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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
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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,
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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 ([email protected]), ([email protected]), ([email protected]), ([email protected]),
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
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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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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
PowerPoint Presentation
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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(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () m/s : : a) b) kg/m kg/m k
63 3 Section 3.1 g 3.1 3.1: : 64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m 3.1. 65 5
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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A Feasibility Study of Direct-Mapping-Type Parallel Processing Method to Solve Linear Equations in Load Flow Calculations Hiroaki Inayoshi, Non-member
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