The Good the Bad and the Awful

Transcription

The Good the Bad and the
Awful-Scientific Simulation and Prediction
Leo P. Kadanoff
([email protected])
The ASC-FLASH program,
University of Chicago
published version:
Leo P. Kadanoff: Excellence in
Computer Simulation, Computers in
Science and Engineering. March-April
2004.
Computational Scenarios. Physics Today, pp.
10-11 (November 2004).
Excellence in Computer Simulations V2.2--For Allegheny- 10-25--09
1
Summary
Worthwhile computer simulations
are done to explore uncharted
territory, resolve a well-posed
scientific or technical question, or
to make a design choice.
Some excellent work is reviewed
Some less happy stories are
recounted.
I then concentrate my attention
upon astrophysical simulations,
showing how they can explore
possible scenarios for stellar
explosions.
2
Sponsors
ASC-FLASH: DOE
Materials Research Lab: NSF
ASC is an alliance of universities and
DOE weapons labs aimed at
improving scientific computations as a
support for the program of stockpile
stewardship. FLASH is Chicago’s part
of this program. We work on
simulating and understanding novae
and supernovae events.
my role, in part, is to explain and
criticize the FLASH efforts. Here
goes:
3
Outline of Talk
The Best: Great Discoveries of the Heroic period
Excellent Recent Work
The Worst: Work which retarded scientific progress
Recent Efforts:
Nano- Jets
Turbulence in Stars
4
Alan Turing:
Turing Machine-purely theoretical,
conceptualization of computer
Enigma, put a “computer” to work in
breaking German WWII codes.
Morphogenesis. Though out process by
which instability could give birth to structure
in embryonic development. Invented
reaction-diffusion system. He conceptualized
morphogenesis as a computer which
produces structures and patterns.
5
Alder and Wainright:
Long range Order from Hard Spheres; Long Time Tails
Berni Alder and Tom Wainright produced two
great discoveries using the molecular dynamics
method. Despite the purely repulsive
interactions, they saw a phase transition from
a fluid state into a solid one. In addition, these
hard spheres, and indeed any colliding fluid
particles, engender through their motion
correlations which persist for a very long time.
(Dorfman.) These “long time tails” are now
pretty well understood as a consequence of
the hydrodynamic motion of the fluid as it
flows past the molecules within the fluid.
New territory yields new insights.
6
Models of Solar Processes
Physics:
High temperatures, nuclear reactions in
sun make neutrinos, which then travel to
earth. Solar model describes sun and
predicts neutrino flux on earth.
Story:
Experiments (Davis) catch neutrinos from sun.
Models (Bachall) predicts neutrino production.
But, simulation disagrees with observation.
After some time, model is validated.
Eventually, new theory of neutrino is
developed. Experiments confirm neutrinos
predictions from theory and simulation.
7
Chaotic behavior, now Ed Lorenz:
Chaos in ODE,
characterized
as weather,
sensitive ‘strange attractor’ structure.
dependence upon initial conditions,
or “the butterfly effect”, was
discovered “accidentally” by
Edward Lorenz working with an
early and very primitive program
for solving linked sets of ordinary
differential equations.
-A study of weather brought about
an important advance in pure
science.
dx/dt= 3 (y-x)
http://www.geom.uiuc.edu/java/Lorenz/
dy/dt= 26.5 x- y -xz
dz/dt= xy - z
8
Feigenbaum:
Period doubling.
Small computers for interactive work.
Mitchell Feigenbaum was using a
desk calculator to study a model
based upon a quadratic formula,
which took a number and
generated another number. That
process was carried on through
many steps by Feigenbaum. And
patterns emerged! These
patterns which showed how
chaos (Yorke)might be born.
x j +1 = rx j (1− x j )
€
And a wonderful world opened
up, unexpectedly.
9
Tom Witten and Len Sander: “DLA”
One of the first examples
of a physical system being
put forward as an
algorithm. Question
answered “How can you
construct a fractal by a
natural process?
T.A. Witten and L. Sander Diffusion-limited
aggregation, a kinetic phenomenon. Phys.
Rev. Lett. 47, 1400, (1981)
Hastings and Levitov
10
The DLA Algorithm
a
b
c
d
Start with
walker
at infinity
It does a
random walk
until it reaches
aggregate
It stops at
nearest
neighbor
site
A walker is
introduced at
infinity once
more
11
Excellent Recent Work
We may suspect that the heroic
age is now passed. The nature of
discoveries is now somewhat
different. I reach for recent
examples to describe the best
things that computational people
are now doing.
Examples:
•Evolution of the Universe
•Solar neutrinos
•nanojets
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Forming Structures in the Universe
Simulators have
explored the early
history of the
Universe.
The hope is that an
extensive process of
simulation of a wide
variety of models
may eliminate all but
but one model, thus
telling us the nature
of the universe.
simulations, Andrey Kravtsov
start with almost uniform universe
13
Structures....
The basic element in this
calculation are many many
smallish clusters of galaxies
In time, gravity produces
instabilities which form
fractal?! structures.
These are large clusters of
galaxies.
clusters of galaxies from simulation
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Structures ...
We can ask of the
simulations: Will they do
the desired job of filtering
out wrong theories?
Is the space of possible
theories too large?
Also the universe is mostly
unobserved “dark matter”.
I am pessimistic about
accurate simulations of
things that have never
been observed.
present day simulation result
looks like our universe?
15
Structures ...
15
Structures ...
piece of the sky
from Sloan digital sky survey
15
The Worst Simulations
Britain’s Transportation Investment Model.
Goal: To get the best transportation system
and while minimizing public spending. Broad mix
of roads, rail, public improvements. Overall
maximization, all expressed in pounds.
Conclusion: Detailed predictions and directions
for public spending. Several peculiar features.
For example, computer result recommends zero
spending on pedestrian road crossings. That’s
strange because flow of pedestrian traffic is
valued in model.
Explanation: Cost......
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Transportation Investment Model
Explanation: Costs of social programs
included in minimization. Pensions are a
debit. Most people killed at road crossings
are old, and the model gives them a negative
value. Hence, maximization gives pedestrian
safety a negative value.
Moral: Design Goals are usually
multidimensional. All sensible modelers ask
not only what comes out but also why did we
get this outcome? Modeling efforts should
include theory and common sense.
17
Cool Fusion
An experiment suggested that fusion was occurring in
a system involving resonant absorption of sound in
deuterated acetone. The paper involved both
experiment and simulations. “[A] roughly tenfold
increase in the external driving pressure was used in
the calculations” beyond the pressure directly
produced by the experimental situation “to
approximately account for the effect of pressure
intensification within the imploding bubble clusters”.
As a result their “[h]ydrodynamic shock code
simulation supported the observed data”. The
refereeing process allowed an apparently uncontrolled
approximation in a key step in the computer
calculation. It would seem that computer simulations
require very little quality control, especially when the
paper seems exciting and provocative to the editor,
here D. Kennedy.
D. Kennedy Science
2002:
Vol. 295. no. p. 1793
R. P. Taleyarkhan, C.
D. West, J. S. Cho, R.
T. Lahey, Jr., R. I.
Nigmatulin, and R.
C. Block Science
295 2002:
1868-1873
18
single bubble sonoluminescence
Sound waves produce pressure
oscillations in fluid, shape of
container focuses sound.
Low pressure makes a bubble.
High pressure produces bubble
collapse, concentration of
energy, higher temperatures
10,000 or 100,000 degrees
and light comes off.
First, experimental discovery.
Then, theory experiment and
simulations explore phenomena.
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Trouble Arises
R. Pecha, B. Gompf, G.
Nick, Z. Q. Wang, and
W. Eisenmenger Phys.
Rev. Lett. 81, 717–720
(1998)
See Lohse,
Brenner,
Hilgenfeldt in Rev
Mod Phys 49
(2002).
However, early workers seem to have been
misled by their enthusiasm for novel energy
sources. Early experiments suggested short
pulse widths implying very high temperatures,
novel methods of generating energy. Early
simulations left out viscosity and got shocks
and very short pulse width. In fact, without
viscosity the width of the shocks would only
be limited by the resolution of the
computation. A “better”, i.e. more expensive,
computation would give sharper shocks and
higher temperature. So early simulations, and
investigators desires, led people in the wrong
direction. After Gompf measured width
correctly, simulators get better results.
20
In contrast, Vuong & Szeri did early
sonoluminescence simulations which
had the right answer: long pulse
widths, low temperatures, no novel
mechanism for energy production. I
report sadly that this correct
conclusions was drowned out by the
calculations with the desired, but
incorrect results.
V. Q.Vuong and A. J.
Szeri, 1996, Physics of
Fluids 8(9), 2354-2364.
It appeared that the early simulations
were performed to support a desired
result, rather than ask “what is
true?.”
21
In contrast, Vuong & Szeri did early
sonoluminescence simulations which
had the right answer: long pulse
widths, low temperatures, no novel
mechanism for energy production. I
report sadly that this correct
conclusions was drowned out by the
calculations with the desired, but
incorrect results.
It appeared that the early simulations
were performed to support a desired
result, rather than ask “what is
true?.”
However, recent experiments show
both high temperatures and low, but
still no novel mechanisms.
V. Q.Vuong and A. J.
Szeri, 1996, Physics of
Fluids 8(9), 2354-2364.
David J. Flannigan and
Kenneth S. Suslick
Phys. Rev. Lett. 95,
044301 (2005)
21
Conclusion of this Section
A program of modeling should either
elucidate new processes or identify
wrong directions. Otherwise there is
no point is carrying it out. In many
examples concerned with novel
mechanisms for the concentration of
energy, the simulations were quite
pointless and played a somewhat
negative role in the advance of the
field.
In the transportation model no sense
led to nonsense.
22
Some Recent Challenges
• Nano-jets
• Rayleigh Taylor
• Type Ia supernova
23
Can one make a nano-jet?
Do molecular dynamics:
Drive pentane through
gold nozzle
From these simulations
this nano-jet almost
works. If it works, It can
be used, for example to
write on chips on the
nanoscale.
For now, the available
driving pressure is not
quite high enough..
Uzi Landman, Michael Moseler Science 289 1165 (2000)
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New science: Look at thin necks
25
Compare with shape
from macroscopic scale
experiment; it’s different
Jens Eggers PRL 89, 084502
(2002) argues that shapes are
different because fluctuations are
important in the nano-study.
experiment: S. Nagel universal shape
26
Rayleigh Taylor Instability
Source of
Instability:
hotter fluid tends to rise
cooler,
more dense, fluid
hotter,
less dense, fluid
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Rayleigh Taylor Instability
Source of
Instability:
hotter fluid tends to rise
cooler,
more dense, fluid
hotter,
less dense, fluid
This instability is very important
for DOE. They saw variability in
their early studies ; they
sponsored 15+ major studies
through ASC program
27
The Raleigh Taylor Instability.
Small deviations from perfect
surface flatness triggers an
instability. The two fluids
penetrate into one another.
Analysis (dimensional and RG
arguments) suggest a
penetration distance
h = αAgt
2
with A being the Atwoods number
(density contrast) and α being
dimensionless---and also Universal (!?).
Kai Kadau...Berni Alder, “Nanohydrodynamics simulation of
R-T Instability”, ‘04. 1.3•108 particles
28
h = αAgt
2
About 15 groups have
measured or calculated
α. Their results are
important for us (a DOE
supported astrophysics
group) because the
instability occurs on the
surface of an exploding
star.
Fluid Mechanics Simulation of RT
instability. “On Validating an Astrophysical
Simulation Code”. A. C. Calder, et al.
Astrophys.J.Supp. 143 201-230 (2002).
The value of α differs from previous
picture by a factor of two.
29
Reynolds number
effects on
Rayleigh–Taylor
instability with
possible
implications for
type Ia supernovae
William H. Cabot
Andrew W. Cook
Nature Physics 2,
562 - 568 (2006)
Result α varies in
course of
experiment.
Rayleigh-Taylor Simulation
30
Resolution Study d=2
denser fluid on top
color codes for density
4
8
16
32
64
128
256
512
1024
2048
(grid points)
Calder et al
31
Summary of Different Studies
A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution
three-dimensional numerical simulations: The Alpha-Group collaboration
Guy Dimonte,et al. Physics of Fluids Vol 16(5) pp. 1668-1693. May 2004
The ‘b’ refers to the bubble, which is the mode of penetration of the light fluid. The heavy
fluid penetrates as spikes.
32
Result
Don’t trust the value of α
It is not universal and depends on
the details of the calculation being
done
Don’t trust any Rayleigh Taylor
calculation with zero surface
tension. Mathematically, it’s an
ill posed problem and answers
depend upon details of what
happens at the earliest time.
33
Nova and Supernova
Unburned material from an
ordinary star accretes
onto a white dwarf star.
The material is then ready
to undergo a very rapid
burn.
In a nova, the burn is
preceded by a mixing
which we argue is caused
by wave action in the
upper layers of the white
dwarf.
cartoon by NASA
34
Nova: Mixing makes burn possible
Breaking carbon/oxygen waves
on a solar mass white dwarf.
The waves are driven by a
resonance interaction with a
wind in the overlying accreted
hydrogen layer, analogously to
terrestrial ocean waves. This
carbon/oxygen spray helps
catalyze the hydrogen
thermonuclear burning that
powers classical novae.
We do not know enough about
wind velocity, etc. for a good
check of theory against
observation.
A. Alexakis, et al., Astrophysical
Journal, in press. Visualization was
done by ANL/Futures Laboratory
35
On to type Ia’s Supernovae:
a really hard problem
A supernova is a white dwarf with
nuclear material all mixed up and
ready to explode. It needs a really
good push to get a nuclear
detonation. It’s hard to see where
that push comes from. Furthermore,
the mix of elements produced by an
artificial detonation is wrong.
A new approach is needed.
a drawing of an ordinary star
feeding “flammable” material
onto a white dwarf
36
A new kind
of trigger. A local
Step I:
fluctuation produces a hot
bubble which rises through
the material. Instabilities
produce a very
unsymmetric bubble.
37
A new kind
of trigger. A local
Step I:
fluctuation produces a hot
bubble which rises through
the material. Instabilities
produce a very
unsymmetric bubble.
37
38
Step II:
Inertial focusing
But after a time it was noted
that the direct effect of this
surfacing was not a
detonation.
Through
insight and simulation Tomaz
Plewa et. al. showed that hot
material would shoot up from
the bubble, fly across the
star, dredge up unburned
material, and the whole mess
would refocus on the other
side.
BOOM
39
Things Learned
Our DOE sponsors came to visit.
We had previously argued that the basic
Rayleigh Taylor simulation was unreliable.
We told the sponsors about the supernova
simulation. But our supernova calculation is
based on the R.T. instability and is at least
equally unreliable. How could we justify their
support?
We argued that our work was an exploratory
simulation and was valuable because, using
calculations of this kind, one could
40
using calculations of this kind, one could......
• produce a new and interesting scenario for
supernovae behavior
• suggest other calculations and observations which
might check this scenario.
41
We further argued that no calculation in which fluid
flow was driven by highly turbulent mixing is likely to
be fully reliable but nonetheless the DOE might use
such calculations to
• discover unexpected behaviors, and thus help
eliminate surprises.
• Start off programs for carefully checking suggested
mechanisms.
• suggest parameter variation exercises to set upper
limits on reliability of their calculations
42
When used this way,
a simulation provides an argument,
How do the power of argumentation provided by
exploratory simulations compare to that of
rhetorical or order-of-magnitude discussions?
Since the simulations must include everything to
make a star go boom, they provide an internal
check of consistency and completeness not
available through words. On the other hand, some
intermediate steps in the argument may have
their weaknesses hidden in unexamined computer
processes. Words may be better than computer
output for showing up weak arguments.
43
But, there are also major dangers in simulations.
Often simulations are directly aimed at confirming our
expectations, thereby throwing away the possibility
of finding anything new. In addition, we simulators
must be most careful to distinguish between
simulations as argument versus simulations as proof.
There is a considerable risk of confounding the two
approaches. It is tempting to say that
"supercomputer simulations show..." when what is
meant is more like "recent investigations have raised
the possibility that...". In our writing, we all are
tempted to replace "it would please us if..." by "we
know that ..". And if we scientists and engineers join
up with all those around us--in places high and low-who confound possibility with proof, and desire with
truth, who then will believe us in anything we say?
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The Good the Bad and the Awful

Transcription

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