Formation process of regular satellites on the circumplanetary disk Hidetaka Okada Department of Earth Sciences, Undergraduate school of Scie
|
|
|
- こうしょ こびき
- 5 years ago
- Views:
Transcription
1 Formation process of regular satellites on the circumplanetary disk Hidetaka Okada Department of Earth Sciences, Undergraduate school of Science, Hokkaido University Planetary and Space Group :
2 ., 60.,,.,,.,,.,,..,., gas-starved accretion disk model) Canup and Ward 2006) A common mass scaling for satellite systems of gaseous planets,., Canup and Ward 2006). Canup and Ward 2006),,. Canup and Ward 2006)
3 i
4 ii Canup and Ward Lubow et al., 1999) Canup and Ward, 2002)
5 iii 3, Canup and Ward, 2002)
6 ,,,,,,.., Mosqueira and Estrada 2003),,.,,,. T 1/r.,,,,.,,.., Canup and Ward 2006), gas-starved accretion disk model)., ).,,,,,,..,,,
7 1 2. T T F 1/4 in, F in, ),,.,,..,, Canup and Ward 2006),. 1.2,,,, 2 ). Canup and Ward 2006) 3 ), 4 ). Canup and Ward 2006) 5 ).
8 2 3 2.,. Canup and Ward 2006),. Hayashi et al., 1985)., Canup and Ward 2006). 2.1.,.,. ),.,,.,,..., 10., Hayashi et al., 1985).,, H 2 O,..,,,.
9 2 4,.,.,,, Lubow et al. 1999) 2. 1.,.... 1,,..,.,.,,.,.,,.,,.,.
10 2 5 1 Lubow et al., 1999).,,..,,.
11 ,.,.,.,,,.,,,.,.,,.,,.,,.,,,,.,.,,.,,.,.,.,,..
12 2 7,. 2., Type I migration)., Type I migration,.,. Type I migration.,. 2.4,.,,,,.,,.. Canup and Ward 2006) M T M P M T /M P ,. 3.7 ) ),, T F 1/4 in Canup and Ward, 2002).,.,
13 Canup and Ward 2006) N, )..,.,,.,.,,.
14 3 9 3,,, Canup and Ward 2006),. 3.1,., -, 3. 3, ρ v t ρ t + ρv) = 0, 1) + v )v = p, 2) p = ρk BT µm u. 3)., k B, µ, m u, v, ρ, p. v = vx, t),ρ = ρx, t), p = px, t)., v 0 = 0, ρ = ρ 0, p = p 0. v = v 1 x, t), ρ = ρ 1 x, t), p = p 1 x, t), v = v 0 + v 1, ρ = ρ 0 + ρ 1, p = p 0 + p 1. 1),2), t ρ 0 + ρ 1 ) + x ρ 1v 1 + ρ 0 v 1 ) = 0, 4) ρ 0 + ρ 1 ) v ) 1 t + v 1 v 1 = x x ρ 0 + ρ 1 ). 5) 2. ρ 0 / t = 0,, ρ 0 / x =
15 , ρ 1 t + ρ v 1 0 x 6) 7) t, x, = 0, 6) ρ 0 v 1 t = p 1 x. 7) 2 ρ 1 t 2 + ρ 2 v 1 0 = 0, 8) t x ρ 0 2 v 1 x t = 2 p 1 x 2. 9) 2 ρ 1 t 2 = 2 p 1 x 2. 10). 10) 3),,, 11), 2 ρ 1 t 2 = k BT µm u 2 ρ 1 x 2. 11) ) 1/2 kb t c s =. 12) µm u 2 ρ t 2. c s. = c s 2 2 ρ x 2. 13). z, z. z, P z = GM Sunρ z r 2 r. 14), M Sun, G, ρ. P = ρk BT µm u, ρ z = GM Sunρ z r 2 r ρ ρ = GM Sun r 3 µm u k B T, 15) µm u z z. k B T 16)
16 3 11 z. z = 0 ρ = ρ0),, ρz) = ρ0) exp GM Sun µm u z 2 ) a 3. 17) k B T 2 H. 2k B T a H = 3 k B T τ K = µm u GM Sun 2µm u π. 18) τ K. 17) ) z 2 ρ = ρ0) exp. 19) H 2. z = H, ρ = ρ0) e 1/e.. 3.2,,,.., 10.,,,, 2007 ).. M c P, T, ρ.,. r F, r, r l., F σ SB [T 4 r) T 4 r + l)] 4σ SB T 3 dt l. 20) dr, σ SB., κ, ρ, l 1/κρ, 20). F 4σ SBT 3 κρ dt dr. 21)
17 3 12 F,,, 4/3,. F 16σ SBT 3 3κρ dt dr. 22),, 16σ SB T 3 dt 3κρ dr = L 4πr 2. 23), L r,.,, M c,. L GM cm c. 24) R c M c, R c,,, M atm., M r. dp dr = GM ρ, r2 25) P = ρk BT. µm u 26) R out,, T out, P out. M c M atm ). T T out, P P out, κ, 23), T = 26), ) 1/4 3κρL. 27) 64πσ SB r P = ρk ) 1/4 B 3κρL. 28) µm u 64πσ SB r
18 ), [ dp dr = d ) ] 1/4 ρk B 3κρL dr µm u 64πσ SB r = GM ρ. 29) r2, GMµmu ρ = k B ) 4 πσ SB 12κL. 30), M atm. M atm = 4πr 2 GMµmu ρdr = R c k B Rout ) 4 π 2 σ SB 3κL ln R out R c. 31) M atm M c, M M c. M M c )., 31) M M = M c + M atm. M c M atm, M atm, M atm., M c M atm, M c, M atm. M c.,,,., M = M atm + M c, dm atm /dm c =. 31) M = M atm + M c, 24) 31), GMatm + M c )µm u M atm = k B ρ c = M c / 4 3 πr c 3, ) 4 π 2 σ SB 3κ R c ln R out. 32) GM c M c R c ) M atm = M atm + M c ) 4 µmu π 2 ) 1/3 σ SB 3Mc G 3 ln R out, 33) k B 3κ 4πρ c M c R c, M atm. M c M atm = β M atm + M c ) 4. 34) M c 2/3
19 3 14, β. β = σ SB κ M c ) 4 µmu π G 3 5 k B 36ρ c ) 1/3 ln R out R c. 35) 34) M c, dm atm /dm c =, M c,crit, M c,crit = ) 3/7 27 M c β M /10 6 yr, lnr out /R c ) 0.5. ) 3/7 κ 1cm 2 g 1 ) 3/7 M. 36),.. Ikoma et al., 2000). ) ) M c fd,atm M c,crit = 10 M /10 6 M. 37) yr f g,atm, , 2, r c. 2. r, r d.,, F in, Ṁ, Ṁ = πr 2 c F in.,, 2., ν = αc s H Shakura and Sunyaev, 1973). ν, α. ν,,.
20 Canup and Ward, 2002), Canup and Ward 2002)., 2,.,.,.,., σ G / t = 0., σ G t = 1 Ṁ 2πr r + F in = 0, 38), σ G, Ṁ r = 2πrF in. 39) Ṁ r, Ṁ = 2πrσ G v r. v r. 1,, 2,.,, v j t + v v i j = 1 P + 1 p ij + x i ρ g x i ρ g x j x j GM r ). 40)
21 3 16, M, p ij. p ij = 2ρ g ν e ij 13 ) e kkδ ij, e ij = 1 vi + v ) j. 41) 2 x j x i 1, 2, 3. 40) r, φ, z). φ, v φ ρ v r r + v φ 1 r v φ φ + v v φ z = ρν 2 v φ + ρν 2 v r r 2 φ ρν 1 r 2 v φ + ν ρ r z + 1 r v φv r vφ r v φ r ) ). 42), v φ., 2 2 = 2 / r 2 + /r r+ 2 /r 2 φ / z 2., φ,,. z,., v z = 0, / φ = 0. z, σ G v r r r2 Ω) r = r r 3 σ G ν Ω ). 43) r, Ω, Ω = v φ /r. Ω Ω K Ω K ), Ω = GM /r 3 43), g r = Ṁ h r. 44) g, g = 3πσ G hν. h, h = rω 2. 38), 44). r r c, Ṁ r c < r < r d, r < r c, r = r c, Ṁ., r c < r < r d. r > r c,, F in = 0., Ṁ,,, Ṁ, Ṁ = Ṁ0 = const. 44) r c r d, Ṁ 0 h h d ) = g g d ) = g. 45), r = r d, g = g d, r = r d, g d = 0.
22 3 17 r < r c. r < r c,, Ṁ r. Ṁdh/dr = dṁh)/dr hdṁ/dr 44), h r 1/2, hṁr) + gr) = 4 5 πf inrch 2 c rph 2 p ) + A. 46), h c = r c 2 Ω c, h d = r d 2 Ω d, r P. A. r = r P, gr P ) = 0., A = Ṁph p 4 5 πf inr 2 ph p., Ṁ P. r = r c., Ṁ = Ṁ0, r = r c, h c Ṁ 0 + Ṁ0h d h c ) = 4 5 πr c 2 h c F in + Ṁph p 4 5 πf inr p 2 h p, 47) Ṁ 0 h d Ṁph p = 4 5 πf inr c 2 h c r p 2 h p ). 48),,,.,, r d,., 48), 49), Ṁp + Ṁ0 = Ṁ πf inr p 2. 49) Ṁ 0 h d πf in r c 2 πf in r p 2 + Ṁ0)h p = 4 5 πf inr c 2 h c r p 2 h p ). 50), h p = r p 2 Ω p,, Ω d = GM GM r 3 d, Ω c = r 3 c, Ω p = GM r 3 p, Ṁ 0 r 1/2 d r 1/2 p ) = πf in r 2 c r 1/2 p πf inr 5/2 p πf inr 5/2 c, 51) [ ) 1/2 2 4 rc Ṁ 0 = πf in r c + 1 ) ] [ 2 rd ) ] 1/2 1 rp ) 5 5 r p r c r p
23 3 18 Ṁ 0, Ṁr > r c), Ṁr < r c ). Ṁr > r c ) = Ṁ0, = πf in r c 2 [ 4 5 rc r p ) 1/ rp r c ) ] [ 2 rd ) ] 1/ r p 53) rc Ṁr < r c) = 2πrF in dr Ṁ0, 54) r [ ) ] 2 2 r = πf in r c 1 4/5)r c/r p ) 1/2 + 1/5)r p /r c ) ) r d /r p ) 1/2 1 r c,, r p /r c ) 2 1, r d /r p ) 1/2 1., [ ) ] 1/2 4 rc Ṁr > r c ) = Ṁ0 Ṁ, 56) 5 r d [ ) 2 r Ṁr < r c ) Ṁ 1 4 ) ] 1/2 rc. 57) 5,. r c r d r > r c ), r < r c ), [ σ G r) 4Ṁ rc 15πν r σ G r) 4Ṁ 15πν rc r d ]. 58) [ 5 4 rc 1 ) ] 2 r. 59) r d 4 r c
24 ,,,,.,.,.. r,, GM P Ṁ/r) r GM P Ṁ r 2 r. 60),, Ėν,,, Ė ν = 9 4 νω2 σ G 2πr r. 61) Ė rad = 2σ SB T d 4 2πr r. 62), T d., T d, 9 4 νω2 σ G 2πr r = 2σ SB T 4 d 2πr r, 63) [ T 4 d 9Ω2 νσ G = 3Ω2 r 2 c F in 1 4 rc 1 ) ] 2 r. 64) 8σ SB 5 r d 5 8σ SB T d F in 1/4, α σ G. r c.,,.,
25 3 20,. Canup and Ward, 2002). [ ) ] 4 T 4 c T 4 d Tneb T d τt d 4. 65) τ.,, T d T c. 3) Canup and Ward 2002).,. 25R J 1000K,, r 20R J 200K,.
26 3 21 3, Canup and Ward, 2002) T d, T c. 4. τ G τ G ) τ G = 10 4 yr, τ G = yr,.
27 , r. r 2πr r/f. f -., m s. τ acc = fm s 2πr rf in. 66) r e, r/r 2e.,,,.,,,.,,. e τ col, τ drag, τ dw., e τ relax, e τ col = τ relax, τ drag = τ relax, τ dw = τ relax., e, τ dw = τ relax., τ dw = τ relax e. Ward 1988), τ dw = 1 ) ) M M c ) 4. 67) C e Ω M σ G r 2 rω,, τ relax = 0.73 ) ) M M v ) 4 [ln 2Λ] 1 Ω M σ S r 2. 68) rω, σ S, v,. τ dw = τ relax,, v
28 3 23 v dw, 67) 68), ) ) 1 M M c ) = C e Ω M σ G r 2 rω Ω v dw = c σs σ G M ) ) vdw M ) 4 [ln 2Λ] 1 M σ S r 2, 69) rω ) 1/4. 70), e. v dw v K σs Γ σ G ) 1/4 ) H e. 71) r Γ 1. r m s, σ S σ S = m s /2πr r., ) 1/4 ) m s H e, 72) 2πr rσ G r ) 1/4 ) H 4πr 2 e 5/4, 73) σ G r ) 1/5 ms. 74) ms e H r 4πrHσ G 74) 66), τ acc fσ G F in ms 4πrHσ G ) 4/5. 75),..,. τ 1. τ 1 = 1 C a Ω Mp m s ) Mp r 2 σ G ) ) 2 H. 76) r C a 1. 76), H/r) c/rω) 0.1.,.
29 τ acc, Type I migration., τ acc τ 1 m s,, m c., m crit /M P. 75) 76), fσ G F in mc 4πrHσ G ) 4/5 = 1 C a Ω Mp m s ) Mp r 2 σ G ) ) 2 H. 77) r, F in F in = M P /τ G πr c 2., τ G = M P dm/dt) 1. 77), fσ G M P πr c 2 τ G mc 4πrHσ G ) 4/5 = 1 C a MP m c ) MP r 2 σ G ) ) 2 H. 78) r, σ G r < r c,. [ σ G = 4F 5 15πν 4 rc 1 ) ] 1/2 r, 79) r d 4 r c 0.2 ) Fin r ) 2 rc ) 2. 80) α Ω H r, ν = αch, H/r c/rω, r/r c = 0.5, r/r d = 0.2., 78), f M P 3 0.2Fin αω ) 6/5 r H ) 12/5 rc ) ) 12/5 4/5 1 2 πrc τ G m 9/5 c = H2 r 4πrH C a r 4. 81), mc M P ) ) 5/9 ) 26/9 ) 10/9 ) 2/3 π H r α 5.4 Ωτ G f) 1/9 82) C a r r C f ) 5/9 ) 26/9 ) 10/9 ) 2/3 3.5 H/r r/rc α/f χ ) C a χ χ [1week/2 /Ω))f/10 2 )τ G /10 7 yr)] 1/9, m crit /M P, 1. H/r), r
30 3 25, H/r) 0.1. r c, r/r c ), 1. m c /M P, α, f. α,..,. - f. 3.7 r. 1 R P < r < r c. MT M P ) = rc m crit/m P ) R P r dr. 84) r, r/r e. e, 74), F in = M P /τ G πr c 2, σ G 80), r H 84), MT M P ) = mc ) 1/5 α 4πrH 0.2 rc R P rc 1 R P r m c 1 M P H 1 C a ) 1/5 πrc 2 τ G Ω M P ) 1/5 ) 2/5 ) 2/5 H r. 85) r r c mc απr 2 ) 1/5 ) 2/5 ) 2/5 c τ G Ω H r dr, 0.8πrHM P r r c 86) ) 4/9 ) 10/9 ) 8/9 ) 1/3 H r α 1 dr. r r c f 1/9 Ωτ G f) 87), H/r, f,, r c R P,. MT M P ) C a χ ) 4/9 ) 10/9 ) 1/3 H α 1 r f ) 4/9 3.5 H/r 0.1 1, α/f). C a. 88) 1/9 Ωτ G f) ) 1/3. 89) ) 10/9 α/f
31 3 26 α.,, α 10 4 < α < 10 2., α 3, M T /M P 1. M T /M P.
32 Canup and Ward 2006)..,,.,, Type I migration.,,,.,,,.,,,,.,,. Canup and Ward 2006),,.,.
33 5 Canup and Ward Canup and Ward 2006 Canup and Ward 2006) A common mass scaling for satellite systems of gaseous planets ) ,,,,, 10,,.,,. )..
34 5 Canup and Ward ,. M T M P, M T /M P ,., ) H + He).,M T /M P ) 10 4 ). M T /M P ) = M T /M P ) ,,,,.,,.,.,,. 10 4,.,,,. 5.3,, ,, ),
35 5 Canup and Ward , Fig ).,.,,,.,.,,.,,...
36 5 Canup and Ward a, ).. b,. F in 1/r) γ in r γ in ), r in r c ). F in f. ν r 2 /ν, ν = αch ). α 1 c H. ν F in / F in in, σ G. γ in = 0, r r c, σ G 0.3F in r c 2 /ν)[1.2 r c /r d r/r C ) 2 /4] 0.21/α) F in Ω 1 )r/h) 2 r c /r) 2 r/r c ) = 0.5, r c /r d ) = 0.2 ref.9 ). r d,ω r. r c 10R P.,,., 10 4 < α < 0.1,r r c 30R P τ ν 1/α).,,,,. f 10 2., f 3 30.,, f.,,, f.
37 5 Canup and Ward ,,. m s /M p ), m s /M p ) 2. m s..,, 1,. e) a) τ e,τ 1, τ e = e/ ė, τ 1 = a/ ȧ. τ 1 = 1 C a Ω Mp m s ) Mp r 2 σ G ) ) 2 H = C e τ e r C a H/r) 2. 5.A.1) C a C e 1. σ G. Ω = GM p /r 3 ) 1/2 r. H, c, H/r) c/rω) 0.1.,., 1.. m s τ acc τ acc fm s /2πr rf in ). F in, f -, 2πr r. e ). r/r 2e, e H/r)m s /4πrHσ G ) 1/5,,. r, τ acc fσ G /F in )m s /4πrHσ G ) 4/5. m crit, 5.A.1) τ acc = 1,m S = m crit., G,. α.
38 5 Canup and Ward G F i n/α).fig.1 ) r c,., F in M P / r C 2 G )., G M P dm/dt 1 M P. ), ) ) 5/9 ) 26/9 ) 10/9 ) 2/3 mc π H r α 5.4 Ωτ G f) 1/9, 5.A.2) M P C a r r C f ) 5/9 ) 26/9 ) 10/9 ) 2/3 3.5 H/r r/rc α/f χ A.3). C a,χ [1week/2 /Ω))f/10 2 )τ G /10 7 yr)] 1/9 1. m crit /M P ) χ G ) 1/9.,. H/r), r, H/r) 0.1. r c,, r/r c ), 1. 5.A.3). α - f.,., 1., f.,. m crit., 1 m crit., 1 acc ).,, m crit,m T. H/r), f,, ) rc MT m crit/m P ) = dr, 5.A.4) M P R P r ) 4/9 ) 10/9 ) 1/3 1 H α C a r f Ωτ G f), 5.A.5) 1/ ) 4/9 ) 10/9 ) 1/3 3.5 H/r α/f χ A.6) C a
39 5 Canup and Ward r C R P. R P. M T /M P ) χ, r c, α/f). 5.5 N,.. F in /f).. 4 α/f). 1. M T /M P ) 5.A.6) M T,, 5.A.3) 5.A.6)., f = 10 2 ) 10, M T /M P =
40 5 Canup and Ward M T, M P τ G M P /dm/dt) 1, dm/dt. τ G = yr, r C = 30R P, γ in = 0. α/f) = 10 6, , ,,. M T m crit 5.A.3) )., M T., m crit,. M T /M P ) α/f) 1/3, α/f) 500, 10. M T /M P ), m crit. α/f), τ G.. M T /M P ). 5.A.3) 5.A.6),..., 5.A.3), 5.A.6) M T /M P ).
41 5 Canup and Ward a. b c m s M P ). b c γ in = 0, r c = 30R P, 1.7 < M in /M T < 10 M in ), τ G, yr yr τ G M in /M T )... b α/f) = , α = 0.05, M T /M P ) = c39 ).,α/f = 10 6 ), α = 10 4 M T /M P ) = α/f) = , α = M T /M P ) = c20 )., α/f) = , α = M T /M P ) = 10 4 c64 ). M T /M P ) = c17 ), α/f) = , α = R P M P, R P C C 7). ). α/f) = c60 ), M T /M P ) = M T,
42 5 Canup and Ward c b M T /M P ). 7 F in t) = F in 0) exp t/τ in ) σ G t) = σ G 0) exp t/τ in ). τ in 10 5 τ in years) ) t = 0., r C /R P = 25, 30, 44).,,,,. a α/f),. b α/f),. 4 ). a,b, r/r c ) = 0.5, c/rω) = 0.1, τ in = 10 6 yr, τ G = τ G,last τ in M P /M T )/f 5.A.3), 5.A.6).. α T P = 500K K = 0.1. ) T P K ). 1,. 1,. 5/2 m Gap /M P C v αh/r). Cv C v = 3, m Gap, < m lgst /m Gap >= , m Gap, τ v τ i n ). 1 M T m S.
43 5 Canup and Ward ,,.,,...,,,, r c ).,,.. α) - f ). M T /M P ) α/f) 1/3 α/f)., α/f) 10 6 < α/f) < ,,. α, f, b c20 ),,.. 75 N = 7.,., N.,
44 5 Canup and Ward m s /M P ) 10 5 N lg = 4. < C lg > 17). r c 25R P r C 44R P 20 < a max /R P < 60). r c a max 2. r c, R H ) j, 3. j j = Ω P R 2/5 H Ω P, R H = a P M P /3M ) 1/3, a P, M ), r r = j 2 /GM P,,,,r /R P r c 1.6r, r c < j >= GM P r.. T eff F 1/4 in,ref.9 )., τ G ), 5.A.3) 5.A.6) f ).,., τ in = 10 6 yr ), 15R P 200K α 10 3, K = O10 1 )cm 2 g 1, 500 K,ref.9 ),.,,,. 7 c17 1),.,,. τ in = 10 6 yr,m T /M P ) O10 4 ) 10, 2,3.
45 5 Canup and Ward ),., 98.,. ),. 27.,....., M T riton /M P ,.,., ).,. ),,. M T riton,, M T /M Neptune O10 4 ).
46 5 Canup and Ward ,3,..,., years ), 10 4 M P, -.
47 5 Canup and Ward ,,...,..
48 43 [1] Canup, Robin M., Ward, William R. : A common mass scaling for satellite systems of gaseous planets. Nature, Volume 441, Issue 7095, pp ). [2] Canup, Robin M., Ward, William R. : Formation of the Galilean Satellites: Conditions of Accretion. The Astronomical Journal, Volume 124, Issue 6, pp ). [3] Ikoma, Masahiro; Nakazawa, Kiyoshi; Emori, Hiroyuki., Formation of Giant Planets: Dependences on Core Accretion Rate and Grain Opacity., The Astrophysical Journal, Volume 537, Issue 2, pp ). [4] Hayashi, C., Nakazawa, K., Nakagawa, Y. : Formation of the solar system. IN: Protostars and planets II A ). Tucson, AZ, University of Arizona Press, pp ). [5] Mosqueira, Ignacio., Estrada, Paul R. : Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites. Icarus, Volume 163, Issue 1, pp ). [6] Lubow, S. H., Seibert, M., Artymowicz, P., Disk Accretion onto High-Mass Planets., The Astrophysical Journal, Volume 526, Issue 2, pp ) [7] Shakura, N. I., Sunyaev, R. A. : Black holes in binary systems. Observational appearance. Astron. Astrophys., Vol. 24, pp ) [8], :.. pp ) [9], : ) [10], : )
Hidetaka Okada Department of Cosmosciences, Graduate School of Science, Hokkaido University
Hidetaka Okada 21372 Department of Cosmosciences, Graduate School of Science, Hokkaido University 212 2 28 , N 2.,.,.,. N 2, Ar. Ar, N 2, NH 3 N 2.. Kuramoto and Matsui (1994),,., 1 5, 5 K,,., Ar, Ar.,,
Contents 1 Jeans (
Contents 1 Jeans 2 1.1....................................... 2 1.2................................. 2 1.3............................... 3 2 3 2.1 ( )................................ 4 2.2 WKB........................
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
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
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 =
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
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
(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
Standard Model for Formation of the Solar System ADACHI Toshitaka Department of Earth Sciences, Undergraduate school of Science, Hokkaido University P
Standard Model for Formation of the Solar System ADACHI Toshitaka Department of Earth Sciences, Undergraduate school of Science, Hokkaido University Planetary Physics Laboratory 2009 4 24 , Hayashi et
.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
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
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) = [](/thumbs/99/141438442.jpg "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
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
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)
/ 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,
gr09.dvi
.1, θ, ϕ d = A, t dt + B, t dtd + C, t d + D, t dθ +in θdϕ.1.1 t { = f1,t t = f,t { D, t = B, t =.1. t A, tdt e φ,t dt, C, td e λ,t d.1.3,t, t d = e φ,t dt + e λ,t d + dθ +in θdϕ.1.4 { = f1,t t = f,t {
(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](/thumbs/104/162595168.jpg "(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
() [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () ) m/s 4. ) 4. AMEDAS
![() [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () ) m/s 4. ) 4. AMEDAS](/thumbs/92/107891201.jpg "() [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () ) m/s 4. ) 4. AMEDAS")
() [REQ] 4. 4. () [REQ] 0m 0 m/s () [REQ] (3) [POS] 4.3(3) ()() () 0 0 4. 5050 0 ) 00 4 30354045m/s 4. ) 4. AMEDAS ) 4. 0 3 ) 4. 0 4. 4 4.3(3) () [REQ] () [REQ] (3) [POS] () ()() 4.3 P = ρ d AnC DG ()
( ) 2002 1 1 1 1.1....................................... 1 1.1.1................................. 1 1.1.2................................. 1 1.1.3................... 3 1.1.4......................................
Formation of hot jupiters by slingshot model Naoya Okazawa Department of Earth Sciences, Undergraduate school of Science, Hokkaido University
Formation of hot jupiters by slingshot model Naoya Okazawa 22070283 Department of Earth Sciences, Undergraduate school of Science, Hokkaido University Planetary and Space Group 2011 4 18 1,.,,.,.,.,..,.,.,,.,.,,,.,.,.,.,,,..
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(
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
ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.
24(2012) (1 C106) 4 11 (2 C206) 4 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 (). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5... 6.. 7.,,. 8.,. 1. (75%)
( ; ) 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 =
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......................
A
A04-164 2008 2 13 1 4 1.1.......................................... 4 1.2..................................... 4 1.3..................................... 4 1.4..................................... 5 2
vol5-honma (LSR: Local Standard of Rest) 2.1 LSR R 0 LSR Θ 0 (Galactic Constant) 1985 (IAU: International Astronomical Union) R 0 =8.5
2.2 1 2.2 2.2.1 (LSR: Local Standard of Rest) 2.1 LSR R 0 LSR Θ 0 (Galactic Constant) 1985 (IAU: International Astronomical Union) R 0 =8.5 kpc, Θ 0 = 220 km s 1. (2.1) R 0 7kpc 8kpc Θ 0 180 km s 1 270
ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.
(1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..
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
( ) ,
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
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](/thumbs/86/94275608.jpg "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
* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H
1 1 1.1 *1 1. 1.3.1 n x 11,, x 1n Nµ 1, σ x 1,, x n Nµ, σ H 0 µ 1 = µ = µ H 1 µ 1 µ H 0, H 1 * σ σ 0, σ 1 *1 * H 0 H 0, H 1 H 1 1 H 0 µ, σ 0 H 1 µ 1, µ, σ 1 L 0 µ, σ x L 1 µ 1, µ, σ x x H 0 L 0 µ, σ 0
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
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
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
n (1.6) i j=1 1 n a ij x j = b i (1.7) (1.7) (1.4) (1.5) (1.4) (1.7) u, v, w ε x, ε y, ε x, γ yz, γ zx, γ xy (1.8) ε x = u x ε y = v y ε z = w z γ yz
1 2 (a 1, a 2, a n ) (b 1, b 2, b n ) A (1.1) A = a 1 b 1 + a 2 b 2 + + a n b n (1.1) n A = a i b i (1.2) i=1 n i 1 n i=1 a i b i n i=1 A = a i b i (1.3) (1.3) (1.3) (1.1) (ummation convention) a 11 x
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..................
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
x E E E e i ω = t + ikx 0 k λ λ 2π k 2π/λ k ω/v v n v c/n k = nω c c ω/2π λ k 2πn/λ 2π/(λ/n) κ n n κ N n iκ k = Nω c iωt + inωx c iωt + i( n+ iκ ) ωx
x E E E e i ω t + ikx k λ λ π k π/λ k ω/v v n v c/n k nω c c ω/π λ k πn/λ π/(λ/n) κ n n κ N n iκ k Nω c iωt + inωx c iωt + i( n+ iκ ) ωx c κω x c iω ( t nx c) E E e E e E e e κ e ωκx/c e iω(t nx/c) I I
untitled
(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
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,
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
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
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)
修士論文
SAW 14 2 M3622 i 1 1 1-1 1 1-2 2 1-3 2 2 3 2-1 3 2-2 5 2-3 7 2-3-1 7 2-3-2 2-3-3 SAW 12 3 13 3-1 13 3-2 14 4 SAW 19 4-1 19 4-2 21 4-2-1 21 4-2-2 22 4-3 24 4-4 35 5 SAW 36 5-1 Wedge 36 5-1-1 SAW 36 5-1-2
untitled
18 1 2,000,000 2,000,000 2007 2 2 2008 3 31 (1) 6 JCOSSAR 2007pp.57-642007.6. LCC (1) (2) 2 10mm 1020 14 12 10 8 6 4 40,50,60 2 0 1998 27.5 1995 1960 40 1) 2) 3) LCC LCC LCC 1 1) Vol.42No.5pp.29-322004.5.
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
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)
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
2009 2 26 1 3 1.1.................................................. 3 1.2..................................................... 3 1.3...................................................... 3 1.4.....................................................
1. : 1.5 2. ( ): 2.5 3. : 1 ( ) / minimum solar nebula model ( ) http://antwrp.gsfc.nasa.gov/apod/ap950917.html ( ) http://www-astro.physics.ox.ac.uk/~wjs/apm_grey.gif ( ) SDSS : d 2 r i dt 2 ÿ j i
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
Microsoft Word - 11問題表紙（選択）.docx
A B A.70g/cm 3 B.74g/cm 3 B C 70at% %A C B at% 80at% %B 350 C γ δ y=00 x-y ρ l S ρ C p k C p ρ C p T ρ l t l S S ξ S t = ( k T ) ξ ( ) S = ( k T) ( ) t y ξ S ξ / t S v T T / t = v T / y 00 x v S dy dx
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 )
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................................
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
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())
Hanbury-Brown Twiss (ver. 2.0) van Cittert - Zernike mutual coherence
Hanbury-Brown Twiss (ver. 2.) 25 4 4 1 2 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 4 3 Hanbury-Brown Twiss ( ) 5 3.1............................................
) 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
A 99% MS-Free Presentation
A 99% MS-Free Presentation 2 Galactic Dynamics (Binney & Tremaine 1987, 2008) Dynamics of Galaxies (Bertin 2000) Dynamical Evolution of Globular Clusters (Spitzer 1987) The Gravitational Million-Body Problem
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)
* 1 1 (i) (ii) Brückner-Hartree-Fock (iii) (HF, BCS, HFB) (iv) (TDHF,TDHFB) (RPA) (QRPA) (v) (vi) *
* 1 1 (i) (ii) Brückner-Hartree-Fock (iii) (HF, BCS, HFB) (iv) (TDHF,TDHFB) (RPA) (QRPA) (v) (vi) *1 2004 1 1 ( ) ( ) 1.1 140 MeV 1.2 ( ) ( ) 1.3 2.6 10 8 s 7.6 10 17 s? Λ 2.5 10 10 s 6 10 24 s 1.4 ( m
2007 5 iii 1 1 1.1.................... 1 2 5 2.1 (shear stress) (shear strain)...... 5 2.1.1...................... 6 2.1.2.................... 6 2.2....................... 7 2.2.1........................
Untitled
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
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
: , 2.0, 3.0, 2.0, (%) ( 2.
2017 1 2 1.1...................................... 2 1.2......................................... 4 1.3........................................... 10 1.4................................. 14 1.5..........................................
i 18 2H 2 + O 2 2H 2 + ( ) 3K
i 18 2H 2 + O 2 2H 2 + ( ) 3K ii 1 1 1.1.................................. 1 1.2........................................ 3 1.3......................................... 3 1.4....................................
/Volumes/NO NAME/gakujututosho/chap1.tex i
2012 4 10 /Volumes/NO NAME/gakujututosho/chap1.tex i iii 1 7 1.1............................... 7 2 11 2.1........................................... 11 2.2................................... 18 2.3...................................
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
( ) 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 ( - )
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)
II (No.2) 2 4,.. (1) (cm) (2) (cm) , (
II (No.1) 1 x 1, x 2,..., x µ = 1 V = 1 k=1 x k (x k µ) 2 k=1 σ = V. V = σ 2 = 1 x 2 k µ 2 k=1 1 µ, V σ. (1) 4, 7, 3, 1, 9, 6 (2) 14, 17, 13, 11, 19, 16 (3) 12, 21, 9, 3, 27, 18 (4) 27.2, 29.3, 29.1, 26.0,
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 )
(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
kawa (Spin-Orbit Tomography: Kawahara and Fujii 21,Kawahara and Fujii 211,Fujii & Kawahara submitted) 2 van Cittert-Zernike Appendix A V 2
Hanbury-Brown Twiss (ver. 1.) 24 2 1 1 1 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 3 3 Hanbury-Brown Twiss ( ) 4 3.1............................................
dynamics-solution2.dvi
1 1. (1) a + b = i +3i + k () a b =5i 5j +3k (3) a b =1 (4) a b = 7i j +1k. a = 14 l =/ 14, m=1/ 14, n=3/ 14 3. 4. 5. df (t) d [a(t)e(t)] =ti +9t j +4k, = d a(t) d[a(t)e(t)] e(t)+ da(t) d f (t) =i +18tj
July 28, H H 0 H int = H H 0 H int = H int (x)d 3 x Schrödinger Picture Ψ(t) S =e iht Ψ H O S Heisenberg Picture Ψ H O H (t) =e iht O S e i
July 8, 4. H H H int H H H int H int (x)d 3 x Schrödinger Picture Ψ(t) S e iht Ψ H O S Heisenberg Picture Ψ H O H (t) e iht O S e iht Interaction Picture Ψ(t) D e iht Ψ(t) S O D (t) e iht O S e ih t (Dirac
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..........
Outline I. Introduction: II. Pr 2 Ir 2 O 7 Like-charge attraction III.
Masafumi Udagawa Dept. of Physics, Gakushuin University Mar. 8, 16 @ in Gakushuin University Reference M. U., L. D. C. Jaubert, C. Castelnovo and R. Moessner, arxiv:1603.02872 Outline I. Introduction:
基礎から学ぶトラヒック理論 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.
基礎から学ぶトラヒック理論 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/085221 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 +α 3 1 2 4 5 1 2 ii 3 4 5 6 7 8 9 9.3 2014 6 iii 1 1 2 5 2.1 5 2.2 7
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/
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
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
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
I A A441 : April 15, 2013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida )
I013 00-1 : April 15, 013 Version : 1.1 I Kawahira, Tomoki TA (Shigehiro, Yoshida) http://www.math.nagoya-u.ac.jp/~kawahira/courses/13s-tenbou.html pdf * 4 15 4 5 13 e πi = 1 5 0 5 7 3 4 6 3 6 10 6 17
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
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....................
arxiv: v1(astro-ph.co)
arxiv:1311.0281v1(astro-ph.co) R µν 1 2 Rg µν + Λg µν = 8πG c 4 T µν Λ f(r) R f(r) Galileon φ(t) Massive Gravity etc... Action S = d 4 x g (L GG + L m ) L GG = K(φ,X) G 3 (φ,x)φ + G 4 (φ,x)r + G 4X (φ)
1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N m 1.
1.1 1. 1.3.1..3.4 3.1 3. 3.3 4.1 4. 4.3 5.1 5. 5.3 6.1 6. 6.3 7.1 7. 7.3 1 1 variation 1.1 imension unit L m M kg T s Q C QT 1 A = C s 1 MKSA F = ma N N = kg m s 1.1 J E = 1 mv W = F x J = kg m s 1 = N
7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
![7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±](/thumbs/91/106462075.jpg "7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±")
7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
) ] [ 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](/thumbs/92/107866707.jpg ") ] [ 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
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)
: 2005 ( ρ t +dv j =0 r m m r = e E( r +e r B( r T 208 T = d E j 207 ρ t = = = e t δ( r r (t e r r δ( r r (t e r ( r δ( r r (t dv j =
72 Maxwell. Maxwell e r ( =,,N Maxwell rot E + B t = 0 rot H D t = j dv D = ρ dv B = 0 D = ɛ 0 E H = μ 0 B ρ( r = j( r = N e δ( r r = N e r δ( r r = : 2005 ( 2006.8.22 73 207 ρ t +dv j =0 r m m r = e E(
10:30 12:00 P.G. vs vs vs 2
1 10:30 12:00 P.G. vs vs vs 2 LOGIT PROBIT TOBIT mean median mode CV 3 4 5 0.5 1000 6 45 7 P(A B) = P(A) + P(B) - P(A B) P(B A)=P(A B)/P(A) P(A B)=P(B A) P(A) P(A B) P(A) P(B A) P(B) P(A B) P(A) P(B) P(B
2 G(k) e ikx = (ik) n x n n! n=0 (k ) ( ) X n = ( i) n n k n G(k) k=0 F (k) ln G(k) = ln e ikx n κ n F (k) = F (k) (ik) n n= n! κ n κ n = ( i) n n k n
. X {x, x 2, x 3,... x n } X X {, 2, 3, 4, 5, 6} X x i P i. 0 P i 2. n P i = 3. P (i ω) = i ω P i P 3 {x, x 2, x 3,... x n } ω P i = 6 X f(x) f(x) X n n f(x i )P i n x n i P i X n 2 G(k) e ikx = (ik) n
20 4 20 i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1.............................