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1 ( )
2 () ( ) SDSS : d 2 r i dt 2 = Gm jr ij j i rij 3
3 = Newton 3 0.1% 19
4 ( ) 3 3 (2 )
5 ,3 Sun L4 L5 Jupiter Figure-8 solution 10 Figure-8 Solution 3 (0.005% )
6 d 2 x = f(x) (1) dt2 x(0) = x 0, dx dt t=0 = v(0) = v 0 (2) 1 dx/dt = f(x) x(t +Δt) =x(t)+δtf(x(t))
7 e Nature : Laskar and Gastineau 2009 ( 0.38mm)
8 1 2
9 = /10
10 ρ R d 2 R dt = πgρr3 /R 2 = 4 πgρr (3) 3 d 2 r dt 2 = 4 3 πgm/r2 (4) M ρr 3 a(t) ρ(t) =ρ 0 /a 3, r = r 0 a (5) 2 a d 2 a dt 2 = 4 3 πρ 0/a 2 (6) 3 2 a 0 t
11 ( ) )
12 ? X X 2 Hot dark matter Cold dark matter
13 1
14 Ill-posed problem??
15 f(x, v) :6 f(x, v)dxdv dxdv f t + v f Φ f v =0, (7) Φ 2 φ = 4πGρ. (8) G ρ ρ = m dvf, (9)
16 . 1996
17 M82 X NASA Chandra X
18 2 2 D = D
19
20 f t = A(f(x)) (10) ( A f 2) (1) df df f 0 (x) A(f 0 (x)) = 0 f = f 0 + df df (2) : df f 0 df : df t = B(df (x)) (11) B(αdf 1 (x)+βdf 2 (x)) = αb(df 1 (x))+βb(df 2 (x)) (12) (3) df 1 df 1 df 1, df 2 df 1 + df 2
21 λ λdf = B(df ) (13) df = e λt df 0 λ f 0 f 0 df df
22 , D =1.05 (2), D =10 λ: (3), D = 100, D = 709
23 , D = 1000 gravothermal instavility V. Antnov (1961) : Hachisu & Sugimoto (1978) Hachisu et al. (1978) : Cohn (1980):
24 3 (Nature Vol 428 No , Formation of massive black holes through runaway collisions in dense young star clusters ) 1. : 2. M82 IMBH 3. : Classic View (Rees 1984) 2...
25 () ( ) 3 merger : ( ) M82 BH Matsumoto et al. ApJL 547, L25 BH 10M BH > 10 6 M
26 M82 IMBH ( ) () >> 10, << 10 6 BH M82 (K band) 700M = IMBH (intermediate-mass BH). M : BH (2) HST NICMOS/Keck NIRSPEC McCrady et al. (astro-ph/ ) IMBH ( ) IMBH IMBH How IMBHs were formed? ()
27 McCrady et al (astro-ph/ ) Cluster #11 (MGG-11) σ r =11.4 ± 0.8km/s half-light radius 1.2 ± 0.17pc IMBH ( ) 3. IMBH ( ) kinetic mass 3.5 ± M Age 10Myrs. M/L ( ) (< 10 Myrs) King model with W 0 = 7-12 Salpeter IMF (as suggested by McCrady et al) Star-by-star simulation for MGG-11 (MGG-9 is scaled) W 0 8 (MGG-11 ) MGG-9 ( )
28 ( ) BH M ( ) IMBH IMBH IMBH / M82 IMBH ( ) (BH2003 talk) 2MASS Chandra M82-X1 MGG Radiation recoil
29 IMBH SMBH Merger SMBH Growth timescale would be too large 3. SMBH IMBH? ( ) Ebisuzaki et al ApJ 562, 19L 1) 2).... 3) 4) IMBH 3. IMBH 4. IMBH IMBH Katz and Gunn 1992 : Cray YMP : 1000
30 Saitoh et al animation GRAPE-5 1 (!) 1 : 1 : 1 : 4-5 :
31 Saitoh et al Star formation with SPH Large scale structure formation with AMR animation (Baba et al 2009) 1 2 SPH Cray XT4 ASURA 10pc ( 500pc) 10K ( 10 4 K) 3000M ( 10 5 M )
32 2006: Xu et al, Science 311, 54 Nov 2008: Burst of results from VLBA Several data from VERA (Compiled by Dr. Asaki)
33 ( 30km/s)
34 ( ) ( ) + (Fujii et al. 2010) animation a1 animation a2 animation b1 Stable against radial mode (a1, a2) Spiral arms form They seem to be maintained for very long time
35
36 148Gflops Gflops 10 (GRAVITY PIPE, GRAPE) GRAPE Host Computer Time integration etc. GRAPE Interaction calculation : :
37 GRAPE 1988 GRAPE GRAPE
38 GRAPE GRAPE = GRAPE: 1/100 GRAPE-6 ( ()) μm μm nm nm 10 GRAPE-DR :
39 GRAPE-DR R i = j f(x i,y j ) (M) 2 y j PEID BBID A x + ALU B T 32W 256W 256 (K M ) W MHz Gflops PCIe 20
40 GRAPE-DR GRAPE-DR : 128-, 128- (105Tflops peak) : Intel Core i7+x GB : x4 DDR LU ( 1A: CPU 2 ) 430Gflops(1 ) 670Gflops(2 ) 1 CPU 11 GDR 4 chips GDR 1 chips GRAPE-6 HD5870 Performance for small N much better than GPU (for treecode, the multiwalk method greatly improves GPU performance, though)
41 Little Green 500, June 2010 (nm) (GF/W) GRAPE-DR GRAPE Tesla C Xeon #2: IBM PowerXCell, #9: NVIDIA Fermi GRAPE-DR 10 GRAPE-6 GRAPE-6 10 : 30 GRAPE-DR FPGA ASIC
42 2 : % A Green /24
1. : 1.5 2. ( ): 2.5 3. : 1 ( ) / minimum solar nebula model ( ) http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) http://www-astro.physics.ox.ac.uk/~wjs/apm_grey.gif ( ) SDSS : d 2 r i dt 2 ÿ j i
A 99% MS-Free Presentation
A 99% MS-Free Presentation 2 Galactic Dynamics (Binney & Tremaine 1987, 2008) Dynamics of Galaxies (Bertin 2000) Dynamical Evolution of Globular Clusters (Spitzer 1987) The Gravitational Million-Body Problem
4 19
I / 19 8 1 4 19 : : f(e, J), f(e) Phase mixing Landau Damping, violent relaxation : 2 2 : ( ) http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) http://www-astro.physics.ox.ac.uk/~wjs/apm_grey.gif
EGunGPU
Super Computing in Accelerator simulations - Electron Gun simulation using GPGPU - K. Ohmi, KEK-Accel Accelerator Physics seminar 2009.11.19 Super computers in KEK HITACHI SR11000 POWER5 16 24GB 16 134GFlops,
/ 18 12 4 ( ) ( ) : : f(e, J), f(e) Phase mixing Landau Damping, violent relaxation : 2 2 : ? m i d 2 x i dt 2 = j i f ij (1) x i m i i f ij j i f ij G f ij = Gm i m j x j x i x j x i 3, (2) ( ) 2 (
Gravothermal Catastrophe & Quasi-equilibrium Structure in N-body Systems
2004/3/1 3 N 1 Antonov Problem & Quasi-equilibrium State in N-body N Systems A. Taruya (RESCEU, Univ.Tokyo) M. Sakagami (Kyoto Univ.) 2 Antonov problem N-body study of quasi-attractivity M15 T Antonov
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THE STAR FORMATION NEWSLETTER No.291-14 March 2017 2017/04/28 16-20 16. X-Shooter spectroscopy of young stellar objects in Lupus. Atmospheric parameters, membership and activity diagnostics 17. The evolution
23 Fig. 2: hwmodulev2 3. Reconfigurable HPC 3.1 hw/sw hw/sw hw/sw FPGA PC FPGA PC FPGA HPC FPGA FPGA hw/sw hw/sw hw- Module FPGA hwmodule hw/sw FPGA h
23 FPGA CUDA Performance Comparison of FPGA Array with CUDA on Poisson Equation (lijiang@sekine-lab.ei.tuat.ac.jp), (kazuki@sekine-lab.ei.tuat.ac.jp), (takahashi@sekine-lab.ei.tuat.ac.jp), (tamukoh@cc.tuat.ac.jp),
1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
sec13.dvi
13 13.1 O r F R = m d 2 r dt 2 m r m = F = m r M M d2 R dt 2 = m d 2 r dt 2 = F = F (13.1) F O L = r p = m r ṙ dl dt = m ṙ ṙ + m r r = r (m r ) = r F N. (13.2) N N = R F 13.2 O ˆn ω L O r u u = ω r 1 1:
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HPC / (CfCA) HPC 2007/11/23-25 CfCA GRAPE GRAPE GRAPE-DR HPC : : 1 1 (II ) Ia 100 1 ( ) 0.1 pc 1 AU 3 : 1 100 Top-down Katz and Gunn 1992 Dark Matter + + DM, : :SPH 10 4 Cray YMP 500-1000 : 10 7 Saitoh
IPSJ SIG Technical Report Vol.2014-ARC-213 No.24 Vol.2014-HPC-147 No /12/10 GPU 1,a) 1,b) 1,c) 1,d) GPU GPU Structure Of Array Array Of
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Note.tex 2008/09/19( )
1 20 9 19 2 1 5 1.1........................ 5 1.2............................. 8 2 9 2.1............................. 9 2.2.............................. 10 3 13 3.1.............................. 13 3.2..................................
arxiv: v1(astro-ph.co)
arxiv:1311.0281v1(astro-ph.co) R µν 1 2 Rg µν + Λg µν = 8πG c 4 T µν Λ f(r) R f(r) Galileon φ(t) Massive Gravity etc... Action S = d 4 x g (L GG + L m ) L GG = K(φ,X) G 3 (φ,x)φ + G 4 (φ,x)r + G 4X (φ)
http://www.ns.kogakuin.ac.jp/~ft13389/lecture/physics1a2b/ pdf I 1 1 1.1 ( ) 1. 30 m µm 2. 20 cm km 3. 10 m 2 cm 2 4. 5 cm 3 km 3 5. 1 6. 1 7. 1 1.2 ( ) 1. 1 m + 10 cm 2. 1 hr + 6400 sec 3. 3.0 10 5 kg
1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l
1 1 ϕ ϕ ϕ S F F = ϕ (1) S 1: F 1 1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l : l r δr θ πrδr δf (1) (5) δf = ϕ πrδr
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2.2 1 2.2 2.2.1 (LSR: Local Standard of Rest) 2.1 LSR R 0 LSR Θ 0 (Galactic Constant) 1985 (IAU: International Astronomical Union) R 0 =8.5 kpc, Θ 0 = 220 km s 1. (2.1) R 0 7kpc 8kpc Θ 0 180 km s 1 270
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2010 KEK (Japan) (Japan) (Japan) Cheoun, Myun -ki Soongsil (Korea) Ryu,, Chung-Yoe Soongsil (Korea) 1. S.Reddy, M.Prakash and J.M. Lattimer, P.R.D58 #013009 (1998) Magnetar : ~ 10 15 G ~ 10 17 19 G (?)
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Formation process of regular satellites on the circumplanetary disk Hidetaka Okada Department of Earth Sciences, Undergraduate school of Scie
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80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = n λ x i e λ x i! = λ n x i e nλ n x i! n n log l(λ) = log(λ) x i nλ log( x i!) log l(λ) λ = 1 λ n x i n =
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NGC1068 Dark Matter Halo baryon gas stars SMBH SMBH 1 SMBHs? (AGN) AGN Seyfertization Taniguchi 1987, ApJ, 317, L57 AGN The dead quasar problem (Rees 1990, Science, 247, 817) T AGN ~ 10 8 yrs AGN AGN
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2003-08-04 1984 VP-1001 CPU, 250 MFLOPS, 128 MB 2004ASCI Purple (LLNL)64 CPU 197, 100 TFLOPS, 50 TB, 4.5 MW PC 2 CPU 16, 4 GFLOPS, 32 GB, 3.2 kw 20028 CPU 640, 40 TFLOPS, 10 TB, 10 MW (ASCI: Accelerated
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