tokieda gresham 2018...2018/05/22 · big research grants cutting-edge proposals. . . all...
Transcript of tokieda gresham 2018...2018/05/22 · big research grants cutting-edge proposals. . . all...
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Toy Models
Tadashi TokiedaGresham Lecture, May 2018
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茶碗の音
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Tap a teacup.
handle
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Tap a teacup.
handle
The cup chimes —the same pitch from all 4 points.
Perhaps this is the note of this cup ?
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Tap a teacup.
handle
The cup chimes —the same pitch from all 4 points.
Perhaps this is the note of this cup ?
But now tap
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Tap a teacup.
handle
The cup chimes —the same pitch from all 4 points.
Perhaps this is the note of this cup ?
But now tap
Again a common pitch,
but a higher pitch than before.
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The inverse problem is interesting.
Suppose we are in a pitch-dark roomand don’t know the make of an object,
but we are allowed to go around tapping itand record the sound pattern.
Can we reconstruct the object from the recorded data ?
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The inverse problem is interesting.
Suppose we are in a pitch-dark roomand don’t know the make of an object,
but we are allowed to go around tapping itand record the sound pattern.
Can we reconstruct the object from the recorded data ?
In general, no :
Can’t tell E, N, W, S
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The inverse problem is interesting.
Suppose we are in a pitch-dark roomand don’t know the make of an object,
but we are allowed to go around tapping itand record the sound pattern.
Can we reconstruct the object from the recorded data ?
In general, no :
Can’t tell E, N, W, S nor 1, 2, 4 handles . . .
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杉の玉・七角
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The sides rounded by a minuscule ε
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the contact point passes continuously
The sides rounded by a minuscule ε
As soon as the rounding εbecomes zero . . .
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the contact point passes continuously
The sides rounded by a minuscule ε
As soon as the rounding εbecomes zero . . .
ouch !
discontinuous passage
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the contact point passes continuously
The sides rounded by a minuscule ε
As soon as the rounding εbecomes zero . . .
ouch !
discontinuous passage
singular perturbation
lim model ≠ modelε➛ 0
ε 0
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帯五角畳み
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N = 72 passes
N = 51 pass
N = 30 pass
Regular N-gons from tying strips into knots then tightening and flattening
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N = 72 passes
N = 51 pass
N = 30 pass
Regular N-gons from tying strips into knots then tightening and flattening
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坂を降りる
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Why did slow down ? Why was immobilized ?
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Why did slow down ? Why was immobilized ?
α
Grains have a characteristic angle of repose :the limit angle α of steepness for a pile of those grains.If we try to make the pile steeper than α , the pile avalanches and resettles at α .
(Static liquids cannot sustain any steepness : for them, α = 0 .)
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For a less-than-full jar, the center of gravity is to the downhill side of the point of contact .
The effect of gravityis to roll the jar downhill.
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β
For a more-than-empty jar, the center of gravity is to the uphill side of the point of contact .
The effect of gravityis to roll the jar uphill,
checking descent.
For a less-than-full jar, the center of gravity is to the downhill side of the point of contact .
The effect of gravityis to roll the jar downhill.
This effect can occur only if α > β .
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DES
CEN
T P
ACE
HOW FULL0% 100%immobile
A cartoon graph of the pace of descent as a function of the fill fraction :
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DES
CEN
T P
ACE
HOW FULL0% 100%immobile
A cartoon graph of the pace of descent as a function of the fill fraction :
Near 100%the grains stick to the wall — cf. viscous fluidsuntil they emerge on the free surface.There they cascade along a sigmoid profile.
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DES
CEN
T P
ACE
HOW FULL0% 100%immobile
A cartoon graph of the pace of descent as a function of the fill fraction :
Near 0% the grains oscillate as a single body,slipping on the wall — cf. inviscid fluids.
Near 100%the grains stick to the wall — cf. viscous fluidsuntil they emerge on the free surface.There they cascade along a sigmoid profile.
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紙風船
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wrin
klie
r smoother
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wrin
klie
r smoother
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wrin
klie
r smoother
relaxation from wrinkles
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wrin
klie
r smoother
relaxation from wrinkles
per cycle, more smoothness
volu
me
time
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wrin
klie
r smoother
relaxation from wrinkles
per cycle, more smoothness
volu
me
time
hit
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wrin
klie
r smoother
relaxation from wrinkles
per cycle, more smoothness
volu
me
time
hit
hit
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wrin
klie
r smoother
relaxation from wrinkles
per cycle, more smoothness
volu
me
time
hit
hit
hit
asymptote: sphere
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wrin
klie
r smoother
relaxation from wrinkles
per cycle, more smoothness
volu
me
time
hit
hit
hit
asymptote: sphere
Energy flow in usual multi-scale processes(e.g. turbulence)
LARGE SCALES
small scales
cascade
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wrin
klie
r smoother
relaxation from wrinkles
per cycle, more smoothness
volu
me
time
hit
hit
hit
asymptote: sphere
But for paper balloon
LARGE SCALES
small scales
inve
rse
casc
ade
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歌う輪・磁石
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motion spin flapping
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analogy bounce ≈ flap
motion spin flapping
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analogy bounce ≈ flap
motion spin flapping
energy E〜 height 〜 time2〜 bounce frequency−2
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analogy bounce ≈ flap
motion spin flapping
dissipation (friction, earthquake) :
energy E〜 height 〜 time2〜 bounce frequency−2
flap frequency
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analogy bounce ≈ flap
motion spin flapping
dissipation (friction, earthquake) :
⟹
energy E〜 height 〜 time2〜 bounce frequency−2
flap frequency
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analogy bounce ≈ flap
motion spin flapping
dissipation (friction, earthquake) :
⟹ ⟹
energy E〜 height 〜 time2〜 bounce frequency−2
flap frequency
frequency
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inverse problems<< phase transition >>singular perturbationviscous/inviscid coalescenceinverse cascadefinite-time singularity
Toys open up an unexpectedly rich ecology of phenomena and ideas :
and more . . .
chiming tea cupswirl vs. circulationrolling/not rolling polygonsjars of grains down a slopepaper balloon singing rim
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labsinstitutesinternetlibrariesclassroomsbig research grantscutting-edge proposals
. . .
all supremely importantthese are where
we expect science to come from
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So why toys ?
labsinstitutesinternetlibrariesclassroomsbig research grantscutting-edge proposals
. . .
all supremely importantthese are where
we expect science to come from
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In all natural phenomena there is something of the marvelous.
[Aristotle, De partibus animalium I 5.645a = DK 22A9]
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In all natural phenomena there is something of the marvelous.
There is a story thatsome visitors once wished to meet Heraclitus,and when they entered and saw him in the kitchen,
warming himself at the stove and playing with children,they hesitated.
[Aristotle, De partibus animalium I 5.645a = DK 22A9]
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In all natural phenomena there is something of the marvelous.
There is a story thatsome visitors once wished to meet Heraclitus,and when they entered and saw him in the kitchen,
warming himself at the stove and playing with children,they hesitated.
But Heraclitus said, “Come in; don’t be afraid.There are gods even here.”
[Aristotle, De partibus animalium I 5.645a = DK 22A9]
εἶναι γὰρ καὶ ἐνταῦθα θεούς
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To my esteemed audiencefor your friendly company
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To my esteemed audiencefor your friendly company
and especially toProf. Chris Budd
for his kind hospitality
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正
To my esteemed audiencefor your friendly company
and especially toProf. Chris Budd
for his kind hospitality