt}}=F}
472:Effort or across power conjugates
25:
520:Flow or through power conjugates
1156:flow rate as the flow variable.
1065:are both expressions of energy.
2045:from the original on 2019-08-10
1982:from the original on 2016-03-05
1649:Mechatronics: An Introduction,
1476:Martinsen & Grimnes, p. 287
1316:General purpose analog computer
202:Mechanical–electrical analogies
1857:, 2nd ed., Van Nostrand, 1958
18:Structural analog (electronic)
1:
1120:Non-power-conjugate analogies
944:Newton's second law of motion
1847:, Colorado University Press.
1214:, to show the same behavior.
1193:Electronic circuit analogies
464:Mobility analogy (Firestone)
268:as a proxy for the study of
159:Creating an analogical model
1868:Regtien, Paul P. L. (2002)
1212:Thévenin equivalent circuit
461:Impedance analogy (Maxwell)
2128:
1914:Basics of analog computers
1709:RF Components and Circuits
1677:Busch-Vishniac, Ilene J.,
1662:Borutzky, Wolfgang (2009)
1557:Taylor & Huang, p. 378
1055:{\displaystyle \int u\,dp}
1025:{\displaystyle \int F\,dx}
829:Faraday's law of induction
199:
36:
29:
2018:Ellerman, David Patterson
1946:Ellerman, David Patterson
1647:Bishop, Robert H. (2005)
1509:Busch-Vishniac, pp. 18-20
1116:first published in 1943.
359:power conjugate variables
1912:Truit and Rogers (1960)
1901:, Boca Raton: CRC Press
1870:Sensors for Mechatronics
1778:Hamill, David C. (1993)
1664:Bond Graph Methodology,
1187:generalised displacement
230:of variables analogous.
39:Analogy (disambiguation)
30:Not to be confused with
1893:10.1109/TAC.2002.803532
1865:(first published 1943).
1707:Carr, Joseph J. (2002)
1282:Philosophical conundrum
1142:gyrator-capacitor model
256:Physiological analogies
1919:Vogel and Ewel (1972)
1810:Libbey, Robert (1994)
1215:
1056:
1026:
986:
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871:
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711:Mechanical rotational
321:differential equations
264:used the study of the
168:
144:operational amplifiers
136:
65:
1692:Care, Charles (2010)
1635:Philosophy of Science
1593:Busch-Vishniac, p. 19
1527:Busch-Vishniac, p. 21
1497:Busch-Vishniac, p. 19
1470:Busch-Vishniac, p. 20
1455:Busch-Vishniac, p. 18
1205:
1128:(mmf) to voltage and
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987:
937:
872:
822:
763:Hamiltonian mechanics
753:Hamiltonian variables
723:Moment of inertia (I)
228:power conjugate pairs
166:
47:
1428:Yeates (2004), p.73.
1419:Yeates (2004), p.71.
1223:functional analogues
1183:generalised momentum
1036:
1006:
950:
903:
835:
788:
717:Angular velocity (ω)
642:Table of equivalents
636:volumetric flow rate
406:mechanical impedance
402:Electrical impedance
223:mechanical impedance
219:electrical impedance
196:Mechanical analogies
52:diagram of a simple
37:For other uses, see
1855:Dynamical Analogies
1617:Borutzky, pp. 27-28
1536:Borutzky, pp. 27-28
1306:Conceptual metaphor
1134:magnetic reluctance
1126:magnetomotive force
1114:dynamical analogies
666:Energy dissipation
648:
455:
390:electromotive force
378:James Clerk Maxwell
352:Dynamical analogies
73:dynamical analogies
32:Analogical modeling
2085:2010-05-13 at the
2059:2019-08-10 at the
1965:pp. 237–268.
1749:Elmore, William C.
1728:2023-04-07 at the
1257:Analogue computers
1219:Functional analogs
1216:
1198:Functional analogs
1150:thermal resistance
1087:mechanical filters
1080:analogue computers
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720:Torsion spring (Îş)
691:Mechanical linear
646:
453:
448:through and across
317:population ecology
169:
91:isomorphic systems
66:
58:electrical network
50:mechanical network
2107:Scientific models
1923:, Addison-Wesley.
1872:, Elsevier, 2012
1829:, Academic Press
1797:Heaviside, Oliver
1792:10.1109/63.223957
1774:978-0-1980-3754-5
1711:, Oxford: Newnes
1631:Achinstein, Peter
1560:Carr, pp. 170–171
1243:hydraulic analogy
1237:Hydraulic analogy
1229:, the concept of
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419:impedance analogy
413:variable and the
371:audio electronics
241:hydraulic analogy
234:Hydraulic analogy
208:impedance analogy
69:Analogical models
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612:electric current
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431:mobility analogy
423:Oliver Heaviside
394:electric current
384:with electrical
302:electromagnetism
277:Formal analogies
245:water integrator
212:mobility analogy
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2047:. Retrieved
1984:. Retrieved
1954:
1928:
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1844:
1826:
1811:
1804:
1783:
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1663:
1648:
1634:
1624:Bibliography
1613:
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1484:
1460:
1451:
1442:
1433:
1424:
1415:
1407:
1403:
1398:
1389:
1379:
1370:
1321:Homomorphism
1287:
1285:
1272:
1260:
1240:
1230:
1222:
1218:
1217:
1207:
1186:
1182:
1178:
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1123:
1113:
1108:
1084:
1072:
1064:
994:
882:displacement
879:
775:flux linkage
756:
737:Pressure (p)
697:Velocity (u)
683:Inductor (L)
631:
622:
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607:
598:
589:
583:
577:
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544:
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483:
479:
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427:
414:
410:
375:
367:mechatronics
355:
216:
205:
182:
170:
152:
137:
133:
122:
119:
114:
110:
106:
100:
83:
80:open systems
77:
72:
68:
67:
61:
2013:(271 pages)
2003:|work=
1814:, Springer
1696:, Springer
1545:Care, p. 76
1356:Wind tunnel
1331:Isomorphism
1241:A fluid or
1227:black boxes
1167:bond graphs
1104:transducers
734:Volume flow
706:Damper (B)
677:Voltage (V)
674:Current (I)
671:Electrical
619:is velocity
298:gravitation
249:integration
148:calibration
103:analogizing
97:Explanation
2096:Categories
2063:(24 pages)
2049:2019-08-09
1986:2019-08-09
1878:0123944090
1835:0080568807
1820:0442308612
1702:1848829485
1687:038798495X
1672:1848828829
1657:1420037242
1651:CRC Press
1363:References
1089:, notably
896:) because
781:) because
731:Hydraulic
714:Torque (T)
700:Spring (K)
580:is voltage
337:Archimedes
282:"The same
190:simulation
2112:Semantics
2033:CiteSeerX
2005:ignored (
1995:cite book
1666:Springer
1208:black box
1040:∫
1010:∫
997:integrand
798:λ
694:Force (F)
339:used the
333:Recursion
325:mechanics
288:solutions
284:equations
270:awareness
128:knowledge
88:black box
54:resonator
2083:Archived
2057:Archived
2043:Archived
1977:Archived
1799:(1893) "
1726:Archived
1386:(1989),
1351:Paradigm
1346:Morphism
1336:Metaphor
1294:See also
1100:Q factor
890:momentum
703:Mass (M)
603:pressure
586:is force
398:velocity
210:and the
124:a priori
107:analogue
2102:Analogy
1863:1450867
1853:(1958)
1843:(1994)
1755:(1949)
1326:Inquiry
1301:Analogy
1247:voltage
1154:entropy
946:), and
831:), and
439:through
386:voltage
310:charges
140:voltage
64:for it.
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746:Valve
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411:effort
341:myriad
306:masses
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574:where
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512:, ω,
499:, ω,
382:force
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1874:ISBN
1859:OCLC
1831:ISBN
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1770:ISBN
1751:and
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1668:ISBN
1653:ISBN
1221:(or
1206:Any
1185:and
1177:and
1032:and
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740:Tank
415:flow
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308:and
300:and
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488:p
484:T
480:F
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312:.
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