Evoltion of onentration by Eler method (Dirihlet) Evoltion of onentration by Eler method (Nemann).2 t n =.4n.2 t n =.4n : t n
|
|
- あゆみ りゅうとう
- 5 years ago
- Views:
Transcription
1 5 t = = (, y, z) t (, y, z, t) t = κ (68) κ [, ] (, ) = ( ) A ( /2)2 ep, A =., t =.. (69) 4πκt 4κt = /2 (, t) = for ( =, ) (Dirihlet ondition) (7) = for ( =, ) (Nemann ondition) (7) (68) (, t) = ( ) ( y)2 ep (y, )dy (72) 4πκt 4κt (69) = y = ((y, ) = δ(y ) δ() (, t) ( (, t) = ep ( ) 2 ) G(, t) (73) 4πκt 4κt N + i = i, i =,,, N t n = n t, n =,, (, t) ( i, t n ) = n i n+ i = n i + κ t ( n 2 i+ 2 n i + n ) i (74) 2
2 Evoltion of onentration by Eler method (Dirihlet) Evoltion of onentration by Eler method (Nemann).2 t n =.4n.2 t n =.4n : t n =.4n : t n =.4n [,] dq dt = Q(t) = (, t) 2 ( d = κ t 2 d = κ (, t)d (75) = = ) = (76) = t (, t) 5.2 Diffsion eqation in D by Simple Eler impliit real*8 (a-h,o-z) integer pot,gdraw,n,tma real*8 kappa parameter(n=5, kappa=., dt=., ibs=) dt parameter(tma=4, gdraw=4) dimension (:n),old(:n) *** d=.d/dfloat(n) d2i=.d/d/d pi=4.d*atan(.d) amp=.d- t_init=. *** 2
3 =d*(n/2) do i=,n =i*d (i)=amp/sqrt(2.*pi*t_init)*ep(-(-)*(-)/4/kappa/t_init) if((i).lt..d-2) (i)=.d *** if(ibs.eq.) then * write(6,*) Dirihlet Condition open(, file= diffsion_d.dat ) * ()=.d (n)=.d else write(6,*) Nemann Condition open(, file= diffsion_n.dat ) * ()=() (n)=(n-) endif *** Write (=/2,t) t=.d write(6,) format(/, Evoltion of (/2,t), /) write(6,) t,(n/2) do i=,n write(,) i*d, (i) write(,) do n=,tma *** * _old do i=,n old(i)=(i) * do i=,n- diff=kappa*(old(i+)-2.d*old(i)+old(i-))*d2i (i)=old(i)+diff*dt *** if(ibs.eq.) then ()=.d (n)=.d else ()=() (n)=(n-) endif * * *** if(mod(n,gdraw).eq.) then do i=,n write(,) i*d, (i) write(,) t=n*dt 22
4 write(6,) t,(n/2) endif format(, pe.3, 2, pe2.6) stop end gnplot gdiffsion.plt ips= ips=, ips= epsfile bondary= if(ips==) set terminal postsript eps pls olor "Times-Itali" 22 set nologsale set nologsale y set range [.:.] set yrange [:.5] set label "" set ylabel "" if(ips== && bondary==) set otpt "diffsion_d.eps" if(bondary==) set title "Evoltion of onentration by Eler method (Dirihlet)";\ plot diffsion_d.dat sing :2 title $t_n=.4n$ with lines ;\ :2-> y pase - "Dirihelt ondition" if(ips== && bondary==) set otpt "diffsion_n.eps" if(bondary==) set title "Evoltion of onentration by Eler method (Nemann)";\ plot diffsion_n.dat sing :2 title $t_n=.4n$ with lines ;\ pase - "Nemann ondition" 5.3. t = (, ) = 2. ) y t > U = t = ν 2, y >, t > (77) y2 (y, t) ν = µ/ρ ν =. (y =, t) = U, (y, t) y (78) (y, ) =. (79) Rayleigh y 23
5 .8 Rayleigh problem t n =.4n.2 Evoltion of onentration by Eler method (Dirihlet) t n =.4n.6.8 y : ν =. t n =.4n 2: t =.2, t n =.4n. y = U e (y (t), t) = U e y (t) = 4νt t t =.2 2 2κ 2, 6) t t + t (, t + t) = = 4π t ep t (8) ( ) ( y)2 (y, t)dy (8) 4κ t G( y, t)(y, t)dy (82) G(, t) (73) t y y + dy (y, t)dy t 24
6 t= = 2k t -D<<D 以内に Q の大部分が含まれているためには t=dt Dt Dt/4 t=2dt D y D/2 y D 3: y Q = t, 2 t [, ] 4: t [, ] [ /2, /2] t/4 Q(t) = = (, t + t)d = (83) G( y, t)d (84) 2, t = y y [G(, t) + 2G(, t) + G(, t)] (85) 2 [, ] 3 G y = (73) 2 4κ t > (86) 4 2 (86) 2 / (2κ t) ( /2, t/2) ( /2) 2 / 2κ( t/2) = 2 / 2κ2 t < (86) t/2 [ /2, /2] 4 25
7 = /5 =.2, 2 /(2κ) = 4 4 /2/. = 2 3 t =. t =.2 Crank-Niolson Sheme n n + n+ i = n i + κ t ( ) 2 2 n+ i+ 2n+ i + n+ i + n i+ 2 n i + n i n+ i n+ Impliit Sheme (87) (87) 2 + b 2 + b 2 + b b 2 + b n+ n+. n+ N n+ N = f n f n. f n N f n N (88) f n i = n i+ (2 b) n i + n i, b = 2 2 κ t. (89) (88) n+ i = n+ i = α i n+ i + β i (9) 2 + b α i n+ i+ + f n i + β i 2 + b α i (9) (9) α i, β i α i = Dirihlet = N = 2 + b α i, β i = f n i + β i 2 + b α i (92) n+ = α n+ + β = α =, β = (93) i = i = N (92) α i, β i n+ N = n+ N = α N n+ N + β N n+ i Gass (8) t =
8 Evoltion of onentration by Crank-Niolson (Dirihlet) dt=.4.2 t n =.4n : t =.4, t n =.4n. 6 t + =, (94) f() (, t) = f( t) ξ = t (, t) = f(ξ) f t = df ξ df = dξ t dξ, f = df ξ dξ = df dξ, t + = df ( + ) = (95) dξ ξ (, t) ξ = t f(ξ) = f( t) = (, t) t = (, ) = f() t > (, t) f() t (94) 6 6. n+ j n j t = n j+ n j 2 { for <.5 Type A (, ) = otherwise (96) (97) 27
9 t -t=ξ -2 -t=ξ - -t= t 2 t A B C D 6: t = ξ (, t) t = 7 > / j = j j, > (98) 8 ) < = j+ j, < (99) (94) n+ j n+ j n j t n j t n+ j n j t = n j+ n j 2 = n j n j, > () = n j+ n j, < () + n j+ 2n j + n j 2 2 (2) 2 9 () 28
10 .5 n+2 Flow diretion.5 n n t j- j j+ 7: Type A (96) 8: n + j n t 6.2. > = 2, 2. < (94) [, L] L L (, t)d = d = ((L, t) (, t)) (3) t (, t) = (L, t) (2) Q(t) t =, Q(t) = L (, t)d = (4) 6.3 (La-Wendroff) n+ j n j t = n j+ n j t ( ) 2 2 n j+ 2 n j + n j (5) 29
11 : Type A () 2: Type A () : Type B 22: Type B : Type B 3
12 2 t/2 2 / 2 2 t/2 2 Type A Type B 2, 22, 6.2 ( Type B (, ) = 2πσ ep ( ) 2 ) 2 σ 2, σ =.5 (6) 6.4 Convetive eqation in D by La-Wendroff or Central Differene *** Choie of the nmerial sheme swith=: Central differene swith=: La-Wendroff *** Choie of the initial ondition init_type=: Top hat init_type=: Gassian impliit real*8 (a-h,o-z) integer kint,kdraw,n,nt,tma,swith parameter(n=, tma=4, kint=2, kdraw=2) parameter(n=, tma=, kint=2, kdraw=2) parameter(=.d, dt=.2, width=.5, init_type=, swith=) dimension (:n),old(:n) harater*2 file(:2) *** Make parameters d=.d/dfloat(n) pi=4.d*atan(.d) sigma2=width*width amp=.d-/sqrt(2.*pi*sigma2) r=*dt/d file()= Central_differene file()= La-Wendroff if(swith==) open(,file= Central_differene.dat ) if(swith==) open(,file= La-Wendroff.dat ) 3
13 write(6,) file(swith),r format(,a2,, Corant Nmber=,pe.3,/) write(6,*) Conservation of Q *** Initial ondition and omptation of total Q(t)=\int (,t)d *** =d*(n/2) do i=,n =i*d (i)=.d if(init_type==.and. abs(-)<=width) (i)=.d if(init_type==) (i)=amp*ep(-.5d*(-)**2/sigma2) *** Otpt data for t= all otpt(,d,dt,n,,kint,kdraw) *** Time advaning by simple Eler do nt=,tma *** Copy to old do i=,n old(i)=(i) *** Choie of the nmerial sheme swith=: La-Wendroff swith=: Central differene do i=,n ipls=mod(i+,n) tmp=old(i)-.5d*r*(old(ipls)-old(i-)) diff=.5d*r*r*(old(ipls)-2.d*old(i)+old(i-)) (i)=tmp+swith*diff *** Enfore periodi bondary ondition ()=(n) *** Otpt data for t> all otpt(,d,dt,n,nt,kint,kdraw) stop end ******************************************************************** sbrotine otpt(,d,dt,n,nt,kint,kdraw) impliit real*8 (a-h,o-z) real*8 (:n) save Q_init if(mod(nt,kint).eq.) then Q=.d do i=,n Q=Q+(i) Q=Q*d if(nt==) Q_init=Q write(6,) nt*dt,q/q_init endif **** write Q 32
14 *** write (,t) if(mod(nt,kdraw).eq.) then do i=,n write(,2) i*d,(i) write(,2) endif format(,2(pe.3,)) 2 format(,2(pe2.5,)) retrn end (, t) t + = ν 2 2 (7) Brgers(948) : (, ) = sin ( > ) 33
PowerPoint プレゼンテーション
Nagoya Institute of Tehnology 中部 CAE 懇話会 流体伝熱基礎講座 第 1 回午後 名古屋工業大学大学院 創成シミュレーション工学専攻 後藤俊幸 Nagoya Institute of Tehnology 数値計算の基礎 x=a の近傍での Taylor 展開 Nagoya Institute of Tehnology Nagoya Institute of Tehnology
More information8 1 1., y y (, +1) (-1, ) (, ) (+1, ) y (, -1) 1.1: (,y ) y y ±1 = ± y ±1 = y ± y (, ), = (,y ) (,y ) +1, = ( +, y )=, + 1, = (, y )=, (1.) (1.3) ( )
7 1 () Brgers 1.1 a + b y + c y + d + e + f + g =0. (1.1) y b 4ac > 0 t c =0 b 4ac =0 t = κ b 4ac < 0 + y =4πGρ 8 1 1., y y (, +1) (-1, ) (, ) (+1, ) y (, -1) 1.1: (,y ) y y ±1 = ± y ±1 = y ± y (, ), =
More information_0212_68<5A66><4EBA><79D1>_<6821><4E86><FF08><30C8><30F3><30DC><306A><3057><FF09>.pdf
More information
情報活用資料
y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 21 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 22 L A x y A L x 23 ls -l gnuplot gnuplot> plot "sine.dat"
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 information3. :, c, ν. 4. Burgers : u t + c u x = ν 2 u x 2, (3), ν. 5. : u t + u u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,.,
B:,, 2017 12 1, 8, 15, 22 1,.,,,,.,.,,,., 1,. 1. :, ν. 2. : u t = ν 2 u x 2, (1), c. u t + c u x = 0, (2), ( ). 1 3. :, c, ν. 4. Burgers : u t + c u x = ν 2 u x 2, (3), ν. 5. : u t + u u x = ν 2 u x 2,
More information3. :, c, ν. 4. Burgers : t + c x = ν 2 u x 2, (3), ν. 5. : t + u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,., ν. t +
B: 2016 12 2, 9, 16, 2017 1 6 1,.,,,,.,.,,,., 1,. 1. :, ν. 2. : t = ν 2 u x 2, (1), c. t + c x = 0, (2). e-mail: iwayama@kobe-u.ac.jp,. 1 3. :, c, ν. 4. Burgers : t + c x = ν 2 u x 2, (3), ν. 5. : t +
More information研修コーナー
l l l l l l l l l l l α α β l µ l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
More informationc y /2 ddy = = 2π sin θ /2 dθd /2 [ ] 2π cos θ d = log 2 + a 2 d = log 2 + a 2 = log 2 + a a 2 d d + 2 = l
c 28. 2, y 2, θ = cos θ y = sin θ 2 3, y, 3, θ, ϕ = sin θ cos ϕ 3 y = sin θ sin ϕ 4 = cos θ 5.2 2 e, e y 2 e, e θ e = cos θ e sin θ e θ 6 e y = sin θ e + cos θ e θ 7.3 sgn sgn = = { = + > 2 < 8.4 a b 2
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 information1 1 x y = y(x) y, y,..., y (n) : n y F (x, y, y,..., y (n) ) = 0 n F (x, y, y ) = 0 1 y(x) y y = G(x, y) y, y y + p(x)y = q(x) 1 p(x) q(
1 1 y = y() y, y,..., y (n) : n y F (, y, y,..., y (n) ) = 0 n F (, y, y ) = 0 1 y() 1.1 1 y y = G(, y) 1.1.1 1 y, y y + p()y = q() 1 p() q() (q() = 0) y + p()y = 0 y y + py = 0 y y = p (log y) = p log
More informationcpall.dvi
55 7 gnuplot gnuplot Thomas Williams Colin Kelley Unix Windows MacOS gnuplot ( ) ( ) gnuplot gnuplot 7.1 gnuplot gnuplot () PC(Windows MacOS ) gnuplot http://www.gnuplot.info gnuplot 7.2 7.2.1 gnuplot
More informationMicrosoft Word - 資料 docx
y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 29 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 30 L A x y A L x 31 plot sine curve program sine implicit
More information1 u t = au (finite difference) u t = au Von Neumann
1 u t = au 3 1.1 (finite difference)............................. 3 1.2 u t = au.................................. 3 1.3 Von Neumann............... 5 1.4 Von Neumann............... 6 1.5............................
More information第86回日本感染症学会総会学術集会後抄録(I)
κ κ κ κ κ κ μ μ β β β γ α α β β γ α β α α α γ α β β γ μ β β μ μ α ββ β β β β β β β β β β β β β β β β β β γ β μ μ μ μμ μ μ μ μ β β μ μ μ μ μ μ μ μ μ μ μ μ μ μ β
More information橡3章波浪取扱.PDF
2 2-2 * -* *EM EM -1- (2.1) Dally x κ ( F cos θ ) + ( F sin θ ) = ( F F s ) 2.1 y d 2-7 F F Stable wave energy flux d F (2.2) F s = E s gs = 1 8 ρgh 2 s gh = 1 8 ρg(γ h) 2 gh 2.2 η (2.3) ds xx = ρgd d
More information2011 8 26 3 I 5 1 7 1.1 Markov................................ 7 2 Gau 13 2.1.................................. 13 2.2............................... 18 2.3............................ 23 3 Gau (Le vy
More information取扱説明書 [N-03A]
235 1 d dt 2 1 i 236 1 p 2 1 ty 237 o p 238 1 i 2 1 i 2 1 u 239 1 p o p b d 1 2 3 0 w 240 241 242 o d p f g p b t w 0 q f g h j d 1 2 d b 5 4 6 o p f g p 1 2 3 4 5 6 7 243 244 1 2 1 q p 245 p 246 p p 1
More information1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 5 3. 4. 5. A0 (1) A, B A B f K K A ϕ 1, ϕ 2 f ϕ 1 = f ϕ 2 ϕ 1 = ϕ 2 (2) N A 1, A 2, A 3,... N A n X N n X N, A n N n=1 1 A1 d (d 2) A (, k A k = O), A O. f
More information66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3) d 1 NN K K 8.1 d σd σd M = σd = E 2 d (8.4) ρ 2 d = I M = EI ρ 1 ρ = M EI ρ EI
65 8. K 8 8 7 8 K 6 7 8 K 6 M Q σ (6.4) M O ρ dθ D N d N 1 P Q B C (1 + ε)d M N N h 2 h 1 ( ) B (+) M 8.1: σ = E ρ (E, 1/ρ ) (8.1) 66 σ σ (8.1) σ = 0 0 σd = 0 (8.2) (8.2) (8.1) E ρ d = 0... d = 0 (8.3)
More information64 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
More information9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x
2009 9 6 16 7 1 7.1 1 1 1 9 2 1 f(x, y) = xy sin x cos y x y cos y y x sin x d (x, y) = y cos y (x sin x) = y cos y(sin x + x cos x) x dx d (x, y) = x sin x (y cos y) = x sin x(cos y y sin y) y dy 1 sin
More informationmeiji_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
More informationsec13.dvi
13 13.1 O r F R = m d 2 r dt 2 m r m = F = m r M M d2 R dt 2 = m d 2 r dt 2 = F = F (13.1) F O L = r p = m r ṙ dl dt = m ṙ ṙ + m r r = r (m r ) = r F N. (13.2) N N = R F 13.2 O ˆn ω L O r u u = ω r 1 1:
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 information,. Black-Scholes u t t, x c u 0 t, x x u t t, x c u t, x x u t t, x + σ x u t, x + rx ut, x rux, t 0 x x,,.,. Step 3, 7,,, Step 6., Step 4,. Step 5,,.
9 α ν β Ξ ξ Γ γ o δ Π π ε ρ ζ Σ σ η τ Θ θ Υ υ ι Φ φ κ χ Λ λ Ψ ψ µ Ω ω Def, Prop, Th, Lem, Note, Remark, Ex,, Proof, R, N, Q, C [a, b {x R : a x b} : a, b {x R : a < x < b} : [a, b {x R : a x < b} : a,
More information(2-1) x, m, 2 N(m, 2 ) x REAL*8 FUNCTION NRMDST (X, M, V) X,M,V REAL*8 x, m, 2 X X N(0,1) f(x) standard-norm.txt normdist1.f x=0, 0.31, 0.5
2007/5/14 II II agata@k.u-tokyo.a.jp 0. 1. x i x i 1 x i x i x i x x+dx f(x)dx f(x) f(x) + 0 f ( x) dx = 1 (Probability Density Funtion 2 ) (normal distribution) 3 1 2 2 ( x m) / 2σ f ( x) = e 2πσ x m
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 informationarxiv: 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)
More informationTOP URL 1
TOP URL http://amonphys.web.fc2.com/ 1 6 3 6.1................................ 3 6.2.............................. 4 6.3................................ 5 6.4.......................... 6 6.5......................
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 information1 911 9001030 9:00 A B C D E F G H I J K L M 1A0900 1B0900 1C0900 1D0900 1E0900 1F0900 1G0900 1H0900 1I0900 1J0900 1K0900 1L0900 1M0900 9:15 1A0915 1B0915 1C0915 1D0915 1E0915 1F0915 1G0915 1H0915 1I0915
More informationMicrosoft Word - 資料 (テイラー級数と数値積分).docx
δx δx n x=0 sin x = x x3 3 + x5 5 x7 7 +... x ak = (-mod(k,2))**(k/2) / fact_k ( ) = a n δ x n f x 0 + δ x a n = f ( n) ( x 0 ) n f ( x) = sin x n=0 58 I = b a ( ) f x dx ΔS = f ( x)h I = f a h h I = h
More information1. 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
More informationi 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....................................
More information. (.8.). t + t m ü(t + t) + c u(t + t) + k u(t + t) = f(t + t) () m ü f. () c u k u t + t u Taylor t 3 u(t + t) = u(t) + t! u(t) + ( t)! = u(t) + t u(
3 8. (.8.)............................................................................................3.............................................4 Nermark β..........................................
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 information201711grade1ouyou.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
More informationTOP URL 1
TOP URL http://amonphys.web.fc.com/ 1 19 3 19.1................... 3 19.............................. 4 19.3............................... 6 19.4.............................. 8 19.5.............................
More informationgr09.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 {
More information9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L) du (L) = f (9.3) dx (9.) P
9 (Finite Element Method; FEM) 9. 9. P(0) P(x) u(x) (a) P(L) f P(0) P(x) (b) 9. P(L) 9. 05 L x P(x) P(0) P(x) u(x) u(x) (0 < = x < = L) P(x) E(x) A(x) P(L) f ( d EA du ) = 0 (9.) dx dx u(0) = 0 (9.2) E(L)A(L)
More information( ) ( )
20 21 2 8 1 2 2 3 21 3 22 3 23 4 24 5 25 5 26 6 27 8 28 ( ) 9 3 10 31 10 32 ( ) 12 4 13 41 0 13 42 14 43 0 15 44 17 5 18 6 18 1 1 2 2 1 2 1 0 2 0 3 0 4 0 2 2 21 t (x(t) y(t)) 2 x(t) y(t) γ(t) (x(t) y(t))
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 informationpositron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) 0.5 1.5MeV : thermalization 10 100 m psec 100psec nsec E total = 2mc 2 + E e + + E e Ee+ Ee-c mc
More information70 5. (isolated system) ( ) E N (closed system) N T (open system) (homogeneous) (heterogeneous) (phase) (phase boundary) (grain) (grain boundary) 5. 1
5 0 1 2 3 (Carnot) (Clausius) 2 5. 1 ( ) ( ) ( ) ( ) 5. 1. 1 (system) 1) 70 5. (isolated system) ( ) E N (closed system) N T (open system) (homogeneous) (heterogeneous) (phase) (phase boundary) (grain)
More informationgrad φ(p ) φ P grad φ(p ) p P p φ P p l t φ l t = 0 g (0) g (0) (31) grad φ(p ) p grad φ φ (P, φ(p )) xy (x, y) = (ξ(t), η(t)) ( )
2 9 2 5 2.2.3 grad φ(p ) φ P grad φ(p ) p P p φ P p l t φ l t = g () g () (3) grad φ(p ) p grad φ φ (P, φ(p )) y (, y) = (ξ(t), η(t)) ( ) ξ (t) (t) := η (t) grad f(ξ(t), η(t)) (t) g(t) := f(ξ(t), η(t))
More information基礎数学I
I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 1....................... 1............
More information2 A I / 58
2 A 2018.07.12 I 2 2018.07.12 1 / 58 I 2 2018.07.12 2 / 58 π-computer gnuplot 5/31 1 π-computer -X ssh π-computer gnuplot I 2 2018.07.12 3 / 58 gnuplot> gnuplot> plot sin(x) I 2 2018.07.12 4 / 58 cp -r
More information9 5 ( α+ ) = (α + ) α (log ) = α d = α C d = log + C C 5. () d = 4 d = C = C = 3 + C 3 () d = d = C = C = 3 + C 3 =
5 5. 5.. A II f() f() F () f() F () = f() C (F () + C) = F () = f() F () + C f() F () G() f() G () = F () 39 G() = F () + C C f() F () f() F () + C C f() f() d f() f() C f() f() F () = f() f() f() d =
More informationTrapezoidal Rule θ = 1/ x n x n 1 t = 1 [f(t n 1, x n 1 ) + f(t n, x n )] (6) 1. dx dt = f(t, x), x(t 0) = x 0 (7) t [t 0, t 1 ] f t [t 0, t 1 ], x x
University of Hyogo 8 8 1 d x(t) =f(t, x(t)), dt (1) x(t 0 ) =x 0 () t n = t 0 + n t x x n n x n x 0 x i i = 0,..., n 1 x n x(t) 1 1.1 1 1 1 0 θ 1 θ x n x n 1 t = θf(t n 1, x n 1 ) + (1 θ)f(t n, x n )
More information3/4/8:9 { } { } β β β α β α β β
α β : α β β α β α, [ ] [ ] V, [ ] α α β [ ] β 3/4/8:9 3/4/8:9 { } { } β β β α β α β β [] β [] β β β β α ( ( ( ( ( ( [ ] [ ] [ β ] [ α β β ] [ α ( β β ] [ α] [ ( β β ] [] α [ β β ] ( / α α [ β β ] [ ] 3
More informationuntitled
. 96. 99. ( 000 SIC SIC N88 SIC for Windows95 6 6 3 0 . amano No.008 6. 6.. z σ v σ v γ z (6. σ 0 (a (b 6. (b 0 0 0 6. σ σ v σ σ 0 / v σ v γ z σ σ 0 σ v 0γ z σ / σ ν /( ν, ν ( 0 0.5 0.0 0 v sinφ, φ 0 (6.
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 informationPart () () 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
More information1. ( ) 1.1 t + t [m]{ü(t + t)} + [c]{ u(t + t)} + [k]{u(t + t)} = {f(t + t)} (1) m ü f c u k u 1.2 Newmark β (1) (2) ( [m] + t ) 2 [c] + β( t)2
212 1 6 1. (212.8.14) 1 1.1............................................. 1 1.2 Newmark β....................... 1 1.3.................................... 2 1.4 (212.8.19)..................................
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 information2 1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a 2 + b 2 α (norm) N(α) = a 2 + b 2 = αα = α 2 α (spure) (trace) 1 1. a R aα =
1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a + b α (norm) N(α) = a + b = αα = α α (spure) (trace) 1 1. a R aα = aα. α = α 3. α + β = α + β 4. αβ = αβ 5. β 0 6. α = α ( ) α = α
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 information1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l
1 1 ϕ ϕ ϕ S F F = ϕ (1) S 1: F 1 1 (1) () (3) I 0 3 I I d θ = L () dt θ L L θ I d θ = L = κθ (3) dt κ T I T = π κ (4) T I κ κ κ L l a θ L r δr δl L θ ϕ ϕ = rθ (5) l : l r δr θ πrδr δf (1) (5) δf = ϕ πrδr
More information7 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
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 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 informationMicrosoft Word - 03-数値計算の基礎.docx
δx f x 0 + δ x n=0 a n = f ( n) ( x 0 ) n δx n f x x=0 sin x = x x3 3 + x5 5 x7 7 +... x ( ) = a n δ x n ( ) = sin x ak = (-mod(k,2))**(k/2) / fact_k 10 11 I = f x dx a ΔS = f ( x)h I = f a h I = h b (
More information第10章 アイソパラメトリック要素
June 5, 2019 1 / 26 10.1 ( ) 2 / 26 10.2 8 2 3 4 3 4 6 10.1 4 2 3 4 3 (a) 4 (b) 2 3 (c) 2 4 10.1: 3 / 26 8.3 3 5.1 4 10.4 Gauss 10.1 Ω i 2 3 4 Ξ 3 4 6 Ξ ( ) Ξ 5.1 Gauss ˆx : Ξ Ω i ˆx h u 4 / 26 10.2.1
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 information( ) 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 ( - )
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 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 information1. A0 A B A0 A : A1,...,A5 B : B1,...,B
1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A B f : A B 4 (i) f (ii) f (iii) C 2 g, h: C A f g = f h g = h (iv) C 2 g, h: B C g f = h f g = h 4 (1) (i) (iii) (2) (iii) (i) (3) (ii) (iv) (4)
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 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(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
More information1
1 2 3 4 5 6 7 8 9 10 A I A I d d d+a 11 12 57 c 1 NIHONN 2 i 3 c 13 14 < 15 16 < 17 18 NS-TB2N NS-TBR1D 19 -21BR -70-21 -70-22 20 21 22 23 24 d+ a 25 26 w qa e a a 27 28 -21 29 w w q q q w 30 r w q!5 y
More informationTOP URL 1
TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7
More informationuntitled
1 4 4 6 8 10 30 13 14 16 16 17 18 19 19 96 21 23 24 3 27 27 4 27 128 24 4 1 50 by ( 30 30 200 30 30 24 4 TOP 10 2012 8 22 3 1 7 1,000 100 30 26 3 140 21 60 98 88,000 96 3 5 29 300 21 21 11 21
More informationB1 Ver ( ), SPICE.,,,,. * : student : jikken. [ ] ( TarouOsaka). (, ) 1 SPICE ( SPICE. *1 OrCAD
B1 er. 3.05 (2019.03.27), SPICE.,,,,. * 1 1. 1. 1 1.. 2. : student : jikken. [ ] ( TarouOsaka). (, ) 1 SPICE ( SPICE. *1 OrCAD https://www.orcad.com/jp/resources/orcad-downloads.. 1 2. SPICE 1. SPICE Windows
More informationf(x) = f(x ) + α(x)(x x ) α(x) x = x. x = f (y), x = f (y ) y = f f (y) = f f (y ) + α(f (y))(f (y) f (y )) f (y) = f (y ) + α(f (y)) (y y ) ( (2) ) f
22 A 3,4 No.3 () (2) (3) (4), (5) (6) (7) (8) () n x = (x,, x n ), = (,, n ), x = ( (x i i ) 2 ) /2 f(x) R n f(x) = f() + i α i (x ) i + o( x ) α,, α n g(x) = o( x )) lim x g(x) x = y = f() + i α i(x )
More information(iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y = 0., y x, y = x. (v) 1x = x. (vii) (α + β)x = αx + βx. (viii) (αβ)x = α(βx)., V, C.,,., (1)
1. 1.1...,. 1.1.1 V, V x, y, x y x + y x + y V,, V x α, αx αx V,, (i) (viii) : x, y, z V, α, β C, (i) x + y = y + x. (ii) (x + y) + z = x + (y + z). 1 (iii) 0 V, x V, x + 0 = x. 0. (iv) x V, y V, x + y
More informationEvolutes and involutes of fronts Masatomo Takahashi Muroran Institute of Technology
Evolutes and involutes of fronts Masatomo Takahashi Muroran Institute of Technology evolute involute, evolvent involute : involvo evolvent : evolvo 6 4 6 4 4 6 4 6 H 3 γ : I R C γ(t) 0, t(t) := γ(t) γ(t),
More information17 1 25 http://grape.astron.s.u-tokyo.ac.jp/pub/people/makino/kougi/stellar_dynamics/index.html http://grape.astron.s.u-tokyo.ac.jp/pub/people/makino/talks/index-j.html d 2 x i dt 2 = j i Gm j x j x i
More information128 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
More informationtokei01.dvi
2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN
More informationZ: Q: R: C: sin 6 5 ζ a, b
Z: Q: R: C: 3 3 7 4 sin 6 5 ζ 9 6 6............................... 6............................... 6.3......................... 4 7 6 8 8 9 3 33 a, b a bc c b a a b 5 3 5 3 5 5 3 a a a a p > p p p, 3,
More information.. ( )T p T = p p = T () T x T N P (X < x T ) N = ( T ) N (2) ) N ( P (X x T ) N = T (3) T N P T N P 0
20 5 8..................................................2.....................................3 L.....................................4................................. 2 2. 3 2. (N ).........................................
More informationy = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f() + f() + f(3) + f(4) () *4
Simpson H4 BioS. Simpson 3 3 0 x. β α (β α)3 (x α)(x β)dx = () * * x * * ɛ δ y = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f()
More informationI A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google
I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59
More information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
More information2 1 κ c(t) = (x(t), y(t)) ( ) det(c (t), c x (t)) = det (t) x (t) y (t) y = x (t)y (t) x (t)y (t), (t) c (t) = (x (t)) 2 + (y (t)) 2. c (t) =
1 1 1.1 I R 1.1.1 c : I R 2 (i) c C (ii) t I c (t) (0, 0) c (t) c(i) c c(t) 1.1.2 (1) (2) (3) (1) r > 0 c : R R 2 : t (r cos t, r sin t) (2) C f : I R c : I R 2 : t (t, f(t)) (3) y = x c : R R 2 : t (t,
More information2 I I / 61
2 I 2017.07.13 I 2 2017.07.13 1 / 61 I 2 2017.07.13 2 / 61 I 2 2017.07.13 3 / 61 7/13 2 7/20 I 7/27 II I 2 2017.07.13 4 / 61 π-computer gnuplot MobaXterm Wiki PC X11 DISPLAY I 2 2017.07.13 5 / 61 Mac 1.
More information第1章 微分方程式と近似解法
April 12, 2018 1 / 52 1.1 ( ) 2 / 52 1.2 1.1 1.1: 3 / 52 1.3 Poisson Poisson Poisson 1 d {2, 3} 4 / 52 1 1.3.1 1 u,b b(t,x) u(t,x) x=0 1.1: 1 a x=l 1.1 1 (0, t T ) (0, l) 1 a b : (0, t T ) (0, l) R, u
More informationnosenote3.dvi
i 1 1 2 5 3 Verlet 9 4 18 5 23 6 26 1 1 1 MD t N r 1 (t), r 2 (t),, r N (t) ṙ 1 (t), ṙ 2 (t),, ṙ N (t) MD a 1, a 2, a 3 r i (i =1,,n) 1 2 T =0K r i + m 1 a 1 + m 2 a 2 + m 3 a 3 (m 1,m 2,m 3 =0, ±1, ±2,,
More information