Size: px
Start display at page:

Download ""

Transcription

1 4

2

3 3 1 Introduction Fokker-Planck

4 A BSS-S

5 ev ev GHz (C.L.Carili.et al 1992) r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) E 0 =1TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s r 0 =(0, 0, 5kpc)

6 3.9 r 0 =(0, 0, 5kpc) ( ) ( ) F (E,R E 0, r 0 ) (3.2.12) r 0 = (0, 0, 5kpc) µ =0.5 µ =0.3 (3.2.13) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) TeV Bohm Diffusion Bohm Diffusion Bohm Diffusion κ B 100 1TeV Bohm Diffusion κ B GeV κ = (E/GeV) 0.6 cm 2 /s κ = (E/GeV) 0.6 cm 2 /s 1TeV κ = (E/GeV) 0.6 cm 2 /s 10GeV

7 4.2 κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 ) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 ) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc)

8 4.9 κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc) κ = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) κ = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) Bohm Diffusion 100 r 0 =(0, 0, 5kpc) Bohm Diffusion 100 r 0 =(0, 0, 10kpc) κ = (E/GeV) 0.6 cm 2 /s (10GeV 1TeV) Bohm Diffusion κ B 100 (10GeV 1TeV) A.1 BSS-S

9 Ginzburg Stecker ( 10kpc) NGC4631 NGC891 NGC253 CANGAROO (Collaboration of Australia and Nippon for a GAmma Ray Observatory in the Out back) NGC253 [Itoh,Enomoto,Yanagita,Yoshida,and Tsuru 2003] π 0 X 1

10 Fokker-Planck Fokker-Planck 2

11 1 Introduction ( ) 1eV/cm 3 0.3eV/cm 3 RXJ π 0 SN pc Ginzburg Stecker Ginzburg Stecker ( 10kpc) 3

12 10kpc 5g/cm 2 n 1atom/cm 3 5g/cm ( 10 Be) Be n 1atom/cm 3 NGC4631 NGC891 NGC253 NGC253 CANGAROO 4

13 ( ) X π 0 3 Fokker-Planck Fokker-Planck 5

14

15 Hess ( ) MeV GeV (> ev) (< MeV) 7

16 2.1.1 (2.1) 10 5 ev ev [Jokipii & Kota,1988] (2.1) ev E ev knee ev ev 3.0 knee ev/n ev ev ev 10 9 ev (path length) Fe MeV/n GeV/n (2.2) IMP

17 2.1: 10 5 ev ev 9

18 (1) (Li Be B(L )) Z (2) H He H He (1) L sub-fe C, N, O L (Path Length) erg/s ev [Yanagita,Nomoto,Hayakawa 1990,Yanagita Nomoto 1999] 10

19 2.2: : ( MeV/n) : ( MeV/n) simpson[1983] 11

20 X ASCA TeV CANGAROO (the Collaboration of Australia and Nippon for a GAmma-Ray Observatory in the Outback) SN TeV [Koyama et al.1995;tanimori et al.,1998] CANGAROO RXJ π 0 [H.Muraishi et al2000] ( ) de = N(3 ln γ +19.8) dt i ev s 1 12

21 γ =(1 v 2 /c 2 ) 1/2 N τ = E (de/dt) i = E(eV) N(3 ln γ +19.8) X 1 E ( de dt ) brems =4NZ 2 r 2 e αcḡ r e α ḡ Gaunt Factor Gaunt Factor ḡ =ln(2γ) 1 3 =lnγ Gaunt Factor ḡ = ln(183z 1 3 )

22 2.2.3 ( ) de dt ad = 1 3 ( v)e ( ) de = 4 dt 3 σ T cγ 2H2 8π sync σ T Thomson γ H 2 /8π X 14

23 ( de dt ) IC = 4 3 σ T cγ 2 U ph σ T Thomson γ U ph ( ) 0.6eV/cm eV/cm 3 (T 2.728K) 3µG (de/dt) IC (de/dt) sync = U rad U mag 1 τ = E de/dt = E 4 3 σ = T cγ 2 U CMBR γ U CMBR 0.262eV/cm 3 15

24

25 3 3.1 Ginzburg Stecker ( 10kpc) NGC4631 NGC891 NGC253 CANGAROO (Collaboration of Australia and Nippon for a GAmma Ray Observatory in the Out back) NGC253 [Itoh,Enomoto,Yanagita,Yoshida,and Tsuru 2003] NGC253 (3.1) [Carili,Holdaway,Ho,and De Pree 1992] 0.33GHz NGC Mpc 19kpc(16 ) 17

26 π 0 X Fokker-Planck Fokker-Planck 3.2 E E

27 ApJ...399L 3.1: 0.33GHz (C.L.Carili.et al 1992) 19

28 Fokker-Placnk (3.2) 10kpc 1kpc 1µG 0.262eV/cm 3 (T=2.728K) 250km/s E E Fokker-Planck 1 [Yamada,1999] Full 20

29 Z I.C. Synchrotron Galactic Wind 250km/s Electron radius:10kpc thickness:1kpc Y Galactic Disk X Magnetic Field : 1 ug Photon Density : 0.262eV/cc 3.2: 21

30 Zhang [Zhang,1999] Fokker-Placnk 2 1 Fokker-Placnk Brown Fokker-Placnk f t = ( κ f Vf)+ 1 3 ( V ) 1 p 2 p (p3 f) (3.2.1) f( r, p, t) κ V Fokker-Planck Full- 22

31 (3.2.1) Fokker-Placnk dx i = V i dt + 2κdW i (i x,y,z) (3.2.2) dp = (dp adi + dp IC + dp syn ) (3.2.3) dx i 1 dp 1 V i 250km/s κ (E/GeV) µ cm 2 /s dp adi dp IC dp syn dw Gauss Wiener P (dw )= ( ) 1 2πdt exp dw 2 2dt (3.2.4) 3 ( ) de = 1 dt 3 ( V )E ad (3.2.5) ( de dt ( de dt ) ) IC sync = 4 3 σ T cγ 2 U ph (3.2.6) = 4 3 σ T cγ 2B2 8π (3.2.7) 23

32 E V 250km/s γ σ T cm 2 U ph 0.262eV/cm 3 B 1µG c cm/s (3.2.2)(3.2.3) Euler t i+1 x i+1 p i+1 x i+1 = x i + V i δt + 2κ(p i )δw (3.2.8) p i+1 = p i + dp adi (t i )+dp IC (t i )+dp syn (t i ) (3.2.9) t i (x i,p i ) δw (3.2.4) Gauss Fokker-Placnk (3.2.1) (3.2.2)(3.2.3) 2 [Yamada 1999] (3.3) 2 ( ) 24

33 Forward in Time Z Final State Fixed Initial Condition Y Galactic Disk X Backward in Time Z Fixed FinalCondition E0,r0 Galactic Disk Y Initial State EnergyDistribution : F(E,R E0,r0) X 3.3: 25

34 (3.2.2)(3.2.3) (3.2.2)(3.2.3) V V dp syn dp IC dp syn dp IC dx i = V i dt + 2κdW i (i x,y,z) (3.2.10) dp = dp adi + dp IC + dp syn (3.2.11) (3.2.10)(3.2.11) r 0 E 0 E F (E,R E 0, r 0 ) r 0 E 0 (3.2.10)(3.2.11) Euler R R (3.2.10)(3.2.11) E (E 0, r 0 ) r 0 E 0 r 0 (3.4) E 0 =1TeV r 0 =(0, 0, 5kpc) E 0 =1TeV r 0 =(5kpc, 0, 5kpc) 2 z x y z (0,0,5kpc) 26

35 : (5kpc,0,5kpc) (0,0,5kpc) (5kpc,0,5kpc) (3.5) r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) κ =10 29 (E/GeV ) 0.5 cm 2 /s F (E,R E 0, r 0 ) E <E 0 F (E,R E 0, r 0 )=0 r 0 =(0, 0, 5kpc) E 0 r 0 =(0, 0, 5kpc) E 0 (3.2.11) r 0 =(0, 0, 5kpc) (3.5) ( r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV) r 0 =(0, 0, 5kpc) (3.6) (3.2.10)(3.2.11) 27

36 0.3 F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 3.5: r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) 28

37 0.25 Arrival Time Distribution (0,0,5kpc) Arrival Time (Year) 3.6: r 0 =(0, 0, 5kpc) r 0 = (0, 0, 5kpc) 29

38 0.14 F(E,R 1TeV,5kpc) Kinetic Energy (GeV) 3.7: r 0 = (0, 0, 5kpc) E 0 =1TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s F (E,R E 0, r 0 ) 30

39 0.25 Arrival Time Distribution(0,0,5kpc) Arrival Time (Year) 3.8: r 0 =(0, 0, 5kpc) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s r 0 =(0, 0, 5kpc) 31

40 (3.5) (3.6) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) 10GeV 100GeV 1TeV 10TeV (3.7) r 0 =(0, 0, 5kpc) E 0 =1TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s F (E,R E 0, r 0 ) 3000 µ µ =0.3 µ =0.5 µ =0.3 (3.8) (3.7) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s r 0 =(0, 0, 5kpc) µ =0.3 µ = TeV (3.5) (3.7) F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) 32

41 r 0 =(0, 0, 5kpc) E 0 r 0 f r0 (E 0 ) F (E,R E 0, r 0 )( (3.5) (3.7)) f R (E) f r0 (E 0 )= E 0 f R (E)F (E,R E 0,r 0 )de (3.2.12) f R (E) f R (E) E 2.2 (3.2.13) (3.9) r 0 =(0, 0, 5kpc) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s ( ) ( ) (3.2.12) E 0 =10GeV 32GeV 100GeV 320GeV 1TeV 3.2TeV 10TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ = (E/GeV) 0.5 cm 2 /s (3.2.13) (3.9) 2 µ =0.3 µ =0.5 µ =0.3 z (3.10) (3.9) 33

42 κ =10 29 (E/GeV) 0.5 cm 2 /s ( ) r 0 =(0, 0, 5kpc) E 0 =10GeV 32GeV 100GeV 320GeV 1TeV 3.2TeV 10TeV ( ) r 0 =(0, 0, 9kpc) E 0 =10GeV 32GeV 100GeV 320GeV 1TeV 3.2TeV 10TeV (3.9) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) r 0 =(0, 0, 9kpc) kpc <x<20kpc 20kpc <y<20kpc 20kpc <z<20kpc (3.11) 2kpc yz (3.11) x (3.12) κ =10 29 (E/GeV) 0.5 cm 2 /s (3.12) 10GeV 100GeV 1TeV 10TeV kpc 34

43 Energy Spectrum (0,0,5kpc) GeV 3.9: r 0 =(0, 0, 5kpc) ( ) ( ) F (E,R E 0, r 0 ) (3.2.12) r 0 =(0, 0, 5kpc) µ =0.5 µ =0.3 (3.2.13) 35

44 10-7 Energy Spectrum GeV 3.10: r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) ( ) ( ) F (E,R E 0, r 0 ) (3.2.12) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) (3.2.13) 36

45 1 10GeV GeV TeV TeV GeV z 10kpc 10GeV GeV z 10kpc 100GeV 5 1TeV z 10kpc 10TeV z 10kpc 1 z 10kpc R L 2(κt cool ) 1/2 [C.Ito,R.Enomoto,S.yanagita,T.Yoshida,T.G.Tsuru 2003] t cool Gauss Gauss (κt cool ) 1/2 2(κt cool ) 1/ z 10GeV 100GeV 1TeV 10TeV 12.1kpc 6.8kpc 3.8kpc 2.2kpc 37

46 0.1 z 10GeV 100GeV 1TeV 10TeV 13kpc 8kpc 4kpc 3kpc (3.13) 1TeV µ (3.12) (3.13) µ =0.4 µ =0.5 µ =0.6 µ =0.7 (3.12) µ =0.4 µ =0.5 µ = µ = µ =0.4 z 10kpc 1TeV 1 µ =0.5 µ =0.6 1TeV 1 µ = µ z 10kpc µ z 10kpc (3.12) R L 2(κt cool ) 1/2 0.1 z R L 1TeV µ =0.4 µ =0.5 µ =0.6 µ = kpc 3.83kpc 5.41kpc 7.64kpc 1TeV 0.1 z µ =0.4 µ =0.5 µ =0.6 µ =0.7 3kpc 4kpc 4.5kpc 9kpc R L (3.13) 38

47 z x 2kpc 2kpc y 3.11: 39

48 kpc kpc kpc kpc kpc kpc 3.12: 10GeV 100GeV 1TeV 10TeV κ =10 29 (E/GeV) 0.5 cm 2 /s 40

49 20 20 kpc kpc kpc kpc kpc kpc kpc kpc 3.13: 1TeV µ =0.4 µ =0.5 µ =0.6 µ =0.7 41

50 3.3 (3.12) (3.13) Ginzburg Stecker TeV 10kpc κ =10 29 (E/GeV) µ cm 2 /s 2 λ r L ξ ξ = λ r L (3.3.1) ξ [Terasawa 2002] Bohm Diffusion Bohm Diffusion κ B 42

51 v κ B = 1 3 r Lv (3.3.2) (3.14) (3.15) Bohm Diffusion κ B z 5kpc Bohm Diffusion κ B 1µG 10GeV 100GeV 1TeV 10TeV cm 2 /s cm 2 /s cm 2 /s cm 2 /s κ =10 29 (E/GeV) µ cm 2 /s Bohm Diffusion κ B ( (3.14)) (3.9) 10GeV 100GeV GeV 10 9 (0,0,5kpc) 100GeV 1000 κ B ( (3.15)) (3.16) (3.17) Bohm Diffusion κ B 100 1TeV 10GeV (3.16) 1TeV (3.17) 10GeV (3.16) z 2kpc 1TeV 0.1 Bohm Diffusion κ B kpc 1TeV 43

52 (3.17) z 6kpc 10GeV 1 Bohm Diffusion κ B 100 6kpc 10GeV Bohm Diffusion κ B 100 Ginzubulg Stecker TeV 10 Be 26 Al 36 Cl 54 Mn Be/B Al/Mg Cl/Ar Mn/Fe B/C κ = (E/GeV) 0.6 cm 2 /s [Webber and Soutoul 1997] (3.18) z 5kpc 3000 (3.18) ( ) κ = (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) 0.6 cm 2 /s ( ) κ = (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) µ cm 2 /s 1/5 (3.19) κ = (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) 0.6 cm 2 /s 1/5 44

53 10-7 Electron Energy Spectrum (0,0,5kpc) GeV 3.14: Bohm Diffusion

54 10-7 Electron Energy Spectrum (0,0,5kpc) GeV 3.15: Bohm Diffusion

55 20 10 kpc kpc 3.16: Bohm Diffusion κ B 100 1TeV

56 20 kpc kpc 3.17: Bohm Diffusion κ B GeV

57 10-7 Electron Energy Spectrum (0,0,5kpc) GeV 3.18: κ = (E/GeV)cm 2 /s ( ) κ =10 29 (E/GeV) 0.6 cm 2 /s 49

58 6kpc TeV (3.20) κ = (E/GeV) 0.6 cm 2 /s 10GeV (3.19) 1TeV (κ = (E/GeV) 0.6 cm 2 /s) 10GeV z 10kpc kpc 10GeV κ = (E/GeV) 0.6 cm 2 /s Ginzbrug Stecker 6kpc TeV 50

59 20 kpc kpc 20 kpc kpc 3.19: κ = (E/GeV) 0.6 cm 2 /s 1TeV κ =10 29 (E/GeV) 0.6 cm 2 /s 1TeV 51

60 20 kpc kpc 3.20: κ = (E/GeV) 0.6 cm 2 /s 10GeV 52

61 Bohm Diffusion κ B B/C κ = (E/GeV) 0.6 cm 2 /s (4.1) 3 10kpc 1kpc xyz 1µG 300km/s E E

62 Z Adiabatic Loss Galactic Wind 300km/s Proton radius:10kpc thickness:1kpc Y Galactic Disk X Magnetic Field : 1uG 4.1: 54

63 4.2 Fokker- Planck Full- dx i = V i dt + 2κdW i (i x,y,z) (4.2.1) dp = dp adi (4.2.2) dx i 1 dp 1 V i 300km/s κ 2 2 κ Bs = 100 κ B cm 2 /s κ com = (E/GeV) 0.6 cm 2 /s κ B Bohm Diffusion (dp adi ) dw Gauss Wiener (3.2.4) (4.2) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.4) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.6) (4.2) r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) κ Bs 55

64 κ com (4.2) (4.6) κ com (4.3) κ com r 0 =(0, 0, 10kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.3) r 0 =(0, 0, 10kpc) (4.4) (4.2) κ com (10GeV 100GeV) (4.4) κ Bs r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.2) (4.4) µ 1 µ (4.4) 4 5 κ Bs κ com kpc 56

65 0.9 F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 4.2: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) F (E,R E 0, r 0 ) 57

66 0.7 F(E,R E0,R0) (0,0,10kpc) Kinetic Energy (GeV) 4.3: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) F (E,R E 0, r 0 ) 58

67 0.7 F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 4.4: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) 59

68 0.7 F(E,R E0,R0) (0,0,10kpc) Kinetic Energy (GeV) 4.5: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 ) 60

69 0.2 Electron F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 4.6: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) F (E,R E 0, r 0 ) 61

70 (4.5) κ Bs r 0 =(0, 0, 10kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) r 0 =(0, 0, 10kpc) (4.5) (4.2) (4.4) κ Bs (4.7) (4.2) r 0 =(0, 0, 5kpc) τ r 0 =(0, 0, 5kpc) (4.8) (4.3) r 0 =(0, 0, 10kpc) (4.9) (4.4) r 0 =(0, 0, 5kpc) (4.4) µ 1 r 0 =(0, 0, 5kpc) (4.10) (4.5) r 0 =(0, 0, 10kpc) 62

71 0.1 Arrival Time Distribution (0,0,5kpc) Arrival Time (Year) 4.7: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) r 0 =(0, 0, 5kpc) 63

72 0.1 Arrival Time Distribution (0,0,10kpc) Arrival Time (Year) 4.8: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) r 0 =(0, 0, 10kpc) 64

73 0.8 Arrival Time Distribution (0,0,5kpc) Arrival Time (Year) 4.9: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) 65

74 1 Arrival Time Distribution (0,0,10kpc) Arrival Time (Year) 4.10: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc) 66

75 4.3 (4.2) (4.5) F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 10kpc) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 10kpc) E 0 r 0 f r0 (E 0 ) F (E,R E 0, r 0 )( (4.2) (4.5)) f R (E) (3.2.12) E E 2.2 (4.11) (4.2) κ com r 0 =(0, 0, 5kpc) (4.12) (4.3) κ com r 0 =(0, 0, 10kpc) r 0 =(0, 0, 5kpc) (4.12) (4.11) (4.12) κ com (4.13) (4.4) κ Bs r 0 =(0, 0, 5kpc) (4.14) (4.5) κ Bs 67

76 r 0 =(0, 0, 10kpc) κ com (4.11) (4.13) κ Bs κ com 10 4 (4.13) (4.13) (4.13) E 2.2 (4.13) 1TeV 10TeV (4.4) µ 1 µ (4.13) (4.14) (4.14) κ Bs 4.4 (4.15) κ com (4.15) 10GeV 1TeV 1 10GeV ( ) TeV ( ) 10GeV z 10kpc GeV z 10kpc 1TeV z 10kpc 68

77 10-7 Proton Energy Spectrum (0,0,5kpc) GeV 4.11: κ = (E/GeV)cm 2 /s r 0 =(0, 0, 5kpc) 69

78 10-7 Proton Energy Spectrum (0,0,10kpc) GeV 4.12: κ = (E/GeV)cm 2 /s r 0 = (0, 0, 10kpc) 70

79 10-7 Proton Energy Spectrum (0,0,5kpc) GeV 4.13: Bohm Diffusion 100 r 0 =(0, 0, 5kpc) 71

80 10-7 Proton Energy Spectrum (0,0,10kpc) GeV 4.14: Bohm Diffusion 100 r 0 =(0, 0, 10kpc) 72

81 TeV z 10kpc 10GeV 1TeV 1TeV (3.12) κ = (E/GeV) 0.6 cm 2 /s TeV 10kpc (4.16) κ Bs (4.16) 10GeV 1TeV 1 10GeV ( ) TeV ( ) GeV z 10kpc 1 10GeV z 10kpc 1TeV z 10kpc 2 1TeV z 10kpc Bohm Diffusion κ B 100 TeV 10kpc 73

82 kpc kpc kpc kpc 4.15: κ = (E/GeV) 0.6 cm 2 /s 10GeV κ = (E/GeV) 0.6 cm 2 /s 1TeV 74

83 kpc kpc kpc kpc 4.16: Bohm Diffusion κ B GeV Bohm Diffusion κ B 100 1TeV 75

84

85 5 Ginzburg Stecker ( 10kpc) ( ) Fokker-Placnk Fokker-Placnk (3.12) (3.13) (3.12) 2 (3.13) µ (3.12) (3.13) κ =10 29 (E/GeV) µ cm 2 /s Bohm Diffusion 77

86 100 κ Bs = 100 κ B B/C κ com = (E/GeV) 0.6 cm 2 /s (3.16) (3.19) κ Bs κ com 1TeV (3.16) κ Bs 10kpc TeV κ com (3.19) 10kpc TeV NGC253 TeV CANGAROO [Itoh,Enomoto,Yanagita,Yoshida,and Tsuru 2003] 10kpc TeV TeV TeV 10kpc TeV NGC253 κ com (3.17) (3.20) κ Bs κ com 10GeV (3.17) κ Bs 10GeV (3.20) 10kpc 10GeV µg GHz (3.1) 10kpc 78

87 µg κ com 10GeV TeV NGC253 κ com κ com Ginzburg Stecker TeV NGC253 10kpc π 0 10kpc (4.15) (4.16) κ com κ Bs 10GeV 1TeV Ginzburg Stecker 79

88 ( 10kpc) 80

89 A BSS-S [Neill,Olinto,Blasi 2001] (A.1) (A.1) bisymmetric even-parity field model(bss-s) (z=0) 0 6µG 3µG B sp = B 0 (r)cos(θ β ln(r/r 0 )) (A.0.1) B 0 (r) = 3ρ 0 r tanh3 ( r )µg r 1 (A.0.2) B(r, θ, z =0)=B sp (sin pˆρ +cospˆθ) (A.0.3) ( B S (r, θ, z) =B(r, θ, z =0) 1 2cosh( z z 1 ) + 1 2cosh( z z 2 ) ) (A.0.4) r 0 =10.55kpc β =1/ tan p p = 10 ρ 0 =8.5kpc r 1 =2kpc z 1 =0.3kpc z 2 =4kpc (κ ) (κ ) 2 d x = ( κ V V d )dt + α σ dw σ (t) (A.0.5) dp = dp adi + dp IC + dp syn (A.0.6) 81

90 A.1: BSS-S z 0 kpc 82

91 (A,0,5) κ x x y z (A,0,7) κ 0 0 κ = 0 κ κ (A.0.7) (A,0,6) dw σ Gauss Wiener (3.2.4) α σ dw σ ασ dw σ (t) = α 1 dw 1 + α 2 dw 2 + α 3 dw 3 (A.0.8) = 2κ dw 1 + 2κ dw 2 + 2κ dw 3 (A.0.9) (r, θ, z) ê r cos χ sin χ 0 ê θ = sin χ cos χ ê φ ê b ê ê z (A.0.10) ê x cos θ sin θ 0 ê r ê y = sin θ cos θ 0 ê θ (A.0.11) ê z ê x cos θ cos χ sin θ sin χ cos θ sin chi sin θ cos χ 0 ê b ê y = cos θ sin chi +sinθcos χ cos θ cos χ sin θ sin χ 0 ê ê z ê z (A.0.12) ê z 83

92 dw x cos θ cos χ sin θ sin χ cos θ sin chi sin θ cos χ 0 2κ dw 1 dw y = cos θ sin chi +sinθcos χ cos θ cos χ sin θ sin χ 0 2κ dw 2 dw z κ dw 3 (A.0.13) χ cos χ = B r B r (A,0,5) V d ( ) V d = pv B 3q B 2 (A.0.14) (A.0.15) (A,0,1) (A,0,4) V dx = pv 2coth 3 ( r r 1 )sec(θ β ln( r r 0 ))(x cos p + y sin p)(z 2 sin( z z 1 )+z 1 sin( z z 2 )) 3q 3r 0 z 1 z 2 (cos( z z 1 )+cos( z z 2 )) 2 (A.0.16) V dy = pv 2coth 3 ( r r 1 )sec(θ β ln( r r 0 ))(y cos p x sin p)(z 2 sin( z z 1 )+z 1 sin( z z 2 )) 3q 3r 0 z 1 z 2 (cos( z z 1 )+cos( z z 2 )) 2 (A.0.17) V dz = pv 3q coth2 ( r )csch 2 ( r )sec 2 (θ β ln( r ))( 12r cos p cos(θ β ln( r )) r 1 r 1 r 0 r 0 +r 1 (3 cos(p + θ β ln( r )) 2β cos p sin(θ β ln( r ))) sinh( 2r )) r 0 r 0 r 1 /6r 0 r 1 (cos( z z 1 )+cos( z z 2 )) (A.0.5) κ (A.0.7) (r, θ, z) κ 84

93 κ 0 0 κ = 0 κ κ = κ ê θ ê θ + κ ê ê + κ ê b ê b (A.0.18) κ cos 2 χ + κ sin 2 χ (κ κ )cosχsin χ 0 κ = (κ κ )cosχsin χ κ cos 2 χ + κ sin 2 χ κ (A.0.19) κ xx κ xy 0 κ = κ yx κ yy κ zz (A.0.20) κ xx = (κ cos 2 χ + κ sin 2 χ)cos 2 θ +(κ cos 2 χ + κ sin 2 χ)sin 2 θ (κ κ )sin2χ κ xy = (κ κ )cosχsin χ(cos 2 θ sin 2 θ)+(κ κ )cos2χ κ yx = (κ κ )cosχsin χ(cos 2 θ sin 2 θ)+(κ κ )cos2χ κ yy = (κ cos 2 χ + κ sin 2 χ)cos 2 θ +(κ cos 2 χ + κ sin 2 χ)sin 2 θ +(κ κ )sin2χ κ zz = κ (A.0.20) κ κ 85

94

95 NGC253 87

96

97 [1] Andrew W. Strong,and Igor V.Moskalenko,Astrophys.J,509, ,1998 [2] C.Itoh.,et al,a&a,396,l1-l4,2002 [3] C.Itoh,R.Enomoto,S.Yanagita,T.Yoshida,and T.G.Tsuru,Astrophys.J,584,L000- L000,2003 [4] D.Breitschwerdt,J.F.McKenzie,and H.J.Volk,A&A,269,54-66,1993 [5] F.W.Stecker,IAUS,84, ,1979 [6] Jokipii,J.R.,and J.Kota,J.Geophys.Res.91, ,1986 [7] Koyama,K.,et al.,nature 378, ,1995 [8] Ming Zhang,Astrophys.J 513, ,1999 [9] R.Enomoto.,et al,nature,416, ,2002 [10] Simpson,J.A.,Ann.Rev.Nucl.Part.Sci.,33, ,1983. [11] S.O Neill,A.Olinto,and P.Blasi,ICRC2001 [12] V.L.Ginzburg,IAUS,84, ,1979 [13] W.R.Webber,and A.Soutoul,Astrophys.J,506, ,1998 [14] Yamada,Y.,S.Yanagita,and T.Yoshida,Adv.Space Res.in press 1999 [15] Yanagita,S.,and N.Nomoto,Proc.3rd Integral Workshop, The Extreme Universe,pub.Kluwer Academic Publishers,in press [16], 10,

98 [17], 12,2000 [18], 14,2002 [19],,,, (1983) [20],, (2002) [21] M.S.Longair,High Energy Astrophysics Second Edition Vol.1 [22] M.S.Longair,High Energy Astrophysics Second Edition Vol.2 [23] Thomas K.Gaisser,Cosmic Rays and Particle Physics, (1997) 90

ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d

ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d A 2. x F (t) =f sin ωt x(0) = ẋ(0) = 0 ω θ sin θ θ 3! θ3 v = f mω cos ωt x = f mω (t sin ωt) ω t 0 = f ( cos ωt) mω x ma2-2 t ω x f (t mω ω (ωt ) 6 (ωt)3 = f 6m ωt3 2.2 u ( v w) = v ( w u) = w ( u v) ma22-9

More information

1 3 1.1.......................... 3 1............................... 3 1.3....................... 5 1.4.......................... 6 1.5........................ 7 8.1......................... 8..............................

More information

No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2

No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2 No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j

More information

W u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)

W u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2) 3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)

More information

The Physics of Atmospheres CAPTER :

The Physics of Atmospheres CAPTER : The Physics of Atmospheres CAPTER 4 1 4 2 41 : 2 42 14 43 17 44 25 45 27 46 3 47 31 48 32 49 34 41 35 411 36 maintex 23/11/28 The Physics of Atmospheres CAPTER 4 2 4 41 : 2 1 σ 2 (21) (22) k I = I exp(

More information

( ; ) C. H. Scholz, The Mechanics of Earthquakes and Faulting : - ( ) σ = σ t sin 2π(r a) λ dσ d(r a) =

( ; ) C. H. Scholz, The Mechanics of Earthquakes and Faulting : - ( ) σ = σ t sin 2π(r a) λ dσ d(r a) = 1 9 8 1 1 1 ; 1 11 16 C. H. Scholz, The Mechanics of Earthquakes and Faulting 1. 1.1 1.1.1 : - σ = σ t sin πr a λ dσ dr a = E a = π λ σ πr a t cos λ 1 r a/λ 1 cos 1 E: σ t = Eλ πa a λ E/π γ : λ/ 3 γ =

More information

pdf

pdf 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

More information

LLG-R8.Nisus.pdf

LLG-R8.Nisus.pdf d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =

More information

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 =

#A A A F, F d F P + F P = d P F, F y P F F x A.1 ( α, 0), (α, 0) α > 0) (x, y) (x + α) 2 + y 2, (x α) 2 + y 2 d (x + α)2 + y 2 + (x α) 2 + y 2 = #A A A. F, F d F P + F P = d P F, F P F F A. α, 0, α, 0 α > 0, + α +, α + d + α + + α + = d d F, F 0 < α < d + α + = d α + + α + = d d α + + α + d α + = d 4 4d α + = d 4 8d + 6 http://mth.cs.kitmi-it.c.jp/

More information

変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,

変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, 変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +

More information

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

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

More information

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H

V(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H 199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)

More information

K E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................

More information

120 9 I I 1 I 2 I 1 I 2 ( a) ( b) ( c ) I I 2 I 1 I ( d) ( e) ( f ) 9.1: Ampère (c) (d) (e) S I 1 I 2 B ds = µ 0 ( I 1 I 2 ) I 1 I 2 B ds =0. I 1 I 2

120 9 I I 1 I 2 I 1 I 2 ( a) ( b) ( c ) I I 2 I 1 I ( d) ( e) ( f ) 9.1: Ampère (c) (d) (e) S I 1 I 2 B ds = µ 0 ( I 1 I 2 ) I 1 I 2 B ds =0. I 1 I 2 9 E B 9.1 9.1.1 Ampère Ampère Ampère s law B S µ 0 B ds = µ 0 j ds (9.1) S rot B = µ 0 j (9.2) S Ampère Biot-Savart oulomb Gauss Ampère rot B 0 Ampère µ 0 9.1 (a) (b) I B ds = µ 0 I. I 1 I 2 B ds = µ 0

More information

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e

N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 3 5 5 5 3 3 7 5 33 5 33 9 5 8 > e > f U f U u u > u ue u e u ue u ue u e u e u u e u u e u N cos s s cos ψ e e e e 3 3 e e 3 e 3 e 3 > A A > A E A f A A f A [ ] f A A e > > A e[ ] > f A E A < < f ; >

More information

21 2 26 i 1 1 1.1............................ 1 1.2............................ 3 2 9 2.1................... 9 2.2.......... 9 2.3................... 11 2.4....................... 12 3 15 3.1..........

More information

1 1.1 ( ). z = a + bi, a, b R 0 a, b 0 a 2 + b 2 0 z = a + bi = ( ) a 2 + b 2 a a 2 + b + b 2 a 2 + b i 2 r = a 2 + b 2 θ cos θ = a a 2 + b 2, sin θ =

1 1.1 ( ). z = a + bi, a, b R 0 a, b 0 a 2 + b 2 0 z = a + bi = ( ) a 2 + b 2 a a 2 + b + b 2 a 2 + b i 2 r = a 2 + b 2 θ cos θ = a a 2 + b 2, sin θ = 1 1.1 ( ). z = + bi,, b R 0, b 0 2 + b 2 0 z = + bi = ( ) 2 + b 2 2 + b + b 2 2 + b i 2 r = 2 + b 2 θ cos θ = 2 + b 2, sin θ = b 2 + b 2 2π z = r(cos θ + i sin θ) 1.2 (, ). 1. < 2. > 3. ±,, 1.3 ( ). A

More information

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 1 16 10 5 1 2 2.1 a a a 1 1 1 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a

More information

液晶の物理1:連続体理論(弾性,粘性)

液晶の物理1:連続体理論(弾性,粘性) The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers

More information

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)

() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi) 0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()

More information

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4

) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4 1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev

More information

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e

Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e 7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z

More information

( ) ( )

( ) ( ) 20 21 2 8 1 2 2 3 21 3 22 3 23 4 24 5 25 5 26 6 27 8 28 ( ) 9 3 10 31 10 32 ( ) 12 4 13 41 0 13 42 14 43 0 15 44 17 5 18 6 18 1 1 2 2 1 2 1 0 2 0 3 0 4 0 2 2 21 t (x(t) y(t)) 2 x(t) y(t) γ(t) (x(t) y(t))

More information

18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb

18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)

More information

29

29 9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n

More information

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)

) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) 4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7

More information

9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) Ĥ0 ψ n (r) ω n Schrödinger Ĥ 0 ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ0 + Ĥint (

9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) Ĥ0 ψ n (r) ω n Schrödinger Ĥ 0 ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ0 + Ĥint ( 9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) 2. 2.1 Ĥ ψ n (r) ω n Schrödinger Ĥ ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ + Ĥint (t)] ψ (r, t), (2) Ĥ int (t) = eˆxe cos ωt ˆdE cos ωt, (3)

More information

Report10.dvi

Report10.dvi [76 ] Yuji Chinone - t t t = t t t = fl B = ce () - Δθ u u ΔS /γ /γ observer = fl t t t t = = =fl B = ce - Eq.() t ο t v ο fl ce () c v fl fl - S = r = r fl = v ce S =c t t t ο t S c = ce ce v c = ce v

More information

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )

II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11

More information

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq

50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq 49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r

More information

( ) ,

( ) , II 2007 4 0. 0 1 0 2 ( ) 0 3 1 2 3 4, - 5 6 7 1 1 1 1 1) 2) 3) 4) ( ) () H 2.79 10 10 He 2.72 10 9 C 1.01 10 7 N 3.13 10 6 O 2.38 10 7 Ne 3.44 10 6 Mg 1.076 10 6 Si 1 10 6 S 5.15 10 5 Ar 1.01 10 5 Fe 9.00

More information

B 1 B.1.......................... 1 B.1.1................. 1 B.1.2................. 2 B.2........................... 5 B.2.1.......................... 5 B.2.2.................. 6 B.2.3..................

More information

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x

x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x [ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),

More information

, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. main.tex 2011/08/13( )

, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. main.tex 2011/08/13( ) 81 4 2 4.1, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. 82 4.2. ζ t + V (ζ + βy) = 0 (4.2.1), V = 0 (4.2.2). (4.2.1), (3.3.66) R 1 Φ / Z, Γ., F 1 ( 3.2 ). 7,., ( )., (4.2.1) 500 hpa., 500 hpa (4.2.1) 1949,.,

More information

Part () () Γ Part ,

Part () () Γ Part , Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35

More information

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t

r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t 1 1 2 2 2r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t) V (x, t) I(x, t) V in x t 3 4 1 L R 2 C G L 0 R 0

More information

(5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b)

(5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b) (5) 74 Re, bondar laer (Prandtl) Re z ω z = x (5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b) (5) 76 l V x ) 1/ 1 ( 1 1 1 δ δ = x Re x p V x t V l l (1-1) 1/ 1 δ δ δ δ = x Re p V x t V

More information

I ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT

I ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345

More information

PDF

PDF 1 1 1 1-1 1 1-9 1-3 1-1 13-17 -3 6-4 6 3 3-1 35 3-37 3-3 38 4 4-1 39 4- Fe C TEM 41 4-3 C TEM 44 4-4 Fe TEM 46 4-5 5 4-6 5 5 51 6 5 1 1-1 1991 1,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV

More information

H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [

H 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [ 3 3. 3.. H H = H + V (t), V (t) = gµ B α B e e iωt i t Ψ(t) = [H + V (t)]ψ(t) Φ(t) Ψ(t) = e iht Φ(t) H e iht Φ(t) + ie iht t Φ(t) = [H + V (t)]e iht Φ(t) Φ(t) i t Φ(t) = V H(t)Φ(t), V H (t) = e iht V (t)e

More information

4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.

4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5. A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c

More information

6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4

6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4 35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m

More information

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1

1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1 1 I 1.1 ± e = = - =1.602 10 19 C C MKA [m], [Kg] [s] [A] 1C 1A 1 MKA 1C 1C +q q +q q 1 1.1 r 1,2 q 1, q 2 r 12 2 q 1, q 2 2 F 12 = k q 1q 2 r 12 2 (1.1) k 2 k 2 ( r 1 r 2 ) ( r 2 r 1 ) q 1 q 2 (q 1 q 2

More information

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k

More information

Gmech08.dvi

Gmech08.dvi 145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2

More information

211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,

More information

z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy

z f(z) f(z) x, y, u, v, r, θ r > 0 z = x + iy, f = u + iv C γ D f(z) f(z) D f(z) f(z) z, Rm z, z 1.1 z = x + iy = re iθ = r (cos θ + i sin θ) z = x iy z fz fz x, y, u, v, r, θ r > z = x + iy, f = u + iv γ D fz fz D fz fz z, Rm z, z. z = x + iy = re iθ = r cos θ + i sin θ z = x iy = re iθ = r cos θ i sin θ x = z + z = Re z, y = z z = Im z i r = z = z

More information

4 5.............................................. 5............................................ 6.............................................. 7......................................... 8.3.................................................4.........................................4..............................................4................................................4.3...............................................

More information

IA

IA IA 31 4 11 1 1 4 1.1 Planck.............................. 4 1. Bohr.................................... 5 1.3..................................... 6 8.1................................... 8....................................

More information

構造と連続体の力学基礎

構造と連続体の力学基礎 II 37 Wabash Avenue Bridge, Illinois 州 Winnipeg にある歩道橋 Esplanade Riel 橋6 6 斜張橋である必要は多分無いと思われる すぐ横に道路用桁橋有り しかも塔基部のレストランは 8 年には営業していなかった 9 9. 9.. () 97 [3] [5] k 9. m w(t) f (t) = f (t) + mg k w(t) Newton

More information

006 11 8 0 3 1 5 1.1..................... 5 1......................... 6 1.3.................... 6 1.4.................. 8 1.5................... 8 1.6................... 10 1.6.1......................

More information

( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e

( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e ( ) Note 3 19 12 13 8 8.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R, µ R, τ R (1a) L ( ) ) * 3) W Z 1/2 ( - )

More information

O x y z O ( O ) O (O ) 3 x y z O O x v t = t = 0 ( 1 ) O t = 0 c t r = ct P (x, y, z) r 2 = x 2 + y 2 + z 2 (t, x, y, z) (ct) 2 x 2 y 2 z 2 = 0

O x y z O ( O ) O (O ) 3 x y z O O x v t = t = 0 ( 1 ) O t = 0 c t r = ct P (x, y, z) r 2 = x 2 + y 2 + z 2 (t, x, y, z) (ct) 2 x 2 y 2 z 2 = 0 9 O y O ( O ) O (O ) 3 y O O v t = t = 0 ( ) O t = 0 t r = t P (, y, ) r = + y + (t,, y, ) (t) y = 0 () ( )O O t (t ) y = 0 () (t) y = (t ) y = 0 (3) O O v O O v O O O y y O O v P(, y,, t) t (, y,, t )

More information

Note.tex 2008/09/19( )

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..................................

More information

30

30 3 ............................................2 2...........................................2....................................2.2...................................2.3..............................

More information

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,

.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =, [ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b

More information

( )

( ) 7..-8..8.......................................................................... 4.................................... 3...................................... 3..3.................................. 4.3....................................

More information

I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co

I-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co 16 I ( ) (1) I-1 I-2 I-3 (2) I-1 ( ) (100 ) 2l x x = 0 y t y(x, t) y(±l, t) = 0 m T g y(x, t) l y(x, t) c = 2 y(x, t) c 2 2 y(x, t) = g (A) t 2 x 2 T/m (1) y 0 (x) y 0 (x) = g c 2 (l2 x 2 ) (B) (2) (1)

More information

i

i 009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3

More information

19 σ = P/A o σ B Maximum tensile strength σ % 0.2% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional

19 σ = P/A o σ B Maximum tensile strength σ % 0.2% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional 19 σ = P/A o σ B Maximum tensile strength σ 0. 0.% 0.% proof stress σ EL Elastic limit Work hardening coefficient failure necking σ PL Proportional limit ε p = 0.% ε e = σ 0. /E plastic strain ε = ε e

More information

I 1

I 1 I 1 1 1.1 1. 3 m = 3 1 7 µm. cm = 1 4 km 3. 1 m = 1 1 5 cm 4. 5 cm 3 = 5 1 15 km 3 5. 1 = 36 6. 1 = 8.64 1 4 7. 1 = 3.15 1 7 1 =3 1 7 1 3 π 1. 1. 1 m + 1 cm = 1.1 m. 1 hr + 64 sec = 1 4 sec 3. 3. 1 5 kg

More information

( 4) ( ) (Poincaré) (Poincaré disk) 1 2 (hyperboloid) [1] [2, 3, 4] 1 [1] 1 y = 0 L (hyperboloid) K (Klein disk) J (hemisphere) I (P

( 4) ( ) (Poincaré) (Poincaré disk) 1 2 (hyperboloid) [1] [2, 3, 4] 1 [1] 1 y = 0 L (hyperboloid) K (Klein disk) J (hemisphere) I (P 4) 07.3.7 ) Poincaré) Poincaré disk) hyperboloid) [] [, 3, 4] [] y 0 L hyperboloid) K Klein disk) J hemisphere) I Poincaré disk) : hyperboloid) L Klein disk) K hemisphere) J Poincaré) I y 0 x + y z 0 z

More information

SFGÇÃÉXÉyÉNÉgÉãå`.pdf

SFGÇÃÉXÉyÉNÉgÉãå`.pdf SFG 1 SFG SFG I SFG (ω) χ SFG (ω). SFG χ χ SFG (ω) = χ NR e iϕ +. ω ω + iγ SFG φ = ±π/, χ φ = ±π 3 χ SFG χ SFG = χ NR + χ (ω ω ) + Γ + χ NR χ (ω ω ) (ω ω ) + Γ cosϕ χ NR χ Γ (ω ω ) + Γ sinϕ. 3 (θ) 180

More information

微分積分 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, 初版 1 刷発行時のものです.

微分積分 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, 初版 1 刷発行時のものです. 微分積分 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. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)

More information

9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x

9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x 2009 9 6 16 7 1 7.1 1 1 1 9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x(cos y y sin y) y dy 1 sin

More information

Bethe-Bloch Bethe-Bloch (stopping range) Bethe-Bloch FNAL (Fermi National Accelerator Laboratory) - (SciBooNE ) SciBooNE Bethe-Bloch FNAL - (SciBooNE

Bethe-Bloch Bethe-Bloch (stopping range) Bethe-Bloch FNAL (Fermi National Accelerator Laboratory) - (SciBooNE ) SciBooNE Bethe-Bloch FNAL - (SciBooNE 21 2 27 Bethe-Bloch Bethe-Bloch (stopping range) Bethe-Bloch FNAL (Fermi National Accelerator Laboratory) - (SciBooNE ) SciBooNE Bethe-Bloch FNAL - (SciBooNE ) Bethe-Bloch 1 0.1..............................

More information

3 filename=quantum-3dim110705a.tex ,2 [1],[2],[3] [3] U(x, y, z; t), p x ˆp x = h i x, p y ˆp y = h i y, p z ˆp z = h

3 filename=quantum-3dim110705a.tex ,2 [1],[2],[3] [3] U(x, y, z; t), p x ˆp x = h i x, p y ˆp y = h i y, p z ˆp z = h filename=quantum-dim110705a.tex 1 1. 1, [1],[],[]. 1980 []..1 U(x, y, z; t), p x ˆp x = h i x, p y ˆp y = h i y, p z ˆp z = h i z (.1) Ĥ ( ) Ĥ = h m x + y + + U(x, y, z; t) (.) z (U(x, y, z; t)) (U(x,

More information

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2

6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2 1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a

More information

K E N Z U 01 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.................................... 4 1..1..................................... 4 1...................................... 5................................

More information

講義ノート 物性研究 電子版 Vol.3 No.1, (2013 年 T c µ T c Kammerlingh Onnes 77K ρ 5.8µΩcm 4.2K ρ 10 4 µωcm σ 77K ρ 4.2K σ σ = ne 2 τ/m τ 77K

講義ノート 物性研究 電子版 Vol.3 No.1, (2013 年 T c µ T c Kammerlingh Onnes 77K ρ 5.8µΩcm 4.2K ρ 10 4 µωcm σ 77K ρ 4.2K σ σ = ne 2 τ/m τ 77K 2 2 T c µ T c 1 1.1 1911 Kammerlingh Onnes 77K ρ 5.8µΩcm 4.2K ρ 1 4 µωcm σ 77K ρ 4.2K σ σ = ne 2 τ/m τ 77K τ 4.2K σ 58 213 email:takada@issp.u-tokyo.ac.jp 1933 Meissner Ochsenfeld λ = 1 5 cm B = χ B =

More information

sec13.dvi

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:

More information

A

A A04-164 2008 2 13 1 4 1.1.......................................... 4 1.2..................................... 4 1.3..................................... 4 1.4..................................... 5 2

More information

(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a

(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a 1 2 2.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a) L ( ) ) * 2) W Z 1/2 ( - ) d u + e + ν e 1 1 0 0

More information

5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1

5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1 4 1 1.1 ( ) 5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1 da n i n da n i n + 3 A ni n n=1 3 n=1

More information

(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

(1.2) 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

More information

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s

[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s [ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =

More information

/ Christopher Essex Radiation and the Violation of Bilinearity in the Thermodynamics of Irreversible Processes, Planet.Space Sci.32 (1984) 1035 Radiat

/ Christopher Essex Radiation and the Violation of Bilinearity in the Thermodynamics of Irreversible Processes, Planet.Space Sci.32 (1984) 1035 Radiat / Christopher Essex Radiation and the Violation of Bilinearity in the Thermodynamics of Irreversible Processes, Planet.Space Sci.32 (1984) 1035 Radiation and the Continuing Failure of the Bilinear Formalism,

More information

chap03.dvi

chap03.dvi 99 3 (Coriolis) cm m (free surface wave) 3.1 Φ 2.5 (2.25) Φ 100 3 r =(x, y, z) x y z F (x, y, z, t) =0 ( DF ) Dt = t + Φ F =0 onf =0. (3.1) n = F/ F (3.1) F n Φ = Φ n = 1 F F t Vn on F = 0 (3.2) Φ (3.1)

More information

meiji_resume_1.PDF

meiji_resume_1.PDF β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E

More information

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 (

1. (8) (1) (x + y) + (x + y) = 0 () (x + y ) 5xy = 0 (3) (x y + 3y 3 ) (x 3 + xy ) = 0 (4) x tan y x y + x = 0 (5) x = y + x + y (6) = x + y 1 x y 3 ( 1 1.1 (1) (1 + x) + (1 + y) = 0 () x + y = 0 (3) xy = x (4) x(y + 3) + y(y + 3) = 0 (5) (a + y ) = x ax a (6) x y 1 + y x 1 = 0 (7) cos x + sin x cos y = 0 (8) = tan y tan x (9) = (y 1) tan x (10) (1 +

More information

main.dvi

main.dvi SGC - 48 208X Y Z Z 2006 1930 β Z 2006! 1 2 3 Z 1930 SGC -12, 2001 5 6 http://www.saiensu.co.jp/support.htm http://www.shinshu-u.ac.jp/ haru/ xy.z :-P 3 4 2006 3 ii 1 1 1.1... 1 1.2 1930... 1 1.3 1930...

More information

B

B B07557 0 0 (AGN) AGN AGN X X AGN AGN Geant4 AGN X X X (AGN) AGN AGN X AGN. AGN AGN Seyfert Seyfert Seyfert AGN 94 Carl Seyfert Seyfert Seyfert z < 0. Seyfert I II I 000 km/s 00 km/s II AGN (BLR) (NLR)

More information

all.dvi

all.dvi 38 5 Cauchy.,,,,., σ.,, 3,,. 5.1 Cauchy (a) (b) (a) (b) 5.1: 5.1. Cauchy 39 F Q Newton F F F Q F Q 5.2: n n ds df n ( 5.1). df n n df(n) df n, t n. t n = df n (5.1) ds 40 5 Cauchy t l n mds df n 5.3: t

More information

C el = 3 2 Nk B (2.14) c el = 3k B C el = 3 2 Nk B

C el = 3 2 Nk B (2.14) c el = 3k B C el = 3 2 Nk B I ino@hiroshima-u.ac.jp 217 11 14 4 4.1 2 2.4 C el = 3 2 Nk B (2.14) c el = 3k B 2 3 3.15 C el = 3 2 Nk B 3.15 39 2 1925 (Wolfgang Pauli) (Pauli exclusion principle) T E = p2 2m p T N 4 Pauli Sommerfeld

More information

Microsoft Word - 章末問題

Microsoft Word - 章末問題 1906 R n m 1 = =1 1 R R= 8h ICP s p s HeNeArXe 1 ns 1 1 1 1 1 17 NaCl 1.3 nm 10nm 3s CuAuAg NaCl CaF - - HeNeAr 1.7(b) 2 2 2d = a + a = 2a d = 2a 2 1 1 N = 8 + 6 = 4 8 2 4 4 2a 3 4 π N πr 3 3 4 ρ = = =

More information

untitled

untitled 50cm 2500mm 300mm 15 CCD 15 100 1 2 3 4 23 SORA Kwak SeungJo 1 1.1 1995 20 2015 6 18 1931 1 2 3 2 ˆ 300mm 2500mm ˆ 2 1.2 WASP 1: 15 2048 2048 CCD 200mm 70 13 WASP 8 1.3 50cm 1 1: CCD 2: 1.4 MOST MOST 15

More information

.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T

.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977

More information

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2

II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2 II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh

More information

5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E

5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E 5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E 2, S 1 N 1 = S 2 N 2 2 (chemical potential) µ S N

More information

2.1: n = N/V ( ) k F = ( 3π 2 N ) 1/3 = ( 3π 2 n ) 1/3 V (2.5) [ ] a = h2 2m k2 F h2 2ma (1 27 ) (1 8 ) erg, (2.6) /k B 1 11 / K

2.1: n = N/V ( ) k F = ( 3π 2 N ) 1/3 = ( 3π 2 n ) 1/3 V (2.5) [ ] a = h2 2m k2 F h2 2ma (1 27 ) (1 8 ) erg, (2.6) /k B 1 11 / K 2 2.1? [ ] L 1 ε(p) = 1 ( p 2 2m x + p 2 y + pz) 2 = h2 ( k 2 2m x + ky 2 + kz) 2 n x, n y, n z (2.1) (2.2) p = hk = h 2π L (n x, n y, n z ) (2.3) n k p 1 i (ε i ε i+1 )1 1 g = 2S + 1 2 1/2 g = 2 ( p F

More information

ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +

ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + 2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j

More information

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google

I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59

More information

23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4

23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 23 1 Section 1.1 1 ( ) ( ) ( 46 ) 2 3 235, 238( 235,238 U) 232( 232 Th) 40( 40 K, 0.0118% ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 2 ( )2 4( 4 He) 12 3 16 12 56( 56 Fe) 4 56( 56 Ni)

More information

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y

(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y [ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)

More information

W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge

W 1983 W ± Z cm 10 cm 50 MeV TAC - ADC ADC [ (µs)] = [] (2.08 ± 0.36) 10 6 s 3 χ µ + µ 8 = (1.20 ± 0.1) 10 5 (Ge 22 2 24 W 1983 W ± Z 0 3 10 cm 10 cm 50 MeV TAC - ADC 65000 18 ADC [ (µs)] = 0.0207[] 0.0151 (2.08 ± 0.36) 10 6 s 3 χ 2 2 1 20 µ + µ 8 = (1.20 ± 0.1) 10 5 (GeV) 2 G µ ( hc) 3 1 1 7 1.1.............................

More information

master.dvi

master.dvi 4 Maxwell- Boltzmann N 1 4.1 T R R 5 R (Heat Reservor) S E R 20 E 4.2 E E R E t = E + E R E R Ω R (E R ) S R (E R ) Ω R (E R ) = exp[s R (E R )/k] E, E E, E E t E E t E exps R (E t E) exp S R (E t E )

More information

nsg02-13/ky045059301600033210

nsg02-13/ky045059301600033210 φ φ φ φ κ κ α α μ μ α α μ χ et al Neurosci. Res. Trpv J Physiol μ μ α α α β in vivo β β β β β β β β in vitro β γ μ δ μδ δ δ α θ α θ α In Biomechanics at Micro- and Nanoscale Levels, Volume I W W v W

More information

TOP URL 1

TOP URL   1 TOP URL http://amonphys.web.fc.com/ 1 19 3 19.1................... 3 19.............................. 4 19.3............................... 6 19.4.............................. 8 19.5.............................

More information