QUERY Meaning of Stock/Level

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""Jay Forrest"" <systems@jayf
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QUERY Meaning of Stock/Level

Post by ""Jay Forrest"" <systems@jayf »

Posted by ""Jay Forrest"" <systems@jayforrest.com>

While following this thread I struggled with the feeling that there was a
difference between models that use soft variables to support exploration of
relatively concrete issues and topics and models that are specifically
concerned with the nature and significance of the soft variable. The former
feels more rational and verifiable, while the latter raises concerns. In
additon, the chaining of soft variables or converging impacts of multiple
soft variables to a node in a quantitative model strikes me as posing a
difficult challenge for both formulation and validation. Jean-Jacques' logic
of striving to make the soft variable dependent on hard variables strikes me
as an appropriate ambition.

Jay Forrest
Posted by ""Jay Forrest"" <systems@jayforrest.com>
posting date Tue, 15 Apr 2008 08:45:17 -0500
_______________________________________________
""Ingram,Allan E - PFR-6"" <a
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QUERY Meaning of Stock/Level

Post by ""Ingram,Allan E - PFR-6"" <a »

Posted by ""Ingram,Allan E - PFR-6"" <aeingram1@bpa.gov>

The example of ratios describing customer preference for new vehicles
presented by Jean-Jacques Laublé’ appeals to me. His modeling allows
examination of his business with varying degrees of new vehicle
preference. Formal or informal customer surveys provide the objective
basis for establishing the business impact of customer preference. This
approach creates a clear connection between customer preference and
business performance that invites regular updates from experience.

I view subjective variables as best modeled by dimensionless weighting
factors affecting efficiency or performance variables or by modifying
delays in information flows. I am uncomfortable creating subjective
stocks with units that influence physical or financial flows.

My discomfort is focused on the impact of subjective variables within
the structure of SD models. SD modeling provides structures that help
us understand how pre-existing mental models lead us astray. For me,
whenever exogenously subjective stocks are put in a stock/flow
structure, they are likely to impose an unverified mental model. Are
there suggestions regarding how to verify a purely subjective stock with
observations or experience? What would a model of truck rental income
per day with an input flow measured in Trust/customer look like?

Posted by ""Ingram,Allan E - PFR-6"" <aeingram1@bpa.gov>
posting date Fri, 18 Apr 2008 16:49:39 -0700
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Mabel Fong <may_belle_66@yaho
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QUERY Meaning of Stock/Level

Post by Mabel Fong <may_belle_66@yaho »

Posted by Mabel Fong <may_belle_66@yahoo.com>

Hi:

I have been following these posts in hopes that someone
might educate me as to the nature of financial stocks as they occur in macroeconomic
systems.

The hard state variables of economics are obviously the
physical stocks of commodities; and the business of economic science is therefore
to account for the distribution of these stocks among economic sectors.

Transactions of physical quanta occur in an ever-changing
price environment, and these give rise to financial flows among the sectors. Financial
flows continuously create financial state variables that are certainly potent
matters of economic causation in capitalist systems: their levels presumably determine
what to produce, what to demand, and the transaction prices themselves.

In sum, the monetary stocks of the economy can be observed operating
in the manner of hard state variables, such as the physical stocks whose levels
determine physical production rates. But their import at a given moment is
entirely contingent on the prices of that moment, even though the dollars now in
a financial state variable were acquired under ‘who knows what’ earlier price
regimes.

I assume SD sets little store by economics’ monetary models
because the unit in which money is measured is subject to constant redefinition
by means that must remain unknowable until monetary flows are separated into
physical flows and the prices at which they occur. But does SD have a handle on
past monetary flows’ effects on current prices’ absolute levels? Or do you hold
that there is no sense in which price levels are absolute in the sense that a
physical stock is absolute?

Or put the question in terms of physical stocks: I observe
that SD models typically record changes in physical stocks, but these seldom
give rise to changes in the values at which those stocks are held – which, it
seems to me, should be at least partly determinative of how the stocks are
disposed.

Where I have seen prices feeding back into the uses made of
physical stocks, these prices have been the artifacts of ‘supply/demand pressures’
having no connection to monetary stocks developed out of the history of prices
and physical flows. Once again, the premise seems to be that price levels are
not hard state variables; and, by inference, neither are financial state
variables.

Mabel
Posted by Mabel Fong <may_belle_66@yahoo.com>
posting date Sat, 19 Apr 2008 14:37:14 -0700 (PDT)
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""John Morecroft"" <jmorecrof
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QUERY Meaning of Stock/Level

Post by ""John Morecroft"" <jmorecrof »

Posted by ""John Morecroft"" <jmorecroft@london.edu>

I fully agree with Bob Eberlein when he says:

""any variable that can change only over time, needs to be treated as a
stock. In fact, even in everyday language, we speak of things such as
building anger, rising emotions, falling into despair. Stocks every
one"".

By coincidence I have recently been re-reading two SD papers that nicely
illustrate the point. Annotated citations are below.

Mass NJ and Senge PM 1975. Understanding Oscillations in Simple Systems,
MIT System Dynamics Group Working Paper, D-2045-2 (available from the
System Dynamics Society on a DVD containing the complete D-memo series
of the MIT System Dynamics Group). The paper begins with a single stock
model of the rabbit population in a field to rigorously demonstrate (by
simulation) that a model containing a single stock accumulation cannot
possibly generate overshoot or cyclical dynamics. A model requires at
least two stocks to generate oscillations. The authors develop an
inventory-workforce model containing two stocks and only four active
equations (eleven equations including constants and initial values) to
rigorously demonstrate the origin of undamped oscillations in a second
order system. Realistic extensions to this tiny model are then used to
explain both expanding and damped oscillations. These structural
variations on the base model are similar to the structural variations
that Mike Radzicki adds to his Romeo and Juliet model to investigate
dynamics and romantic styles (see citation below).

Radzicki MJ 1993. Dyadic Processes, Tempestuous Relationships, and
System Dynamics, System Dynamics Review, 9 (1), 79-94. In this paper
Mike Radzicki translates Steven Strogatz's differential equation models
of Romeo and Juliet into visual stocks, flows and feedback loops. He
explains the corresponding algebraic model and uses simulation to
demonstrate cyclical dynamics of the two stock variables: Juliet's love
for Romeo and Romeo's love for Juliet. The simulated dynamics include
undamped, damped and expanding oscillations. These different dynamics
are shown to arise from a range of romantic styles (such as 'eager
beaver' and 'cautious lover') according to the choice of parameters that
characterise the relationship between Romeo and Juliet. Mike also
developed an interesting and challenging homework assignment based on
Romeo and Juliet (Homework #6 from Course SS 1510, Introduction to
System Dynamics Modeling, Worcester Polytechnic Institute). The
assignment requires students to build the full range of oscillating
models described in the paper.

_________________________________

John Morecroft | Senior Fellow
Management Science and Operations
London Business School
Posted by ""John Morecroft"" <jmorecroft@london.edu>
posting date Sun, 20 Apr 2008 11:28:06 +0100
_______________________________________________
Jack Harich <register@thwink.
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QUERY Meaning of Stock/Level

Post by Jack Harich <register@thwink. »

Posted by Jack Harich <register@thwink.org>

> any variable that can change only over time, needs to be treated as a
> stock.

Perhaps this principle is incomplete. As stated it would mean, for
example, that the temperature of an object must be modeled as a stock.
Temperature cannot change instantaneously. It can only change gradually,
over time. The same could be said for intelligence, trust, political
power, etc.

Maybe it's more like nouns versus verbs. Variables that are verbs
(rates) have a unit per time period, like persons/year. Nouns have only
the unit, like persons. Verbs cannot be a stock, but nouns can
optionally be a stock. It's just a question of which nouns you want to
emphasize in the model's structure by making then stocks.

That such contentious principles have not been nailed down would seem to
be an indicator of how young the field of system dynamics remains.

Jack
Posted by Jack Harich <register@thwink.org>
posting date Sun, 20 Apr 2008 08:19:04 -0400
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Bill Harris <bill_harris@faci
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QUERY Meaning of Stock/Level

Post by Bill Harris <bill_harris@faci »

Posted by Bill Harris <bill_harris@facilitatedsystems.com>

""SDMAIL Jack Harich"" <register@thwink.org> writes:

> > Maybe it's more like nouns versus verbs. Variables that are verbs
> > (rates) have a unit per time period, like persons/year. Nouns have only

""Flowing water"" sounds like a potential flow to me, with units of
gallons per minute perhaps, thinking of the bathtub metaphor, but it is
(or functions as) a noun. See, for example,
http://www.chompchomp.com/terms/gerund.htm.

Thinking back quickly on the models I've done, I'm hard-pressed to think
of a variable of any sort that wasn't a noun. That's consistent with
John Sterman's injunction in §5.2.6 of BD: ""Variable Names Should Be
Nouns or Noun Phrases."" While that's in the chapter on CLDs, he next
says that ""varible names in causal diagrams and models should be nouns
or noun phrases"" (I presume that ""models"" refers to equations or at
least to the set of stock-and-flow diagrams, which includes equations),
and he doesn't seem to contradict that by word or precept in chapter 6
on stock-and-flow diagrams.

> That such contentious principles have not been nailed down would seem to
> be an indicator of how young the field of system dynamics remains.

While it may be hard to explain in short emails here, the concept of a
stock (state variable) seems to have been quite stable for decades.
Think of the output of integrators in an analog computer program, the
concept of state as defined in any text on the state variable approach
to control systems or filter design, or chapter 6 of BD. I'd throw in
circuit design, too, but that's a bit further afield from SD.

The two challenges I've seen arise when trying to give non-technical
guidelines for differentiating stocks and flows and when discussing
non-independent stocks and the resulting order of the system.

Did I miss something?

Bill
- --
Bill Harris
Posted by Bill Harris <bill_harris@facilitatedsystems.com>
posting date Mon, 21 Apr 2008 10:47:55 -0700
_______________________________________________
George Richardson <gpr@albany
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QUERY Meaning of Stock/Level

Post by George Richardson <gpr@albany »

Posted by George Richardson <gpr@albany.edu>

On Apr 21, 2008, at 6:38 AM, SDMAIL Jack Harich wrote:
> Maybe it's more like nouns versus verbs. Variables that are verbs
> (rates) have a unit per time period, like persons/year. Nouns have only
> the unit, like persons. Verbs cannot be a stock, but nouns can
> optionally be a stock. It's just a question of which nouns you want to
> emphasize in the model's structure by making then stocks.

Richmond argued for that link to language for years. See his excellent
""An Introduction to Systems Thinking: STELLA"" published by High
Performance Systems (now iSee Systems) in various versions beginning in
1992 (my most recent copy is 2001). It is why he pressed for flows to
be labeled with ""ing"" words: hiring, ordering, producing, and the like.

The slight glitch in this is that all quantities (e.g., in a formal
system dynamics model) are nouns: the amount of hiring (people/month)
is a quantity, and all quantities are nouns. ""ing"" words work to flag
verb-like flows because they are verbs turned into nouns (gerunds).

Another slight glitch, which Forrester addressed way back in Industrial
Dynamics, is that one can not use units to flag types of variables. One
example he gave is the Average Sales Rate in a company: its units would
be units/month (or some such), but as an average over time it would be a
stock (probably captured as a SMOOTH). So units that sound ""verb-like""
may belong to variables that ought to modeled as stocks.

But Richmond reportedly had considerable success teaching people to
think of stocks and nouns and flows as verbs, so the main thrust of that
thinking appears to be more helpful than hurtful even though it's not
strictly correct.

> That such contentious principles have not been nailed down would seem to
> be an indicator of how young the field of system dynamics remains.

I'm not convinced about that conclusion. A lot has been written, some
very clearly, on the topic we've been discussing (meaning of stock) over
the last fifty years. Some of the questions and responses suggest that
some of the old wisdom is not currently in vogue or salient -- not that
it's not there, but rather that we are not keeping it alive. That's a
function of the age of the field, not its youth.

Another potential source of the impression that we don't have this stuff
""nailed down"" is that the selection of stocks appropriate to study a
particular dynamic problem can be difficult, involving subtleties linked
to the time frame of the phenomena, the meaning of quantities, and the
use of them in the model. There's some ""art"" to selecting stocks, and
one sees that by sensing that some of our practitioners are particularly
gifted and insightful in selecting stocks (again Richmond comes to
mind). I tried to write down some of that art about stocks in the old
Richardson and Pugh text in section 4.3, called ""What is a Level?""

..George
Posted by George Richardson <gpr@albany.edu>
posting date Mon, 21 Apr 2008 12:53:22 -0400
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""Jack Homer"" <jhomer@comcas
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QUERY Meaning of Stock/Level

Post by ""Jack Homer"" <jhomer@comcas »

Posted by ""Jack Homer"" <jhomer@comcast.net>

In regard to the definition of stocks, Jack Harich says:
> That such contentious principles have not been nailed down would seem to
> be an indicator of how young the field of system dynamics remains.

This is a much more a reflection of the dynamics of this listserve than of
the field of SD. The fact is that many questions that are discussed in this
listserve (""what is a stock?"", ""what is exogenous?"", ""what should we do with
soft variables?"", ""why do we speak of dynamic hypotheses rather than root
causes?"", ""how should we work with clients to ensure best results?""...) have
been asked and answered in books and articles going back decades, starting
most obviously with Forrester's Industrial Dynamics in 1961.

I mean offense to no one, but what we have seen for a number of years is
that the most frequent and most voluminous contributions to this listserve
tend to come from the least experienced in the field. Many of these
contributors have not read Industrial Dynamics nor Sterman's Business
Dynamics nor any other foundational texts, nor have they taken a proper
course in SD, but they rather hope to absorb what they need to know from a
discussion group. When an experienced person does bother to contribute,
their knowledge is not valued above that of inexperienced contributors, and
their remarks are lost in the din of uneducated response. I think this is
largely because it is not really possible to give a quick and adequate
answer to most of the questions that are asked. To really understand what
should be considered a stock, or what should be considered exogenous, one
needs to be properly immersed in the subject, and not just view it as a
programming tool or an analytical approach without deep philosophical
underpinnings. The knowledgeable cannot give a quickie answer to these
questions, but the unknowledgeable are only too happy to rush in and do so.
So, the unknowledgeable end up dominating the discussion and drive away the
knowledgeable to more worthwhile pursuits...like actually doing the SD
projects and writing the published works and teaching the students who want
to understand SD in depth and not in a superficial way.

Sometimes I wish Bob Eberlein would just step in and say, ""This is an old
question and has been answered."" But, of course, he doesn't want to shut
off the free flow of conversation, and after all, there are many periods
when the flow of even uneducated conversation slows to a trickle. But, just
think, what if the reason for that trickle is that the knowledgeable have
been driven away by the din of uneducated chatter? What if we bit the
bullet and gently told the unknowledgeable to keep quiet on most matters
until they had read the foundational texts and/or taken a proper course in
SD? Is it possible the knowlegeable would come back and lead the listserve
in a constructive new direction? Maybe it's worth a try.

Jack Homer
Posted by ""Jack Homer"" <jhomer@comcast.net>
posting date Mon, 21 Apr 2008 09:56:37 -0400
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""Dhr. Nijland"" <lukkenaer@p
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QUERY Meaning of Stock/Level

Post by ""Dhr. Nijland"" <lukkenaer@p »

Posted by ""Dhr. Nijland"" <lukkenaer@planet.nl>

Jack Harich wrote:
> Maybe it's more like nouns versus verbs. Variables that are verbs
> (rates) have a unit per time period, like persons/year. Nouns have only
> the unit, like persons. Verbs cannot be a stock, but nouns can
> optionally be a stock. It's just a question of which nouns you want to
> emphasize in the model's structure by making then stocks.

Two remarks:
1) I think, in some cases, a variable may be represented as ""state
variable"" and ""rate variable"" in the same model, even without
representing ""material"" stocks and flows.
Studying the dynamics of position, velocity, acceleration and mass
of satelites in a gravitational field by means of a numeric simulation
model:
The ""velocity"" (m/sec) of the satelite may be modelled as a rate
variable with respect to ""covered distance (or position)"" (m), the
latter being a state variable with respect to the first.
The same rate variable ""velocity"" (m/sec), however, is a state variable
with respect to another rate variable ""acceleration of the satelite""
((m/sec)/sec).
It may be noted that the ""mass of the satelite"" according to relativity
theory variates with ""velocity of the satelite"", but there is /_no need
to model this mass variable as a ""state""_,/ though it evidently
represents ""matter"". At their turn ""mass"" and ""position""
determine ""gravitational force"", and ""gravitational force"" determines
the rate variable ""acceleration"". So three causal loops are formed: 1)
velocity > position > gravitational force > accelleration > velocity; 2)
velocity > mass > gravitational force > acceleration > velocity; 3)
velocity > mass > acceleration > velocity. Is this model conceptually
correct?
So the material variable ""mass"" is not represented as a state variable,
while the non-material variables ""acceleration"" and ""velocity"" are
reprented as rate and state.

2) Cannot any variable in a model formally be represented as a
combination of state variable and rate variables? And any constant too?
For a constant may be regarded as a state variable of which the sum of
inrates and outrates are zero.

Best regards,
Geert Nijland
Posted by ""Dhr. Nijland"" <lukkenaer@planet.nl>
posting date Mon, 21 Apr 2008 20:43:04 +0200
_______________________________________________
Keith Linard <linard.keith@gm
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QUERY Meaning of Stock/Level

Post by Keith Linard <linard.keith@gm »

Posted by Keith Linard <linard.keith@gmail.com>

Re Jack Harich's post:
> Maybe it's more like nouns versus verbs.
> Variables that are verbs (rates) have a unit per time period, like persons/year.
> ... Verbs cannot be a stock

Consider velocity: (displacement/time)
Velocity can be either a flow variable or a stock variable, depending on
whether one's focus is on displacement or acceleration. That is,
Velocity can be considered either as a noun or a verb, depending on context,
just as in the English language we distinguish between a word being used as
a verb or a gerund.


Keith Linard
150 Lacote Road
Greendale
VIC 3341
Posted by Keith Linard <linard.keith@gmail.com>
posting date Tue, 22 Apr 2008 08:34:27 +1000
_______________________________________________
""Alan McLucas"" <a.mclucas@a
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QUERY Meaning of Stock/Level

Post by ""Alan McLucas"" <a.mclucas@a »

Posted by ""Alan McLucas"" <A.McLucas@adfa.edu.au>

I disagree with Jack's example. Maybe it's just inappropriately chosen?
We might have a stock of heat, but never a stock of temperature. Perhaps
this thread has past its use-by date.
Regards,
Alan

Dr Alan McLucas
School of Information Technology and Electrical Engineering
Posted by ""Alan McLucas"" <A.McLucas@adfa.edu.au>
posting date Tue, 22 Apr 2008 07:49:03 +1000
_______________________________________________
""Antoni Oliva"" <aoliva@22si
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QUERY Meaning of Stock/Level

Post by ""Antoni Oliva"" <aoliva@22si »

Posted by ""Antoni Oliva"" <aoliva@22sistema.com>

My humble opinion in relation to the Stock/level discussion, and after my
experience in modelling (specially social matters) is that the consideration
of a variable either as an stock or as a rate is indeed defining the model:
not only the scale but also the approach we are giving to the problem.
I have found often solutions (solutions in terms of a more clarifying
structure, or more straight approach..., not matemathical solutions) in the
model process by changing one of the main variables from stock to rate or
viceversa

This explanation would complete the sentence from George Richardson:
There's some ""art"" to selecting stocks, and one sees that by sensing that
some of our practitioners are particularly gifted and insightful in
selecting stocks.

Antoni
Posted by ""Antoni Oliva"" <aoliva@22sistema.com>
posting date Tue, 22 Apr 2008 13:45:26 +0200
_______________________________________________
<richard.dudley@attglobal.net
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QUERY Meaning of Stock/Level

Post by <richard.dudley@attglobal.net »

Posted by <Richard.Dudley@attglobal.net>


>> > > Maybe it's more like nouns versus verbs. Variables that are verbs
>> > > (rates) have a unit per time period, like persons/year. Nouns have
>> > > only

I agree with some other views that stocks can certainly have units of
Posted by <Richard.Dudley@attglobal.net>
posting date Wed, 23 Apr 2008 09:08:33 +0700
_______________________________________________
David Rees <david.rees@synerg
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QUERY Meaning of Stock/Level

Post by David Rees <david.rees@synerg »

Posted by David Rees <david.rees@synergia.co.nz>

Jack wrote:

>This is a much more a reflection of the dynamics of this listserv than of the
>field of SD.

Absolutely! This thread began with an interesting and subtle question about the
representation of intangibles as stocks. Some of the responses were interesting,
informative and thought provoking. Some were not.

One sign that a field has confidence in itself is that it builds on its body of
knowledge and demands that participants in the field study and learn that body
of knowledge BEFORE making pronouncements about what the field is or is not. If
you want to debate the merits of one rugby team over another with me you'd
better understand the special role played by the 'loose forwards' in today's
game. If you don't I'll just change the topic and drink my beer. I'd also be
happy, by the way, to explain their importance if you wanted to learn something
about this strange game. Surely, those who are really experienced leaders in our
field must continually mutter - very politely no doubt - 'just go and read
Industrial Dynamics then come back and we'll continue the conversation'.

I am all for debate but let's start demanding, at least a base level of
knowledge amongst those who want to get involved. Maybe some of those involved
in this thread should have first asked ""could someone please direct me to good
references that deal with the meaning of stocks and the issues surrounding
intangibles"". I have no doubt they would have had many helpful replies. Having
read those books and papers they could have come back into the conversation and
made a useful contribution.

I would hate for the Jack Homer's, George Richardson's, Tom Fiddaman's, John
Morecroft's etc. etc. of this field to pull back from this listserv as they are
the leaders in the field who know a lot more than most of us and from whom we
can learn a lot. They are all willing to share their knowledge and willing to
get involved in challenging debates. However, let's be a bit more respectful
and first ensure our pronouncements are based on a sound understanding of what
has already been written. Those who make major breakthroughs, and even those of
us who make minor breakthroughs, tend to do so because we have invested in the
core knowledge first, as it is only then that we can build on it and really
challenge it.

David Rees
Posted by David Rees <david.rees@synergia.co.nz>
posting date Wed, 23 Apr 2008 22:49:18 +1200
_______________________________________________
""richard dudley"" <richard
Junior Member
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QUERY Meaning of Stock/Level

Post by ""richard dudley"" <richard »

Posted by ""'richard dudley'"" <richard.dudley@attglobal.net>


Resend of scrambled message [don't ever put multiple x's together in a post]

> Maybe it's more like nouns versus verbs. Variables that are verbs
> (rates) have a unit per time period, like persons/year. Nouns
> have only

I agree with some other views that stocks can certainly have units of something
per time unit.

Oil production capacity is usually measured in barrels/year. But like other
capacities this is modeled as a stock. Changes to this stock are in units
of barrels/year/year.

Thus we can also model river discharge (i.e. river ""flow"") as a stock with
units M3/s and its change in flow as m3/s/s.


Richard
Posted by ""'richard dudley'"" <richard.dudley@attglobal.net>
posting date Wed, 23 Apr 2008 19:57:08 +0700
_______________________________________________
Jack Harich <register@thwink.
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QUERY Meaning of Stock/Level

Post by Jack Harich <register@thwink. »

Posted by Jack Harich <register@thwink.org>



Posted by ""Alan McLucas"" <A.McLucas@adfa.edu.au>
> I disagree with Jack's example. Maybe it's just inappropriately
> chosen? We might have a stock of heat, but never a stock of
> temperature. Perhaps this thread has past its use-by date. Regards,
> Alan

Alan,

Thanks. I really like your distinction between heat and temperature.

John Morecroft wrote: ""I fully agree with Bob Eberlein when he says:
'any variable that can change only over time, needs to be treated as a
stock. In fact, even in everyday language, we speak of things such as
building anger, rising emotions, falling into despair. Stocks every one'.""

Jack Harich replied: ""Perhaps this principle is incomplete. As stated it
would mean, for example, that the temperature of an object must be
modeled as a stock. Temperature cannot change instantaneously. It can
only change gradually, over time. The same could be said for
intelligence, trust, political power, etc.""

So again, it appears we have these two premises:
1. ""any variable that can change only over time, needs to be treated as
a stock.""
2. ""Temperature cannot change instantaneously. It can only change
gradually, over time.""

Thus the conclusion follows that:
3. Temperature needs to be treated as a stock.

To Bob's list of ""building anger, rising emotions, falling into despair.
Stocks every one."" we could add ""rising temperature.""

Above is the SD viewpoint. The scientific viewpoint starts with the
definition of temperature, which is ""a measure of the internal energy or
enthalpy, that is the level of elementary motion giving rise to heat
transfer."" Note that temperature is independent of the mass of an object.

This agrees with your position, that temperature should not be treated
as a stock. I feel the same way, which is why I brought the subject up.

However, based on the many useful posts on this subject, I can see there
are occasional cases where temperature could be usefully treated as a
stock.

Perhaps we could modify Bob's definition of a stock slightly, to this:
""A stock is any variable whose behavior is best represented as changing
over time, due to rates of increase and decrease."" or more briefly as ""A
stock is any variable best represented as an accumulation."" or even more
briefly as ""A stock is an accumulation."" The last is how Sterman defines
it, on page 192.

The ""best represented"" aspect is why an element in one model is an
auxiliary variable, in another model is a stock, and in yet another
model is a constant.

Regarding my statement that: ""Maybe it's more like nouns versus verbs.
Variables that are verbs (rates) have a unit per time period, like
persons/year. Nouns have only the unit, like persons. Verbs cannot be a
stock, but nouns can optionally be a stock. It's just a question of
which nouns you want to emphasize in the model's structure by making
then stocks.""

Thanks to the many patient posters who have pointed out the error in
this. I was wrong. Whether a variable is a noun or verb does not affect
its potential to be a stock. Neither does its units. The ultimate
criteria seems to be usefulness in the model as a stock.

SDMAIL Jack Homer wrote:
> Posted by ""Jack Homer"" <jhomer@comcast.net>
> I mean offense to no one, but what we have seen for a number of years
> is that the most frequent and most voluminous contributions to this
> listserve tend to come from the least experienced in the field. Many
> of these contributors have not read Industrial Dynamics nor Sterman's
> Business Dynamics nor any other foundational texts, nor have they
> taken a proper course in SD, but they rather hope to absorb what they
> need to know from a discussion group.
Thanks. This is a thoughtful post. Allow me to reply, because I may be
one of the offenders.

I've considered ordering a copy of Industrial Dynamics several times,
but based on the price and the fact that nearly 100% of it has probably
been incorporated into Business Dynamics and Urban Dynamics, I have not.

I've read Business Dynamics twice. But apparently I need to read it a
third time, because it has an example of a stock that is not a noun. :-)

I've not taken a proper course in SD. I have, however, done 50 practice
models of various simple problems. I have also developed a formal
process on how to apply SD to difficult social problems. I suspect that
this practice work and a process that fits the problem domain is far
more important than whether one has taken a proper course or not. But I
do see what Jack Homer is trying to say in general--that novices barging
into a high level forum are like a bull in a china shop.

I use SD as one of many problem solving skills. Thus my needs are
different from those who are specialists and SD experts. This second
type of user goes around looking for problems to apply SD to.

The first type of user is what will cause SD to sink or swim. If SD can
mature to the point where the average college educated problem solver
can learn and apply it when the need arises, then SD will swim.
Otherwise, SD will continue to exist in a relatively small world. (Kim -
There's a goal in here.)


> When an experienced person does bother to contribute, their knowledge
> is not valued above that of inexperienced contributors, and their
> remarks are lost in the din of uneducated response.
This has long been a huge problem of public forums. The only workable,
scalable solution I've seen is the message ratings approach used by
Slashdot.org and others. I was sorry to see that ratings were not in
version 3.0 of PHPBB, the forum software I use. However, several people
are working on mods for ratings, using the ""karma"" terminology of slashdot.

Message ratings work roughly like this: Regular forum readers receive a
certain number of points per week or so. They cannot save them up. As
they read messages, they can rate them for usefulness. Particularly bad
posts can even receive negative ratings. In a few days or hours,
depending on board volume, all messages will have an average rating.

The beauty of this approach is the forum can have a default rating.
Below that, no messages are shown, unless you change the default. This
would resolve the issue Jack Homer raises, that low quality messages can
spoil the value of a high quality forum.

The need for mechanisms like this arise from the fact that in virtual
conversation, the usual social feedback loops are missing. We cannot
look across the table or the room and see frowns when a bad statement is
made, or nods when a good one appears. The usual peer pressure norms are
missing.

Actually, we are probably lucky the quality of this list is as high as
it is. We can certainly thank certain people for this.


> I think this is largely because it is not really possible to give a
> quick and adequate answer to most of the questions that are asked. To
> really understand what should be considered a stock, or what should be
> considered exogenous, one needs to be properly immersed in the
> subject, and not just view it as a programming tool or an analytical
> approach without deep philosophical underpinnings.
I see your point. But I wonder, can we improve on the presentation,
organization and definitions of our key terms and concepts?

An example that has value for me is, as I was probing the social agent
side of the sustainability problem, I needed to study foundational
concepts on agent behavior. Agents in a social system behave much like
species members in an ecological system, so I set off to study ecology.
Using the book ""Ecology"" by Mackenzie, Ball, and Virdee (Part of the
Instant Notes series) I was able to get up to speed in a few weeks. The
book has clear, understandable, short definition and discussions of
several hundred key terms/concepts. The book gave me several
tremendously useful concepts (competitive exclusion, importance of
niches, niche succession) that I have used in my analysis and SD models.

The book is incredibly well organized along the lines of the concepts.
Each chapter (itself a key concept) begins with a list of the key terms
and their short definitions. This is then elaborated upon in the rest of
the chapter.

As far as I know, the field of SD has nothing like this book.

See: http://www.amazon.com/Instant-Notes-Eco ... 1859962572


> The knowledgeable cannot give a quickie answer to these questions, but
> the unknowledgeable are only too happy to rush in and do so. So, the
> unknowledgeable end up dominating the discussion and drive away the
> knowledgeable to more worthwhile pursuits...like actually doing the SD
> projects and writing the published works and teaching the students who
> want to understand SD in depth and not in a superficial way.
>
But isn't there occasionally some value in what some of these supposedly
unknowledgeable newcomers have to say? This, I suspect, is the basic
tradeoff between a closed an open forum.

This problem could be reduced by the use of message ratings.

> Sometimes I wish Bob Eberlein would just step in and say, ""This is an
> old question and has been answered."" But, of course, he doesn't want
> to shut off the free flow of conversation, and after all, there are
> many periods when the flow of even uneducated conversation slows to a
> trickle. But, just think, what if the reason for that trickle is that
> the knowledgeable have been driven away by the din of uneducated
> chatter? What if we bit the bullet and gently told the
> unknowledgeable to keep quiet on most matters until they had read the
> foundational texts and/or taken a proper course in SD? Is it possible
> the knowlegeable would come back and lead the listserve in a
> constructive new direction? Maybe it's worth a try.
>
It's one option. But there are others, as I have pointed out above.

This was a terrific post. I suspect it said what many have been
thinking, but did not dare verbalize....

Thanks,

Jack

Posted by Jack Harich <register@thwink.org>
posting date Wed, 23 Apr 2008 09:08:07 -0400
_______________________________________________
""Ralph Levine"" <leviner@msu
Junior Member
Posts: 2
Joined: Fri Mar 29, 2002 3:39 am

QUERY Meaning of Stock/Level

Post by ""Ralph Levine"" <leviner@msu »

Posted by ""Ralph Levine"" <leviner@msu.edu>

As the discussion about representing soft variables as stocks continues,
a number of new points about the usefulness of including soft variables
in models have emerged. There are many points we agree with. First, we
agree that the modeler must formulate and understand the specific goals
of the model, and, at least, at first, not push the model outside of its
usefulness, as Jean-Jacques Lauble suggests. This rule of thumb applies
to the inclusion of any variable, intangible or not. We suggest
starting from formulating the dynamic hypothesis representing the
processes modeled in the loop structures. Again, Jean-Jacques Lauble’s
example of getting a satisfactory result with a small model that was
composed of only 8 loops, without the inclusion of soft variables and
additional processes (13 loops), makes a lot of sense to us. From a
slightly different example, going back to the history of system
dynamics, the urban dynamics model was criticized by some reviewers as
being deficient because the model did not include a suburban component.
One could argue that the structure formulated by Forrester to account
for urban growth and decay was sufficient to evaluate suggested policy
interventions without adding the suburbs. This was essentially a
boundary issue. As in Jean-Jacques Lauble’s case, adding loop
structure to capture the dynamics of the suburbs and the interaction of
the suburbs with the city was not necessary to achieve the original set
of goals. Walter Schroeder expanded the boundaries of the original urban
model by including a suburban component. The new model was
significantly more complex. However, the augmented model essentially
""reaffirms the policy recommendations presented Urban Dynamics.""
(Schrioeder, 1975). Forrester’s original dynamic hypothesis was
sufficient to account for the problem.

The other side of the coin: When there needs to be more structure.
Getting back to the topic of including soft variables in one’s models,
perhaps the best reason for doing that is that the inclusion of soft
variables may lead to better understanding and insight into what caused
the problem and perhaps what changes in policies should be initiated to
make things better in the long run. Here is an example of such a case
where including soft variables paid off. The work of John Heinbokel and
Jeff Potash, who developed a SD model of the pneumonic plague comes to
mind. Epidemiological compartment (S-E-I-R) models are well known to
system dynamicists (e.g., see John Sterman’s text, Chapter 9). John and
Jeff’s model was formulated with the best science available. The first
iteration contained no subjective variables. After developing the
model, they looked for data to see if the model fit a real instance of
the plague. They found time series data from an outbreak of the plague
in Surat, India in 1994. Their first model fit those data miserably.
The model predicted many more new cases and a much longer course of the
disease than was found in the time series data. Why did the epidemic die
out so fast? John and Jeff began to get the details of what happened by
rereading a very detailed account of the incident written by Ghanshyam
Shah Shah’s book contained both quantitative data and as well as a
vast amount of qualitative data dealing with differences in coping
responses of the residents and the decision processes used by officials
and health care providers. In addition to the eventual distribution of
prophylactic antibiotics (and the indication that those antibiotics were
not typically used correctly), they discovered that a large proportion
of the population fled the city, and those who remained self-isolated
themselves. Epidemiological models, in general, do not include these
behavioral mechanisms to cope within the framework of the model. John
and Jeff then (1) estimated antibiotic usage, (2) included a drainage
(fleeing) process out of the stocks of (a) people at risk and (b) people
incubating the disease, and (3) incorporated a change in the mixing
coefficient to capture the effect of self-isolation. A combination of
both processes accounted for an excellent fit to the quantitative data.

As system dynamicists, they realized that the changes they had made to
the model were exogenous in nature. The parameters were in fact dynamic
and most likely part of the internal loop structure. Thus, they sought
to endogenize those behavioral processes by developing an additional set
of loops that would account for the behavioral responses of fleeing and
self-isolating. As part of expanding the boundary of the model, they
consulted with social scientists (RL was among them) as domain experts
to help them incorporate such processes as (1) risk perceptions as one
of the drivers for fleeing and accepting medicine and (2) trust in the
authorities in communication those risks. We should emphasize that a
good fit of the augmented model does not mean that other very different
mechanisms might also generate an equally good fit. However, the
behavioral processes used in the model reflected the best scientific
information currently known and accepted. The output of the model also
was consistent with a recent study by the WHO on those behavioral
processes included in the model, any one of which, if mishandled, could
result in undermining effective communication and response strategies.
This provides at least an initial basis for validating the model from an
independent source.

Briefly, we want to comment about the issue of when to use a soft
variable as a stock and when to treat it as a weight or index that is a
function of conserved stocks. We differ somewhat from John Barton’s
handling of the intangible variable, ""reputation."" He points out that
reputation is a function of ""easily recognized measurables.""
Presumably, if those input variables change, the organization’s
reputation will change. However, in many cases, the input variable can
change up and down, but it take times to generate a good reputation and
respond to variability in the input variables that would make up the
index. In this particular case, we suggest thinking about making
reputation an information delay of some order. This is what we described
in our last post. It was also suggested by Jean-Jacques Lauble in
handling the willingness of the client to fulfill needs his or her needs
with the considered project.

The use of the smooth in this case may work and be simple enough to
capture the delay in the cognitive system and be consistent with
original goals of the model. Let us point out, however, that for
variables, such as reputation, the dynamics may be a bit more
complicated. For example, reputations have to be maintained, which may
make including a drainage process desirable. The drainage process would
represent those factors that are unaccountable by the structural loops
associated with the inputs, such as perhaps competition from other
firms, if that process is not in the model. In our estimation, the
adding a drainage process to a smooth is certainly possible ( which
would generate a steady state error )is problematical, but that is
material for another post.



Forrester, J. (1969). Urban Dynamics. Cambridge, MA: Wright Allen Press

Heinbokel, J, & Potash, J. (2003). Modeling behavior ;as a factor in
the Dynamics of an outbreak of pneumonic plague. Proceedings of the
international Conference of the System Dynamics Society, New York, July
20-24.

Heinbokel, J., & Potash, J. Endogenous ;human behaviors in pneumonic
plague simulation: Psychological & behavioral theories as small ""generic
models. Proceedings of the international Conference of the System
Dynamics Society, Boston, July 17-21.

Shah, G. (1997). Public health and urban development: The plague in
Surat. New Delhi: Sage Publication

Schroeder,W,. W. (1975). Urban dynamics and the suburbs. In W. W.
Schroeder , R. E. Sweeney, L. E.

Alfeld (Eds.) Readings in Urban Dynamics: Vol. 2, Cambridge, MA:
Wright-Allen Press

Sterman, J.D. (2000) Business dynamics: Systems thinking and modeling
for a complex world. Boston: McGraw Hill.

World Health Organization. (2005) WHO outbreak communication guidelines.

Respectfully,

Ralph Levine, Ph.D.
Professor Emeritus (On Call)
Departments of Community, Agriculture, Recreation, and Resource Studies And
Department of Psychology
Michigan State University
East Lansing, MI 48823

AND

David W. Lounsbury, Ph.D.
Asst. Attending Psychologist, Beh. Sci. Service
Community Outreach and Health Disparities
Dept. of Psychiatry & Behavioral Sciences
Memorial Sloan-Kettering Cancer Center
641 Lexington Ave, 7th Floor
New York, NY 10022

Posted by ""Ralph Levine"" <leviner@msu.edu>
posting date Wed, 23 Apr 2008 18:07:15 -0400
_______________________________________________
Tom Fiddaman <tom@ventanasyst
Member
Posts: 25
Joined: Fri Mar 29, 2002 3:39 am

QUERY Meaning of Stock/Level

Post by Tom Fiddaman <tom@ventanasyst »

Posted by Tom Fiddaman <tom@ventanasystems.com>

I think Jack's latest missive has clarified the debate:
> So again, it appears we have these two premises:
> 1. ""any variable that can change only over time, needs to be treated as
> a stock.""
> 2. ""Temperature cannot change instantaneously. It can only change
> gradually, over time.""
>
> Thus the conclusion follows that:
> 3. Temperature needs to be treated as a stock.

This is a good characterization of the argument, and highlights the
problem with the first premise: a thing that can change only over time
might be a stock (heat) or something that changes as a function of an
underlying stock (temperature). Thus ""can it change only over time?"" is
a helpful question to ask oneself when seeking the stocks in a model,
but may not be sufficient to pin down the best representation.

> Above is the SD viewpoint. The scientific viewpoint starts with the
> definition of temperature, which is ""a measure of the internal energy or
> enthalpy, that is the level of elementary motion giving rise to heat
> transfer."" Note that temperature is independent of the mass of an object.
>
> This agrees with your position, that temperature should not be treated
> as a stock. I feel the same way, which is why I brought the subject up.

I would argue that the SD viewpoint is not different from the scientific
viewpoint, or at least shouldn't be.

In the case of temperature, there's a good physical argument to make
heat or enthalpy the underlying stock. In a system with constant mass
and no phase transitions, treating temperature as a stock could be a
perfectly reasonable simplification. In some cases, it might be useful
to further simplify by ignoring the stock of heat, treating temperature
as an auxiliary. For example, in a model of glacial cycles one might use
and auxiliary representing the equilibrium temperature of the
atmosphere, rather than explicitly modeling the dynamics of heat
accumulation, because the time constant (<1yr) is so short with respect
to the period of interest (>100,000yr).

In other cases, there isn't a clear argument for one or another
mathematically equivalent formulation - should one model the position
and velocity of a body, or the position and momentum? I prefer the
latter, but either way we will have velocity and momentum, one of which
will be a stock, the other an auxiliary related to the stock by mass,
with neither changing instantaneously.

> Perhaps we could modify Bob's definition of a stock slightly, to this:
> ""A stock is any variable whose behavior is best represented as changing
> over time, due to rates of increase and decrease."" or more briefly as ""A
> stock is any variable best represented as an accumulation."" or even more
> briefly as ""A stock is an accumulation."" The last is how Sterman defines
> it, on page 192.
>
> The ""best represented"" aspect is why an element in one model is an
> auxiliary variable, in another model is a stock, and in yet another
> model is a constant.

Right. One could even go a bit further and describe a stock as something
best represented by an integration, but the definition becomes a bit
tautological. The real need is for a menu of criteria one might apply in
order to make good choices among competing, possibly equivalent options.
The notion of accumulation is helpful toward that end, but perhaps not
in all cases - I don't find it particularly helpful for thinking about a
pipeline delay (infinite order), for example. The menu might include:
- accumulation (of inflows and outflows or simply net changes)
- delay, inertia, momentum
- persistence, memory, or ergodicity (the ""stop time"" thought experiment)
- gradual vs. instantaneous change
- measurability (the idea that flows are uselessly noisy when viewed at
fine time scales)
- integral vs. derivative
- units of measure
Most of this was laid out pretty clearly in Industrial Dynamics, Chapter 6.

I rather doubt that even modestly experienced modelers would get into
protracted arguments over the fundamental nature of a particular
variable. Where there will be disagreement is over the philosophically
impure tradeoffs (include or neglect a stock, at what level of
aggregation?) that need to be made in order to yield a model that is
useful. This is generally regarded as art. I think it is an art to the
extent that we as a field haven't really formalized a method for making
choices efficiently. However, it's also a science in the sense that any
given assumption can be tested against alternatives (disaggregate the
population by gender, change the order of delays, etc.).

Tom

****************************************************
Tom Fiddaman
Ventana Systems, Inc.
Posted by Tom Fiddaman <tom@ventanasystems.com>
posting date Thu, 24 Apr 2008 10:34:31 -0600
_______________________________________________
""Jay Forrest"" <systems@jayf
Junior Member
Posts: 6
Joined: Fri Mar 29, 2002 3:39 am

QUERY Meaning of Stock/Level

Post by ""Jay Forrest"" <systems@jayf »

Posted by ""Jay Forrest"" <systems@jayforrest.com>

Good email, Tom. I was behind and just got to Jack's email. The temperature
example is great - and a lot like the ""trust"" model in that temperature is a
somewhat arbitrary indicator/measure rather than an consistent, universal
amount. The underlying stock is ""contained energy"" and the phase transitions
and heat capacity differences among materials defy universal treatment as a
stock. OTOH, over a finite range, for a given pool, the stock designation
could be not only highly simplifying but also quite accurate.

The integration requirement for stocks seems appropriate and useful for
separating pseudostocks (trust, temperature, price) from true stocks though
I suspect differences of perception would still make this distinction a bit
fuzzy. One thing I like about the integration concept is that it provides a
clear logic for testing the appropriateness of using the stock designation
for a variable wherein we can compare flow units to the stock (temperature
uits do not flow but rather thermal units) and as we shift from extreme to
extreme the continued integration remains valid (no discontinuities such as
phase transitions where adding more heat doesn't increase temp, etc.).

Thanks!
Jay Forrest
Posted by ""Jay Forrest"" <systems@jayforrest.com>
posting date Fri, 25 Apr 2008 07:54:21 -0500
_______________________________________________
""Kim Warren"" <Kim@strategyd
Member
Posts: 36
Joined: Fri Mar 29, 2002 3:39 am

QUERY Meaning of Stock/Level

Post by ""Kim Warren"" <Kim@strategyd »

Posted by ""Kim Warren"" <Kim@strategydynamics.com>

As I recall my limited physics, temperature is something to do with the
amount of heat divided by the quantity of matter amongst which the heat
is spread ? If so, is it not the heat that accumulates, rather than
temperature - to take SD's favourite metaphor of the bath-tub, the
bath's temperature falls if cold water is added. The amount of total
energy - the stock - in the water rises [unless the temperature of added
water is zero], but rises less fast than the stock of water. [Apologies
to serious physicists for this gross simplification].
This also questions whether the fact that something can change only
slowly over time is a good guide - temperature can be changed almost
instantly, e.g. if a pulse of cold water [e.g. a bucketful] is thrown in
all at once. The stock of my bank balance would also change instantly if
someone kindly gave me a cheque for $1million [I wish!] - but it's still
a stock.

Kim Warren
Posted by ""Kim Warren"" <Kim@strategydynamics.com>
posting date Sun, 27 Apr 2008 11:59:37 +0100
_______________________________________________
""Jay Forrest"" <systems@jayf
Junior Member
Posts: 6
Joined: Fri Mar 29, 2002 3:39 am

QUERY Meaning of Stock/Level

Post by ""Jay Forrest"" <systems@jayf »

Posted by ""Jay Forrest"" <systems@jayforrest.com>

Hi Kim!

While I am not a physicist, I am a chemical engineer which requires a
significant level of thermodynamics so I feel at least partially qualified
to address your comments.

The concept of temperature relates to an intensive property that has subtle
nuances that lead it to be easily misconstrued. Intensive properties are
properties that describe the specific characteristics of a substance in a
given state and are independent of the amount of substance considered.
(Densiy is another intensive property that my be more easily comprehended).
In Thermodynamics by Lewis and Randall, temperature is ""qualitatively
defined as follows: If there can be no thermal flow from one body to
another, the bodies are at the same temperature, but if one can lose
temperature to the other by thermal flow, the temperature of the former is
greater."" The authors then go on to build a quantitative set of rules for
temperature that basically says the same thing as comprehensive rules
covering all cases. It is not about heat content per se but about conditions
that result in heat flow.

The most obvious failing of temperature as a stock lies in boiling water.
One places a pan of water over a flame. Being colder that the flame, the
water absorbs energy and warms - until it reaches the boiling point
(nominally 100 C at sea level). At that point the water continues to absorb
heat but does NOT increase in temperature and the temperature fo the steam
is still 100 C but has much greater heat content.

Temperature is an arbitrary measure related to the heat contained in a unit
of matter. It is important to not consider it an extensive property or
universal. Heat capacities (the amount of energy required to raise the
temperature of a substance by a fixed amount) are not consistent, either
across materials or even within a given material (i.e. the heat capacity
varies with temperature).

As I alluded previously with a given substance and a narrow (fuzzy word)
range temperature can be somewhat ""stocky"". If we mix liquid water at one
temperature with liquid water at another the resulting temperature will be
pretty close to a weighted average of the component temperatures (1 cup of
water at 50 degrees added to 1 cup at 60 degrees will give 2 cups at
essentially 55 degrees. But Aluminum has a heat capacity about 1/4 that of
Iron such that if we have a pound of Aluminum at 600 degrees and a pound of
iron at 100 degrees and place them in contact and insulate them so they have
no external heat losses, you would end up with them both at 200 degrees.

A similar problem arises if we add a small amount of water at 40 degrees to
a block of ice at 0 C. The result will be at 0 C. The conservation principle
of stocks is defied. The reason is that temperature doesn't flow... Thermal
energy flows....

Hope this is helpful!
Jay Forrest
Posted by ""Jay Forrest"" <systems@jayforrest.com>
posting date Sun, 27 Apr 2008 08:48:34 -0500
_______________________________________________
""Zahed Sheikh"" <zahed.sheik
Junior Member
Posts: 2
Joined: Fri Mar 29, 2002 3:39 am

QUERY Meaning of Stock/Level

Post by ""Zahed Sheikh"" <zahed.sheik »

Posted by ""Zahed Sheikh"" <zahed.sheikh@gmx.com>

Temperature is just a measure we have created as a tool to rank the
level of hotness or coldness. In general when you add heat to a material
its temperature goes up unless a change of phase is taking place. So,
when water starts boiling, the temperature stays constant as you add
heat because this added heat will be used to supply the energy needed
for phase change. Temperature of an object can change instantaneously if
its resistance to heat is zero (infinite thermal conductivity). In
reality any material has a time constant that has to do with its
physical properties as well as its environmental conditions.

We have a dimensionless number called the Biot number which is the ratio
of the internal resistance to heat transfer to the external resistance
(due to the environment through convective heat transfer). When this
ratio is less that 0.1, we are safe to assume that the object is
isothermal and the equation governing the change in T becomes

dT/dt = (T-Tref)*A

where T ref is a reference or ambient T and A depends on the physical
properties, external conditions as well as volume and surface area of
the object exposed to the ambient. Looking at this equation just from a
mathematical angle, you can see that T can be used as a stock.

But we do not really accumulate T in nature. This is somehow similar to
representing price as stock. We do it in some situations because it
makes sense. Price is just an attribute we assign to something that
represents its perceived value, etc. It is hard to visualize price as an
accumulation process but it is easy to see that it is a variable that
goes up and down.

In short, I think that representing something like temperature as stock
depends of the situation.

What Kim refers to applies to the change in temperature and not the
temperature itself. DT = Q/(m*Cp) where DT is change in Temperature. Cp
is the specific heat. This, of course, applies when we don't have phase
change.

Zahed Sheikholeslami
Simtegra, LLC
Posted by ""Zahed Sheikh"" <zahed.sheikh@gmx.com>
posting date Sun, 27 Apr 2008 11:15:05 -0400
_______________________________________________
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