() () () 15%85% ( 10 9 kg m 3 ) (10 21 kg m 3 ) C C C C... () Instroduction : 15 2
|
|
|
- ありさ あさま
- 7 years ago
- Views:
Transcription
1 URL: / Introduction() () () / 1
2 () () () 15%85% ( 10 9 kg m 3 ) (10 21 kg m 3 ) C C C C... () Instroduction : 15 2
3 (A4 2 )(100 ) 30 3
4 1 1.1 : km 4m 4m (1 AU ) km (tab1) AU 1/ αcen (4.3 ) 30 km 1 1? π 10 7 sec sec 4
5 1 1 2πR /4 = 1 km (1) 1AU () = 1 5 km (2) 1ly () = c 1 (3) = m (4) 1pc () = 3.26ly (5) /100 1/ m 4 km (1) cm (2) cm (3) cm () 5
6 3 1. (1AU) () 100bun 6
7 1.2 () ( = ) ( = ) 4 () kouseiq (kouseiq)
8 () 10m 10km 100km 1000km 10000km 8
9 5 10 m 120km km m m αcen 4.3 ly 30pc 8.5kpc 50kpc kpc 6647km/s 150 9
10 () 1 km = 1000 m = 10 3 m 1 cm = = 10 2 m 1 AU = m ( ) 1 pc = m = 1 AU / 1 =3.26 ly 1 ly = m = tera T = giga G = 10 9 mega M = 10 6 kilo k = 10 3 hecto h = 10 2 deca da = 10 deci d = 10 1 centi c = 10 2 milli m = 10 3 micro µ = 10 6 nano n = 10 9 pico p = : = π = : 1 = 60 = =1 1 = 1 : l = rθ () : = days = s : = c = m/s : = (km/s)/mpc x log x x = 10 a x a log x = 10 a a = log x. (6) 10
11 1.4 () v = H 0 d (7) v d H 0 71(km/sec)/(Mpc) (hubble/p.tex)! 11
12 Mpc km /s NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC Mpc km /s NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC NGC (Proc. Nat. Acad. Sci., 15, 168) [4] 12
13 1000 km/sec Mpc () 13
14 1.5 ( )1/2 = θ = l D (8) l:d: 6 1 radian arcmin 1. : m m 2. : km km 3. : 25 ly ly 4. M13: 98 ly ly 5. M31: 50 kpc kpc 6. : 1 Mpc 6647 km/sec () 1.6 (parallax) 1 / 14
15 0 ( annual parallax) (arc sec) p D = 1 p pc (9) 1.7 file = LandF.tex ( [Watt/m 2 ] [erg/sec cm 2 ]) (Flux) ( [W] [erg/sec]) (luminosity) F L F = D L 4πD 2 (10) 7 L = W (flux) () 2mm 15
![tex ( [Watt/m 2 ] [erg/sec cm 2 ]) (Flux) ( [W]](/docs-images/41/22743482/images/page_15.jpg "[erg/sec]) (luminosity) F L F = D L 4πD 2 (10)")
16 () LandF-Q f = L/4πD W 4π( ) 2 m 2 = W/m 2 πr 2 r = W 1.8 file = scale.tex () () (magnitute) b = 10 a a = log b (11)..., 1/10, 1, 10, 100, , 1, 0, 1, 2, 3,... (12) : 2 1/12 = f/f 0 2 0/ Do 1 2 1/ / Re 9/8 = / / Mi 5/4 = / Fa 4/3 = / / Sol 3/2 = / / La 5/3 = / / Si 15/8 = / Do 16
17 = n = 12 log 2 f f 0 (13) f f 0 = 2 n/12 (14) M = 2 3 log 10 E 11.8 (15) f[hz] (Do, Re, Mi,..) () F [W/m 2 ] m 6 () (magnitude) = m 1 m 0 = 5 2 log 10 F 1 F 0 = (m 1 m 0 ) F 1 F 0 = 5 2 log 10 () (16) (17) Linear Scale Log Scale () 0 () F ν F ν = [W/m 2 Hz] (AB ) 8?? 17
![.) () F [W/m 2 ] m 6 () 5 100 (magnitude) = m 1 m 0 = 5 2 log 10 F 1 F 0](/docs-images/41/22743482/images/page_17.jpg "= 10 2 5 (m 1 m 0 ) F 1 F 0 = 5 2 log 10 () (16) (17) Linear Scale Log")
18 () scale 9 f do f re f mi f fa f sol f la f si f DO (1) f sol f do > f DO f sol (2) f sol f do f DO f sol (1) f sol f do < f DO f sol () doremi 1.9 file = mag.tex 10pc () () L (luminosity) Joul/sec = W M (absolute magnitude) 10pc () f (flux) Joul/m 2 sec m (apparent magnitude) 4.7 m M m M = 5 log D(in pc ) 5 (18) 18
19 L = 4πD 2 f (19) = 4π10 2 f 10pc (20) (21) f f 10pc = L/4πD2 L/4π10 2 = 102 D 2 (22) ( ) f log 10 f 10pc = 2 log 10 D + 2 (23) (24) ( ) 5 2 log f = m M (25) f 10pc (23) (25) (M m) 2 5 = 2 log 10 D + 2 (26) M m = 5 log 10 D + 5 (27) M L ( ) L M M = ( ) L 2 log (28) L L = W = erg/sec (Bolometric magnitude, Bolometric luminosity) ( ) () ( CCD) () bolometric () (18) 19
20 (Type I SNR) () M snr (m snr ) () (magniq)? (α CMa) m = 1.5, d = 2.7pc (α Ori) m = 0.8, d = 150pc 20
21 2 2.1 file = col.tex ( ) (photon) ν( [Hz]) = 1/P ; P ( [sec]) ω = 2πν; λ( [m] or [cm], [nm],...); k = 2π/λ k c = cm/sec () (...) ϵ = hν = hω h erg sec p = hk h = h/2π p = h/λ () cp = c ν = λ (29) x E(x, t) = E 1 sin(ωt kx) (30) B(x, t) = (k E 1 ) sin(ωt kx) (31) 4 k µ (k 0, k 1, k 2, k 3 ) = (ω/c, k x, k y, k z ) (32) 21
22 1 1 (3Volt) ev = C 1V = J = erg (33) MeV m e c 2 = (1/2)MeV (76.2MHz FM ) 4m X 3eV kev MeV, GeV, TeV,......Hz 1000GHz...m 0.3mm 390 (550) 720nm () () () (colq) λ, ν, hν 390nm () 720nm 22
23 () Hz, ev 10 x V x ω n = (n x, n y, n z ) k (k x, k y, k z ) = (kn x, kn y, kn z ) ω (k x, k y, k z) ω, k x, k y, k z ω, k x, k y, k z (Doppler effect) (abberation) () dopplerq 2.2 telsc.tex CCD () 1 1 () 23
24 θ θ 1.22 λ D (34) D ( VLBI )VLA(), VSOP () () E/E λ/λ 10msec () F ()O F P F l = P F OF b2 f 2π l/λ OF = f, OP = b O O P Φ(b) b 2π l + Φ(b) = 0 (36) λ F P Q P Q = f 2 + (b + x) 2 (37) OF P Q OF = f { 1 + (35) } 1 2 (b + x)2 f 2 f (38) = b2 f + bx f = l + bx f (39) 24
25 O F 2π l λ bx bx + Φ(b) + 2π = 2π λf λf b Q a(x) = A(b) P 2πb/λ = Y, x/f = x a(x) = (40) A(b)e (2πbx/λf)i db (41) A(Y )e XY i dy (42) A(b) A(b) δ - A(b) θ XY 1, πd λ x f = θ (43) 11 f 1 f 2 12 () diffrq 25
26 2.3 :flux Instenisty fi.tex () de da t t + dt ν ν + dν F ν = de dt da dν () flux [erg/sec cm 2 Hz] dω (44) I ν = de dt da dν dω (45) Specific Intensity ( Brightness) [erg/sec cm 2 Hz str ] F ν = I ν cos θdω (46) θ net flux 3 2 = 6 m box (6 ) (3 π/180) (2 π/180) = π 2 /5400str () dθ dφ sin θdφ!) dω = sin θdθdφ (47) 26
27 : Instensity : 6 (x, y, z, p x, p y, p z ) (snap shot ) dn = f ph (r, p)dxdydzdp x dp y dp z (48) = h 3 f ph c 3 ν2 dνdωdv (49) = f ν (r, θ, φ)dνdωdv (50) (p x, p y, p z ) (p, θ, ϕ) p = hν/c f ν (θ, φ) dω ( ν ν + dν ) da dt : I ν = cf ν hν (51) D R I ν de R dω D 2 de dω D 2 ( ) I ν I ν = (52) ν ν + dν F ν dν, I ν dν, L ν dν, 27
28 F ν, I ν, L ν ν F = F ν dν, I = I ν dν, L = L ν dν, m 2 (Instensity) ν ν + dν I ν flux F ν ( πi ν ) 2. flux F ν ( 0) () fluxq () I = 0 I ν dν erg/sec cm kw/m 2 flux F = 0 F ν dν () intensityq 15 F ν [W/m 2 Hz] 1 AU () I ν [W/m 2 Hz str] F ν I ν () telscq 2.4 intf.tex 28
29 D λ/d D λ/d D D D D 2 D web pages 16 VLA (Rreen Bank, West Virgnia, USA, National Radio Astronomical Observatory). 27km 1cm 10cm () intfa θ = 1.22 λ D () intfq = 1.22 (1 10)cm cm = ( ) 10 6 rad = arcsec (53) π (arcsec) 2.5 spec.tex : ( ) () 29
30 E(t) E(t) = Ê(ω) = 1 E(t)e iωt dt (54) 2π flux () F ω = c Ê(ω) 2 flux F = (c/4π) E(t) 2 dt Parseval s theorem E(t) 2 dt = 2π Ê(ω) 2 dω4π 0 Ê(ω) 2 dω (55) F = 0 F ω dω (56) () Dopper effect (Dark matter ) web pages 2.6 () black.tex T T I ν T B ν I ν = B ν (T ) (57) Planck function I ν = 2hν3 /c 2 e hν/kt 1 B ν(t ) (58) 30
31 planck () hν max 2.82kT (59) B ν ν B λ (T ) = 8πhc λ 5 1 e hc/λkt 1 (60) λ max hc/4.97kt hν kt Raylei-Jeans law hν kt Wean law I ν 2hν3 c 2 I ν 2ν2 kt (61) c2 ( exp hν ) kt (62) hν max 2.82kT F ν = I ν cos θdω = πi ν = πb ν (63) 2π str F = π 0 B ν (T )dν = 2π5 k 4 15c 2 h 3 T 4 σt 4 (64) 0 x 3 π4 e x dx = 1 15 Stefan-Boltzmann law F = σt 4 σ = 2π5 k 4 31 (65) 15c 2 h 3 T 4 = erg/cm 3 deg 4 sec (66)
32 17 p = u/3 u () T ds = du + pdv ds = V du T dt dt + 4 u dv (67) ( ) 3 T ( ) S S = dt + dv (68) T V 2 S/ T V V u = at 4 Stefan-Boltzmann law (69) V U T () StefanQ (StefanQ: ) du = d(v u) = V du + udv p = u/3 ( T ( ( ) S V T ( ) ) S V T V T ds = V du + 4 udv (70) 3 V ) T = T = ( ) V du V T dt ( ) 4 u = 4 3 T 3 T du dt = 1 T T ( 1 T 2 u + 1 T ) du dt (71) (72) 4dT/T = du/u ln T 4 = ln u + const., or u = at 4 (73) 18 ν advance () blackq 2.7 efftemp.tex 32
33 () F F obs R D ( ) 2 D F = F obs (74) R σt 4 (75) F DR L = 4πR 2 F 4πR 2 σt 4 (76) (effective temperature) T eff LRT; L = 4πR 2 σt 4 eff (77) T eff () F U,B,V,R,I () m 2 m 1 = 5 2 log ( Bλ1 B λ1 B λ1 = λ5 2 e hc/λ2kt 1 B λ1 λ 5 1 e hc/λ 1kT 1 ) 5 2 log λ5 2 λ 5 + hc ( 1 1 ) = a + b 1 kt λ 2 λ 1 T (78) (79) a,b 2.8 HR HRzu.tex 33
34 O A... O B A F G S K M R N (Russell s students in Princeton O Be A Fine Girl Kiss Me Right Now, Smack!) () HR (Hertzsprung-Russel Diagram) HR (77) HR = () HR HR HR HR HR 19 L T R 34
35 () efftempq 20 HR () HRzuQ 21 HR () HR2Q (HR2Q: ) HR ( ) ( ) T F = σt 4 σ R L = 4πR 2 σt 4 HR 22 (α CMa) m = pc M (α Ori) m = pc M () startypeq (startypeq: ) M = m 5 log D + 5 m pc D M = log(2.7) + 5 = 1.3 (or 1.4) (80) log ( ) 0.7 = () (81) log 2.7 = log 3 + log 9 1 = 0.431() (82) 35
36 M = log(150) + 5 = 5.1 (83) log 150 = log () (84) log 150 = log 3 + log = 2.176() (85) 10pc 15 10pc 15 2 = = pc 1/ = = = L L = 4πσR 2 T 4 (86) (1) A 1 (10000/6000) 4 = 7.7 (5/2) log 7.7 = (2) M ( ) 400 HR
37 (M core > M ch ) (He ) (RGB) () L M 3.5 He 2 3α CO (AGB:Asymptotoic Giant Branch) CO < 8M 10M CO H He CO 56 Fe () H,Si,(O,Ne,Mg),(C,O),He,H 1.3 2M () 56 Fe 13 4 He + 4n 124.4MeV (87) 4 He 2p + 2n 28.3MeV (88) 161MeV
38 1: (10 8 K) (20M ) H pp CNO 4 He He 12 C He 12 C + 12 C 1 6O + γ 14 C 16 O 1.5 C 12 C + 12 C 23 Na + p 12 C + 12 C 20 Ne + α Ne, Na Mg, Al Ne 20 Ne + γ 16 O + α 20 Ne + α 24 Mg + γ O Mg 15 O 16 O + 16 O 28 Si + α 16 O + 16 O 28 P + p Si, P, S Cl, Ar, Ca 3 28 Si + γ 24 Mg + α Si 24 Mg + γ 23 Na + p 24 Mg + γ 20 Ne + α Cr, Mn Ge, Co, Ni, Cu 40 M /m F e = erg GM /R 2 NR = erg R NS 10km 2.9 radtransfer.tex Intensity I ν I ν = B ν (T ) T 6000K I ν = B ν (T room ) T room 300K 38
39 (absorption) (emission) (radiation)( ) () ( ) Radiation emission [] ν σ ν n dl κ ν = nσ ν dl [] (emission coefficient) j [erg/cm 3 sec str]: ν ν + dν monochromatic emission coefficient j ν (Intensity)I di ν ds = α νi ν + j ν (89) s (radiation transfer equation) di ν /ds = 0I ν = B ν (T ) j ν /α ν = B ν (T ) T j ν α ν = B ν (T ) (90) Kirchoff s Law L α ν ()( I 0 ) I ν = I 0 e ανl (91) 39
40 l ν l ν = κ 1 ν τ ν = α ν ds (92) () τ ν 1 τ ν 1 (Source function) S ν = j ν α ν (93) : di ν dτ ν = I ν + S ν (94) I ν > S ν I ν (95) I ν < S ν I ν (96) I ν τ ν I ν S ν, (97) S ν B ν (T ) 23 F ν [W/m 2 Hz] 1 AU () I ν [W/m 2 Hz str] F ν I ν () telscq 2.10 α ν l ν ν E = hν 0 (T 1 ) (T 2 ) 40
41 ν 0 I ν0 = B ν0 (T 1 ) I ν0 = B ν0 (T 2 ) I ν0 = B ν0 (T 2 ) ν 0 I ν = B ν (T 1 ) I ν I ν0 () = B ν0 (T 2 ) (98) I ν () = B ν (T 1 ) (99) T 1 > T 2 B ν (T 1 ) > B ν0 (T 2 ) (line absorption) ν 0 (line emission) (line absorption) (line emission) 10 6 K 6000K () 6000K 41
42 3 : : : SN1087A : (): : () crossing time () t cross = R v (100) R v V 250km/s 50kpc t coss 10 8 yr 35 ( ) m 1 m 2 () r F = G m 1m 2 r 2 (101) G = dyn/cm 2 g 2 42
43 1 : F 1 = F 2 + F 2 + F F n (102) () 24 g :T = 27.3 :R = m g/g g = 9.8m/s 2 2 R (R = ) 2 (R/R ) 2 () 2 inv2q g = R(2π/T ) 2 = m/s g/g = (R/R ) 2 = Virial () () I 1 2 N m i ri 2 (103) i=2 d 2 I/dt 2 d 2 I = W + 2T (104) dt2 T = 1 2 m ivi 2 = (105) W = G m im j (106) r ij allpairs 43
44 W + 2T W + 2T = 0 M = m i v 2 = 2T/M (): r g W = GM 2 /r g v 2 = GM r g (107) : m/s () newtonjq 26 () () () kyoriq (kyoriq: ) () θ R 0 D = θr 0 44
45 () ()( ) ( ) () M m ( D [pc] m M = 5 log D 5 ) (): v D v = H d H 71 km/s Mpc v 27 () iroirotelq (K) () suntempq 29 () globq 30 85% (dark matter) () darkmq ( darkmq) () v 2 /R R (dark matter) 45
46 31 A B (1) A B (2) A (3) B (4) A B (5) () expq 32 () impressq 46
47 () x log x x = 10 a x a log x = 10 a a = log x. (108) log( ) log log 10 = log (log 7 log 6) + log 6 = log 6.4 = log(64/10) = 2 log 8 1 = π = G = dyncm3/g 2 c = cm/s h = ergs e = esu m p = g m e = g σ SB = erg/scm 2 K 4 1eV = erg M = cm M = g L = erg/s 1AU = cm 1pc = cm 1ly = cm (109) σ SB Stefan Boltzman const. 47
24.15章.微分方程式
m d y dt = F m d y = mg dt V y = dy dt d y dt = d dy dt dt = dv y dt dv y dt = g dv y dt = g dt dt dv y = g dt V y ( t) = gt + C V y ( ) = V y ( ) = C = V y t ( ) = gt V y ( t) = dy dt = gt dy = g t dt
untitled
(1) 100 100 60% (2) (3) - 1 - 1 2 3 4 100 200-2 - 1 2 3-3 - 4 5 6 7......... (1) (2) (3) 1) 2) 3) 8(5) - 4 - 0.5 27.3 3 0.05 27.30 4 0.005 Système International d'unités 7218 1 (1) Pas Pas J/molK J/(molK)
7 9 7..................................... 9 7................................ 3 7.3...................................... 3 A A. ω ν = ω/π E = hω. E
B 8.9.4, : : MIT I,II A.P. E.F.,, 993 I,,, 999, 7 I,II, 95 A A........................... A........................... 3.3 A.............................. 4.4....................................... 5 6..............................
A9RF112.tmp.pdf
9 1-1 9 9 10 11 13 17 1-2 18 18 19 20 21 21 22 23 24 26 2-1 26 26 26 30 33 35 2-2 36 36 38 40 44 44 45 3-1 45 45 47 49 51 53 58 3-2 59 59 60 62 64 68 69 70 4-1 70 70 72 4-2 73 73 74 74 75 76 77 77 79 80
1 180m g 10m/s 2 2 6 1 3 v 0 (t=0) z max t max t z = z max 1 2 g(t t max) 2 (6) 1.3 2 3 3 r = (x, y, z) e x, e y, e z r = xe x + ye y + ze z. (7) v =
1. 2. 3 3. 4. 5. 6. 7. 8. 9. I http://risu.lowtem.hokudai.ac.jp/ hidekazu/class.html 1 1.1 1 a = g, (1) v = g t + v 0, (2) z = 1 2 g t2 + v 0 t + z 0. (3) 1.2 v-t. z-t. z 1 z 0 = dz = v, t1 dv v(t), v
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..................
( ) ,
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
5 36 5................................................... 36 5................................................... 36 5.3..............................
9 8 3............................................. 3.......................................... 4.3............................................ 4 5 3 6 3..................................................
Report10.dvi
[76 ] Yuji Chinone - t t t = t t t = fl B = ce () - Δθ u u ΔS /γ /γ observer = fl t t t t = = =fl B = ce - Eq.() t ο t v ο fl ce () c v fl fl - S = r = r fl = v ce S =c t t t ο t S c = ce ce v c = ce v
34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2 ガウス 型 関 数 1.2 1 関 数 値 0.8 0.6 0.4 0.2 0 15 10 5 0 5 10
33 2 2.1 2.1.1 x 1 T x T 0 F = ma T ψ) 1 x ψ(x) 2.1.2 1 1 h2 d 2 ψ(x) + V (x)ψ(x) = Eψ(x) (2.1) 2m dx 2 1 34 2 2 h = h/2π 3 V (x) E 4 2 1 ψ = sin kxk = 2π/λ λ = h/p p = h/λ = kh/2π = k h 5 2 ψ = e ax2
2 X-ray 6 gamma-ray 7 1 17.1 0:38m 0:77m nm 17.2 Hz Hz 1 E p E E = h = ch= (17.2) p = E=c = h=c = h= (17.3) continuum continuous spectrum line spectru
1 17 object 1 observation 17.1 X electromagnetic wave photon 1 = c (17.1) c =3 10 8 ms ;1 m mm = 10 ;3 m m =10 ;6 m nm = 10 ;9 m 1 Hz 17.1 spectrum radio 2 infrared 3 visual light optical light 4 ultraviolet
2 (f4eki) ρ H A a g. v ( ) 2. H(t) ( ) Chapter 5 (f5meanfp) ( ( )? N [] σ e = 8π ( ) e mc 2 = cm 2 e m c (, Thomson cross secion). Cha
![2 (f4eki) ρ H A a g. v ( ) 2. H(t) ( ) Chapter 5 (f5meanfp) ( ( )? N [] σ e = 8π ( ) e mc 2 = cm 2 e m c (, Thomson cross secion). Cha](/thumbs/43/23149233.jpg "2 (f4eki) ρ H A a g. v ( ) 2. H(t) ( ) Chapter 5 (f5meanfp) ( ( )? N [] σ e = 8π ( ) e mc 2 = cm 2 e m c (, Thomson cross secion). Cha")
http://astr-www.kj.yamagata-u.ac.jp/~shibata P a θ T P M Chapter 4 (f4a). 2.. 2. (f4cone) ( θ) () g M θ (f4b) T M L 2 (f4eki) ρ H A a g. v ( ) 2. H(t) ( ) Chapter 5 (f5meanfp) ( ( )? N [] σ e = 8π ( )
23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4
23 1 Section 1.1 1 ( ) ( ) ( 46 ) 2 3 235, 238( 235,238 U) 232( 232 Th) 40( 40 K, 0.0118% ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 2 ( )2 4( 4 He) 12 3 16 12 56( 56 Fe) 4 56( 56 Ni)
QMI_10.dvi
... black body radiation black body black body radiation Gustav Kirchhoff 859 895 W. Wien O.R. Lummer cavity radiation ν ν +dν f T (ν) f T (ν)dν = 8πν2 c 3 kt dν (Rayleigh Jeans) (.) f T (ν) spectral energy
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
atomic line spectrum emission line absorption line atom proton neutron nuclei electron Z atomic number A mass number neutral atom ion energy
1 22 22.1 atomic line spectrum emission line absorption line atom proton neutronnuclei electron Z atomic number A mass number neutral atom ion energy level ground stateexcited state ionized state 22.2
Gmech08.dvi
145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
(Blackbody Radiation) (Stefan-Boltzmann s Law) (Wien s Displacement Law)
( ) ( ) 2002.11 1 1 1.1 (Blackbody Radiation).............................. 1 1.2 (Stefan-Boltzmann s Law)................ 1 1.3 (Wien s Displacement Law)....................... 2 1.4 (Kirchhoff s Law)...........................
1.3 (heat transfer with phase change) (phase change) (evaporation) (boiling) (condensation) (melting) (solidification) 1.4 (thermal radiation) 4 2. 1
CAE ( 6 ) 1 1. (heat transfer) 4 1.1 (heat conduction) 1.2 (convective heat transfer) (convection) (natural convection) (free convection) (forced convection) 1 1.3 (heat transfer with phase change) (phase
untitled
10 log 10 W W 10 L W = 10 log 10 W 10 12 10 log 10 I I 0 I 0 =10 12 I = P2 ρc = ρcv2 L p = 10 log 10 p 2 p 0 2 = 20 log 10 p p = 20 log p 10 0 2 10 5 L 3 = 10 log 10 10 L 1 /10 +10 L 2 ( /10 ) L 1 =10
2 p T, Q
270 C, 6000 C, 2 p T, Q p: : p = N/ m 2 N/ m 2 Pa : pdv p S F Q 1 g 1 1 g 1 14.5 C 15.5 1 1 cal = 4.1855 J du = Q pdv U ( ) Q pdv 2 : z = f(x, y). z = f(x, y) (x 0, y 0 ) y y = y 0 z = f(x, y 0 ) x x =
E F = q b E (2) E q a r q a q b N/C q a (electric flux line) q a E r r r E 4πr 2 E 4πr 2 = k q a r 2 4πr2 = 4πkq a (3) 4πkq a 1835 4πk 1 ɛ 0 ɛ 0 (perm
1 1.1 18 (static electricity) 20 (electric charge) A,B q a, q b r F F = k q aq b r 2 (1) k q b F F q a r?? 18 (Coulomb) 1 N C r 1m 9 10 9 N 1C k 9 10 9 Nm 2 /C 2 1 k q a r 2 (Electric Field) 1 E F = q
4 2 4.1: =, >, < π dθ = dφ = 0 3 4 K = 1/R 2 rdr + udu = 0 dr 2 + du 2 = dr 2 + r2 1 R 2 r 2 dr2 = 1 r 2 /R 2 = 1 1 Kr 2 (4.3) u iu,r ir K = 1/R 2 r R
1 4 4.1 1922 1929 1947 1965 2.726 K WMAP 2003 1. > 100Mpc 2. 10 5 3. 1. : v = ȧ(t) = Ha [ ] dr 2. : ds 2 = c 2 dt 2 a(t) 2 2 1 kr 2 + r2 (dθ 2 + sin 2 θdφ 2 ) a(t) H k = +1 k *1) k = 0 k = 1 dl 2 = dx
30
3 ............................................2 2...........................................2....................................2.2...................................2.3..............................
03J_sources.key
Radiation Detection & Measurement (1) (2) (3) (4)1 MeV ( ) 10 9 m 10 7 m 10 10 m < 10 18 m X 10 15 m 10 15 m ......... (isotope)...... (isotone)......... (isobar) 1 1 1 0 1 2 1 2 3 99.985% 0.015% ~0% E
) ] [ 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
2 Chapter 4 (f4a). 2. (f4cone) ( θ) () g M. 2. (f4b) T M L P a θ (f4eki) ρ H A a g. v ( ) 2. H(t) ( )
http://astr-www.kj.yamagata-u.ac.jp/~shibata f4a f4b 2 f4cone f4eki f4end 4 f5meanfp f6coin () f6a f7a f7b f7d f8a f8b f9a f9b f9c f9kep f0a f0bt version feqmo fvec4 fvec fvec6 fvec2 fvec3 f3a (-D) f3b
hirameki_09.dvi
2009 July 31 1 2009 1 1 e-mail: mtakahas@auecc.aichi-edu.ac.jp 2 SF 2009 7 31 3 1 5 1.1....................... 5 1.2.................................. 6 1.3..................................... 7 1.4...............................
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
0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ). f ( ). x i : M R.,,
2012 10 13 1,,,.,,.,.,,. 2?.,,. 1,, 1. (θ, φ), θ, φ (0, π),, (0, 2π). 1 0.,,., m Euclid m m. 2.., M., M R 2 ψ. ψ,, R 2 M.,, (x 1 (),, x m ()) R m. 2 M, R f. M (x 1,, x m ), f (x 1,, x m ) f(x 1,, x m ).
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
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
example2_time.eps
Google (20/08/2 ) ( ) Random Walk & Google Page Rank Agora on Aug. 20 / 67 Introduction ( ) Random Walk & Google Page Rank Agora on Aug. 20 2 / 67 Introduction Google ( ) Random Walk & Google Page Rank
B
B07557 0 0 (AGN) AGN AGN X X AGN AGN Geant4 AGN X X X (AGN) AGN AGN X AGN. AGN AGN Seyfert Seyfert Seyfert AGN 94 Carl Seyfert Seyfert Seyfert z < 0. Seyfert I II I 000 km/s 00 km/s II AGN (BLR) (NLR)
CAT. No. 1154b 2008 C-9
T CAT. o. 1154b IS SK µm D K mm & Dmp 1 ea µm d CS mm & Bs K ia & dmp V dp & dmp & Hs 1 mm d & ds & & B2s d2s & Hs & A1s d d B C B2 H A1 SjD d2 H d µm d & dmp & d1mp & dmp V dp 1 mm d d d B & dmp & d1mp
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(
E B m e ( ) γma = F = e E + v B a m = 0.5MeV γ = E e m =957 E e GeV v β = v SPring-8 γ β γ E e [GeV] [ ] NewSUBARU.0 957 0.999999869 SPring-8 8.0 5656
![E B m e ( ) γma = F = e E + v B a m = 0.5MeV γ = E e m =957 E e GeV v β = v SPring-8 γ β γ E e [GeV] [ ] NewSUBARU.0 957 0.999999869 SPring-8 8.0 5656](/thumbs/39/20055634.jpg "E B m e ( ) γma = F = e E + v B a m = 0.5MeV γ = E e m =957 E e GeV v β = v SPring-8 γ β γ E e [GeV] [ ] NewSUBARU.0 957 0.999999869 SPring-8 8.0 5656")
SPring-8 PF( ) ( ) UVSOR( HiSOR( SPring-8.. 3. 4. 5. 6. 7. E B m e ( ) γma = F = e E + v B a m = 0.5MeV γ = E e m =957 E e GeV v β = v SPring-8 γ β γ E e [GeV] [ ] NewSUBARU.0 957 0.999999869 SPring-8
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..............
i 0 1 0.1 I................................................ 1 0.2.................................................. 2 0.2.1...........................
2008 II 21 1 31 i 0 1 0.1 I................................................ 1 0.2.................................................. 2 0.2.1............................................. 2 0.2.2.............................................
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,
C:/KENAR/0p1.dvi
2{3. 53 2{3 [ ] 4 2 1 2 10,15 m 10,10 m 2 2 54 2 III 1{I U 2.4 U r (2.16 F U F =, du dt du dr > 0 du dr < 0 O r 0 r 2.4: 1 m =1:00 10 kg 1:20 10 kgf 8:0 kgf g =9:8 m=s 2 (a) x N mg 2.5: N 2{3. 55 (b) x
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
(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
m d2 x = kx αẋ α > 0 (3.5 dt2 ( de dt = d dt ( 1 2 mẋ kx2 = mẍẋ + kxẋ = (mẍ + kxẋ = αẋẋ = αẋ 2 < 0 (3.6 Joule Joule 1843 Joule ( A B (> A ( 3-2
3 3.1 ( 1 m d2 x(t dt 2 = kx(t k = (3.1 d 2 x dt 2 = ω2 x, ω = x(t = 0, ẋ(0 = v 0 k m (3.2 x = v 0 ω sin ωt (ẋ = v 0 cos ωt (3.3 E = 1 2 mẋ2 + 1 2 kx2 = 1 2 mv2 0 cos 2 ωt + 1 2 k v2 0 ω 2 sin2 ωt = 1
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..............
C: PC H19 A5 2.BUN Ohm s law
C: PC H19 A5 2.BUN 19 8 6 3 19 3.1........................... 19 3.2 Ohm s law.................... 21 3.3.......................... 24 4 26 4.1................................. 26 4.2.................................
ma22-9 u ( v w) = u v w sin θê = v w sin θ u cos φ = = 2.3 ( a b) ( c d) = ( a c)( b d) ( a d)( b c) ( a b) ( c d) = (a 2 b 3 a 3 b 2 )(c 2 d 3 c 3 d
A 2. x F (t) =f sin ωt x(0) = ẋ(0) = 0 ω θ sin θ θ 3! θ3 v = f mω cos ωt x = f mω (t sin ωt) ω t 0 = f ( cos ωt) mω x ma2-2 t ω x f (t mω ω (ωt ) 6 (ωt)3 = f 6m ωt3 2.2 u ( v w) = v ( w u) = w ( u v) ma22-9
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
BH BH BH BH Typeset by FoilTEX 2
GR BH BH 2015.10.10 BH at 2015.09.07 NICT 2015.05.26 Typeset by FoilTEX 1 BH BH BH BH Typeset by FoilTEX 2 1. BH 1.1 1 Typeset by FoilTEX 3 1.2 2 A B A B t = 0 A: m a [kg] B: m b [kg] t = t f star free
2 g g = GM R 2 = 980 cm s ;1 M m potential energy E r E = ; GMm r (1.4) potential = E m = ;GM r (1.5) r F E F = ; de dr (1.6) g g = ; d dr (1.7) g g g
1 1 (gravitation) 1.1 m F a ma = F (1.1) F a m F 1.1 m F a (1.1) m a F m F a m a F F a m 0 0 1.2 (universal gravitation) (potential) M m gravitational force F r F = ; GMm r 2 (1.2) G = 6:67 10 ;8 dyn cm
Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3. 39. 4.. 4.. 43. 46.. 46..
Cotets 6 6 : 6 6 6 6 6 6 7 7 7 Part. 8. 8.. 8.. 9..... 3. 3 3.. 3 3.. 7 3.3. 8 Part. 4. () 4.. () 4.. 3 5. 5 5.. 5 5.. 6 5.3. 7 Part 3. 8 6. 8 6.. 8 6.. 8 7. 8 7.. 8 7.. 3 8. 3 9., 34 9.. 34 9.. 37 9.3.
2011de.dvi
211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37
1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0
A c 2008 by Kuniaki Nakamitsu 1 1.1 t 2 sin t, cos t t ft t t vt t xt t + t xt + t xt + t xt t vt = xt + t xt t t t vt xt + t xt vt = lim t 0 t lim t 0 t 0 vt = dxt ft dft dft ft + t ft = lim t 0 t 1.1
閨75, 縺5 [ ｨ ﾁ573, 縺 ｨ ｨ
39ｨ 8 998 3. 753 68, 7 86 ﾀ7 9 9989769 438 縺48 縺55 3783645 ﾀ5 縺473 ﾀ7996495 ｨ 59754 8554473 9 8984473 3553 7. 95457357, 4.3. 639745 5883597547 6755887 67996499 ｨ 597545 4953473 9 857473 3553, 536583, 89573,
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります
A B 5 C 9 3.4 7 mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3
π 9 3 7 4. π 3................................................. 3.3........................ 3.4 π.................... 4.5..................... 4 7...................... 7..................... 9 3 3. p
IA
IA 31 4 11 1 1 4 1.1 Planck.............................. 4 1. Bohr.................................... 5 1.3..................................... 6 8.1................................... 8....................................
/ 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,
I 1
I 1 1 1.1 1. 3 m = 3 1 7 µm. cm = 1 4 km 3. 1 m = 1 1 5 cm 4. 5 cm 3 = 5 1 15 km 3 5. 1 = 36 6. 1 = 8.64 1 4 7. 1 = 3.15 1 7 1 =3 1 7 1 3 π 1. 1. 1 m + 1 cm = 1.1 m. 1 hr + 64 sec = 1 4 sec 3. 3. 1 5 kg
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
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)
168 13 Maxwell ( H ds = C S rot H = j + D j + D ) ds (13.5) (13.6) Maxwell Ampère-Maxwell (3) Gauss S B 0 B ds = 0 (13.7) S div B = 0 (13.8) (4) Farad
13 Maxwell Maxwell Ampère Maxwell 13.1 Maxwell Maxwell E D H B ε 0 µ 0 (1) Gauss D = ε 0 E (13.1) B = µ 0 H. (13.2) S D = εe S S D ds = ρ(r)dr (13.3) S V div D = ρ (13.4) ρ S V Coulomb (2) Ampère C H =
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
genron-3
" ( K p( pasals! ( kg / m 3 " ( K! v M V! M / V v V / M! 3 ( kg / m v ( v "! v p v # v v pd v ( J / kg p ( $ 3! % S $ ( pv" 3 ( ( 5 pv" pv R" p R!" R " ( K ( 6 ( 7 " pv pv % p % w ' p% S & $ p% v ( J /
. 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.........
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..................................
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)
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
i
009 I 1 8 5 i 0 1 0.1..................................... 1 0.................................................. 1 0.3................................. 0.4........................................... 3
1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e
No. 1 1 1 H Li Be Na M g B A l C S i N P O S F He N Cl A e K Ca S c T i V C Mn Fe Co Ni Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb T e I X e Cs Ba F Ra Hf Ta W Re Os I Rf Db Sg Bh
0 s T (s) /CR () v 2 /v v 2 v = T (jω) = + jωcr (2) = + (ωcr) 2 ω v R=Ω C=F (b) db db( ) v 2 20 log 0 [db] (3) v R v C v 2 (a) ω (b) : v o v o =
![0 s T (s) /CR () v 2 /v v 2 v = T (jω) = + jωcr (2) = + (ωcr) 2 ω v R=Ω C=F (b) db db( ) v 2 20 log 0 [db] (3) v R v C v 2 (a) ω (b) : v o v o =](/thumbs/91/105491855.jpg "0 s T (s) /CR () v 2 /v v 2 v = T (jω) = + jωcr (2) = + (ωcr) 2 ω v R=Ω C=F (b) db db( ) v 2 20 log 0 [db] (3) v R v C v 2 (a) ω (b) : v o v o =")
RC LC RC 5 2 RC 2 2. /sc sl ( ) s = jω j j ω [rad/s] : C L R sc sl R 2.2 T (s) ( T (s) = = /CR ) + scr s + /CR () 0 s T (s) /CR () v 2 /v v 2 v = T (jω) = + jωcr (2) = + (ωcr) 2 ω v R=Ω C=F (b) db db(
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
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 = = =
3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α
![3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α](/thumbs/42/22937190.jpg "3 3.3. I 3.3.2. [ ] N(µ, σ 2 ) σ 2 (X 1,..., X n ) X := 1 n (X 1 + + X n ): µ X N(µ, σ 2 /n) 1.8.4 Z = X µ σ/ n N(, 1) 1.8.2 < α < 1/2 Φ(z) =.5 α z α")
2 2.1. : : 2 : ( ): : ( ): : : : ( ) ( ) ( ) : ( pp.53 6 2.3 2.4 ) : 2.2. ( ). i X i (i = 1, 2,..., n) X 1, X 2,..., X n X i (X 1, X 2,..., X n ) ( ) n (x 1, x 2,..., x n ) (X 1, X 2,..., X n ) : X 1,
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
http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 2 N(ε 1 ) N(ε 2 ) ε 1 ε 2 α ε ε 2 1 n N(ɛ) N ɛ ɛ- (1.1.3) n > N(ɛ) a n α < ɛ n N(ɛ) a n
http://www2.math.kyushu-u.ac.jp/~hara/lectures/lectures-j.html 1 1 1.1 ɛ-n 1 ɛ-n lim n a n = α n a n α 2 lim a n = 1 n a k n n k=1 1.1.7 ɛ-n 1.1.1 a n α a n n α lim n a n = α ɛ N(ɛ) n > N(ɛ) a n α < ɛ
基礎地学I.ppt
I torutake@mail.sci.hokudai.ac.jp http://geotec.sci.hokudai.ac.jp/geotec/ I 800 2940 7/26 8/9 2/3 9 15 10% 6/1 20% 70% 15% 30% 40% 15% R=6400 km θ (S) θ/360 o =S/2πR (1) GPS (Global Positioning System)
4 1 Ampère 4 2 Ampere 31
4. 2 2 Coulomb 2 2 2 ( ) electricity 2 30 4 1 Ampère 4 2 Ampere 31 NS 2 Fleming 4 3 B I r 4 1 0 1.257 10-2 Gm/A µ 0I B = 2πr 4 1 32 4 4 A A A A 4 4 10 9 1 2 12 13 14 4 1 16 4 1 CH 2 =CH 2 28.0313 28 2
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
C el = 3 2 Nk B (2.14) c el = 3k B C el = 3 2 Nk B
I ino@hiroshima-u.ac.jp 217 11 14 4 4.1 2 2.4 C el = 3 2 Nk B (2.14) c el = 3k B 2 3 3.15 C el = 3 2 Nk B 3.15 39 2 1925 (Wolfgang Pauli) (Pauli exclusion principle) T E = p2 2m p T N 4 Pauli Sommerfeld
6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4
35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m
2019 1 5 0 3 1 4 1.1.................... 4 1.1.1......................... 4 1.1.2........................ 5 1.1.3................... 5 1.1.4........................ 6 1.1.5......................... 6 1.2..........................
467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 B =(1+R ) B +G τ C C G τ R B C = a R +a W W ρ W =(1+R ) B +(1+R +δ ) (1 ρ) L B L δ B = λ B + μ (W C λ B )
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
ii
ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................
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
2 1 7 - TALK ABOUT 21 μ TALK ABOUT 21 Ag As Se 2. 2. 2. Ag As Se 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 1 Sb Ga Te 2. Sb 2. Ga 2. Te 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 1 1 2 3 4
空き容量一覧表（154kV以上）
1/3 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量 覧 < 留意事項 > (1) 空容量は 安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 熱容量を考慮した空き容量を記載しております その他の要因 ( や系統安定度など ) で連系制約が発 する場合があります (3) 表 は 既に空容量がないため
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......................
2/8 一次二次当該 42 AX 変圧器 なし 43 AY 変圧器 なし 44 BA 変圧器 なし 45 BB 変圧器 なし 46 BC 変圧器 なし
1/8 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( や系統安定度など ) で連系制約が発生する場合があります (3)
36 th IChO : - 3 ( ) , G O O D L U C K final 1
36 th ICh - - 5 - - : - 3 ( ) - 169 - -, - - - - - - - G D L U C K final 1 1 1.01 2 e 4.00 3 Li 6.94 4 Be 9.01 5 B 10.81 6 C 12.01 7 N 14.01 8 16.00 9 F 19.00 10 Ne 20.18 11 Na 22.99 12 Mg 24.31 Periodic
m dv = mg + kv2 dt m dv dt = mg k v v m dv dt = mg + kv2 α = mg k v = α 1 e rt 1 + e rt m dv dt = mg + kv2 dv mg + kv 2 = dt m dv α 2 + v 2 = k m dt d
m v = mg + kv m v = mg k v v m v = mg + kv α = mg k v = α e rt + e rt m v = mg + kv v mg + kv = m v α + v = k m v (v α (v + α = k m ˆ ( v α ˆ αk v = m v + α ln v α v + α = αk m t + C v α v + α = e αk m
1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +
( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n
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()
ver 0.3 Chapter 0 0.1 () 0( ) 0.2 3 4 CHAPTER 0. http://www.jaist.ac.jp/~t-yama/k116 0.3 50% ( Wikipedia ) ( ) 0.4! 2006 0.4. 5 MIT OCW ( ) MIT Open Courseware MIT (Massachusetts Institute of Technology)
1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0
1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 0 < t < τ I II 0 No.2 2 C x y x y > 0 x 0 x > b a dx
( )
18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................
基礎数学I
I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 1....................... 1............
E 1/2 3/ () +3/2 +3/ () +1/2 +1/ / E [1] B (3.2) F E 4.1 y x E = (E x,, ) j y 4.1 E int = (, E y, ) j y = (Hall ef
![E 1/2 3/ () +3/2 +3/ () +1/2 +1/ / E [1] B (3.2) F E 4.1 y x E = (E x,, ) j y 4.1 E int = (, E y, ) j y = (Hall ef](/thumbs/81/83176619.jpg "E 1/2 3/ () +3/2 +3/ () +1/2 +1/ / E [1] B (3.2) F E 4.1 y x E = (E x,, ) j y 4.1 E int = (, E y, ) j y = (Hall ef")
4 213 5 8 4.1.1 () f A exp( E/k B ) f E = A [ k B exp E ] = f k B k B = f (2 E /3n). 1 k B /2 σ = e 2 τ(e)d(e) 2E 3nf 3m 2 E de = ne2 τ E m (4.1) E E τ E = τe E = / τ(e)e 3/2 f de E 3/2 f de (4.2) f (3.2)
b3e2003.dvi
15 II 5 5.1 (1) p, q p = (x + 2y, xy, 1), q = (x 2 + 3y 2, xyz, ) (i) p rotq (ii) p gradq D (2) a, b rot(a b) div [11, p.75] (3) (i) f f grad f = 1 2 grad( f 2) (ii) f f gradf 1 2 grad ( f 2) rotf 5.2