Ozeco will surely respond to this,...
Mind reader....
I see that there are several questions I need to address. Let's see if I can tackle them in some logical order. Starting with this:
Great writeup you've provided here Ozeco,...
Thank you!
but I have a question for the sake of clarity.
Would you apply the same reasoning to Bazant's limiting case?
Yes - but I would make explicit some things I left unsaid. Those being:
1) "Are the assumptions valid for the purpose?" and
2) "Are the claims made legitimate within the assumptions?"
The answers to those are "Yes" and "Yes" for Bazant.**
They are undefined for Nemec et al....
Let's see why. This is Bazant and Zhou's abstract:
Abstract: This paper presents a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed.
So we have a "simplified approximate analysis" which shows that the tower was doomed if something allowed the top portion of tower to start falling.
I state it that way because that is exactly the starting point assumed by Nemec et al. i.e. the top part of the tower had started falling. So we have like starting points for comparison. Apples with apples if you prefer the colloquialism.
From there Bazant assumed all columns in place - the safest for survival assumption - and showed that there was more than enough energy to cause collapse. Since the actual situation was some columns not carrying load the actual collapse occurred validly within the scope of Bazant's assumptions. So, as I said, "Yes" and "Yes" for Bazant. Bazant was correct.**
Now Nemec et al's abstract says:
Abstract: The differential equation of collapse of a high building is derived taking into account many influences. Computer simulation of the collapse of the WTC building is presented using two independent programs for some variations of parameters. The results of both, differential equation and computer simulation, are compared.
Note it claims "simulation of the collapse of the WTC building" and has an aim of comparing "The results of both, differential equation and computer simulation..." So the only reference to WTC is that it is to be a simulation and that simulation used to compare two methods - this latter not tied to the real collapse.
So:
For me, Bazant's limiting case suffers from the same criticism you apply,...
Whilst the two are superficially similar Bazant uses the "all columns in play" to perform a "simplified approximate analysis" through which he forms valid conclusions about the real behaviour of WTC Twin Towers. Contrast with Nemec et al's use which only sets out to compare methods - not form conclusions about the real event. the aim of comparing two methods probably achieved. But that does not interest me because it is not validly related to the real WTC 9/11 events. Specifically their intended method was to "simulate" and you cannot simulate by using a wrong mechanism. You can put a limit case around a real event and Bazant did so.
So the core of Nemec's claims was "simulation" which he didn't achieve whilst the core of Bazant's claim was "a valid approximation" which he did achieve.
Bazant deliberately used a wrong mechanism but properly allowed for the effects of the simplifying assumption. Nemec et al's assumption could not support a claim of "simulation". And, unlike Bazant, they made no allowance for the scope of the assumption.
however I find it of value and completely relevant. If Bazant's inputs and calculations are accurate (which I believe they are) his case proves global collapse under the best case scenario. Should we not apply the same uniformity of logic to this paper?
Sure - I just spent a couple of hours trying to - there's nothing in the Nemec paper which could be the basis of applying "the same uniformity of logic".
The "uniformity" you should be seeking is not the uniformity of assuming all columns in place. It is how that bit of assumption fits into the argument being made. Bazant's arguments were directed to a valid real world claim about WTC Twin towers. He achieved that aim.
What is Nemec trying to achieve? Does he achieve it? Validly?
I suggest he hasn't even clearly stated an objective.
Which is why, at this stage, I'm not answering a number of questions members have posed. We ain't sure what we are discussing.
We need to get clear what it is we want to discuss before we can progress this mini-discussion.
In my opinion this paper fails because the inputs and calculations are inadequate, not because it fails to mimic the nature of the actual collapse events.
I suggest that neither of those is the reason it fails - see the above material.
** I am specifically and deliberately referring to Bazant and Zhou. The rest of Bazant's work raises a can of worms set of issues. Set them aside till we get this easy one under control. 