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| Finite Simple Group (of Order Two) |
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Finite Simple Group (of Order Two)
The Klein Four Group
The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my
heart
You're my Axiom of Choice, you know it's true
But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll
find
We're a finite simple group of order two
I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way
Since every time I see you, you just quotient
out
The faithful image that I map into
But when we're one-to-one you'll see what I'm
about
'Cause we're a finite simple group of order
two
Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our
two-forms
Now everything is so complexified
When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense
I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel
trap
But we're a finite simple group of order two
I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple
group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")
I've proved my proposition now, as you can
see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.
Tags : Finite Simple Group of Order Two The Klein Four Math |
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Affichage : 368513
Durée : 183 s |
| Re: WTC Finite Element Analysis |
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This FEA analysis shows that the a number of
WTC core columns in the North Tower sustained
extensive damage across most of the floors of
impact.
The original description of the video is as
follows:
Although most Americans believe they know
what brought down the World Trade Center twin
towers on Sept. 11, 2001, civil engineers are
still seeking answers to questions that could
save lives in the future.
Structural engineers need to know from a
scientific perspective what happened to the
buildings during the terrorist attacks in
order to prevent future failures. The search
for answers continues with the help of a
state-of-the-art animated visualization
created by researchers at Purdue University.
Christoph Hoffmann, a professor of computer
science and director of Purdue's Rosen Center
for Advanced Computing, a division of
Information Technology at Purdue, says the
animation reveals more information than could
be conveyed through a scientific simulation
alone.
"Scientific simulations restrict us to
showing the things that are absolutely
essential to the engineer," Hoffmann says.
"This gives us a simulation that doesn't
deliver much visual information to a
layperson. Our animation takes that
scientific model and adds back the visual
information required to make it a more
effective communication tool."
The scientific simulation, the completion of
which was announced last September, required
several test runs before the researchers were
satisfied; the final test run required more
than 80 hours of high-performance computing.
The simulation depicts how a plane tore
through several stories of the World Trade
Center north tower within a half-second and
found that the weight of the fuel acted like
a flash flood of flaming liquid, knocking out
essential structural columns within the
building and removing fireproofing insulation
from other support structures. The simulation
used lines and dots to show the aircraft and
building during the event.
To develop the new animated visualization,
Voicu Popescu, an assistant professor of
computer science, developed a translator
application that creates a link between
computer simulations and computer
visualization systems to automatically
translate simulation data into a 3-D
animation scene.
"This translator is scalable and can be used
in other simulations," Popescu says.
In the animation, elements that were not part
of the scientific simulation, such as flames
and smoke, are clearly rendered, although the
visualization does not show the subsequent
effects of the fire.
Even though details were added in this
animation, Popescu says the visualization was
intentionally kept "non-descript" so that
they would not be exploitive of the horrific
attack.
"For example, on the airplane there are no
airline insignia or windows," Popescu says.
Still, Popescu says the visualization has a
realism never seen before.
"The crashes and computer models you often
see on television are not scientifically
accurate," he says. "This provides an
alternative that is useful to the nonexpert
but is also scientifically accurate, so it
provides a more realistic picture of the
event."
The visualization begins with a Google Earth
map of lower Manhattan as it appeared on
Sept. 11, 2001. The video then shows the
damage caused by the aircraft as it hit the
north tower, follows the disintegrating plane
through the interior, and then shows the
airplane metal, ignited fuel, dust and smoke
exiting the building on the opposite side.
The simulation found that the airplane's
metal skin peeled away shortly after impact
and shows how the titanium jet engine shafts
flew through the building like bullets.
As with an earlier simulation developed by
this team that examined the 9/11 attack on
the Pentagon, the World Trade Center
simulation showed that it was the weight of
the 10,000 gallons of fuel more than anything
else that caused the damage.
"It is the weight, the kinetic energy of the
fuel that causes much of the damage in these
events," Hoffmann says. "If it weren't for
the subsequent fire, the structural damage
might be almost the same if the planes had
been filled with water instead of fuel."
Mete Sozen, Purdue's Kettlehut Distinguished
Professor of Structural Engineering and a
principal investigator on the simulation
project, says the researchers worked for
years and used the best computing resources
available to recreate the event.
"To estimate the serious damage to the World
Trade Center core columns, we assembled a
detailed numerical model of the impacting
aircraft as well as a detailed numerical
model of the top 20 stories of the building,"
Sozen says. "We then used weeks of
supercomputer time over a number of years to
simulate the event in many credible angles of
impact of the aircraft."
Sozen says the actual damage to the
building's facade that was observed was
identical to the damage shown by the
numerical simulation.
"We calibrated our calculations using data
from experiments we had conducted to evaluate
the energy imparted from fluid moving at high
speed to solid targets," he says. "We
concluded that the damage map we calculated
for our numerical model of the building would
correspond closely to the actual extent of
the damage."
The simulation represented the plane and its
mass as a mesh of hundreds of thousands of
"finite elements," or small squares
containing specific physical characteristics.
In the visualization, these scientific data
points are used to show how airplane
components swept through the building and out
through the other side as the fuel ignited.
"The aircraft moved through the building as
if it were a hot and fast lava flow," Sozen
says. "Consequently, much of the fireproofing
insulation was ripped off the structure. Even
if all of the columns and girders had
survived the impact - an unlikely event - the
structure would fail as the result of a
buckling of the columns. The heat from an
ordinary office fire would suffice to soften
and weaken the unprotected steel. Evaluation
of the effects of the fire on the core column
structure, with the insulation removed by the
impact, showed that collapse would follow
whatever the number of columns cut at the
time of the impact."
The animation is the latest in a series of
projects by the Purdue team that arose after
9/11 to determine the structural damage that
occurs when an airplane collides with a
building. Although one goal was to develop
structures that can withstand a terrorist
attack, the team also has used this research
to investigate other scenarios, such as an
airplane inadvertently crashing into a
building located near an airport.
"This is important work that has many more
applications than we first thought," Hoffmann
says. "The important thing is that we are
learning so much in so many different areas."
The research was funded in part by the
National Science Foundation.
Others involved in the research are civil
engineering assistant professors Ayhan
Irfanoglu and Santiago Puiol, computer
science doctoral student Paul Rosen, and
civil engineering doctoral students Oscar
Ardila and Ingo Brachmann.
Writer: Steve Tally, (765) 494-9809
Sources: Christoph Hoffmann, (765) 494-6185,
cmh@cs.purdue.edu
Voicu Popescu, (765) 496-7347,
popescu@cs.purdue.edu
Mete Sozen, (765) 494-2186, sozen@purdue.edu
Purdue News Service: (765) 494-2096;
purduenews@purdue.edu (more) (less)
Tags : wtc wtc1 wtc2 core fea world trade center animation simulation fema nist truss 911 9/11 |
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Affichage : 16862
Durée : 300 s |
| FINITE - Short Film |
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Nothing lasts forever.
When a relationship is forced to change, how
does one come to terms with the past and
reconcile? Ultimately, relationships like
life simply exist, persist, and endure for a
limited period of time.
(FINITE is the second short film by Directors
Eric and Dusty.)
Tags : short film sci-fi sci fi scifi science fiction drama |
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Affichage : 26812
Durée : 532 s |
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