微粒子合成化学・講義
|
|
- ぎんと つちかね
- 5 years ago
- Views:
Transcription
1 1
2 2
3 1 mol/l KCl 3
4 4
5 Derjaguin Landau Verway Overbeek B.V.Derjaguin and L.Landau;Acta Physicochim.,URSS, 14, E.J.W.Verwey and J.Th G Overbeek; Theory of the Stability of Lyophobic Colloids,
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14
15 -Si-O-H -Si-O + H + 15
16 16
17 17
18 18
19 19
20 0 Helmholtz 0 20
21 0 Gouy-Chapman 0 21
22 0 Stern Stern Stern 0 Slip 22
23 23
24 0=Stern d 0 24
25 25
26 z+ eψ n+ = n + exp (1) 0 kt z eψ n = n0 exp kt n: n 0 : z: k: T: ψ: +,-: 26
27 ψ0 c RT c ψ 0 = ln zf c (2) R: c 0 : c at ψ 0 =
28 Poisson ψ ψ ψ ρ Δ ψ = div (grad ψ ) = + + = x y z ε ε ε r : ε 0 : ρ: r 0 (3) 28
29 29 ρ: n n n z z z = = = = , = = = + kt ze nze kt ze kt ze nze n n ze ψ ψ ψ ρ sinh 2 exp exp ) ( (4)
30 Poisson-Boltzmann (3),(4) x 2 d ψ 2nze zeψ = sinh (5) 2 dx ε ε kt r 0 (5) zeψ zeψ 0 tanh = tanh exp( κx) 4kT 4kT (6) 30
31 zeψ kt <<1 (5) d dx 2 ψ 2 2 = κ ψ κ = nz e ε ε kt r κ = z c (7) ψ = ψ exp( κ ) 0 x (7) (8) (9) (10) Debye-Huckel 31
32 32
33 : h P P = P E + P O P P E O = = ( n ε + r ε n 2 dψ dx ) kt 2nkT (15) (16) 33
34 P O P E ψ 0 P E (1) (16) P O P R (h) P R zeψ h / 2 ( h) = 2nkT cosh 1 kt ψ 2/h : (17) 34
35 ψ h/2 ψ s(h/2) zeψ / 4kT << 1 then tanh( zeψ / 4kT) zeψ / 4kT (6) ψ<20 mv ψ γ ( h / 2) = 8kT h = γ exp κ ze 2 zeψ 0 tanh 4kT (18) (19) 35
36 (17) ze ψ 2 h / 2 / kt << 1 then PR ( h) nkt{ zeψ h / 2 / kt} (18) κh>1 h cosh y 1 + y 2 P R 2 ( h) = 64nkTγ exp( κh) (20) 36
37 V R ( h) h = P R ( h) dh = 64nkT κ γ 2 exp( κ h) (21) 37
38 38
39 Derjaguin Derjaguin : a 1 a 2 H H<<a 1,a 2 P R ( H ) = 2π a a 1 2 V ( a H 1 a R + 2 (21) (22) a 1 =a 2 =a P R ( H ) = 64 π ankt κ γ 2 exp( ) κ h) (22) (23) 39
40 a V R ( H H ) = PR ( H ) dh 64πankT 2 = γ exp( κh) (24) 2 κ 40
41 zeψ 0 / 4kT << 1 then tanh( zeψ 0 / 4kT) zeψ 0 / 4kT (23),(24) zeψ 0 =4kT 1:1 25 ψ 0 =103 mv ψ 0 =20 mv zeψ 0 /4kT tanh{ zeψ 0 /4kT} 1% P V R R 20mV ( H ( H ) ) = = 2 2 π π a a ε ε r r ε ε (13) 2 0κψ 0 exp( κh) 2 0ψ 0 exp( κh) (25) (26) 41
42 42 ) exp( 2 ) ( h a H P r R κ κψ ε ε π = ) exp( 2 ) ( h a H V r R κ ψ ε ε π = (13) ) exp( 2 ) ( 0 2 H a H P r R κ ε κε σ π = ) exp( 2 ) ( H a H V r R κ ε ε κ σ π = (25) (26) (27) (28) κψ ε ε σ r = (13)
43 van der Waals aa P A ( H ) = 12H aa V A ( H ) = 12H A Hamaker 2 (29) (30) 43
44 ) exp( 2 ) ( H aa H a H P r T = κ ε κε σ π H aa H a H V r T 12 ) exp( 2 ) ( = κ ε ε κ σ π H aa h a H V r T 12 ) exp( 2 ) ( = κ ψ ε ε π (31) (32) (33)
45 45
46 V T ( H ) = 2 π a ε r ε ψ 2 0 κ 0 exp( H ) aa 12 H ε r, ε 0, ψ 0, A a κ 46
47 2 2 κ = ε nz r ε 0 2 e 2 kt e ε r ε 0 k n z T 47
48 n z T κ 48
49 V T ( H ) 2 a r 0 0 exp( H ) = π ε ε ψ κ 2 aa 12 H 49
50 van der Waals 50
51 51
52 van der Waals 52
53 53
54 54
55 55
56 56
57 57
58 58
59 59
60 60
61 61
62 62
63 63
64 64
65 65
66 66
67 67
68 68
69 KCl 1 mol/l KCl 69
70 70
71 71
72 72
73 73
74 74
75 75
76 76
77 77
78 78
79 79
80 80
81 81
82 82
83 83
84 84
85 85
86 86
87 87
88 88
89 89
90 90
91 91
92 92
93 93
94 94
95 95
96 2,3,7,8- ppm O- n- cm/day ppb 2 96
97 97
98 98
99 99
100 No data
101 (8.01%) 49 (16.67%) 242 (3.62%) 59 (0.81%) 1 (0.34%) 2 (0.03%) 54 (0.74%) 11 (3.74%) 26 (0.39%) 914 (12.47%) (4.65%) 81 (1.11%) 16 (5.44%) 29 (0.43%) 1614 (22.03%) 61 (20.75%) 581 (8.68%)
102 (A) [%] (B) [%] B/A
103 103
104 104
105 105
106 gteq/ ( ) ( )
107 107
108 108
109 109
110 ( C) (ng-teq/nm 3 ) ( 1111)
111 111
112 112
113 113
114 114
115 115
微粒子合成化学・講義
http://www.tagen.tohoku.ac.jp/labo/muramatsu/mura/main.html E-mail: mura@tagen.tohoku.ac.jp 1 Derjaguin Landau Verway Overbeek B.V.Derjaguin and L.Landau;Acta Physicochim.,URSS, 14, 633 1941. E.J.W.Verwey
More informationコロイド化学と界面化学
環境表面科学講義 http://res.tagen.tohoku.ac.jp/~liquid/mura/kogi/kaimen/ E-mail: mura@tagen.tohoku.ac.jp 村松淳司 分散と凝集 ( 平衡論的考察! 凝集! van der Waals 力による相互作用! 分散! 静電的反発力 凝集 分散! 粒子表面の電位による反発 分散と凝集 考え方! van der Waals
More informationナノ粒子のサイズ・形態制御と 構造敏感型触媒プロセスへの応用
環境表面科学講義 http://res.tagen.tohoku.ac.jp/~liquid/mura/kogi/kaimen/ E-mail: mura@tagen.tohoku.ac.jp 村松淳司 DLVO 理論 分散と凝集をどう扱うか それぞれを別の 2 つの力とする 3 分散と凝集 考え方 V total = V H + V el V H : van der Waals 力による相互作用エネルギー
More information. 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.........
More informationI-2 (100 ) (1) y(x) y dy dx y d2 y dx 2 (a) y + 2y 3y = 9e 2x (b) x 2 y 6y = 5x 4 (2) Bernoulli B n (n = 0, 1, 2,...) x e x 1 = n=0 B 0 B 1 B 2 (3) co
16 I ( ) (1) I-1 I-2 I-3 (2) I-1 ( ) (100 ) 2l x x = 0 y t y(x, t) y(±l, t) = 0 m T g y(x, t) l y(x, t) c = 2 y(x, t) c 2 2 y(x, t) = g (A) t 2 x 2 T/m (1) y 0 (x) y 0 (x) = g c 2 (l2 x 2 ) (B) (2) (1)
More informationmaster.dvi
4 Maxwell- Boltzmann N 1 4.1 T R R 5 R (Heat Reservor) S E R 20 E 4.2 E E R E t = E + E R E R Ω R (E R ) S R (E R ) Ω R (E R ) = exp[s R (E R )/k] E, E E, E E t E E t E exps R (E t E) exp S R (E t E )
More information( )
7..-8..8.......................................................................... 4.................................... 3...................................... 3..3.................................. 4.3....................................
More information, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. main.tex 2011/08/13( )
81 4 2 4.1, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. 82 4.2. ζ t + V (ζ + βy) = 0 (4.2.1), V = 0 (4.2.2). (4.2.1), (3.3.66) R 1 Φ / Z, Γ., F 1 ( 3.2 ). 7,., ( )., (4.2.1) 500 hpa., 500 hpa (4.2.1) 1949,.,
More information4.6 (E i = ε, ε + ) T Z F Z = e βε + e β(ε+ ) = e βε (1 + e β ) F = kt log Z = kt log[e βε (1 + e β )] = ε kt ln(1 + e β ) (4.18) F (T ) S = T = k = k
4.6 (E i = ε, ε + ) T Z F Z = e ε + e (ε+ ) = e ε ( + e ) F = kt log Z = kt loge ε ( + e ) = ε kt ln( + e ) (4.8) F (T ) S = T = k = k ln( + e ) + kt e + e kt 2 + e ln( + e ) + kt (4.20) /kt T 0 = /k (4.20)
More informationH22環境地球化学4_化学平衡III_ ppt
1 2 3 2009年度 環境地球化学 大河内 温度上昇による炭酸水の発泡 気泡 温度が高くなると 溶けきれなくなった 二酸化炭素が気泡として出てくる 4 2009年度 環境地球化学 圧力上昇による炭酸水の発泡 栓を開けると 瓶の中の圧力が急激に 小さくなるので 発泡する 大河内 5 CO 2 K H CO 2 H 2 O K H + 1 HCO 3- K 2 H + CO 3 2- (M) [CO
More informationNo δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2
No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j
More information30
3 ............................................2 2...........................................2....................................2.2...................................2.3..............................
More information( ) ,
II 2007 4 0. 0 1 0 2 ( ) 0 3 1 2 3 4, - 5 6 7 1 1 1 1 1) 2) 3) 4) ( ) () H 2.79 10 10 He 2.72 10 9 C 1.01 10 7 N 3.13 10 6 O 2.38 10 7 Ne 3.44 10 6 Mg 1.076 10 6 Si 1 10 6 S 5.15 10 5 Ar 1.01 10 5 Fe 9.00
More informationnm (T = K, p = kP a (1atm( )), 1bar = 10 5 P a = atm) 1 ( ) m / m
.1 1nm (T = 73.15K, p = 101.35kP a (1atm( )), 1bar = 10 5 P a = 0.9863atm) 1 ( ).413968 10 3 m 3 1 37. 1/3 3.34.414 10 3 m 3 6.0 10 3 = 3.7 (109 ) 3 (nm) 3 10 6 = 3.7 10 1 (nm) 3 = (3.34nm) 3 ( P = nrt,
More information成長機構
j im πmkt jin jim π mkt j q out j q im π mkt jin j j q out out π mkt π mkt dn dt πmkt dn v( ) Rmax bf dt πmkt R v ( J J ), J J, J J + + T T, J J m + Q+ / kt Q / kt + ( Q Q+ )/ ktm l / ktm J / J, l Q Q
More informationall.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
More information2,200 WEB * Ξ ( ) η ( ) DC 1.5 i
mailto: tomita@phys.h.kyoto-u.ac.jp 2002 2003 1.5 2003 2004 2005 2,200 WEB * Ξ ( ) η ( ) DC 1.5 i 1 1 1.1............................. 1 1.2..................................... 2 1.3.................................
More informationW u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)
3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
More informationuntitled
1907(40) 100 100 21 1 1 21 21 21 21 21 1891(M24) 1920(T9)1 2 1932(S7) 1947(S22) 1968(S43)12 2001(H13) 1955(S30) 1 24 9 7 22 43 13 2 100 6 200300t 1896M29 3876 1536 1 15 1907(M7) 11 6 1898(M31) 5 6 2 1912(M45)
More information2 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
More information[ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 i,j S i S j (4.39) i, j z 5 2 z = 4 z = 6 3
4.2 4.2.1 [ ] (Ising model) 2 i S i S i = 1 (up spin : ) = 1 (down spin : ) (4.38) s z = ±1 4 H 0 = J zn/2 S i S j (4.39) i, j z 5 2 z = 4 z = 6 3 z = 6 z = 8 zn/2 1 2 N i z nearest neighbors of i j=1
More informationω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j
More information25 7 18 1 1 1.1 v.s............................. 1 1.1.1.................................. 1 1.1.2................................. 1 1.1.3.................................. 3 1.2................... 3
More informationIA
IA 31 4 11 1 1 4 1.1 Planck.............................. 4 1. Bohr.................................... 5 1.3..................................... 6 8.1................................... 8....................................
More information微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
More information120 9 I I 1 I 2 I 1 I 2 ( a) ( b) ( c ) I I 2 I 1 I ( d) ( e) ( f ) 9.1: Ampère (c) (d) (e) S I 1 I 2 B ds = µ 0 ( I 1 I 2 ) I 1 I 2 B ds =0. I 1 I 2
9 E B 9.1 9.1.1 Ampère Ampère Ampère s law B S µ 0 B ds = µ 0 j ds (9.1) S rot B = µ 0 j (9.2) S Ampère Biot-Savart oulomb Gauss Ampère rot B 0 Ampère µ 0 9.1 (a) (b) I B ds = µ 0 I. I 1 I 2 B ds = µ 0
More informationII ( ) (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
More information8 300 mm 2.50 m/s L/s ( ) 1.13 kg/m MPa 240 C 5.00mm 120 kpa ( ) kg/s c p = 1.02kJ/kgK, R = 287J/kgK kPa, 17.0 C 118 C 870m 3 R = 287J
26 1 22 10 1 2 3 4 5 6 30.0 cm 1.59 kg 110kPa, 42.1 C, 18.0m/s 107kPa c p =1.02kJ/kgK 278J/kgK 30.0 C, 250kPa (c p = 1.02kJ/kgK, R = 287J/kgK) 18.0 C m/s 16.9 C 320kPa 270 m/s C c p = 1.02kJ/kgK, R = 292J/kgK
More informationQMII_10.dvi
65 1 1.1 1.1.1 1.1 H H () = E (), (1.1) H ν () = E ν () ν (). (1.) () () = δ, (1.3) μ () ν () = δ(μ ν). (1.4) E E ν () E () H 1.1: H α(t) = c (t) () + dνc ν (t) ν (), (1.5) H () () + dν ν () ν () = 1 (1.6)
More informationThe Physics of Atmospheres CAPTER :
The Physics of Atmospheres CAPTER 4 1 4 2 41 : 2 42 14 43 17 44 25 45 27 46 3 47 31 48 32 49 34 41 35 411 36 maintex 23/11/28 The Physics of Atmospheres CAPTER 4 2 4 41 : 2 1 σ 2 (21) (22) k I = I exp(
More informationb3e2003.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
More information: 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(
More information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
More information液晶の物理1:連続体理論(弾性,粘性)
The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers
More information.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T
NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977
More information,., 5., ,. 2.2,., x z. y,.,,,. du dt + α p x = 0 dw dt + α p z + g = 0 α dp dt + pγ dα dt = 0 α V dα dt = 0 (2.2.1), γ = c p /c
29 2 1 2.1 2.1.1.,., 5.,. 2.1.1,. 2.2,., x z. y,.,,,. du dt + α p x = 0 dw dt + α p z + g = 0 α dp dt + pγ dα dt = 0 α V dα dt = 0 (2.2.1), γ = c p /c v., V = (u, w), = ( / x, / z). 30 2.1.1: 31., U p(z),
More information(5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b)
(5) 74 Re, bondar laer (Prandtl) Re z ω z = x (5) 75 (a) (b) ( 1 ) v ( 1 ) E E 1 v (a) ( 1 ) x E E (b) (a) (b) (5) 76 l V x ) 1/ 1 ( 1 1 1 δ δ = x Re x p V x t V l l (1-1) 1/ 1 δ δ δ δ = x Re p V x t V
More information4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
More informationx 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
More informationNote.tex 2008/09/19( )
1 20 9 19 2 1 5 1.1........................ 5 1.2............................. 8 2 9 2.1............................. 9 2.2.............................. 10 3 13 3.1.............................. 13 3.2..................................
More information³ÎΨÏÀ
2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p
More information1
1 1.. ( ) ( ) ( ) (A) E icb φ Et = + cdiva ct (H3) (B) ( ) ct ct ' ctct ' + ' = ' ct ' + ct ' i( ') (H3,H18) 3 (i) cosh Ψ = cosh ΘcoshΩ sinhψ sinhθ sinhω cosh Ψ cosh Θ cosh Ω = sinhψ sinhθ sinhω tanhψ
More information現代物理化学 2-1(9)16.ppt
--- S A, G U S S ds = d 'Q r / ΔS = S S = ds =,r,r d 'Q r r S -- ds = d 'Q r / ΔS = S S = ds =,r,r d 'Q r r d Q r e = P e = P ΔS d 'Q / e (d'q / e ) --3,e Q W Q (> 0),e e ΔU = Q + W = (Q + Q ) + W = 0
More information006 11 8 0 3 1 5 1.1..................... 5 1......................... 6 1.3.................... 6 1.4.................. 8 1.5................... 8 1.6................... 10 1.6.1......................
More informationKENZOU
KENZOU 2008 8 2 3 2 3 2 2 4 2 4............................................... 2 4.2............................... 3 4.2........................................... 4 4.3..............................
More information1 s 1 H(s 1 ) N s 1, s,, s N H({s 1,, s N }) = N H(s k ) k=1 Z N =Tr {s1,,s N }e βh({s 1,,s N }) =Tr s1 Tr s Tr sn e β P k H(s k) N = Tr sk e βh(s k)
19 1 14 007 3 1 1 Ising 4.1................................. 4................................... 5 3 9 3.1........................ 9 3................... 9 3.3........................ 11 4 14 4.1 Legendre..............................
More information211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,
More informationuntitled
D nucleation 3 3D nucleation Glucose isomerase 10 V / nm s -1 5 0 0 5 10 C - C e / mg ml -1 kinetics µ R K kt kinetics kinetics kinetics r β π µ π r a r s + a s : β: µ πβ µ β s c s c a a r, & exp exp
More information2 1 x 2 x 2 = RT 3πηaN A t (1.2) R/N A N A N A = N A m n(z) = n exp ( ) m gz k B T (1.3) z n z = m = m ρgv k B = erg K 1 R =
1 1 1.1 1827 *1 195 *2 x 2 t x 2 = 2Dt D RT D = RT N A 1 6πaη (1.1) D N A a η 198 *3 ( a =.212µ) *1 Robert Brown (1773-1858. *2 Albert Einstein (1879-1955 *3 Jean Baptiste Perrin (187-1942 2 1 x 2 x 2
More information( ; ) C. H. Scholz, The Mechanics of Earthquakes and Faulting : - ( ) σ = σ t sin 2π(r a) λ dσ d(r a) =
1 9 8 1 1 1 ; 1 11 16 C. H. Scholz, The Mechanics of Earthquakes and Faulting 1. 1.1 1.1.1 : - σ = σ t sin πr a λ dσ dr a = E a = π λ σ πr a t cos λ 1 r a/λ 1 cos 1 E: σ t = Eλ πa a λ E/π γ : λ/ 3 γ =
More information理想気体ideal gasの熱力学的基本関係式
the equipartition law of energy ( )kt k Boltzmann constant 5 Longman Dictionary of Physics (/)kt q Bq (/)kt equipartition law of energy mol (3/)kT (3/)RT (3/)R (5/)R 3R kt - equipartition of energy The
More information1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2
2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
More informationH.Haken Synergetics 2nd (1978)
27 3 27 ) Ising Landau Synergetics Fokker-Planck F-P Landau F-P Gizburg-Landau G-L G-L Bénard/ Hopfield H.Haken Synergetics 2nd (1978) (1) Ising m T T C 1: m h Hamiltonian H = J ij S i S j h i S
More information,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising
,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising Model 1 Ising 1 Ising Model N Ising (σ i = ±1) (Free
More informationBlack-Scholes [1] Nelson [2] Schrödinger 1 Black Scholes [1] Black-Scholes Nelson [2][3][4] Schrödinger Nelson Parisi Wu [5] Nelson Parisi-W
003 7 14 Black-Scholes [1] Nelson [] Schrödinger 1 Black Scholes [1] Black-Scholes Nelson [][3][4] Schrödinger Nelson Parisi Wu [5] Nelson Parisi-Wu Nelson e-mail: takatoshi-tasaki@nifty.com kabutaro@mocha.freemail.ne.jp
More informationEinstein 1905 Lorentz Maxwell c E p E 2 (pc) 2 = m 2 c 4 (7.1) m E ( ) E p µ =(p 0,p 1,p 2,p 3 )=(p 0, p )= c, p (7.2) x µ =(x 0,x 1,x 2,x
7 7.1 7.1.1 Einstein 1905 Lorentz Maxwell c E p E 2 (pc) 2 = m 2 c 4 (7.1) m E ( ) E p µ =(p 0,p 1,p 2,p 3 )=(p 0, p )= c, p (7.2) x µ =(x 0,x 1,x 2,x 3 )=(x 0, x )=(ct, x ) (7.3) E/c ct K = E mc 2 (7.4)
More informationN/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/
More informationTOP URL 1
TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7
More informationm(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
More information18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb
r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)
More informationchap03.dvi
99 3 (Coriolis) cm m (free surface wave) 3.1 Φ 2.5 (2.25) Φ 100 3 r =(x, y, z) x y z F (x, y, z, t) =0 ( DF ) Dt = t + Φ F =0 onf =0. (3.1) n = F/ F (3.1) F n Φ = Φ n = 1 F F t Vn on F = 0 (3.2) Φ (3.1)
More informationII 2 II
II 2 II 2005 yugami@cc.utsunomiya-u.ac.jp 2005 4 1 1 2 5 2.1.................................... 5 2.2................................. 6 2.3............................. 6 2.4.................................
More information) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)
4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7
More information68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1
67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10
More information01_教職員.indd
T. A. H. A. K. A. R. I. K. O. S. O. Y. O. M. K. Y. K. G. K. R. S. A. S. M. S. R. S. M. S. I. S. T. S. K.T. R. T. R. T. S. T. S. T. A. T. A. D. T. N. N. N. Y. N. S. N. S. H. R. H. W. H. T. H. K. M. K. M.
More information2019 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..........................
More informationH 0 H = H 0 + V (t), V (t) = gµ B S α qb e e iωt i t Ψ(t) = [H 0 + V (t)]ψ(t) Φ(t) Ψ(t) = e ih0t Φ(t) H 0 e ih0t Φ(t) + ie ih0t t Φ(t) = [
3 3. 3.. H H = H + V (t), V (t) = gµ B α B e e iωt i t Ψ(t) = [H + V (t)]ψ(t) Φ(t) Ψ(t) = e iht Φ(t) H e iht Φ(t) + ie iht t Φ(t) = [H + V (t)]e iht Φ(t) Φ(t) i t Φ(t) = V H(t)Φ(t), V H (t) = e iht V (t)e
More information5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E
5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E 2, S 1 N 1 = S 2 N 2 2 (chemical potential) µ S N
More informationhttp://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....................
More informationHanbury-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............................................
More information2 A B A B A A B Ea 1 51 Ea 1 A B A B B A B B A Ea 2 A B Ea 1 ( )k 1 Ea 1 Ea 2 Arrhenius 53 Ea R T k 1 = χe 1 Ea RT k 2 = χe 2 Ea RT 53 A B A B
5. A B B A B A B B A A B A B 2 A [A] B [B] 51 v = k[a][b] 51 A B 3 0 273.16 A B A B A B A A [A] 52 v= k[a] 52 A B 55 2 A B A B A A B Ea 1 51 Ea 1 A B A B B A B B A Ea 2 A B Ea 1 ( )k 1 Ea 1 Ea 2 Arrhenius
More informationOnsager SOLUTION OF THE EIGENWERT PROBLEM (O-29) V = e H A e H B λ max Z 2 Onsager (O-77) (O-82) (O-83) Kramers-Wannier 1 1 Ons
Onsager 2 9 207.2.7 3 SOLUTION OF THE EIGENWERT PROBLEM O-29 V = e H A e H B λ max Z 2 OnsagerO-77O-82 O-83 2 Kramers-Wannier Onsager * * * * * V self-adjoint V = V /2 V V /2 = V /2 V 2 V /2 = 2 sinh 2H
More information[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s
[ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =
More information1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2
filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin
More information第3章
5 5.. Maxwell Maxwell-Ampere E H D P J D roth = J+ = J+ E+ P ( ε P = σe+ εe + (5. ( NL P= ε χe+ P NL, J = σe (5. Faraday rot = µ H E (5. (5. (5. ( E ( roth rot rot = µ NL µσ E µε µ P E (5.4 = ( = grad
More information1 2 1 a(=,incident particle A(target nucleus) b (projectile B( product nucleus, residual nucleus, ) ; a + A B + b a A B b 1: A(a,b)B A=B,a=b 2 1. ( 10
1 2 1 a(=,incident particle A(target nucleus) b (projectile B( product nucleus, residual nucleus, ) ; a + A B + b a A B b 1: A(a,b)B A=B,a=b 2 1. ( 10 14 m) ( 10 10 m) 2., 3 1 =reaction-text20181101b.tex
More information1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1
1 I 1.1 ± e = = - =1.602 10 19 C C MKA [m], [Kg] [s] [A] 1C 1A 1 MKA 1C 1C +q q +q q 1 1.1 r 1,2 q 1, q 2 r 12 2 q 1, q 2 2 F 12 = k q 1q 2 r 12 2 (1.1) k 2 k 2 ( r 1 r 2 ) ( r 2 r 1 ) q 1 q 2 (q 1 q 2
More informationIntroduction to Numerical Analysis of Differential Equations Naoya Enomoto (Kyoto.univ.Dept.Science(math))
Introduction to Numerical Analysis of Differential Equations Naoya Enomoto (Kyoto.univ.Dept.Science(math)) 2001 1 e-mail:s00x0427@ip.media.kyoto-u.ac.jp 1 1 Van der Pol 1 1 2 2 Bergers 2 KdV 2 1 5 1.1........................................
More information1
016 017 6 16 1 1 5 1.1............................................... 5 1................................................... 5 1.3................................................ 5 1.4...............................................
More information30 (11/04 )
30 (11/04 ) i, 1,, II I?,,,,,,,,, ( ),,, ϵ δ,,,,, (, ),,,,,, 5 : (1) ( ) () (,, ) (3) ( ) (4) (5) ( ) (1),, (),,, () (3), (),, (4), (1), (3), ( ), (5),,,,,,,, ii,,,,,,,, Richard P. Feynman, The best teaching
More informationS I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d
S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....
More information9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) Ĥ0 ψ n (r) ω n Schrödinger Ĥ 0 ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ0 + Ĥint (
9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) 2. 2.1 Ĥ ψ n (r) ω n Schrödinger Ĥ ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ + Ĥint (t)] ψ (r, t), (2) Ĥ int (t) = eˆxe cos ωt ˆdE cos ωt, (3)
More information1: 3.3 1/8000 1/ m m/s v = 2kT/m = 2RT/M k R 8.31 J/(K mole) M 18 g 1 5 a v t πa 2 vt kg (
1905 1 1.1 0.05 mm 1 µm 2 1 1 2004 21 2004 7 21 2005 web 2 [1, 2] 1 1: 3.3 1/8000 1/30 3 10 10 m 3 500 m/s 4 1 10 19 5 6 7 1.2 3 4 v = 2kT/m = 2RT/M k R 8.31 J/(K mole) M 18 g 1 5 a v t πa 2 vt 6 6 10
More information80 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
More informationi
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
More informationuntitled
40 4 4.3 I (1) I f (x) C [x 0 x 1 ] f (x) f 1 (x) (3.18) f (x) ; f 1 (x) = 1! f 00 ((x))(x ; x 0 )(x ; x 1 ) (x 0 (x) x 1 ) (4.8) (3.18) x (x) x 0 x 1 Z x1 f (x) dx ; Z x1 f 1 (x) dx = Z x1 = 1 1 Z x1
More information) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4
1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev
More informationall.dvi
5,, Euclid.,..,... Euclid,.,.,, e i (i =,, ). 6 x a x e e e x.:,,. a,,. a a = a e + a e + a e = {e, e, e } a (.) = a i e i = a i e i (.) i= {a,a,a } T ( T ),.,,,,. (.),.,...,,. a 0 0 a = a 0 + a + a 0
More informationm 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
More information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
More informationK E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................
More information19 /
19 / 1 1.1............................... 1. Andreev............................... 3 1.3..................................... 3 1.4..................................... 4 / 5.1......................................
More informationK E N Z U 01 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.................................... 4 1..1..................................... 4 1...................................... 5................................
More information