BH BH BH BH Typeset by FoilTEX 2
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- ぜんすけ さわい
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1 GR BH BH BH at NICT Typeset by FoilTEX 1
2 BH BH BH BH Typeset by FoilTEX 2
3 1. BH Typeset by FoilTEX 3
4 1.2 2 A B A B t = 0 A: m a [kg] B: m b [kg] t = t f star free fall x x x t = t f t = 0 : Typeset by FoilTEX 4
5 3 Step 1 K inertia b K rest w.r.t. star star b Typeset by FoilTEX 5
6 Step 2 K free fall K b = K b K-system star Typeset by FoilTEX 6
7 Step 3 star free fall for a long time Typeset by FoilTEX 7
8 A v a = A A A light A A-system ( if v a = constant ) K Inertia light A A-system ( v a increases ) accelerate! A = v a [m/s] light Typeset by FoilTEX 8
9 2 A star K free fall = light light K-system (free fall system) Typeset by FoilTEX 9
10 Abell1689 Typeset by FoilTEX 10
11 Typeset by FoilTEX 11
12 Typeset by FoilTEX 12
13 ( paper ) ( sphere ) Typeset by FoilTEX 13
14 1.5 Einstein R(P) G c 4 ρ(p) L 1 R 1 < R 2 < R 3 P 2 R(P) 1 P 1 L 2 L(P) 2 L 3 P 3 ρ(p) P [erg/cm 3 ] R(P) P [1/cm 2 ] G/c 4 [cm/erg] L(P) ct P x. =. ct P x Typeset by FoilTEX 14
15 1.6 BH BH light cone 1.1 ct x light { ct y x Typeset by FoilTEX 15
16 BH BH horizon L BH = 2GM c 2 Black hole Singularity: ρ = ct light cone BH lights core of a star M [kg] L BH BH x Typeset by FoilTEX 16
17 BH BH BH BH BH BH light BH BH BH Typeset by FoilTEX 17
18 BH Schwarzschild BH r(λ) ( ) dr(λ) 2 ( L 2 c 2 ) ( + dλ r 2 (µc 2 ) 2 1 r ) BH r { µ 0 µ µ = 0 E L = E 2 λ Typeset by FoilTEX 18
19 BH E, L BH µ 0 { µ = 0 potential µ = 0 µ = 0 3_ 2 r BH 3 r BH BH BH r Typeset by FoilTEX 19
20 L = 0 Singularity O ct Black Hole (Trapped Region) R BH gravity Light Cone r ct Singularity O Grav. Doppler Light Cone Trapped Region (Black Hole) R BH world sheet of a wave source r Typeset by FoilTEX 20
21 1.7 BH OK Typeset by FoilTEX 21
22 OK OK Typeset by FoilTEX 22
23 OK BH BH Typeset by FoilTEX 23
24 BH BH (A) BH (B) BH (A) BH (B) BH Typeset by FoilTEX 24
25 1 BH Typeset by FoilTEX 25
26 2. BH BH 2.1 BH BH BH BH Typeset by FoilTEX 26
27 BH BH 3 M : J : Q : Q = 0 Typeset by FoilTEX 27
28 BH Einstein Schwarzschild BH r BH = 2m, m = GM c 2 [cm] BH 0 Typeset by FoilTEX 28
29 BH Einstein Kerr BH r BH = m + m 2 a 2, a = J Mc [cm] BH BH 0 a < m r erg = m + m 2 a 2 cos 2 θ θ BH r < r erg BH Typeset by FoilTEX 29
30 Kerr BH BH a = 0.8 m Typeset by FoilTEX 30
31 2.2 BH BH BH BH M a ( a := J Mc ) BH BH 0 a < m = GM c 2 Typeset by FoilTEX 31
32 2.3 BH BH VLBI { Typeset by FoilTEX 32
33 2.4 BH BH source W 0 earth W 1 W 0 0 W 1 1 Typeset by FoilTEX 33
34 W 0 W 1 BH t obs E obs = E 1 E 0 BH M a BH source W 1 W 0 earth Typeset by FoilTEX 34
35 2.5 Gouy phase shift E 0 W oscillation of observed wave at ONE telescope E 1 Hilbert Trans. of W E t obs t obs t obs t obs E 1 W Zenginoglu &Galley PRD86(2012)064030, YouTube source BH 10 W 1 W 0 20 earth Typeset by FoilTEX 35
36 Gouy Phase Shift (GPS) (caustic) 1 Fourier π/2 Fourier +π/2 Hilbert caustic BH caustic (ex. non-rot. BH) For each beam [cross section] = 0 Typeset by FoilTEX 36
37 F obs E obs 2 E obs F obs (t obs ) GPS W 0 W 1 t obs 2 3 Hilbert GPS BH Typeset by FoilTEX 37
38 2.6 E obs Oscillation of observed wave at ONE telescope Τ 0 (ex. line emission) E Τ 1 obs W 0 W 1 t obs t obs { t obs, E obs BH T 0 T 1 Typeset by FoilTEX 38
39 3 M : BH a : BH ν 1 /ν 0 : (= T 0 /T 1 ) BH BH M, a Typeset by FoilTEX 39
40 W 0 W 1 Gouy Phase Shift intensity (photon no.) W 0 an example W1 source ν Typeset by FoilTEX 40
41 2.7 Step1: A, B Step2: B Hilbert E obs Step3: A B E original data (A) W 0 W 1 t obs strong corelation W 0 W t obs modulated data (B) W 0, W 1 t obs, E obs, ν 1 /ν 0 VLBI Typeset by FoilTEX 41
42 ( t obs, E obs, ν 1 /ν 0 ) E obs = F obs (1) F obs (0) Specific Flux Typeset by FoilTEX 42
43 Specific Flux [erg/s cm 2 Hz] F obs (ν obs ) = I obs (ν obs ) Ω obs = I(ν) ( νobs ν s = ν s (ν obs ) ν s ) 3Is (ν s ) Ω obs Specific Intensity I(ν) [erg/s cm 2 Hz ste-rad] ν 3 = const. Ω obs 1 ν 2 obs Typeset by FoilTEX 43
44 3.2 BH (M, a) M = 1, a = 0.8 obs. φ φ=0 BH θ = 0.7π 2.2 r BH source v s = φ ZAMO W 0 W 1 v s Typeset by FoilTEX 44
45 図 A 光線 これらの光線は 遠方に居る同一観測者に届く しかし 到着時刻がずれて 観測強度も異なる Caustic point on the light orbit 光源がバースト的に発光 赤線はエルゴ領域の赤道 光線ではない
46 φ obs F 1 /F 0 ν 1 /ν 0 φ obs φ obs 0 2π t obs /M F 1 /F 0 ν 1 /ν 0 O(0.1) Typeset by FoilTEX 46
47 W 0 W 1 Gaussian Power law Planckian (θ obs, ϕ obs ) E obs Mathematica file Typeset by FoilTEX 47
48 3.3 VLBI W 0, W 1 { BH W1 W 0 source u s BH Typeset by FoilTEX 48
49 4. BH M, a BH BH ( t obs, F 1 /F 0, ν 1 /ν 0 ) Typeset by FoilTEX 49
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..................
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
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II 14 14-7-8 8/4 II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ 6/ ] Navier Stokes 3 [ ] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I 1 balance law t (ρv i )+ j
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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
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)
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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 =
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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
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1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
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(a) (b) (c) (d) Wunderlich 2.5.1 = = =90 2 1 (hkl) {hkl} [hkl] L tan 2θ = r L nλ = 2dsinθ dhkl ( ) = 1 2 2 2 h k l + + a b c c l=2 l=1 l=0 Polanyi nλ = I sinφ I: B A a 110 B c 110 b b 110 µ a 110
(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
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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()
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QCD ( ), ( ) 8 23 Typeset by FoilTEX Introduction:QCD Phase diagram of QCD system Critical end point Quark Gluon Plasma T c Temperature 1st order phase transition line Hadron 0 CSC 0 Chemical potential
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())
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
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m(ẍ + γẋ + ω 0 x) = ee (2.118) e iωt P(ω) = χ(ω)e = ex = e2 E(ω) m ω0 2 ω2 iωγ (2.119) Z N ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.120)
2.6 2.6.1 mẍ + γẋ + ω 0 x) = ee 2.118) e iωt Pω) = χω)e = ex = e2 Eω) m ω0 2 ω2 iωγ 2.119) Z N ϵω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j 2.120) Z ω ω j γ j f j f j f j sum j f j = Z 2.120 ω ω j, γ ϵω) ϵ
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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
CMP Technical Report No. 4 Department of Computational Nanomaterials Design ISIR, Osaka University 2 2................................. 2.2......................... 2 3 3 3................................
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k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i σ ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m σ A σ σ σ σ f i x
k m m d2 x i dt 2 = f i = kx i (i = 1, 2, 3 or x, y, z) f i ij x i e ij = 2.1 Hooke s law and elastic constants (a) x i (2.1) k m A f i x i B e e e e 0 e* e e (2.1) e (b) A e = 0 B = 0 (c) (2.1) (d) e
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)
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1 2 (90cm 70cm 2015) 3 (68cm 28cm 30cm 12kg 2015) (77.5 109.5cm 2015) 4 (22cm 50cm 50cm 4.6kg 2015) (45cm 62.5cm 2015) (47.4cm 62.5cm 2014) 5 (28.5cm 23.5cm) (45cm 62cm 2015) (97cm 107cm 2015) 6 7 8 9
6 12 10661 93100 227213202 222208197 85kg cm 20 64.521 106856142 2 1 4 3 9767 100 35 cm 7747 208198 90kg 23 5828 10661 93100 cm 227213202 10639 61 64.521 85kg 78kg 70kg 61 100 197204.5 cm 15 61
180 140 22
21 180 140 22 23 25 50 1 3 350 140 500cm 600 140 24 25 26 27 28 29 30 31 1/12 8.3 1/15 6.7 10 1/8 12.5 1/20 140 90 75 150 60 150 10 30 15 35 2,000 30 32 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 % 100 50 33.3
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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
s = 1.15 (s = 1.07), R = 0.786, R = 0.679, DW =.03 5 Y = 0.3 (0.095) (.708) X, R = 0.786, R = 0.679, s = 1.07, DW =.03, t û Y = 0.3 (3.163) + 0
7 DW 7.1 DW u 1, u,, u (DW ) u u 1 = u 1, u,, u + + + - - - - + + - - - + + u 1, u,, u + - + - + - + - + u 1, u,, u u 1, u,, u u +1 = u 1, u,, u Y = α + βx + u, u = ρu 1 + ɛ, H 0 : ρ = 0, H 1 : ρ 0 ɛ 1,
,, 2. Matlab Simulink 2018 PC Matlab Scilab 2
(2018 ) ( -1) TA Email : [email protected], [email protected] : 411 : 10 308 1 1 2 2 2.1............................................ 2 2.2..................................................
数学の基礎訓練I
I 9 6 13 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 3 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............
進化
YouTuber - 白 石 達 也 - -----Original Message------ YouTuber ------End Of Message------- 3 3 1 100 10 120Kg 1 7 5 2 5 1 2 3 4 5 2 3 YouTuber 37 37 63 3 9 5 ( ========= 1) ========= 5 Point1 Point2 Point3