|
|
|
- ありさ けいれい
- 5 years ago
- Views:
Transcription
1
2 Fabry-Perot FP
3 A 40 A A A A A A A A A A A A B 46 B B B C 48 C C D 51 D D D E 56 E E F 61 2
4 1 1.1 [1, 2, 3] 2001 [4] 2003 [5] 2005 [6]2006 SN [7] [8] Q Fabry-Perot 3
5
6 2 Fabry-Perot 2.1 Fabry-Perot Fabry-Perot ( FP ) ( 2.1) FP 1,2 r 1, r 2 t 1, t 2 ν λ l δ = 2πl/λ A A r A r = Ar 1 + At 1 ( r 2 )t 1 e 2iδ + At 1 ( r 2 )( r 1 )( r 2 )t 1 e 2iδ + = Ar 1 + At 2 1( r 2 )e (r 2iδ 1 r 2 e 2iδ) n n=0 = A (r 1 r 2t 2 ) 1 e 2iδ 1 r 1 r 2 e 2iδ (2.1) A A t A t = At 1 t 2 e iδ + At 1 ( r 2 )( r 1 )t 2 e 3iδ + At 1 ( r 2 )( r 1 )( r 2 )( r 1 )t 2 e 5iδ + = At 1 t 2 e (r iδ 1 r 2 e 2iδ) n n=0 = A t 1t 2 e iδ 1 r 1 r 2 e 2iδ (2.2) r F P C, t F P C r F P C = r 1 t2 1 r 2e 2iδ 1 r 1 r 2 e 2iδ (2.3) t F P C = t 1t 2 e iδ 1 r 1 r 2 e 2iδ (2.4) 5
7 2.1. FABRY-PEROT : FP P r P r = A r 2 = {(r2 1 + t2 1 )r 2 r 1 } 2 + 4r 1 r 2 (r1 2 + t2 1 ) sin2 δ (1 r 1 r 2 ) 2 (1 + F sin 2 A 2 (2.5) δ) P t P t = A t 2 = t 2 1 t2 2 1 (1 r 1 r 2 ) F sin 2 δ A 2 (2.6) F = 4r 1 r 2 /(1 r 1 r 2 ) 2 δ 2.2 δ = nπ l δ = 2π l λ = 2π lν c = nπ ν = nc 2l (2.7) Free Spectral Range(FSR) ν F SR = c 2l (2.8) ν FWHM r 1 r 2 (2.6) F sin 2 (πlν FWHM /c) = 1 2 (2.9) ν FWHM ν FSR sin ν FWHM = c πl F (2.10) 6
8 Transmittance π -π 0 π 2π Phase 2.2: FP ν FWHM ν FSR Finesse F F = ν FWHM = π r1 r 2 (2.11) ν FSR 1 r 1 r 2 FP FP 2.2 FP ν 0 = ω 0 /2π δν = δω/2π ν m = ω m /2π m A i A i (t) = A 0 e i(ω 0t+m sin ω mt) = A 0 J n (m)e i(ω 0+nω m)t (2.12) A 0 = A i (0) P i = A i 2 P 0 = A 0 2 J n (m) n Bessel m n = 0, ±1 FP P r (t) (2.3) r FPC ω P r (t) = r(δω)j 0 (m) + 2ir(ω m + δω)j 1 (m) sin ω m t 2 P 0 (2.13) 7
9 δω r(δω) r(0)+r (0)δω ν FWHM ν m r(ω m + δω) 1 P r (t) = { J0 2 (m) r(δω) 2 + J1 2 (m) } { t 2 } 1 P 0 + 8J 0 (m)j 1 (m) ω 2 sin ω m tp 0 l 2J 2 1 (m) cos 2ω m tp 0 (2.14) ω = 2πν FWHM FP sin ω m t t 2 1 P rd (t) = 8J 0 (m)j 1 (m) ω 2 δω (2.15) l FP FP 2.3 ϕ(t) A i (t) = A 0 e i(ω 0t+m sin ω mt+ϕ(t)) (2.16) ϕ(t) 0 ϕ(t) ω F ϕ F ϕ(t) = ϕ F e iω F t + ϕ F e iω F t (2.17) ϕ F 1 ϕ F A i (t) = A 0 e iω 0t J n (m)e inωmt ( 1 + iϕ F e iω F t + iϕ F e iω F t ) (2.18) A r (t) = J n (m)e inωmt {r(ω 0 + nω m ) + iϕ F r(ω 0 + nω m + ω F ) +iϕ F r(ω 0 + nω m ω F )}A 0 e iω 0t (2.19) n = 0, ±1 ν FWHM ν m r(±ω m ) 1 A r (t) = J 0 (m) { r(0) + iϕ F e iω F t r(ω F ) + iϕ F e iω F t r( ω F ) } A 0 e iω 0t +2iJ 1 (m) sin ω m t ( 1 + iϕ F e iω F t + iϕ F e iω F t ) A 0 e iω 0t 1 r F P C(ω) r(ω) (2.20) 8
10 sin ω m t FP P rd (t) = 2iJ 0 (m)j 1 (m) { iϕ F e iω F t (r(ω F ) r(0)) + iϕ F e iω F t (r( ω F ) r(0)) } + (c.c.) (2.21) (2.3) e 2iω F l 1 2iω F l 1 r 1 r 2 1 r(ω F ) r(0) = t 2 2iω F 1 ω 2 l [ 1 + ( ) ] ωF e iθ F (2.22) ω tan θ F = 2ω F ω (2.21) t 2 1 P rd (t) = 8J 0 (m)j 1 (m) ω 2 l [ 1 + ( ) ] ( 2ωF ϕ t + θ ) F ω ω F (2.23) (2.24) θ F 1 ω F ω t 2 1 P rd (t) = 8J 0 (m)j 1 (m) ω 2 l ϕ (t) (2.25) FP 9
11 3 FP FP FP 3.1 FP FP l ν 0 n ν 0 = nc 2l (3.1) n l δl δν 0 = nc 2 1 l 2 δl = ν δl 0 l (3.2) 1 FP FP 3.2 FP n x F V = F (t)x (3.3) 1 δl n 10
12 (3.3) Z Z(ω) F (ω) iωx(ω) (3.4) F (ω) X(ω) F (t) x(t) Z R(ω) Re[Z(ω)] (3.5) Z(ω) Y (ω) 1 Z(ω) (3.6) σ(ω) Re[Y (ω)] (3.7) H(ω) H(ω) X(ω) F (ω) (3.8) x G x (f) G x (f) G x (f) = 4k BT ω 2 σ(ω) (3.9) H(ω) 3.9 G x (f) = 4k BT ω Im[H(ω)] (3.10) 0 G F (f) G F (f) = 4k B T R(ω) (3.11) m d2 x dt 2 + mω2 0x = 0 (3.12) 11
13 ω 0 (3.12) m d2 x dt 2 + mω2 0x = F (t) (3.13) mω 2 X(ω) + mω 2 0X(ω) = F (ω) (3.14) mω0 2 [1 + iϕ(ω)] mω 2 X(ω) + mω 2 0(1 + iϕ(ω))x(ω) = F (ω) m[ω 2 + ω 2 0{1 + iϕ(ω)}]x(ω) = F (ω) (3.15) ϕ(ω) loss angle Q = 1/ϕ(ω 0 ) Q ϕ(ω) ϕ(ω) = 1/Q G F (f) = 4mω2 0 k BT Qω (3.16) G x (f) = 4k BT ω ω 2 0 mq ω 2 + ω 2 0 [1 + iϕ(ω)] 2 (3.17) G x (f) = 4k BT ω 1 mqω 2 0 (ω ω 0 ) (3.18) G x (f) = 4k BT ω ω 2 0 mqω 4 (ω ω 0 ) (3.19) ϕ(ω) 1 ϕ(ω) 2 1. T 2. Q Q (Q 10 8 ) FP 2 ϕ(ω)
14 (3.18) m M m = M 2 (3.20) E, ρ ω 0 = E π ρ l (3.21) (3.18) G x (f) = 4k BT Q sp ω 2ρl2 π 2 EM (3.22) Q sp Q M R M = ρπr 2 l G x (f) = 4k BT Q sp ω ρl π 3 ER 2 (3.23) 3.1 Gx (f = 1 Hz) = [1/ Hz] (3.24) l l R 20 cm 10 cm E 135 GPa Q sp 10 8 ρ kg/m 3 T 3.5 K 3.1: 13
15 [8] G x (f) = 4k BT Q su ω 1 γ2 πew0 (3.25) w 0, γ Q su Q FP 3.2 Gx (f = 1 Hz) = [1/ Hz] (3.26) l E 135 GPa Q su 10 8 T 3.5 K γ 0.22 w mm 3.2: [15] G x (f) = k BT 2d(1 + γ)(1 2γ)2 Q co ω πw0 2E(1 γ) (3.27) d Q co Q FP Gx (f = 1 Hz) l = [1/ Hz] (3.28) 3 14
16 E 80 GPa Q co 2500 T 3.5 K γ 0.17 w mm d 8 µm 3.3: [15] G x (f) = 16k BT 2 (1 + γ) 2 α 2 κ πcw 3 0 ω 2 (3.29) α, κ, C 3.4 Gx (f = 1Hz) = [1/ Hz] (3.30) l T 3.5 K γ 0.17 w 0 C 0.5 mm J/m 3 K κ m 2 /s α /K 3.4: (S(f)) ( ) 1 Hz 2 S(f) 10 7 m/ Hz (3.31) f 15
17 f 2 x = a 0 b(f) sin 2πft df (3.32) a = x (2πf) 2 = 4π 2 f 2 x (3.33) S a (f) S a (f) (m/s 2 )/ Hz (3.34) 1/(m/s 2 ) A S x (f) = AlS a (f) (3.35) 3.5 S x (f = 1 Hz) l = [1/ Hz] (3.36) A /(m/s 2 ) S(f) 10 9 /f 2 m/ Hz 3.5: FP FP G x (f) = 2(n 0 1) 2 (A 0 /V 0 )πw 2 0 ( p p 0 ) ( T0 T ) τr 2 (3.37) [16] A 0, V 0, p 0, T 0, n 0 τ R τ R = w 0 u 0 T0 T (3.38) 16
18 u 0 (3.37) Gx (f = 1 Hz) = [1/ Hz] (3.39) l n A V m 3 w 0 p p 0 T 0 T u m Pa Pa K 3.5 K 526 m/s 3.6: FP α S T (f) S x (f) = αls T (f) (3.40) FP 18 K T 3 (3.40) 3.7 S x (f = 1 Hz) l 4 = [1/ Hz] (3.41) 17
19 α /K S T (f) 100/f nk/ Hz 3.7: S x (f) = ( ) h[1 ω(1 r1 r 2 ) + F sin 2 (lω/c)] (3.42) α c sin(lω/c) 2ω 0 ηp 0 [16] η, ω 0 α c α c = t2 1 r 2 1 r 1 r 2 (3.43) lω/c 1 1 r 1 1, 1 r τ s S x (f) = hλ[1 + (τ sω) 2 ] 4πcηP 0 τ 2 s τ s = l F c (3.44) 3.8 (3.44) (3.45) S x (f = 1 Hz) l = [1/ Hz] (3.46) δν ν = 10 Hz (3.47) 18
20 t r r F ω rad/s η 0.7 P 0 l 1 mw 20 cm 3.8: 1e-015 1e-016 1e-017 spacer thermal noise substrate thermal noise coating thermal noise thermoelastic noise seismic noise residual gas noise temperature fluctuation noise shot noise total frequency spectrum [1/rtHz] 1e-018 1e-019 1e-020 1e-021 1e frequency [Hz] 3.1: 19
21 δl/l [1/ Hz : 20
22 Q 1/2 Q Q 18 K cm 20 cm 1 in 3 m 0.5 mm 8 µm : (ECDL) ECDL 4.3 Sr 698 nm 1396 nm 698 nm ECDL (MC) ECDL 21
23 : 4.3: ECDL 22
24 A = 0 A = 0 A = [1/(m/s 2 )] 3.35 S a (f) < (m/s 2 )/ Hz (4.1) 4.4: 23
25 st 2nd 2nd 2nd 4.5: 24
26 : Gx (f) < / Hz (4.2) l p < 4.7 Pa (4.3)
27 n V m 3 w 0 p 0 T 0 T u m Pa K 4 K 526 m/s 4.2: Q = ε eff σt 4 W/m 2 (4.4) σ = W/K 4 m 2 ε eff T = 300 K ε eff = 1 (4.4) Q = 460 W/m 2 (4.5) 2nd 1st
28 : (3.40) S x (f) l = αs T (f) < / Hz (4.6) 4 K α /K (4.7) S T (f) < 100 nk/ 1 Hz (4.8) 27
29 :
30 ( 5.2) 1 5 mm 1 5.2: 1 4 K 20 29
31 MC khz khz 1e-009 error signal 1e-010 frequency fluctuation spectrum [1/rtHz] 1e-011 1e-012 1e-013 1e-014 1e frequency [Hz] 5.3: 30
32 error signal gain [db] e+006 1e+007 1e+008 frequency [Hz] 5.4: 200 error signal phase [deg] e+006 1e+007 1e+008 frequency [Hz] 5.5: 31
33 C cu (T ) Q cu = C cu (T ) dt J (5.1) C si (T ) Q si = C si (T ) dt J (5.2) 17 τ = 17 Q cu + Q si Q cu 40 hour (5.3) cushield custack alshield festack 200 temperature [K] time [hour] 5.6: 32
34 : 33
35 gain [db] frequency [Hz] 5.8: ( ) gain [db] frequency [Hz] 5.9: 34
36 S cus T (f) = ( ) 2+ ( 2 ST cush (f)h cush (f) S fes T (f)) (f)hfes (5.4) S T cus (f), Scush T (f), S fes T (f) H cush (f), H fes (f) (5.4) (T n ) 2 1 Hz 5.13 T n 7.4 µk/ Hz (5.5) S T (f) < 400 nk/ Hz (5.6) 2 D.3 35
37 e-001 1e-002 voltage spectrum [V/rtHz] 1e-003 1e-004 1e-005 1e frequency [Hz] 5.10: 1e+000 1e-001 voltage spectrum [V/rtHz] 1e-002 1e-003 1e-004 1e-005 1e frequency [Hz] 5.11: 36
38 e+000 1e-001 voltage spectrum [V/rtHz] 1e-002 1e-003 1e-004 1e frequency [Hz] 5.12: 1e-003 1e-004 1e-005 temperature spectrum [db] 1e-006 1e-007 1e-008 1e-009 1e frequency [Hz] 5.13: 37
39 (MC) ECDL MC ν/ν = Hz Hz S T (f) < 400 nk/ Hz
40 nk/ Hz ν/ν = 10 Hz 39
41 A A GHz S/N 10 6 S/N A.2 v ν abs = ν 0 + k v 2π ν 0 2 ( ) v h k 2 c 2π 2m (A.1) ν 0 k 40
42 A.3. A. (A.1) ν 0 A.3 ω m ε(t) = ε 0 sin ωt ε(t) = ε 0 sin (ωt + η sin ω m t) (A.2) ε(t) = ε 0 J n (η) sin(ω + nω m )t (A.3) ω ± nω m η ω = 2πx max ω m λ ω = kx max < 1 (A.4) ω = ωω mx max c = 2πω mx max λ x max d < 2x max d < λ π (A.5) (A.6) η < 1 Ψ = n x n y n z = n (A.7) h k σ = σ 0 n + m exp(i k x) n 2 (A.8) 41
43 A.4. A. k x 1 A.8 σ = n + m 1 + i k x + n 2 n + m n 2 = δ n+m,n (A.9) A.4 ω ε(t) = ε 0 cos ωt g E g = 1 2 α(ω) ε(t) 2 (A.10) α(ω) = 2 h n ω ng ω 2 ng ω 2 e n d g 2 (A.11) ω ng, e n d g g e n g, e ω eg > ω E g < 0 ε(z, t) = ε 0 (cos(kz ωt) + cos( kz ωt)) (A.12) A.10 E g = U(z) = U cos 2kz 2 (A.13) U 0 = 1 2 α(ω)(2ε2 0 ) A.13 z = 0( ) U(z) = U (2U 0k 2 )z 2 + O(z 4 ) (A.14) m 2U0 Ω = k m (A.15) h d = 2mΩ 42 (A.16)
44 A.5. A. Ω η k clock η = k clock d (A.17) A.5 g 0 e 0 λ trap ν clock = ν (α g 0 (λ trap ) α e0 (λ trap )) ε(t) 2 (A.18) α g0 (λ magic ) = α e0 (λ magic ) (A.19) λ magic P E = αp + βp 2 + O(P 3 ) (A.20) A.19 A.4 ω eg < ω E g > 0 43
45 A.6. A. A.6 A nm g 1 S 0 e 1 P µm 1 W E1 S 0 = J T = E1 S 0 k B = K (A.21) 1 µk Ω = 2π 74 khz (A.22) d = 28 nm (A.23) 698 nm η = 0.25 (A.24) A.6.2 λ magic = 813 nm (A.25) A.5 λ magic = 389 nm (A.26)
46 A.7. A. A.7 A.7.1 GPS GRACE mm GRACE 400 km Φ ν clock ν clock ν clock ν clock = Φ c 2 (A.27) ν clock /ν clock = Φ = J/kg 1 cm A.7.2 Hartree-Fock ν = ν 0 + qx (A.28) q ( ) α 2 x = 1 2δα (A.29) α 0 α 0 q α 0 A
47 B B.1 τ 0 t = τ 0, 2τ 0,, nτ 0 y = y 1, y 2,, y n τ = mτ 0 σ(τ) = 1 2 (y k+m y k ) 2 (B.1) m x x x k+m x k = N m 1 x n+m x n N m n=1 (B.2) (B.1) σ(τ) = N m 1 (x n+m x n ) 2 (B.3) 2(N m) n=1 B.2 σ(τ) S(f) σ(τ) = 2 0 S(f) sin4 (πfτ) df (B.4) (πfτ) 2 B.3 τ σ(τ) B.1 σ(τ) τ B.1 τ 46
48 B.3. B. B.1: σ(τ) τ τ 2 τ 1 τ 0 τ 1 τ 2 B.1: τ 47
49 C C.1 ε A, T Q = εσat 4 (C.1) σ = W/m 2 K 4 ε I Q = εi (C.2) ε 1, ε 2, A 1 = A 2 = A, T 1, T 2 C.1 Q 12 = ε 1 ε 2 σat1 4 [ 1 + (1 ε2 )(1 ε 1 ) + (1 ε 2 ) 2 (1 ε 1 ) 2 + ] = σat1 4 ε 1 ε 2 ε 1 + ε 2 ε 1 ε 2 Q 21 = σat2 4 ε 1 ε 2 ε 1 + ε 2 ε 1 ε 2 (C.3) (C.4) Q = Q 12 Q 21 = ε 1 ε 2 ε 1 + ε 2 ε 1 ε 2 σa(t 4 1 T 4 2 ) ε 1 ε 2 ε eff = ε 1 + ε 2 ε 1 ε 2 (C.5) (C.6) Q = ε eff σa(t 4 1 T 4 2 ) (C.7) 48
50 C.2. C. C.1: C.2 1,2 n C.2 ε eff σa(t 4 i 1 T 4 i ) = ε eff σa(t 4 i T i+1 4 ) (i = 1, 2,, n) (C.8) 2 Q 2 = ε eff σa(t 4 n T 4 n+1) (C.9) C.8 Q 2 = ε eff σa T 4 T 4 n + 1 (C.10) (C.7) Q 2 Q = 1 n + 1 (C.11) 1/(n + 1) 49
51 C.2. C. C.2: 50
52 D D.1 D.1: 51
53 D.1. D. D.2: D.3: 52
54 D.2. D. D.2 T R v n = 4k B T R [V/ Hz] (D.1) v n i n D.1 D.1, D.2, D.3 IC D.2 1 v n = 45 nv/ Hz (D.2) 3.5 K dr dt Ω/K (D.3) i = 10 µa dv dt = idr 27 mv/k dt (D.4) T n = v n dt dv = 2 µk/ Hz (D.5) 2 µk/ Hz 1,2,4,6,7,8 OP27 v n = 3.2 nv/ Hz i n = 400 fa/ Hz 3,5 OPA627 v n = 4.8 nv/ Hz i n = 2.5 fa/ Hz D.1: 1 IC ADR445 53
55 D.2. D. R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R IC 0.2 nv/ Hz 0.2 nv/ Hz 0.2 nv/ Hz 0.2 nv/ Hz 0.2 nv/ Hz 0.2 nv/ Hz 1.3 nv/ Hz 1.3 nv/ Hz 1.3 nv/ Hz 1.3 nv/ Hz 1.3 nv/ Hz 0.2 nv/ Hz 1.5 nv/ Hz 13 nv/ Hz 13 nv/ Hz 13 nv/ Hz 13 nv/ Hz 22 nv/ Hz 0.1 nv/ Hz 0.1 nv/ Hz 0.1 nv/ Hz 4.8 nv/ Hz 3.2 nv/ Hz 10 nv/ Hz 5.2 nv/ Hz 13 nv/ Hz 2.8 nv/ Hz 45 nv/ Hz D.2: 54
56 D.3. D. D.3 D.1 D.4 R = 7 kω v n = 4k B T R 10.8 nv/ Hz (D.6) v n = 45 nv/ Hz 1e-002 1e-003 voltage spectrum [V/rtHz] 1e-004 1e-005 1e-006 1e-007 1e frequency [Hz] D.4: 55
57 E E (negative g factor) 2. (positive g factor) E.1 E.1: negative g factor 1 56
58 E.2. E. FP Finesse 100,000 3 m Finesse 1,000 FP E.2 E.2,E.3 E.4,E.5 1 Hz 10 9 m/ Hz S a (1 Hz) = (m/s 2 )/ Hz (E.1) S a (1 Hz) < E.6, E.7 1 Hz 10 Hz 57
59 E.2. E. 1e-005 1e-006 1e-007 vibration spectrum [m/rthz] 1e-008 1e-009 1e-010 1e-011 1e frequency [Hz] E.2: ) 1e-004 1e-005 1e-006 vibration spectrum [m/rthz] 1e-007 1e-008 1e-009 1e-010 1e-011 1e frequency [Hz] E.3: 58
60 E.2. E. 1e-005 1e-006 1e-007 vibration spectrum [m/rthz] 1e-008 1e-009 1e-010 1e-011 1e-012 1e frequency [Hz] E.4: 1e-005 1e-006 1e-007 vibration spectrum [m/rthz] 1e-008 1e-009 1e-010 1e-011 1e-012 1e frequency [Hz] E.5: 59
61 E.2. E gain [db] frequency [Hz] E.6: gain [db] frequency [Hz] E.7: 60
62 F F.1: F.2: 61
63 F. F.3: F.4: 62
64 F. F.5: F.6: 63
65 [1] T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen and J. Ye: Nature Photonics 6, (2012) A sub-40-mhz-linewidth laser based on a silicon single-crystal optical cavity [2] Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma and C. W. Oates: Nature Photonics 5, (2011) Making optical atomic clocks more stable with level laser stabilization [3] : Vol. 7, No. 1 1 Hz [4] H. Katori in Proc. 6th Symp. on Frequency Standards and Metrology ed. P. Gill World Scientific, Singapore, 2002 [5] M. Takamoto and H. Katori: Phys. Rev. Lett. 91, Spectroscopy of the 1 S 0-3 P 0 Clock Transition of 87 Sr in an Optical Lattice [6] M. Takamoto, F-L Hong, R. Higashi and H. Katori: Nature 435, An optical lattice clock [7] M. Takamoto, T. Takano, and H. Katori: Nature Photonics 5, (2011) Frequency comparison of optical lattice clocks beyond the Dick limit [8] K. Numata, A. Kemery, and J. Camp: Phys. Rev. Lett. 93, (2004) Thermal-Noise Limit in the Frequency Stabilization of Lasers with Rigid Cavities [9] : (1991) Nd:YAG khz [10] : (1998) 2 Fabry-Perot [11] : (1999) [12] : (2001) Fabry-Perot [13]
66 F. [14] : (2000) Study of the thermal noise caused by inhomogeneously distributed loss [15] K. Somiya and K. Yamamoto: Phys. Rev. D 79, (2009) Coating thermal noise of a finite-size cylindrical mirror [16] ( ) [17] K. G. Lyon, G. L. Salinger, C. A. Swenson, and G. K. White: J. Appl. Phys. 48, 865 (1977) Linear thermal expansion measurements on silicon from 6 to 340 K [18] GUY K. WHITE and PHILIP J. MEESON: Experimental Thchniques in Low- Temperature Physics (OXFORD SCIENCE PUBLICATIONS) [19] [20] David W. Allan, Neil Ashby, Clifford C. Hodge: Hewlett Packard Application Note 1289 The Science of Timekeeping [21] : Vol. 4, No. 3 [22] : Vol. 8, No. 2 65
67 ERATO 4 66
68 F. 67
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
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......................
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..................................
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
(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
[Ver. 0.2] 1 2 3 4 5 6 7 1 1.1 1.2 1.3 1.4 1.5 1 1.1 1 1.2 1. (elasticity) 2. (plasticity) 3. (strength) 4. 5. (toughness) 6. 1 1.2 1. (elasticity) } 1 1.2 2. (plasticity), 1 1.2 3. (strength) a < b F
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
http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................
QMII_10.dvi
65 1 1.1 1.1.1 1.1 H H () = E (), (1.1) H ν () = E ν () ν (). (1.) () () = δ, (1.3) μ () ν () = δ(μ ν). (1.4) E E ν () E () H 1.1: H α(t) = c (t) () + dνc ν (t) ν (), (1.5) H () () + dν ν () ν () = 1 (1.6)
untitled
161 3-5 Development of an Ultra-Narrow Line-Width Clock Laser LI Ying, NAGANO Shigeo, MATSUBARA Kensuke, KOJIMA Reiko, KUMAGAI Motohiro, ITO Hiroyuki, KOYAMA Yasuhiro, and HOSOKAWA Mizuhiko An optical
Undulator.dvi
X X 1 1 2 Free Electron Laser: FEL 2.1 2 2 3 SACLA 4 SACLA [1]-[6] [7] 1: S N λ [9] XFEL OHO 13 X [8] 2 2.1 2(a) (c) z y y (a) S N 90 λ u 4 [10, 11] Halbach (b) 2: (a) (b) (c) (c) 1 2 [11] B y = n=1 B
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
untitled
MRR Physical Basis( 1.8.4) METEK MRR 1 MRR 1.1 MRR 24GHz FM-CW(frequency module continuous wave) 30 r+ r f+ f 1.2 1 4 MRR 24GHz 1.3 50mW 1 rf- (waveguide) (horn) 60cm ( monostatic radar) (continuous wave)
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)
n ξ n,i, i = 1,, n S n ξ n,i n 0 R 1,.. σ 1 σ i .10.14.15 0 1 0 1 1 3.14 3.18 3.19 3.14 3.14,. ii 1 1 1.1..................................... 1 1............................... 3 1.3.........................
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(
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
() n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (5) (6 ) n C + nc + 3 nc n nc n (7 ) n C + nc + 3 nc n nc n (
3 n nc k+ k + 3 () n C r n C n r nc r C r + C r ( r n ) () n C + n C + n C + + n C n n (3) n C + n C + n C 4 + n C + n C 3 + n C 5 + (4) n C n n C + n C + n C + + n C n (5) k k n C k n C k (6) n C + nc
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
. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n
003...............................3 Debye................. 3.4................ 3 3 3 3. Larmor Cyclotron... 3 3................ 4 3.3.......... 4 3.3............ 4 3.3...... 4 3.3.3............ 5 3.4.........
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)
1 1 sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω 1 ω α V T m T m 1 100Hz m 2 36km 500Hz. 36km 1
sin cos P (primary) S (secondly) 2 P S A sin(ω2πt + α) A ω ω α 3 3 2 2V 3 33+.6T m T 5 34m Hz. 34 3.4m 2 36km 5Hz. 36km m 34 m 5 34 + m 5 33 5 =.66m 34m 34 x =.66 55Hz, 35 5 =.7 485.7Hz 2 V 5Hz.5V.5V V
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
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
) 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
I ( ) 2019
I ( ) 2019 i 1 I,, III,, 1,,,, III,,,, (1 ) (,,, ), :...,, : NHK... NHK, (YouTube ),!!, manaba http://pen.envr.tsukuba.ac.jp/lec/physics/,, Richard Feynman Lectures on Physics Addison-Wesley,,,, x χ,
飽和分光
3 Rb 1 1 4 1.1 4 1. 4 5.1 LS 5. Hyperfine Structure 6 3 8 3.1 8 3. 8 4 11 4.1 11 5 14 5.1 External Cavity Laser Diode: ECLD 14 5. 16 5.3 Polarization Beam Splitter: PBS 17 5.4 Photo Diode: PD 17 5.5 :
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](/thumbs/92/109118076.jpg "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
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
08-Note2-web
r(t) t r(t) O v(t) = dr(t) dt a(t) = dv(t) dt = d2 r(t) dt 2 r(t), v(t), a(t) t dr(t) dt r(t) =(x(t),y(t),z(t)) = d 2 r(t) dt 2 = ( dx(t) dt ( d 2 x(t) dt 2, dy(t), dz(t) dt dt ), d2 y(t) dt 2, d2 z(t)
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
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..................
Proposal of a next-generation GW detector using huge mirrors abstract April 10, introduction 1 2 design parameters and sensitivity 2 3 mirror c
Proposal of a next-generation GW detector using huge mirrors abstract April 10, 2001 1 introduction 1 2 design parameters and sensitivity 2 3 mirror considerations 3 3.1 huge substrate availability.....................................
1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π
![1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π](/thumbs/101/149329485.jpg "1. 4cm 16 cm 4cm 20cm 18 cm L λ(x)=ax [kg/m] A x 4cm A 4cm 12 cm h h Y 0 a G 0.38h a b x r(x) x y = 1 h 0.38h G b h X x r(x) 1 S(x) = πr(x) 2 a,b, h,π")
. 4cm 6 cm 4cm cm 8 cm λ()=a [kg/m] A 4cm A 4cm cm h h Y a G.38h a b () y = h.38h G b h X () S() = π() a,b, h,π V = ρ M = ρv G = M h S() 3 d a,b, h 4 G = 5 h a b a b = 6 ω() s v m θ() m v () θ() ω() dθ()
吸収分光.PDF
3 Rb 1 1 4 1.1 4 1. 4 5.1 5. 5 3 8 3.1 8 4 1 4.1 External Cavity Laser Diode: ECLD 1 4. 1 4.3 Polarization Beam Splitter: PBS 13 4.4 Photo Diode: PD 13 4.5 13 4.6 13 5 Rb 14 6 15 6.1 ECLD 15 6. 15 6.3
2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP
1. 1 213 1 6 1 3 1: ( ) 2: 3: SF 1 2 3 1: 3 2 A m 2. 2 P M A 2 F = mmg AP AP 2 AP (G > : ) AP/ AP A P P j M j F = n j=1 mm j G AP j AP j 2 AP j 3 P ψ(p) j ψ(p j ) j (P j j ) A F = n j=1 mgψ(p j ) j AP
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
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
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 =
( ) ) ) ) 5) 1 J = σe 2 6) ) 9) 1955 Statistical-Mechanical Theory of Irreversible Processes )
( 3 7 4 ) 2 2 ) 8 2 954 2) 955 3) 5) J = σe 2 6) 955 7) 9) 955 Statistical-Mechanical Theory of Irreversible Processes 957 ) 3 4 2 A B H (t) = Ae iωt B(t) = B(ω)e iωt B(ω) = [ Φ R (ω) Φ R () ] iω Φ R (t)
Microsoft Word - 学士論文（表紙）.doc
GHz 18 2 1 1 3 1.1....................................... 3 1.2....................................... 3 1.3................................... 3 2 (LDV) 5 2.1................................ 5 2.2.......................
基礎数学I
I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 1....................... 1............
( ; ) 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 =
<4D F736F F D B B83578B6594BB2D834A836F815B82D082C88C60202E646F63>
通信方式第 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/072662 このサンプルページの内容は, 第 2 版発行当時のものです. i 2 2 2 2012 5 ii,.,,,,,,.,.,,,,,.,,.,,..,,,,.,,.,.,,.,,.. 1990 5 iii 1 1
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
II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re
![II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re](/thumbs/94/118770263.jpg "II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re")
II 29 7 29-7-27 ( ) (7/31) II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I Euler Navier
201711grade1ouyou.pdf
2017 11 26 1 2 52 3 12 13 22 23 32 33 42 3 5 3 4 90 5 6 A 1 2 Web Web 3 4 1 2... 5 6 7 7 44 8 9 1 2 3 1 p p >2 2 A 1 2 0.6 0.4 0.52... (a) 0.6 0.4...... B 1 2 0.8-0.2 0.52..... (b) 0.6 0.52.... 1 A B 2
( ) 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](/thumbs/98/136160482.jpg "( ) 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 ( - )
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
LD
989935 1 1 3 3 4 4 LD 6 7 10 1 3 13 13 16 0 4 5 30 31 33 33 35 35 37 38 5 40 FFT 40 40 4 4 4 44 47 48 49 51 51 5 53 54 55 56 Abstract [1] HDD (LaserDopplerVibrometer; LDV) [] HDD IC 1 4 LDV LDV He-Ne Acousto-optic
1 2 2 (Dielecrics) Maxwell ( ) D H
2003.02.13 1 2 2 (Dielecrics) 4 2.1... 4 2.2... 5 2.3... 6 2.4... 6 3 Maxwell ( ) 9 3.1... 9 3.2 D H... 11 3.3... 13 4 14 4.1... 14 4.2... 14 4.3... 17 4.4... 19 5 22 6 THz 24 6.1... 24 6.2... 25 7 26
2000年度『数学展望 I』講義録
2000 I I IV I II 2000 I I IV I-IV. i ii 3.10 (http://www.math.nagoya-u.ac.jp/ kanai/) 2000 A....1 B....4 C....10 D....13 E....17 Brouwer A....21 B....26 C....33 D....39 E. Sperner...45 F....48 A....53
(Bessel) (Legendre).. (Hankel). (Laplace) V = (x, y, z) n (r, θ, ϕ) r n f n (θ, ϕ). f n (θ, ϕ) n f n (θ, ϕ) z = cos θ z θ ϕ n ν. P ν (z), Q ν (z) (Fou
(Bessel) (Legendre).. (Hankel). (Laplace) V = (x, y, z) n (r, θ, ϕ) r n f n (θ, ϕ). f n (θ, ϕ) n f n (θ, ϕ) z = cos θ z θ ϕ n ν. P ν (z), Q ν (z) (Fourier) (Fourier Bessel).. V ρ(x, y, z) V = 4πGρ G :.
S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt
S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............
80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t = 0 i r 0 t(> 0) j r 0 + r < δ(r 0 x i (0))δ(r 0 + r x j (t)) > (4.2) r r 0 G i j (r, t) dr 0
79 4 4.1 4.1.1 x i (t) x j (t) O O r 0 + r r r 0 x i (0) r 0 x i (0) 4.1 L. van. Hove 1954 space-time correlation function V N 4.1 ρ 0 = N/V i t 80 4 r ˆρ i (r, t) δ(r x i (t)) (4.1) x i (t) ρ i ˆρ i t
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 ; >
1. z dr er r sinθ dϕ eϕ r dθ eθ dr θ dr dθ r x 0 ϕ r sinθ dϕ r sinθ dϕ y dr dr er r dθ eθ r sinθ dϕ eϕ 2. (r, θ, φ) 2 dr 1 h r dr 1 e r h θ dθ 1 e θ h
IB IIA 1 1 r, θ, φ 1 (r, θ, φ)., r, θ, φ 0 r
t = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z
I 1 m 2 l k 2 x = 0 x 1 x 1 2 x 2 g x x 2 x 1 m k m 1-1. L x 1, x 2, ẋ 1, ẋ 2 ẋ 1 x = 0 1-2. 2 Q = x 1 + x 2 2 q = x 2 x 1 l L Q, q, Q, q M = 2m µ = m 2 1-3. Q q 1-4. 2 x 2 = h 1 x 1 t = 0 2 1 t x 1 (t)
128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds
127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
i
009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3
,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.
9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,
ohpr.dvi
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
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) 0.5 1.5MeV : thermalization 10 100 m psec 100psec nsec E total = 2mc 2 + E e + + E e Ee+ Ee-c mc
.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
keisoku01.dvi
2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 5 Mon, 2006, 401, SAGA, JAPAN Dept.
磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp May 14, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 262 Today s Lecture: Mode-mode Coupling Theory 100 / 262 Part I Effects of Non-linear Mode-Mode Coupling Effects of Non-linear
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 = = =
1 7 ω ω ω 7.1 0, ( ) Q, 7.2 ( Q ) 7.1 ω Z = R +jx Z 1/ Z 7.2 ω 7.2 Abs. admittance (x10-3 S) RLC Series Circuit Y R = 20 Ω L = 100
7 7., ) Q, 7. Q ) 7. Z = R +jx Z / Z 7. 7. Abs. admittance x -3 S) 5 4 3 R Series ircuit Y R = Ω = mh = uf Q = 5 5 5 V) Z = R + jx 7. Z 7. ) R = Ω = mh = µf ) 7 V) R Z s = R + j ) 7.3 R =. 7.4) ) f = π.
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
最新耐震構造解析 ( 第 3 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 3 版 1 刷発行時のものです.
最新耐震構造解析 ( 第 3 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/052093 このサンプルページの内容は, 第 3 版 1 刷発行時のものです. i 3 10 3 2000 2007 26 8 2 SI SI 20 1996 2000 SI 15 3 ii 1 56 6
TOP URL 1
TOP URL http://amonphys.web.fc2.com/ 1 30 3 30.1.............. 3 30.2........................... 4 30.3...................... 5 30.4........................ 6 30.5.................................. 8 30.6...............................
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
( ) ,
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
3 3.1 R r r + R R r Rr [ ] ˆn(r) = ˆn(r + R) (3.1) R R = r ˆn(r) = ˆn(0) r 0 R = r C nn (r, r ) = C nn (r + R, r + R) = C nn (r r, 0) (3.2) ( 2.2 ) C
![3 3.1 R r r + R R r Rr [ ] ˆn(r) = ˆn(r + R) (3.1) R R = r ˆn(r) = ˆn(0) r 0 R = r C nn (r, r ) = C nn (r + R, r + R) = C nn (r r, 0) (3.2) ( 2.2 ) C](/thumbs/94/119172213.jpg "3 3.1 R r r + R R r Rr [ ] ˆn(r) = ˆn(r + R) (3.1) R R = r ˆn(r) = ˆn(0) r 0 R = r C nn (r, r ) = C nn (r + R, r + R) = C nn (r r, 0) (3.2) ( 2.2 ) C")
3 3.1 R r r + R R r Rr [ ] ˆn(r) = ˆn(r + R) (3.1) R R = r ˆn(r) = ˆn(0) r 0 R = r C nn (r, r ) = C nn (r + R, r + R) = C nn (r r, 0) (3.2) ( 2.2 ) C nn (r r ) = C nn (R(r r )) [2 ] 2 g(r, r ) ˆn(r) ˆn(r
a L = Ψ éiγ c pa qaa mc ù êë ( - )- úû Ψ 1 Ψ 4 γ a a 0, 1,, 3 {γ a, γ b } η ab æi O ö æo ö β, σ = ço I α = è - ø çèσ O ø γ 0 x iβ γ i x iβα i
解説 4 matsuo.mamoru jaea.go.jp 4 eizi imr.tohoku.ac.jp 4 maekawa.sadamichi jaea.go.jp i ii iii i Gd Tb Dy g khz Pt ii iii Keywords vierbein 3 dreibein 4 vielbein torsion JST-ERATO 1 017 1. 1..1 a L = Ψ
総研大恒星進化概要.dvi
The Structure and Evolution of Stars I. Basic Equations. M r r =4πr2 ρ () P r = GM rρ. r 2 (2) r: M r : P and ρ: G: M r Lagrange r = M r 4πr 2 rho ( ) P = GM r M r 4πr. 4 (2 ) s(ρ, P ) s(ρ, P ) r L r T
I
I 6 4 10 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............
all.dvi
72 9 Hooke,,,. Hooke. 9.1 Hooke 1 Hooke. 1, 1 Hooke. σ, ε, Young. σ ε (9.1), Young. τ γ G τ Gγ (9.2) X 1, X 2. Poisson, Poisson ν. ν ε 22 (9.) ε 11 F F X 2 X 1 9.1: Poisson 9.1. Hooke 7 Young Poisson G
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](/thumbs/94/121802164.jpg "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
1 9 v.0.1 c (2016/10/07) Minoru Suzuki T µ 1 (7.108) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1)
1 9 v..1 c (216/1/7) Minoru Suzuki 1 1 9.1 9.1.1 T µ 1 (7.18) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1) E E µ = E f(e ) E µ (9.1) µ (9.2) µ 1 e β(e µ) 1 f(e )
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.............................
untitled
BELLE TOP 12 1 3 2 BELLE 4 2.1 BELLE........................... 4 2.1.1......................... 4 2.1.2 B B........................ 7 2.1.3 B CP............... 8 2.2 BELLE...................... 9 2.3
eto-vol2.prepri.dvi
( 2) 3.4 5 (b),(c) [ 5 (a)] [ 5 (b)] [ 5 (c)] (extrinsic) skew scattering side jump [] [2, 3] (intrinsic) 2 Sinova 2 heavy-hole light-hole ( [4, 5, 6] ) Sinova Sinova 3. () 3 3 Ṽ = V (r)+ σ [p V (r)] λ
5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â 0 = Tr Âe βĥ0 Tr e βĥ0 = dγ e βh 0(p,q) A(p, q) dγ e βh 0(p,q) (5.2) e βĥ0
![5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â 0 = Tr Âe βĥ0 Tr e βĥ0 = dγ e βh 0(p,q) A(p, q) dγ e βh 0(p,q) (5.2) e βĥ0](/thumbs/99/141438380.jpg "5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â 0 = Tr Âe βĥ0 Tr e βĥ0 = dγ e βh 0(p,q) A(p, q) dγ e βh 0(p,q) (5.2) e βĥ0")
5 H Boltzmann Einstein Brown 5.1 Onsager [ ] Tr Tr Tr = dγ (5.1) A(p, q) Â = Tr Âe βĥ Tr e βĥ = dγ e βh (p,q) A(p, q) dγ e βh (p,q) (5.2) e βĥ A(p, q) p q Â(t) = Tr Â(t)e βĥ Tr e βĥ = dγ() e βĥ(p(),q())
untitled
( ) c a sin b c b c a cos a c b c a tan b a b cos sin a c b c a ccos b csin (4) Ma k Mg a (Gal) g(98gal) (Gal) a max (K-E) kh Zck.85.6. 4 Ma g a k a g k D τ f c + σ tanφ σ 3 3 /A τ f3 S S τ A σ /A σ /A
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 =
05Mar2001_tune.dvi
2001 3 5 COD 1 1.1 u d2 u + ku =0 (1) dt2 u = a exp(pt) (2) p = ± k (3) k>0k = ω 2 exp(±iωt) (4) k
(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](/thumbs/100/144882653.jpg "(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
橡実験IIINMR.PDF
(NMR) 0 (NMR) 2µH hω ω 1 h 2 1 1-1 NMR NMR h I µ = γµ N 1-2 1 H 19 F Ne µ = Neh 2mc ( 1) N 2 ( ) I =1/2 I =3/2 I z =+1/2 I z = 1/2 γh H>0 2µH H=0 µh I z =+3/2 I z =+1/2 I z = 1/2 I z = 3/2 γh H>0 2µH H=0
S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d
S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....
QMI_09.dvi
25 3 19 Erwin Schrödinger 1925 3.1 3.1.1 3.1.2 σ τ 2 2 ux, t) = ux, t) 3.1) 2 x2 ux, t) σ τ 2 u/ 2 m p E E = p2 3.2) E ν ω E = hν = hω. 3.3) k p k = p h. 3.4) 26 3 hω = E = p2 = h2 k 2 ψkx ωt) ψ 3.5) h
TOP URL 1
TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7
QMI_10.dvi
25 3 19 Erwin Schrödinger 1925 3.1 3.1.1 σ τ x u u x t ux, t) u 3.1 t x P ux, t) Q θ P Q Δx x + Δx Q P ux + Δx, t) Q θ P u+δu x u x σ τ P x) Q x+δx) P Q x 3.1: θ P θ Q P Q equation of motion P τ Q τ σδx
x A Aω ẋ ẋ 2 + ω 2 x 2 = ω 2 A 2. (ẋ, ωx) ζ ẋ + iωx ζ ζ dζ = ẍ + iωẋ = ẍ + iω(ζ iωx) dt dζ dt iωζ = ẍ + ω2 x (2.1) ζ ζ = Aωe iωt = Aω cos ωt + iaω sin
2 2.1 F (t) 2.1.1 mẍ + kx = F (t). m ẍ + ω 2 x = F (t)/m ω = k/m. 1 : (ẋ, x) x = A sin ωt, ẋ = Aω cos ωt 1 2-1 x A Aω ẋ ẋ 2 + ω 2 x 2 = ω 2 A 2. (ẋ, ωx) ζ ẋ + iωx ζ ζ dζ = ẍ + iωẋ = ẍ + iω(ζ iωx) dt dζ
A
A04-164 2008 2 13 1 4 1.1.......................................... 4 1.2..................................... 4 1.3..................................... 4 1.4..................................... 5 2
= hυ = h c λ υ λ (ev) = 1240 λ W=NE = Nhc λ W= N 2 10-16 λ / / Φe = dqe dt J/s Φ = km Φe(λ)v(λ)dλ THBV3_0101JA Qe = Φedt (W s) Q = Φdt lm s Ee = dφe ds E = dφ ds Φ Φ THBV3_0102JA Me = dφe ds M = dφ ds
untitled
( 9:: 3:6: (k 3 45 k F m tan 45 k 45 k F m tan S S F m tan( 6.8k tan k F m ( + k tan 373 S S + Σ Σ 3 + Σ os( sin( + Σ sin( os( + sin( os( p z ( γ z + K pzdz γ + K γ K + γ + 9 ( 9 (+ sin( sin { 9 ( } 4
N/m f x x L dl U 1 du = T ds pdv + fdl (2.1)
23 2 2.1 10 5 6 N/m 2 2.1.1 f x x L dl U 1 du = T ds pdv + fdl (2.1) 24 2 dv = 0 dl ( ) U f = T L p,t ( ) S L p,t (2.2) 2 ( ) ( ) S f = L T p,t p,l (2.3) ( ) U f = L p,t + T ( ) f T p,l (2.4) 1 f e ( U/
II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R
![II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R](/thumbs/95/125540821.jpg "II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R")
II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =
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,