VPM Overview
Gopichand Paturi
gopichandpaturi at gmail.com
Tue Mar 11 11:03:29 PDT 2014
On Tue, Mar 11, 2014 at 7:47 PM, Robert Helling <helling at atdotde.de> wrote:
>
> On 10.03.2014, at 08:41, Gopichand Paturi <gopichandpaturi at gmail.com>
> wrote:
>
> Hi Robert (atdotde),
>
> I guess you are here summarizing the webpage you were referring to on
> deepocean.net.
>
Yes, That's what I have been precisely learning. I wrote the gist of
all that I understood abstracting the equations and technical details.(It
just an essence/abstract which I felt because you were asking me about the
theoritical details previously.)
>
> I have read that page now. I still do have a number of questions:
>
> Thankyou for having a deep look into the reference.
> 1) Do you have any idea where their eq. (18a) comes from? It even seems
> wrong unit wise all terms but the last being of unit pressure while the
> last is has units of pressure^4).
>
> Yes, As far as a dimensional analysis is concerned you are absolutely
right.
But I think that's a printing error there. If you see eqn 18a ...the (P in)
term is replaced by saturation pressure and Pamb by Pf.
So, I have a feeling that the Pf is pointing to that value with a
superscript of 3(=). If you take units of the remaining expression as you
rightly said even that is pressure which can be got from eqn 5b(I think so,
by equating reservoir pressure to zero since the bubble is permeable(This
is just my guess, I'm not sure though)). Also Pf being final ambient
pressure supports this fact.
> 2) I don't see how you get (19) from the others but maybe I have not tried
> hard enough.
>
Yes, It is perfectly valid derivation sir. I have checked and confirmed
it in the actual VPM published research paper, which I am uploading with
this mail.
>
> I completely don't get the section on "mechanical equilibrium, but partly
> because I don't even understand the symbols, single \partial's don't make
> sense to me. But my impression it is just the derivative of the previous
> section (as in work vs force).
>
> Even I have emphasized more on thermodynamic equilibrium part only, and
limiting myself to checking the both results are same. They are indeed the
same.
Sir, If you check actual research paper that I uploaded Yount himself did
the proof by Mechanical equilibrium with which the answers coincide.
Probably this explanation of VPM has comeup recently by looking it in
Thermodynamic way(probably backtracking from force to work).
> The whole point of "number of bubbles" and "total volume" seem bogus to me
> (these being extensive quantitates while all the rest is about intensive
> quantities. Plus the fact that the initial distribution f(r ) is not really
> know. But maybe this does't matter as the condition could be reformulated
> in terms of the minimal radius of bubbles that will eventually grow.
>
> Yes sir, the number of bubbles is a fact that hasn't been calculated. If
you see the total process of derivation, everything is built up on the
theory that maintaining safe bubble count, but it is never calculated. I
felt that it is just built to support the theory and the math. All that was
done is a simple proportional analysis as far as I see it which made role
of radius of the bubble critical.
In the name of bubble they calculated the critical radius and also used
this value to find pressures.(Finding the actual number of bubbles is
always bypassed).
But as far as Volume is concerned I found it convincing and intuitive
because, I think reaching a certain levels of volumes of free gas in the
solution could trigger bubble formation.
(I understand that you are a physics professor & you don't accept things
like that, same with my prof here :-) ), Frankly speaking I did not find a
better explanation.
Everywhere it's given it's proportional and nothing else. (Probably this is
a experimental result !!)
> I have more to say about the later parts of that web page (from "applying
> VPM to diving"). But have to rush now.
>
> Sure, Please let me know them later.(Even I need to work more in this
regard).
> Other things to do: Do you have the python code running as well as the
> fortran (or translated to C) code? Do they indeed give the same schedules?
> Have you identified the key equations from the webpage in the python code?
>
> Yes, I have the code that you gave me. I'm verifying the some application
specifics with that code like critical minimum radius etc.
I am correlating my understanding with the code you gave, as I sent you
a link showing the proof to assign independent bubbles to inert gases in
the chat on IRC. I am also correlating the equations.
But I haven't checked if they give the same results.
I want to do that aspects once
I'm done with the GSoC application formalities, because you need to review
it once/twice, & there is very less time left.
(But if you think I must be doing these before the application phase, let
me know, I will do them. I am postponing these things because of my current
time constraint).
Once you tell me it's ok with the theory,
I would proceed to the implementation part, as it involves getting used to
subsurface's helper functions as well as running the fortran/python/c code
on my system to verify later.
> For a start, we should ignore trimix (N2+O2 should be enough for now) as
> well as repetitive diving.
>
Yes, I think this is a good idea. Dealing with one inert gas initially and
successfully implementing along with testing phase, it would help us to
easily write code for the trimix later (probably could be implemented by
just initializing another bubble in every compartment, and dealing with
some trivial aspects).
This helps in removing some complications involved also during debugging.
I strongly believe I have lots to learn about VPM further, because every
time I go thru it I'm getting a better picture. I think this is a continous
process until I start my hands on work for the summer.
Thanks & Regards,
Gopichand.
> --
>
> .oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oO
> Robert C. Helling Elite Master Course Theoretical and Mathematical
> Physics
> Scientific Coordinator
> Ludwig Maximilians Universitaet Muenchen, Dept.
> Physik
> Phone: +49 89 2180-4523 Theresienstr. 39, rm. B339
> http://www.atdotde.de
>
>
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