The Universe in a (Pretty Big) Box:

Transcription

1 The Universe in a (Pretty Big) Box: From Cells to Galaxies Using Super-Computers Diego Muñoz Michael Long Amanda Peters Randles

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8 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 Astrophysics Department of Astronomy, Harvard University

9 Computational power Computational methods Image source: Public Domain

10 Computational power Computational methods Image source: Public Domain

11 Computational power Computational methods Larger, faster computers Better, more efficient techniques and approximations Image source: Public Domain

12 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. Sir Isaac Newton, portrait by Sir Godfrey Kneller

13 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. Sir Isaac Newton, portrait by Sir Godfrey Kneller

14 Gravity "The Blue Marble" photograph of Earth, taken from Apollo 17. Source: Wikipedia Image credit: NASA / JPL-Caltech / R. Hurt. Source: Wikipedia

15 Asteroid Discovery Credit: Scott Manley Gravity

16 Gravity Whirlpool Galaxy/ M51a. Author: NASA and European Space Agency

17 A galaxy... Gravity at Cosmic Scales HST Image of NGC 4414 /Image source: wikimedia commons

18 A galaxy... Gravity at Cosmic Scales km or 1 quintillion km HST Image of NGC 4414 /Image source: wikimedia commons

19 A galaxy... Gravity at Cosmic Scales HST Image of NGC 4414 /Image source: wikimedia commons

20 Gravity at Cosmic Scales A cluster of galaxies... Burrell Schmidt telescope image of the Virgo cluster. Credit Chris Mihos et al.using the /Image source: wikimedia commons

21 Gravity at Cosmic Scales A cluster of galaxies km or 100 quintillion km Burrell Schmidt telescope image of the Virgo cluster. Credit Chris Mihos et al.using the /Image source: wikimedia commons

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23 0.15 sextillion km 6 sextillion km 0.7 sextillion km

24 Gravity Newton postulated, the the gravitational force between two bodies of masses m 1 and m 2 has a magnitude of Sir Isaac Newton, portrait by Sir Godfrey Kneller

25 Gravity Newton postulated, the the gravitational force between two bodies of masses m 1 and m 2 has a magnitude of m1 m2 Sir Isaac Newton, portrait by Sir Godfrey Kneller

26 Gravity Newton postulated, the the gravitational force between two bodies of masses m 1 and m 2 has a magnitude of m1 m2 Sir Isaac Newton, portrait by Sir Godfrey Kneller

27 Gravity Newton postulated, the the gravitational force between two bodies of masses m 1 and m 2 has a magnitude of m1 r m2 Sir Isaac Newton, portrait by Sir Godfrey Kneller

28 Gravity Newton postulated, the the gravitational force between two bodies of masses m 1 and m 2 has a magnitude of m1 r m2 where r is the distance between the bodies and G is the universal gravitational constant. Sir Isaac Newton, portrait by Sir Godfrey Kneller

29 Gravity Image license: Stock photo, photo.xchng Image ID:

30 Gravity Image license: Stock photo, photo.xchng Image ID:

31 Gravity Image license: Stock photo, photo.xchng Image ID:

32 Gravity Moon Earth Image license: Stock photo, photo.xchng Image ID:

33 Gravity Moon Earth Image license: Stock photo, photo.xchng Image ID:

34 Gravity Moon m2 Earth m1 Image license: Stock photo, photo.xchng Image ID:

35 Gravity Moon m2 Earth m1 Image license: Stock photo, photo.xchng Image ID:

36 Questions?

37 Calculating Gravitational Forces with Supercomputers

38 Calculating Gravitational Forces with Supercomputers a particle

39 Calculating Gravitational Forces with Supercomputers 1

40 Calculating Gravitational Forces with Supercomputers 2 1

41 Calculating Gravitational Forces with Supercomputers 1 2 1

42 Calculating Gravitational Forces with Supercomputers

43 Calculating Gravitational Forces with Supercomputers

44 Calculating Gravitational Forces with Supercomputers

45 Calculating Gravitational Forces with Supercomputers

46 Calculating Gravitational Forces with Supercomputers

47 Calculating Gravitational Forces with Supercomputers

48 Calculating Gravitational Forces with Supercomputers

49 Calculating Gravitational Forces with Supercomputers for N particles:

50 Calculating Gravitational Forces with Supercomputers Gravitational 3 systems require 4 an 5 enormous amount of operations for N particles:

51 Human Brain versus Computer Thinking Man by Rodin

52 Human Brain versus Computer 1 second per operation for operations Thinking Man by Rodin

53 Human Brain versus Computer 1 second per operation for operations Thinking Man by Rodin (10 billion) 2 /2 seconds to calculate gravity for a Galaxy = 1 trillion years

54 Calculating Gravitational Forces with Supercomputers Computers help us perform large numbers of operations Super-computers allow us to carry the operations out simultaneously

55 Calculating Gravitational Forces with Supercomputers 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.

56 Calculating Gravitational Forces with Supercomputers 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. CAN WE CALCULATE GRAVITY APPROXIMATELY?

57 Why Computers?

58 Why Computers? 5 = x +3

59 Why Computers? 5 = x +3 x = 2

60 Why Computers?

61 Why Computers? x = 1 2 x

62 Why Computers? x = 1 2 x

63 Why Computers? x = 1 2 x x = 0?

64 Why Computers? x = 0? 0 = 1 x = 1 2 x

65 Why Computers? x = 0? 0 = 1 x = 1? x = 1 2 x

66 Why Computers? x = 0? 0 = 1 x = 1 2 x x = 1? 1 = 1/2

67 Why Computers? x = 0? 0 = 1 x = 1 2 x x = 1? 1 = 1/2 0 1

68 Why Computers? x = 0? 0 = 1 x = 1 2 x x = 1? 1 = 1/

69 Why Computers? x = 0? 0 = 1 x = 1 2 x x = 1? 1 = 1/2 x = 0.5?

70 Why Computers? x = 0? 0 = 1 x = 1 2 x x = 1? 1 = 1/2 x = 0.5? 0.5 =

71 Why Computers? x = 0? 0 = 1 x = 1 2 x x = 1? 1 = 1/2 x = 0.5? 0.5 = x = ?

72 Why Computers? x = 0? 0 = 1 x = 1 2 x x = 1? 1 = 1/2 x = 0.5? 0.5 = x = ?

73 Why Computers? until it is good enough... Image credit:

74 Why Computers? x =

75 What is Good Enough?

76 What is Good Enough?

77 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

78 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 astronomy: The mass of the Milky Way is known only within a 50% error: billion times the mass of the Sun

79 Questions?

80 Gravity in Astrophysics

81 Gravity in Astrophysics Images: HST publicly released images, hubblesite.org/newscenter

82 Gravity in Astrophysics Images: HST publicly released images, hubblesite.org/newscenter

83 Gravity in Astrophysics Images: HST publicly released images, hubblesite.org/newscenter

84 Calculating Gravitational Forces with Supercomputers office.microsoft.com/en-us/images/

85 Calculating Gravitational Forces with Supercomputers

86 Calculating Gravitational Forces with Supercomputers

87 ...this is called domain decomposition

88 (Mihos & Hernquist 1996) Credit: NASA, ESA, and F. Summers (STScI) Simulation Data: Chris Mihos (Case Western Reserve University) and Lars Hernquist (Harvard University)

89 credit: Philip Hopkins, UC Berkeley

90 The Universe in a Box: What is the shape of the Universe??

91 Sloan Digital Sky Survey

92 Aquarius Simulation -- Virgo Consortium

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