The Universe in a (Pretty Big) Box · 2013. 4. 14. · Kneller GRAVITY is one of the fundamental forces of the Universe, that is, it originates with the universe itself. However,

The Universe in a (Pretty Big) Box:From Cells to Galaxies Using Super-Computers

Diego Muñoz Michael Long

Amanda Peters Randles

Thursday, October 25, 12







The Universe in a (Pretty Big) Box:From Cells to Galaxies Using Supercomputers

Part I 14 Billion Years of History told by 10 Billion

Particles: A Simulated Universe

Diego Muñoz Harvard-Smithsonian Center for AstrophysicsDepartment of Astronomy, Harvard University


Computational power Computational methods

Image source: www.clker.com, Public Domain


http://www.clker.com








Larger, faster computers Better, more efficient techniquesand approximations





Gravity

Sir Isaac Newton, portrait by Sir Godfrey Kneller

GRAVITY is one of the fundamental forces of the Universe, that is, it originates with the universe itself.

However, it was not understood until Isaac Newton’s Principia Matematica (1687). The term originates from the Latin gravitas, which means weight.


Gravity


GRAVITY is one of the fundamental forces of the Universe, that is, it originates with the universe itself.

However, it was not understood until Isaac Newton’s Principia Matematica (1687). The term originates from the Latin gravitas, which means weight.


Gravity

"The Blue Marble" photograph of Earth, taken from Apollo 17. Source: Wikipedia

Image credit: NASA / JPL-Caltech / R. Hurt. Source: Wikipedia


GravityAsteroid Discovery 1980-2010. Credit: Scott Manley


Gravity

Whi

rlpoo

l Gal

axy/

M51

a . A

utho

r: N

AS

A an

d E

urop

ean

Spa

ce A

genc

y


Gravity at Cosmic Scales

HST Image of NGC 4414 /Image source: wikimedia commons

A galaxy...




1000000000000000000 kmor 1 quintillion km

A galaxy...




A galaxy...



Burrell Schmidt telescope image of the Virgo cluster. Credit Chris Mihos et al.using the /Image source: wikimedia commons

A cluster of galaxies...



Burrell Schmidt telescope image of the Virgo cluster. Credit Chris Mihos et al.using the /Image source: wikimedia commons

100000000000000000000 kmor 100 quintillion km

A cluster of galaxies...



6 sextillion km

0.7 sextillion km

0.15 sextillion km


Gravity


Newton postulated, the the gravitational force between two bodies of masses m1 and m2 has a magnitude of


Gravity



m1 m2


Gravity



m1 m2


Gravity



m1 m2 r


Gravity



m1 m2 r

where r is the distance between the bodies and G is the universal gravitational constant.


Gravity

Image license: Stock photo, photo.xchng Image ID: 909780


Gravity



Gravity



Gravity


Earth

Moon


Gravity


Earth

Moon


Gravity


Earth

Moon

m1

m2


Gravity


Earth

Moon

m1

m2


Questions?


Calculating Gravitational Forces with Supercomputers



a “particle”



1



1

2



1

21



1

21

3



1

21

23

3



1

21

23

3

4



1

21

23

3

4

4

5

6



1

21

23

3

4

4

5

6

5



1

21

23

3

4

4

5

6

5

8 79

10



1

21

23

3

4

4

5

6

5

8 79

10



1

21

23

3

4

4

5

6

5

8 79

10for N particles:



1

21

23

3

4

4

5

6

5

8 79

10

Gravitational systems require an enormous amount of operations

for N particles:


Human Brain versus Computer

Thinking Man by Rodin




1 second per operationfor operations




(10 billion)2/2 seconds to calculate gravity for a Galaxy = 1 trillion years

1 second per operationfor operations



• Computers help us perform large numbers of operations

• Super-computers allow us to carry the operations out simultaneously





• Super-computers allow us to calculate approximate solutions in an efficient manner.





• Super-computers allow us to calculate approximate solutions in an efficient manner.

CAN WE CALCULATE GRAVITY APPROXIMATELY?


Why Computers?


Why Computers?

5 = x +3


Why Computers?

5 = x +3x = 2


Why Computers?


Why Computers?

x = 1 2x


Why Computers?

x = 1 2x


Why Computers?

x = 1 2x

x = 0?


Why Computers?

x = 1 2x

x = 0? 0 = 1


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1?


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1? 1 = 1/2


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1? 1 = 1/2

0 1


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1? 1 = 1/2

0 10.5


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1? 1 = 1/2

0 1

x = 0.5?

0.5


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1? 1 = 1/2

0 1

x = 0.5? 0.5 = 0.707...

0.5


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1? 1 = 1/2

0 1

x = 0.5? 0.5 = 0.707... x = 0.6411?

0.5


Why Computers?

x = 1 2x

x = 0? 0 = 1x = 1? 1 = 1/2

0 1

x = 0.5? 0.5 = 0.707... x = 0.6411? 0.6411 0.64122...

0.5


Why Computers?

Image credit:http://www.shiftingstates.com

until it is “good enough”...


http://www.shiftingstates.com

http://www.shiftingstates.com

Why Computers?

0.6411857445049 8598448620048211482366656282095719110...

x =


What is “Good Enough”?





In physics: the fine structure constant is known within 10 significant figures. Its relative standard of uncertainty is 0.32 parts per billion



In physics: the fine structure constant is known within 10 significant figures. Its relative standard of uncertainty is 0.32 parts per billion

In astronomy: The mass of the Milky Way is known only within a 50% error: 1.0 - 1.5 billion times the mass of the Sun


Questions?


Gravity in Astrophysics



Images: HST publicly released images, hubblesite.org/newscenter









http://openclipart.orgoffice.microsoft.com/en-us/images/






...this is called domain decomposition


(Mihos & Hernquist 1996)Credit: NASA, ESA, and F. Summers (STScI) 2008

Simulation Data: Chris Mihos (Case Western Reserve University) and Lars Hernquist (Harvard University)

http://hubblesite.org/newscenter/archive/releases/2008/16/video/d/


http://www.nasa.gov/

http://www.nasa.gov/

http://www.spacetelescope.org/

http://www.spacetelescope.org/

http://www.stsci.edu/

http://www.stsci.edu/

credit: Philip Hopkins, UC Berkeley Thursday, October 25, 12

The Universe in a Box:

What is the shape of the Universe??


Sloan Digital Sky Survey http://www.sdss.org


http://www.sdss.org

http://www.sdss.org

Aquarius Simulation -- Virgo Consortium




Documents

The Universe in a (Pretty Big) Box · 2013. 4. 14. · Kneller GRAVITY is one of the fundamental forces of the Universe, that is, it originates with the universe itself. However,