流体とブラックホールの間に見られる類似性・双対性
|
|
- のぶのすけ ひのと
- 5 years ago
- Views:
Transcription
1 (MIYAMOTO, Umpei) Department of Physics, Rikkyo University 1 : ( $)$ 1 [ 1: ( $BH$ )
2 $(r, \theta, \phi)$ $t$ 4 $(x^{a})_{a=0,1,2,3}:=$ $c$ $(ct, r, \theta, \phi)$ $x^{a}$ $x^{a}+dx^{a}$ $ds^{2}= \sum_{a,b=0}^{3}g_{ab}dx^{a}dx^{b}$ (1) $g_{ab}$ ( $\Sigma$ ) $G_{ab}+ \Lambda g_{ab}=\frac{8\pi G}{c^{4}}T_{ab}$ (2) $G_{ab}$ $A$ 2 $G$ $T_{ab}$ (2) (2) ( ) $T_{ab}=(\rho+P)u_{a}u_{b}+Pg_{ab}$ (3) $(u_{a}, \rho, P)$ $(T_{ab}=\Lambda=0)$ 4 ( ) 2.2 (2) $T_{ab}=\Lambda=0$ ( ) $d s^{2}=-f(r)c^{2}dt^{2}+\frac{dr^{2}}{f(r)}+r^{2}d\omega_{2}^{2}, f(r)=1-\frac{r_{0}}{r}$ (4) $d\omega_{2}^{2}:=d\theta^{2}+\sin^{2}\theta d\phi^{2}$ $M$ 2 $r_{0}$ $r_{0}= \frac{2gm}{c^{2}}$ (5)
3 $\kappa$ 58 $r_{0}=0$ $f(r)\equiv 1$ $(r,\theta, \phi)$ 3 $r_{0}>0$ $r<r_{0}$ $r=0$ ( $)$ $r=r_{0}$ $M$ $r$ $m$ $v$ ( $)$ $\frac{1}{2}mv^{2}-g\frac{mm}{r}=0$ (6) $v=v_{esc}:=\sqrt{\frac{2gm}{r}}$ (7) ( ) (7) $v_{e8c}arrow c$ $rarrow r_{0}=2gm/c^{2}$ $r$ $r_{0}$ $M$ $r_{0}$ $A=4\pi r_{0}^{2}$ $A$ $A+\delta A(\delta A\geq 0)$ $\delta(mc^{2})$ $\delta(mc^{2})=\frac{c^{2}}{8\pi G}\kappa\delta A$ (8) 2 $\kappa$ ( $\kappa=c^{2}/2r_{0}$ ) $Mc^{2}$ $U$ $T$ $A$ $S$ (8) $\delta U=T\delta S$ $i$ $r_{0}$ $\delta J$ 2 $J$ $Q$ (8) $\delta Q$
4 59 ( ) $T= \frac{\hslash}{2\pi ck_{b}}\kappa$ (9) ( ) $k_{b}$ 3 (8) ( ) $S= \frac{c^{3}k_{b}}{4g\hslash}a=\frac{k_{b}}{4\ell_{p}^{2}}a$ (10) $\ell_{p}:=\sqrt{g\hslash}/c^{3}$ $(\sim 10^{-33} cm)$ (10) 4 $(c, G, \hslash, k_{b})$ ( $e^{i\pi}=-1$ ) [ (4) $f(r) arrow 1-(\frac{r_{0}}{r})^{n},$ $d\omega_{2}^{2}arrow d\omega_{n+1}^{2},$ $n=1,2,3,$ $\ldots$ (11) 4 $r_{0}$ $(n+1)$ $S^{n+1}$ 5 $+dz^{2}$ $z$ $(n+4)$ $r_{0}$ $(n+1)$ $S^{n+1}$ $z$ ( $2[a]$ ) 3 $c=g=\hslash=k_{b}=1$ $c=g=\hslash=k_{b}=1$ 4 (2)
5 60 2: $[(a)arrow(b)arrow(c)arrow(d)$ $z$ $(r\cdot=0)$ $S^{n+1}$ $]$ $z=$ $(n+1)$ 3.2 (2) (Gregory-Laflamme) [1] $\delta g_{ab}\propto\exp(-i\omega t+ikz)$ (12) $\omega^{2}<0$ ( $\omega$ ) ( 3) $\lambda:=2\pi/k$ $L$ $L>\lambda_{c^{\backslash },}:=2\pi/k_{ }\sim r_{0}/\sqrt{n}$ $k(0<k<k_{c}\sim\sqrt{n}/r_{0})$ $L$ $(r_{0}\gg$ $r_{0}$ $L)$ $r_{0}\lessapprox L$ $r_{0}$ ( ) 5 6 $n\geq n_{c}:=10$ $[3]$ [5] (5 ) $[$ $2(c)]$ $[$ $2(d)]$ $[$ $2(b)]$ $r\cdot(t)\propto(t_{0}-t)$ ( $t_{0}$ ) 5 $-\cdot$ 6 [2]
6 61 3: $\delta g_{ab}\propto\exp(-i\omega t+ikz)$ $\omega(k)$ $0<k<k_{c}\sim\sqrt{n}/r_{0}$ $(-i\omega>0)$ 7 [ ( ) ( ) ( ) $[6]_{0}$ ( 2 ) $(n>n_{c})\sim$ [7] $P$ $v^{i}(i=$ $\rho$ $1,2,$ $\ldots,p)$ $\partial_{t}\rho+\partial_{i}(\rho v^{i})=0,$ $\partial_{t} (\rho v^{i})+\partial_{j}\pi^{ij}=0$ (13) 7 [1] ( )
7 $\nu$ $\zeta$ 62 ( ) $\Pi_{ij}=\Pi_{ij}^{(0)}+\Pi_{ij}^{(1)}$ $\Pi_{ij}^{(0)}=pv_{i}v_{j}+P\delta_{ij}$ $\Pi_{ij}^{(1)}=-\eta(\partial_{i}v_{j}+\partial_{j}v_{\dot{t}}-\frac{2}{p}\delta_{ij}\partial_{k}v^{k})-\zeta\delta_{ij}\partial_{k}v^{k}$ (14) $\eta$ $\eta$ $\Pi_{ij}^{(0)}$ $\Pi_{1j}^{(.1)}$ $x\vdash-$ (13) ( ) $T_{\mu\nu}$ $\partial_{\mu}t^{\mu\nu}=0, x^{l^{\iota}};=(ct, z^{i})$ (15) ) $\eta,$ (13) ( $P$ $\rho$ $\Pi_{ij}^{(0)}+\Pi_{ij}^{(1)}$ $\Pi_{ij}^{(m)}$ $\Pi_{ij}^{(m\geq 2)}$ $m$ $\partial_{\mu}t^{\mu\nu}=0, T^{\mu\nu}=\sum_{m=0}^{\infty}\epsilon^{m}T_{(m)}^{\mu\nu}$ (16) $\epsilon$ ; $T_{(m>1)}^{\mu\nu}$ $\epsilon(<1)$ $O(\epsilon)$ $T_{(0)}^{\mu\nu}=\rho u^{\mu}u^{\nu}+pp^{\mu\nu}$ (17) $T_{(1)}^{\mu\nu}=-2_{\mathcal{C}7 }\sigma^{\mu\nu}-c\zeta P^{\mu\nu}\partial_{\alpha}u^{\alpha}$ $T^{\mu\nu}$ $(0)$ (3) $P^{\mu\nu}:=u^{\mu}u^{\nu}+\eta^{\mu\nu}$ $\eta^{\mu\nu}=$ diag $(-1,1, \ldots, 1)$ 1 ) $\mu$ ( $\sigma^{\mu\nu}:=(1/2)p^{\mu a}p^{\nu\beta}[\partial_{\alpha}u_{\beta}+\partial_{\beta}u_{\alpha}-(2/p)p_{\alpha\beta}\partial_{\gamma}u^{\gamma}]$ 4.2 $\delta\rho\propto\exp(-i\omega t+ikz)$
8 $c_{s}^{2}$ 63 (13) ( ) $\omega^{2_{=c_{s}^{2}k^{2}}^{j}}, c_{s}^{2};=\frac{dp}{d\rho}$ (18) $P=P(\rho)$ $c_{\hslash}^{2}<0$ ( ) 5 [lo] 5.1 : $z$ $p(\geq 1)$ $(n+3)$ $+ \sum_{i=1}^{p}(dz^{i})^{2}$ $p$ $S^{n+1}$ $x^{a}:=(x^{\mu}, r);=(ct, z^{i},r)$ (19) $z^{i}$ $p$ ( ) $(p+1)$ $(u^{\mu}u_{\mu}=-1)$ $(r_{0}, u^{/1})$ $r_{0}$ $T= \frac{n\hslash c}{4\pi k_{b}r_{0}}$ (20) $p$ $p$ $z^{2}\underline{\nearrow\sim}\prime z^{1}$ 4: 2
9 64 $\delta g_{ab}$ (2) (16) $z^{i}$ $p$ $p(\geq 2)$ $p=1$ 2 4 $p$ $r_{0}$ $u^{\mu}$ $T(r_{0})$ $(r_{0}, u^{\mu})arrow(r_{0}(x^{\nu}), u^{\mu}(x^{\nu}))$ (21) $x^{\nu}=(t, z^{i})$ 4 ( $)$ $T$ $u^{\mu}$ ( $r_{0}$ ) (2) $g_{ab}^{(0)}$ $p$ (2) $g_{ab}^{(0)}+\delta g_{ab}$ $\delta g_{ab}$ $X;=(r_{0}(x^{\nu}), u^{\mu}(x^{\nu}), \delta g_{ab}(x^{a}))$ (22) $X^{\int\iota}$ $\lambda:= \frac{x}{\partial_{\mu}x} $ (23) $(\lambda\gg r_{0})$ ( 2(b) ) $r_{0}$ $r_{0}/\lambda$ $X= \sum_{m=0}^{\infty}\epsilon^{m}x_{(m)}, \epsilon:=\frac{r_{0}}{\lambda}\ll 1$ (24) (2) $\sum_{n=1}^{\infty}\epsilon^{m}g_{(m)}^{ab}=0$ (25) $m=1$ $r_{0}\partial_{\mu}\ln X=O(\epsilon)$ (2) $\partial_{\mu}arrow\epsilon\partial_{\mu}$ (2) (25) (derivative expansion) $r$ Kd ( $V$ $)$ [11]
10 $\rho$ 65 $G_{(m\geq 1)}^{ab}=0$ $(x^{\mu}, r)$ $r$ $(r=r_{0})$ $(r=\infty)$ $x^{\mu}$ (24) $J\triangleright$ $\epsilon=r_{0}/\lambda$ $\epsilon$ (16) ( ) ( ) (16) (17) $\partial_{\mu}t_{(,n-1)}^{\mu\nu}=0$ $(n+3+p)$ 1 $\epsilon G_{(1)}^{ab}=0$ $P=- \frac{\rho}{n+1}=-\frac{\omega_{n+1}c^{4}}{16\pi G}r_{0}^{n}$ (26) $P$ $(p+1)$ $\partial_{\mu}t_{(0)}^{\mu\nu}=0$ $\Omega_{n+1}$ $(n+1)$ 2 $\epsilon G_{(J)}^{ab}+\epsilon^{2}G_{(2)}^{ob}=0$ $\eta=\frac{\omega_{n+1}c^{3}}{16\pi G}r_{0}^{n+1},$ $\zeta=\frac{\omega_{n+1^{c^{3}}}}{8\pi G}r_{0}^{n+1}(\frac{1}{p}+\frac{1}{n+1})$ (27) 8 $\vdash-$ $\partial_{\mu}(t_{(0)}^{l^{\iota\nu}}+\epsilon T_{(1)}^{\mu.\nu})=0$ 4 (2) (16) (26) (27) $r_{0}$ (16) $T_{(m\geq 2)}^{\mu\nu}$ $G_{(m\geq 3)}^{ab}$ $=$ 0 ( $)$ 5.2 (26) $c_{s}^{2};= \frac{dp}{d\rho}=-\frac{1}{n+1}<0$ (28) $p$ $p$ [10]. (27) 3 $\epsilon\sim \partial_{z}r_{0} \ll 1$ $r_{0}$ $ u^{\mu} $ 8 $(r_{0} (t, z), u^{z}(t, z))$ $(p=1)\iota_{\llcorner}^{\sim}$ (2)
11 66 ( ) [5] ( ) ro $\propto(t_{0}-t)$ 2 $n_{c}$ $\partial_{\mu}t_{(m\geq 2)}^{\mu\nu}=0$ $(r_{0}arrow 0)$ 6 $(T_{ab}=\Lambda=0)$ (2) $(A <0)$ $AdS/$CFT(ailti-de Sitter/conformal field theory) [12] ( ) $[13]_{0}$ ( ) [14] $r(t)\propto(t_{0}-t)$ $[$15, $16]$ ($AdS/$CFT $(AdS/$CFT $l$ $)$ ) $AdS/$CFT [17,18] 5
12 $\eta$ 67 5: 5 RHIC (Relativistic Heavy Ion Collider) LHC (Large Hadron Collider) ( ) 5 ( ) RHIC $\eta$ ( ) $\frac{\eta}{s}=\frac{\hslash}{4\pi k_{b}}$ (29) [19] (29) 5 $p$ $p$ (10) $s= \frac{\omega_{n+1}c^{3}k_{b}}{4g\hslash}r_{0}^{n+1}$ (30) $\mathcal{s}$ (27) $r_{0}$ ( (29) [1] R. Gregory and R. Laflamme: Black strings and $p$-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837, [arxiv:hep-th/ ]. [2] G. T. Horowitz and K. Maeda: Fate of the black string instability, Phys. Rev. Lett. 87 (2001) , [arxiv:hep-th/ ]. [3] E. Sorkin: $A$ critical dimension in the black-string pha.se transition, Phys. Rev. Lett. 93 (2004) , [arxiv:hep-th/ ].
13 68 [4] H. Kudoh and U. Miyamoto: On non-uniform smeared black branes, Class. Quant. Grav. 22 (2005) 3853, [arxiv:hep-th/ ]. [5] L. Lehner and F. Pretorius: Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship, Phys. Rev. Lett. 105 (2010) , $[arxiv: $ [hep-th] $].$ [6] V. Cardoso and O. J. C. Dias: Gregory-Laflamme and Rayleigh-Plateau instabilities, Phys. Rev. Lett. 96 (2006) [arxiv:hep-th/ ]. $i$ [7] U. Miyamoto and $K.$. Maeda: Liquid bridges and black strings in higher dimensions, Phys. Lett. $B664$ (2008) 103, $[arxiv: $ [hep-th] $].$ [8] M. M. Caldarelli, O. J. C. Dias, R. Emparan and D. Klemm, Black holes as lumps of fluid, JHEP 0904, 024 (2009), $[arxiv: $ [hep-th] $].$ [9] U. Miyamoto: Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme, Phys. Rev. $D78$ (2008) , $[arxiv: $ [hep-th] $].$ [10] J. Camps, R. Emparan and N. Haddad, Black Brane Viscosity and the Gregory- Laflammc $I_{Ilstab;]ity},$ JHEP 1005 (2010) 042, $[arxiv: $ [hep-th] $].$ [11] 1995 [12] S. Bhattacharyya, V. E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 0802 (2008) 045, $[arxiv: $ [hep-th] $].$ [13] O. Aharony, S. Minwalla and T. Wiseman: Plasma-balls in large $N$ gauge theories and localized black holes, Class. Quant. Grav. 23 (2006) 2171, [arxiv:hep-th/ ]. $i$ [14] $K.$. Maeda and U. Miyamoto: Black hole-black string phase transitions from hydrodynamics, JHEP 0903 (2009) 066, $[arxiv: $ [hep-th] $].$ [15] J. Eggers, Nonlinear dynamics and breakup of free-surface flows, Rev. Mod. Phys. 69, 865 (1997). [16] U. Miyamoto: One-Dimensional Approximation of Viscous Flows, JHEP 1010 (2010) 011, $[arxiv: $ [hep-th] $].$ [17] $AdS/CFT$ 54-3(2010)110 [18] $94-3(2010)350$ [19] P. Kovtun, D. T. Son and A. O. Starinets, Viscosity in strongly interacting quantum field theories from black hole $p1_{1}$ysics, Phys. Rev. Lett. 94, (2005) [hep- $th/ ].$
流体としてのブラックホール : 重力物理と流体力学の接点
1890 2014 136-148 136 : Umpei Miyamoto Research and Education Center for Comprehensive Science, Akita Prefectural University E mail: umpei@akita-pu.ac.jp 1970 ( ) 1 $(E=mc^{2})$, ( ) ( etc) ( ) 137 ( (duality)
More information1 1 (November 15, 2018) 1975 ** ** ( ** ) 015-**** ***** () * * * **** 090-****-****
Contents Contents 1 2 2 5 2.1........................................... 5 2.2......................................... 5 2.3................................. 5 2.4....................................
More informationssastro2016_shiromizu
26 th July 2016 / 1991(M1)-1995(D3), 2005( ) 26 th July 2016 / 1. 2. 3. 4. . ( ) 1960-70 1963 Kerr 1965 BH Penrose 1967 Hawking BH Israel 1971 (Carter)-75(Robinson) BH 1972 BH theorem(,, ) Hawk 1975 Hawking
More informationD-brane K 1, 2 ( ) 1 K D-brane K K D-brane Witten [1] D-brane K K K K D-brane D-brane K RR BPS D-brane
D-brane K 1, 2 E-mail: sugimoto@yukawa.kyoto-u.ac.jp (2004 12 16 ) 1 K D-brane K K D-brane Witten [1] D-brane K K K K D-brane D-brane K RR BPS D-brane D-brane RR D-brane K D-brane K D-brane K K [2, 3]
More information467 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 )
More information24.15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
More information橡超弦理論はブラックホールの謎を解けるか?
1999 3 (Can String Theory Solve the Puzzles of Black Holes?) 305-0801 1-1 makoto.natsuume@kek.jp D-brane 1 Schwarzschild 60 80 2 [1] 1 1 1 2 2 [2] 25 2.2 2 2.1 [7,8] Schwarzschild 2GM/c 2 Schwarzschild
More information基礎から学ぶトラヒック理論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
基礎から学ぶトラヒック理論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/085221 このサンプルページの内容は, 初版 1 刷発行時のものです. i +α 3 1 2 4 5 1 2 ii 3 4 5 6 7 8 9 9.3 2014 6 iii 1 1 2 5 2.1 5 2.2 7
More information第86回日本感染症学会総会学術集会後抄録(II)
χ μ μ μ μ β β μ μ μ μ β μ μ μ β β β α β β β λ Ι β μ μ β Δ Δ Δ Δ Δ μ μ α φ φ φ α γ φ φ γ φ φ γ γδ φ γδ γ φ φ φ φ φ φ φ φ φ φ φ φ φ α γ γ γ α α α α α γ γ γ γ γ γ γ α γ α γ γ μ μ κ κ α α α β α
More information(Tokyo Institute of Technology) Seminar at Ehime University ( ) 9 3 U(N C ), N F /2 BPS ( ) 12 5 (
(Tokyo Institute of Technology) Seminar at Ehime University 2007.08.091 1 2 1.1..................... 2 2 ( ) 9 3 U(N C ), N F 11 4 1/2 BPS ( ) 12 5 ( ) 19 6 Conclusion 23 1 1.1 GeV SU(3) SU(2) U(1): W
More information( ) : (Technocolor)...
( ) 2007.5.14 1 3 1.1............................. 3 1.2 :........... 5 1.3........................ 7 1.4................. 8 2 11 2.1 (Technocolor)................ 11 2.2............................. 12
More information(Osamu Ogurisu) V. V. Semenov [1] :2 $\mu$ 1/2 ; $N-1$ $N$ $\mu$ $Q$ $ \mu Q $ ( $2(N-1)$ Corollary $3.5_{\text{ }}$ Remark 3
Title 異常磁気能率を伴うディラック方程式 ( 量子情報理論と開放系 ) Author(s) 小栗栖, 修 Citation 数理解析研究所講究録 (1997), 982: 41-51 Issue Date 1997-03 URL http://hdl.handle.net/2433/60922 Right Type Departmental Bulletin Paper Textversion
More information高密度荷電粒子ビームの自己組織化と安定性
1885 2014 1-11 1 1 Hiromi Okamoto Graduate School of Advanced Sciences ofmatter, Hiroshima University ( ( ) $)$ ( ) ( ) [1],, $*1$ 2 ( $m,$ q) $*1$ ; $\kappa_{x}$ $\kappa_{y}$ 2 $H_{t}=c\sqrt{(p-qA)^{2}+m^{2}c^{2}}+q\Phi$
More informationhirameki_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...............................
More information多孔質弾性体と流体の連成解析 (非線形現象の数理解析と実験解析)
1748 2011 48-57 48 (Hiroshi Iwasaki) Faculty of Mathematics and Physics Kanazawa University quasi-static Biot 1 : ( ) (coup iniury) (contrecoup injury) 49 [9]. 2 2.1 Navier-Stokes $\rho(\frac{\partial
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 informationMD $\text{ }$ (Satoshi Yukawa)* (Nobuyasu Ito) Department of Applied Physics, School of Engineering, The University of Tokyo Lennar
1413 2005 36-44 36 MD $\text{ }$ (Satoshi Yukawa)* (Nobuyasu Ito) Department of Applied Physics, School of Engineering, The University of Tokyo Lennard-Jones [2] % 1 ( ) *yukawa@ap.t.u-tokyo.ac.jp ( )
More information一般相対性理論に関するリーマン計量の変形について
1896 2014 137-149 137 ( ) 1 $(N^{4}, g)$ $N$ 4 $g$ $(3, 1)$ $R_{ab}- \frac{1}{2}rg_{ab}=t_{ab}$ (1) $R_{ab}$ $g$ $R$ $g$ ( ) $T_{ab}$ $T$ $R_{ab}- \frac{1}{2}rg_{ab}=0$ 4 $R_{ab}=0$ $\mathbb{r}^{3,1}$
More information7 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..............................
More information“‡”�„³…u…›…b…N…z†[…‰
2009 8 31 / 4 : : Outline 4 G MN T t g x mu... g µν = G MN X M x µ X N x ν X G MN c.f., : X 5, X 6,... g µν : : g µν, A µ : R µν 1 2 Rg µν = 8πGT µν : G MN : R MN 1 2 RG MN = 0 ( ) Kaluza-Klein G MN =
More information日本糖尿病学会誌第58巻第1号
α β β β β β β α α β α β α l l α l μ l β l α β β Wfs1 β β l l l l μ l l μ μ l μ l Δ l μ μ l μ l l ll l l l l l l l l μ l l l l μ μ l l l l μ l l l l l l l l l l μ l l l μ l μ l l l l l l l l l μ l l l l
More information1.3 (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
More informationuntitled
Global Quantitative Research / -2- -3- -4- -5- 35 35 SPC SPC REIT REIT -6- -7- -8- -9- -10- -11- -12- -13- -14- -15- -16- -17- 100m$110-18- Global Quantitative Research -19- -20- -21- -22- -23- -24- -25-
More information(Nobumasa SUGIMOTO) (Masatomi YOSHIDA) Graduate School of Engineering Science, Osaka University 1., [1].,., 30 (Rott),.,,,. [2].
1483 2006 112-121 112 (Nobumasa SUGIMOTO) (Masatomi YOSHIDA) Graduate School of Engineering Science Osaka University 1 [1] 30 (Rott) [2] $-1/2$ [3] [4] -\mbox{\boldmath $\pi$}/4 - \mbox{\boldmath $\pi$}/2
More information合併後の交付税について
(1) (2) 1 0.9 0.7 0.5 0.3 0.1 2 3 (1) (a), 4 (b) (a), (c) (a) 0.9 0.7 0.5 0.3 0.1 (b) (d),(e) (f) (g) (h) (a) (i) (g) (h) (j) (i) 5 (2) 6 (3) (A) (B) (A)+(B) n 1,000 1,000 2,000 n+1 970 970 1,940 3.0%
More informationHierarchical model and triviality of $\phi_{4}^{4}$ abstract (Takashi Hara) (Tetsuya Hattori) $\mathrm{w}\mathrm{a}\mathrm{t}\mat
1134 2000 70-80 70 Hierarchical model and triviality of $\phi_{4}^{4}$ abstract (Takashi Hara) (Tetsuya Hattori) $\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{b}\mathrm{e}$ (Hiroshi
More informationSUSY DWs
@ 2013 1 25 Supersymmetric Domain Walls Eric A. Bergshoeff, Axel Kleinschmidt, and Fabio Riccioni Phys. Rev. D86 (2012) 085043 (arxiv:1206.5697) ( ) Contents 1 2 SUSY Domain Walls Wess-Zumino Embedding
More information$\mathrm{c}_{j}$ $u$ $u$ 1: (a) (b) (c) $y$ ($y=0$ ) (a) (c) $i$ (soft-sphere) ( $m$:(mj) $\sigma$:(\sigma j) $i$ $(r_{1j}.$ $j$ $r_{i}$ $r_{j}$ $=r:-
1413 2005 60-69 60 (Namiko Mitarai) Frontier Research System, RIKEN (Hiizu Nakanishi) Department of Physics, Faculty of Science, Kyushu University 1 : [1] $[2, 3]$ 1 $[3, 4]$.$\text{ }$ [5] 2 (collisional
More information(Hiroshi Okamoto) (Jiro Mizushima) (Hiroshi Yamaguchi) 1,.,,,,.,,.,.,,,.. $-$,,. -i.,,..,, Fearn, Mullin&Cliffe (1990),,.,,.,, $E
949 1996 128-138 128 (Hiroshi Okamoto) (Jiro Mizushima) (Hiroshi Yamaguchi) 1 $-$ -i Fearn Mullin&Cliffe (1990) $E=3$ $Re_{C}=4045\pm 015\%$ ( $Re=U_{\max}h/2\nu$ $U_{\max}$ $h$ ) $-t$ Ghaddar Korczak&Mikic
More information$\hat{\grave{\grave{\lambda}}}$ $\grave{\neg}\backslash \backslash ^{}4$ $\approx \mathrm{t}\triangleleft\wedge$ $10^{4}$ $10^{\backslash }$ $4^{\math
$\mathrm{r}\mathrm{m}\mathrm{s}$ 1226 2001 76-85 76 1 (Mamoru Tanahashi) (Shiki Iwase) (Toru Ymagawa) (Toshio Miyauchi) Department of Mechanical and Aerospaoe Engineering Tokyo Institute of Technology
More information「諸雑公文書」整理の中間報告
30 10 3 from to 10 from to ( ) ( ) 20 20 20 20 20 35 8 39 11 41 10 41 9 41 7 43 13 41 11 42 7 42 11 41 7 42 10 4 4 8 4 30 10 ( ) ( ) 17 23 5 11 5 8 8 11 11 13 14 15 16 17 121 767 1,225 2.9 18.7 29.8 3.9
More information112 Landau Table 1 Poiseuille Rayleigh-Benard Rayleigh-Benard Figure 1; 3 19 Poiseuille $R_{c}^{-1}-R^{-1}$ $ z ^{2}$ 3 $\epsilon^{2}=r_{\mathrm{c}}^{
1454 2005 111-124 111 Rayleigh-Benard (Kaoru Fujimura) Department of Appiied Mathematics and Physics Tottori University 1 Euclid Rayleigh-B\ enard Marangoni 6 4 6 4 ( ) 3 Boussinesq 1 Rayleigh-Benard Boussinesq
More informationKaluza-Klein(KK) SO(11) KK 1 2 1
Maskawa Institute, Kyoto Sangyo University Naoki Yamatsu 2016 4 12 ( ) @ Kaluza-Klein(KK) SO(11) KK 1 2 1 1. 2. 3. 4. 2 1. 標準理論 物質場 ( フェルミオン ) スカラー ゲージ場 クォーク ヒッグス u d s b ν c レプトン ν t ν e μ τ e μ τ e h
More informationPart. 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.
More information0.,,., 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 ).
More information確率論と統計学の資料
5 June 015 ii........................ 1 1 1.1...................... 1 1........................... 3 1.3... 4 6.1........................... 6................... 7 ii ii.3.................. 8.4..........................
More informationChern-Simons Jones 3 Chern-Simons 1 - Chern-Simons - Jones J(K; q) [1] Jones q 1 J (K + ; q) qj (K ; q) = (q 1/2 q
Chern-Simons E-mail: fuji@th.phys.nagoya-u.ac.jp Jones 3 Chern-Simons - Chern-Simons - Jones J(K; q) []Jones q J (K + ; q) qj (K ; q) = (q /2 q /2 )J (K 0 ; q), () J( ; q) =. (2) K Figure : K +, K, K 0
More informationMicrosoft Word - Wordで楽に数式を作る.docx
Ver. 3.1 2015/1/11 門 馬 英 一 郎 Word 1 する必要がある Alt+=の後に Ctrl+i とセットで覚えておく 1.4. 変換が出来ない場合 ごく稀に以下で説明する変換機能が無効になる場合がある その際は Word を再起動するとまた使えるようになる 1.5. 独立数式と文中数式 数式のスタイルは独立数式 文中数式(2 次元)と文中数式(線形)の 3 種類があ り 数式モードの右端の矢印を選ぶとメニューが出てくる
More information20 $P_{S}=v_{0}\tau_{0}/r_{0}$ (3) $v_{0}$ $r_{0}$ $l(r)$ $l(r)=p_{s}r$ $[3 $ $1+P_{s}$ $P_{s}\ll 1$ $P_{s}\gg 1$ ( ) $P_{s}$ ( ) 2 (2) (2) $t=0$ $P(t
1601 2008 19-27 19 (Kentaro Kanatani) (Takeshi Ogasawara) (Sadayoshi Toh) Graduate School of Science, Kyoto University 1 ( ) $2 $ [1, ( ) 2 2 [3, 4] 1 $dt$ $dp$ $dp= \frac{dt}{\tau(r)}=(\frac{r_{0}}{r})^{\beta}\frac{dt}{\tau_{0}}$
More information110 $\ovalbox{\tt\small REJECT}^{\mathrm{i}}1W^{\mathrm{p}}\mathrm{n}$ 2 DDS 2 $(\mathrm{i}\mathrm{y}\mu \mathrm{i})$ $(\mathrm{m}\mathrm{i})$ 2
1539 2007 109-119 109 DDS (Drug Deltvery System) (Osamu Sano) $\mathrm{r}^{\mathrm{a}_{w^{1}}}$ $\mathrm{i}\mathrm{h}$ 1* ] $\dot{n}$ $\mathrm{a}g\mathrm{i}$ Td (Yisaku Nag$) JST CREST 1 ( ) DDS ($\mathrm{m}_{\mathrm{u}\mathrm{g}}\propto
More informationLHC ATLAS Large Hadron Collider 27km 2010 7TeV ~48pb -1 ATLAS LHC Higgs Muon spectrometer MDT RPC,TGC
LHC ATLAS Large Hadron Collider 27km 2010 7TeV ~48pb -1 ATLAS LHC Higgs Muon spectrometer MDT RPC,TGC TGC RPC ATLAS r : φ : θ : y-z : η=-ln(tan(θ/2)) Resistive Plate Chamber η
More information2 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 =
More informationTitle 非線形シュレディンガー方程式に対する3 次分散項の効果 ( 流体における波動現象の数理とその応用 ) Author(s) 及川, 正行 Citation 数理解析研究所講究録 (1993), 830: Issue Date URL
Title 非線形シュレディンガー方程式に対する3 次分散項の効果 ( 流体における波動現象の数理とその応用 ) Author(s) 及川 正行 Citation 数理解析研究所講究録 (1993) 830: 244-253 Issue Date 1993-04 URL http://hdlhandlenet/2433/83338 Right Type Departmental Bulletin Paper
More information橡scb79h16y08.PDF
S C B 05 06 04 10 29 05 1990 05 0.1 90 05 0.2 06 90 05 06 06 04 04 10 1.9 90 12 2.0 13 10 10 18.0 16.0 6.1 1 10 1.7 10 18.5 0.8 03 04 1 04 42.9 10 20.5 10 4.2 0.7 0.2 0.6 01 00 100 97 11 102.5 04 91.5
More informationφ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1)
φ 4 Minimal subtraction scheme 2-loop ε 28 University of Tokyo Atsuo Kuniba version 2/Apr/28 Formulas Γ n + ɛ = n n! ɛ + ψn + + Oɛ n =,, 2, ψn + = + 2 + + γ, 2 n ψ = γ =.5772... Euler const, log + ax x
More information共役類の積とウィッテンL-関数の特殊値との関係について (解析的整数論 : 数論的対象の分布と近似)
数理解析研究所講究録第 2013 巻 2016 年 1-6 1 共役類の積とウィッテン \mathrm{l} 関数の特殊値との関係に ついて 東京工業大学大学院理工学研究科数学専攻関正媛 Jeongwon {\rm Min} Department of Mathematics, Tokyo Institute of Technology * 1 ウィツテンゼータ関数とウィツテン \mathrm{l}
More information$\Downarrow$ $\Downarrow$ Cahn-Hilliard (Daisuke Furihata) (Tomohiko Onda) 1 (Masatake Mori) Cahn-Hilliard Cahn-Hilliard ( ) $[1]^{1
$\Downarrow$ $\Downarrow$ 812 1992 67-93 67 Cahn-Hilliard (Daisuke Furihata (Tomohiko Onda 1 (Masatake Mori Cahn-Hilliard Cahn-Hilliard ( $[1]^{1}$ reduce ( Cahn-Hilliard ( Cahn- Hilliard Cahn-Hilliard
More information第 1 章 書 類 の 作 成 倍 角 文 字 SGML 系 書 類 のみ 使 用 できます 文 字 修 飾 改 行 XML 系 書 類 では 文 字 修 飾 ( 半 角 / 下 線 / 上 付 / 下 付 )と 改 行 が 使 用 できます SGML 系 書 類 では 文 字 修 飾 ( 半 角
1.2 HTML 文 書 の 作 成 基 準 1.2.2 手 続 書 類 で 使 用 できる 文 字 全 角 文 字 手 続 書 類 で 使 用 できる 文 字 種 類 文 字 修 飾 について 説 明 します 参 考 JIS コードについては 付 録 J JIS-X0208-1997 コード 表 をご 覧 ください XML 系 SGML 系 共 通 JIS-X0208-1997 情 報 交 換 用
More informationhttp://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
More information<30345F90BC96EC90E690B65F E706466>
15 特集 国際宇宙ステーション日本実験棟 きぼう における流体実験 * Space Experiment on the Instability of Marangoni Convection in Liquid Bridge Koichi NISHINO, Department of Mechanical Engineering, Yokohama National University 1 thermocapillary
More informationNote5.dvi
12 2011 7 4 2.2.2 Feynman ( ) S M N S M + N S Ai Ao t ij (i Ai, j Ao) N M G = 2e2 t ij 2 (8.28) h i μ 1 μ 2 J 12 J 12 / μ 2 μ 1 (8.28) S S (8.28) (8.28) 2 ( ) (collapse) j 12-1 2.3 2.3.1 Onsager S B S(B)
More informationベクトルの近似直交化を用いた高階線型常微分方程式の整数型解法
1848 2013 132-146 132 Fuminori Sakaguchi Graduate School of Engineering, University of Fukui ; Masahito Hayashi Graduate School of Mathematics, Nagoya University; Centre for Quantum Technologies, National
More informationカルマン渦列の発生の物理と数理 (オイラー方程式の数理 : カルマン渦列と非定常渦運動100年)
1776 2012 28-42 28 (Yukio Takemoto) (Syunsuke Ohashi) (Hiroshi Akamine) (Jiro Mizushima) Department of Mechanical Engineering, Doshisha University 1 (Theodore von Ka rma n, l881-1963) 1911 100 [1]. 3 (B\
More information1/2 ( ) 1 * 1 2/3 *2 up charm top -1/3 down strange bottom 6 (ν e, ν µ, ν τ ) -1 (e) (µ) (τ) 6 ( 2 ) 6 6 I II III u d ν e e c s ν µ µ t b ν τ τ (2a) (
August 26, 2005 1 1 1.1...................................... 1 1.2......................... 4 1.3....................... 5 1.4.............. 7 1.5.................... 8 1.6 GIM..........................
More informationL \ L annotation / / / ; / ; / ;.../ ;../ ; / ;dash/ ;hyphen/ ; / ; / ; / ; / ; / ; ;degree/ ;minute/ ;second/ ;cent/ ;pond/ ;ss/ ;paragraph/ ;dagger/
L \ L annotation / / / ; /; /;.../;../ ; /;dash/ ;hyphen/ ; / ; / ; / ; / ; / ; ;degree/ ;minute/ ;second/ ;cent/;pond/ ;ss/ ;paragraph/ ;dagger/ ;ddagger/ ;angstrom/;permil/ ; cyrillic/ ;sharp/ ;flat/
More informationカルマン渦列の消滅と再生成のメカニズム
1822 2013 97-108 97 (Jiro Mizushima) (Hiroshi Akamine) Department of Mechanical Engineering, Doshisha University 1. [1,2]. Taneda[3] Taneda 100 ( d) $50d\sim 100d$ $100d$ Taneda Durgin and Karlsson[4]
More information第88回日本感染症学会学術講演会後抄録(III)
!!!! β! !!μ μ!!μ μ!!μ! !!!! α!!! γδ Φ Φ Φ Φ! Φ Φ Φ Φ Φ! α!! ! α β α α β α α α α α α α α β α α β! β β μ!!!! !!μ !μ!μ!!μ!!!!! !!!!!!!!!! !!!!!!μ! !!μ!!!μ!!!!!! γ γ γ γ γ γ! !!!!!! β!!!! β !!!!!! β! !!!!μ!!!!!!
More informationD 2009 A * 1 ( ) *1 ( ) 0 1 1 6 2 32 2.1............................................. 32 2.2.................................. 41 2.3...................................... 47 3 65 3.1..............................................
More information研究成果報告書
Simulation Study of Interaction between Alfvén Eigenmodes and Energetic Particles (TAE ) TAE TAE MHD ITER We studied the interaction between Alfvén eigenmodes and energetic particles in fusion plasmas
More informationボールねじ
A A 506J A15-6 A15-8 A15-8 A15-11 A15-11 A15-14 A15-19 A15-20 A15-24 A15-24 A15-26 A15-27 A15-28 A15-30 A15-32 A15-35 A15-35 A15-38 A15-38 A15-39 A15-40 A15-43 A15-43 A15-47 A15-47 A15-47 A15-47 A15-49
More informationi 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.............................................
More informationOTO研究会スライド
OTO @, 2017 5 26 2 CFT OTO ) PTEP 2016 (2016) no.11, 113B06 (arxiv1602.06542[hep-th]) Collaboration with P. Caputa(YITP) and A.Veliz-Osorio(Queen Mary U.) i i +1 H = X i i z z i+1 + h X i i x i z = 1
More information~ ~.86 ~.02 ~.08 ~.01 ~.01 ~.1 6 ~.1 3 ~.01 ~.ω ~.09 ~.1 7 ~.05 ~.03 ~.01 ~.23 ~.1 6 ~.01 ~.1 2 ~.03 ~.04 ~.01 ~.1 0 ~.1 5 ~.ω ~.02 ~.29 ~.01 ~.01 ~.11 ~.03 ~.02 ~.ω 本 ~.02 ~.1 7 ~.1 4 ~.02 ~.21 ~.I
More information5 36 5................................................... 36 5................................................... 36 5.3..............................
9 8 3............................................. 3.......................................... 4.3............................................ 4 5 3 6 3..................................................
More informationNatural Convection Heat Transfer in a Horizontal Porous Enclosure with High Porosity Yasuaki SHIINA*4, Kota ISHIKAWA and Makoto HISHIDA Nuclear Applie
Natural Convection Heat Transfer in a Horizontal Porous Enclosure with High Porosity Yasuaki SHIINA*4, Kota ISHIKAWA and Makoto HISHIDA Nuclear Applied Heat Technology Division, Japan Atomic Energy Agency,
More information40 $\mathrm{e}\mathrm{p}\mathrm{r}$ 45
ro 980 1997 44-55 44 $\mathrm{i}\mathrm{c}\mathrm{h}\mathrm{i}$ $-$ (Ko Ma $\iota_{\mathrm{s}\mathrm{u}\mathrm{n}}0$ ) $-$. $-$ $-$ $-$ $-$ $-$ $-$ 40 $\mathrm{e}\mathrm{p}\mathrm{r}$ 45 46 $-$. $\backslash
More information本文/報告2
1024 QAM Demodulator Robust to Phase Noise of Cable STB Tuners Takuya KURAKAKE, Naoyoshi NAKAMURA and Kimiyuki OYAMADA ABSTRACT NHK R&D/No.127/2011.5 41 42 NHK R&D/No.127/2011.5 a ka k I a Q kk a k a I
More information60 1: (a) Navier-Stokes (21) kl) Fourier 2 $\tilde{u}(k_{1})$ $\tilde{u}(k_{4})$ $\tilde{u}(-k_{1}-k_{4})$ 2 (b) (a) 2 $C_{ijk}$ 2 $\tilde{u}(k_{1})$
1051 1998 59-69 59 Reynolds (SUSUMU GOTO) (SHIGEO KIDA) Navier-Stokes $\langle$ Reynolds 2 1 (direct-interaction approximation DIA) Kraichnan [1] (\S 31 ) Navier-Stokes Navier-Stokes [2] 2 Navier-Stokes
More informationEndoPaper.pdf
Research on Nonlinear Oscillation in the Field of Electrical, Electronics, and Communication Engineering Tetsuro ENDO.,.,, (NLP), 1. 3. (1973 ),. (, ),..., 191, 1970,. 191 1967,,, 196 1967,,. 1967 1. 1988
More information1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 () - 1 - - 2 - - 3 - - 4 - - 5 - 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
More informationL A TEX ver L A TEX LATEX 1.1 L A TEX L A TEX tex 1.1 1) latex mkdir latex 2) latex sample1 sample2 mkdir latex/sample1 mkdir latex/sampl
L A TEX ver.2004.11.18 1 L A TEX LATEX 1.1 L A TEX L A TEX tex 1.1 1) latex mkdir latex 2) latex sample1 sample2 mkdir latex/sample1 mkdir latex/sample2 3) /staff/kaede work/www/math/takase sample1.tex
More informationDS II 方程式で小振幅周期ソリトンが関わる共鳴相互作用
1847 2013 157-168 157 $DS$ II (Takahito Arai) Research Institute for Science and Technology Kinki University (Masayoshi Tajiri) Osaka Prefecture University $DS$ II 2 2 1 2 $D$avey-Stewartson $(DS)$ $\{\begin{array}{l}iu_{t}+pu_{xx}+u_{yy}+r
More informationRX501NC_LTE Mobile Router取説.indb
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 19 20 21 22 1 1 23 1 24 25 1 1 26 A 1 B C 27 D 1 E F 28 1 29 1 A A 30 31 2 A B C D E F 32 G 2 H A B C D 33 E 2 F 34 A B C D 2 E 35 2 A B C D 36
More information168 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 =
More informationMicrosoft PowerPoint _9JPS_Tanaka_reduced_
Black Holes in Modified Gravity Takahiro Tanaka (YITP) Inspiraling-coalescing binaries 連星系からの重力波からは様々な情報を引き出せる Inspiral phase (large separation) クリーンな系 質点近似がよい星の内部構造はほとんど無視できる 正確な波形の予測が可能 for detection
More information2007 5 iii 1 1 1.1.................... 1 2 5 2.1 (shear stress) (shear strain)...... 5 2.1.1...................... 6 2.1.2.................... 6 2.2....................... 7 2.2.1........................
More information点集合置換法による正二十面体対称準周期タイリングの作成 (準周期秩序の数理)
1725 2011 1-14 1 (Nobuhisa Fujita) Institute of Multidisciplinary Research for Advanced Materials, Tohoku University 1. (Dirac peak) (Z-module) $d$ (rank) $r$ r $\backslash$ (Bravais lattice) $d$ $d$ $r$
More information1 2
1 2 4 3 5 6 8 7 9 10 12 11 0120-889-376 r 14 13 16 15 0120-0889-24 17 18 19 0120-8740-16 20 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 38 37 40 39 42 41 44 43 46 45 48 47 50 49 52 51 54 53 56 55 58
More information3 5 6 7 7 8 9 5 7 9 4 5 6 6 7 8 8 8 9 9 3 3 3 3 8 46 4 49 57 43 65 6 7 7 948 97 974 98 99 993 996 998 999 999 4 749 7 77 44 77 55 3 36 5 5 4 48 7 a s d f g h a s d f g h a s d f g h a s d f g h j 83 83
More information1: Pauli 2 Heisenberg [3] 3 r 1, r 2 V (r 1, r 2 )=V (r 2, r 1 ) V (r 1, r 2 ) 5 ϕ(r 1, r 2 ) Schrödinger } { h2 2m ( 1 + 2 )+V (r 1, r 2 ) ϕ(r 1, r 2
Hubbard 2 1 1 Pauli 0 3 Pauli 4 1 Vol. 51, No. 10, 1996, pp. 741 747. 2 http://www.gakushuin.ac.jp/ 881791/ 3 8 4 1 1: Pauli 2 Heisenberg [3] 3 r 1, r 2 V (r 1, r 2 )=V (r 2, r 1 ) V (r 1, r 2 ) 5 ϕ(r
More information受賞講演要旨2012cs3
アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート アハ ート α β α α α α α
More information. ------------------------------------. ----------------------------------------------- ------------------------------------- -------------------. ---
. ------------------------------------. ----------------------------------------------- ------------------------------------- -------------------. -----------------------------------------------. -----------------------------------------------
More information