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きみのしんしもかさ
5 years ago
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2 Lennad-Jones L-J Hamonic Multiple time step Phantom τ S τ A τ AS τ A...41

3 3...45

4 4

5 5 1.1 T 0 Á T 1 T A B T [K] q[w/m ] R contact esistance R = θ [m K /W] (1.1) q 1-

6 6 1-3 A A B B

7 7 1. MD MC MC MD MD MC MD MD MC

8 8 1.3

9 9

10 Lennad-Jones 5 non-pola Lennad-Jones L-J L-J 1 6 σ σ φ ( ) = 4ε (.1) ε σ ε σ A 1 ε = (J) (.) A σ A = ( m) (.3) L =

11 11 φ 0 σ 1/6 σ σ ε -1 Lennad-Jones potential

12 1.1. k σ S φ 1 = S (.4) () k( σ ) hamonic 3 m S = kg k = 46.8 N/m σ S =.77 Å 4 σ S =.77 Å

13 13. Lennad-Jones +d Lennad-Jones Lennad-Jones c c c 0 () = c c S σ σ σ σ ε φ.5 c c 0 () + = c c c c c SF σ σ σ σ σ σ ε φ.6 () + = c c c SF d d σ σ σ σ ε φ (.7) c = 3.5σ

14 14.3 Newton i t i Fi (t) m i i (t) d F i ( t) = mi ( t) i.8 dt i (t) i Φ i F i i ( t) =.9 i F i () t t t tfi () t vit + = vit +.10 m t i t i( t + t) = i( t) + tvit +.11 i i

15 L-J L-J / σ t ε Φ( / σ ) ε Φ ( / σ ) = m d dt.1 = / σ t = t / τ Φ( ) = mσ ετ d.13 dt mσ = 1.14 ετ σ τ = m.15 ε τ τ = 1 t τ τ = t = (s)

16 16.4. Hamonic Hamonic Lennad-Jones d φ k = d L J () = = 3 7ε σ S 6 σ S S (.16) (.17) 7m τ S S = 3 (.17) k τ S = s t S = s.4.3 Multiple time step Lennad-Jones Hamonic vs t v t t S () t S t F S, = v t + t (.18) S m S t () t S () t t F + F, + = v t + t (.19) x ( t + t ) = x ( t) + t v t + (.0) t m steps ts vs t + x S ts = vs t + t S FS m t S ( t + t ) = x ( t) + t v t + S S S S () t S (.1) t = t (.) S

17 i

18 18 c j -3-3

19 v 0 T 0 v 0 3kT b 0 =.3 m k b m v 0

20 T 0 T v = v T T 0.4 v v.7. Phantom Phantom Phantom Phantom Phantom -4 = kg/s =46.8 N/m

21 1 move Phantom molecules Fixed molecules F α veticalk hoizonta0.5k veticalk hoizonta3.5k -4 Phantom

23 3 3- L-J int (J) (J) Å K 100 K 10 K 048 fcc 110(K) 500(ps) phantom (110K) 1000(ps) 10(K), 100(K) phantom 4000(ps) 3-1 z L R q L evap q L cond T evap JUMP Heat q evap W q V M Mass Liquid Vapo Solid T JUMP cond Liquid Solid q W cond L R 3-1

24 4 } 3 solid layes Cooling Liquid A Vapo Liquid } 3 solid layes Heating A A 3-

25 5 3. int = (J) (evap.) (cond.) (S) (L) (V) T N q v ps 000ps evap N v N v cond evap cond N L N v N L evap cond N v N L 000ps 000ps 000ps 5000ps T V T S evap T L evap Numbe of Molecules Tempeatue [K] T S cond q V N L cond Time [ps] N L evap T L cond N V Heat Flux [MW/m ] 3-3

26 ps 0 phantom q w Enegy budget [J/m ] Evap. Side Cond. Side 55.3 MW/m Enegy Flux 60.3 MW/m Time [ps] ps 5000ps z ps 3500ps 5000ps 100ps

27 7 Tempeatue [K] Density [1/Å 3 ] Velocity [m/s] ps 5000 ps 000 ps 3500 ps Tempeatue jump: 5.98 K 5.90K <v z > Positon [Å] ps 000ps 5000ps T jump Fig_ q w R T int = (J) (J) 3-

28 8 Label ε INT q W ( 10-1 J) (MW/m ) T JUMP (K) 3- R T (m K/W) λ L (W/m K) L R (nm) dn L /dt (1/ns) evap E cond evap E3 cond evap E4 cond evap E5 cond evap E6 cond q L q V M (MW/m ) (MW/m ) (kg/m s) int R T int q w L W/m?K 110K W/m?K L R = L?R T 3-

29 9 Themal Resistance R T [m K /MW] ε int [x10 1 J] int R T int R T int R T int R T int

30 30

31 τ τ m m S k L-J ε σ ε Á σ Á τ ÂÃ τ Á τ mσ = (4.1) ε 7m τ S S = 3 (4.) k τ AS m AS S = (4.3) m m m + m S L-J ε AS σ AS τ AS masσ AS = (4.4) ε AS τ S 7m ε S = 3 kmσ τ (4.5) τ AS = masε σ AS msε σ AS τ = mε ASσ ( m + ms ) ε ASσ τ (4.6) 3 τ

32 3 4. L-J - L-J Hamonic L-J 4-1 L-J σ (Å) ε ( 10-1 J) m( 10-3 kg/mol) Hamonic 4- Hamonic 0 (Å) k (N m) m( 10-3 kg/mol) τ Å 3 110K 100K 10K fcc 110(K) 100(ps) 10(K) 100(K) phantom 4000(ps)

33 41.6A 33 Cooling 8.8A 7.7A Heating 4-1

34 τ τ Pt τ τ A = (s) (4.7) τ Pt = τ S = (s) (4.8) τ AS = (s) (4.9) τ Pt = τ S = 0.9τ A (4.10) τ AS = 1.8τ A (4.11) τ (4.5) (4.6) τ S 7m ε S = 3 kmσ τ τ AS msε σ AS = ( m + ms ) ε ASσ τ τ τ k m S σ AS ε AS τ S =τ A τ AS =.0τ A 3 k (N/m) 4-4 m S ( 10-3 kg/mol) σ AS (Å) ε AS ( 10-1 J)

35 35 000ps 5000ps 0.06 Density[1/Å 3 ] Tempeatue[K] K : Tempeatue jump 1.91K Position[Å] Density[1/Å 3 ] Tempeatue[K] K : Tempeatue jump 4.9K Position[Å] 4-3

36 Density[1/Å 3 ] Tempeatue[K] K : Tempeatue jump 3.63K Position[Å] T jump (K) 4-5 q W (MW/m ) R T (m /MW) L R (Å) ε σ τ ε σ σ

37 τ S τ A τ s τ A τ AS = 1.8 τ A τ AS τ A τ A τ S = 0.9τ A τ S 4-5 τ τ S 7m ε S = 3 kmσ τ k τ S τ A τ S τ S = 0.9τ A τ S = 0.5τ A τ S = τ A 4-6 τ k τ k (N m) τ S = 0.9τ A 46.8 τ S = 0.5τ A 16.1 τ S = τ A 4.03 τ k 4-6

38 ps 000ps 000ps 10 Tempeatue[K] Time[ps] 4-6

39 Enegy budget[j/m ] MW/m MW/m Time[ps] ps phantom 000ps ps 5000ps T jump q W R T L R 3 τ 4-7 L R

40 Density[1/Å 3 ] Tempeatue[K] K : Tempeatue jump 4.6K Position[Å] τ S τ S k (N/m) T jump (K) q W (MW/m ) R T (m /MW) L R (Å) τ S = 0.9τ A τ S = 0.5τ A τ S = τ A

41 41 τ s τ A τ s τ A τ s τ A τ AS τ A τ s τ A τ S = τ A τ AS =τ A τ AS =3.0τ A τ AS =0.7τ A ε AS τ S τ AS τ AS τ A τ AS = τ S = τ A τ AS = 0.7τ A τ AS =τ A τ AS = 3.0τ A τ AS = 1.8 τ A τ AS τ A = τ S τ AS = τ A τ A = τ S τ AS = 0.7τ A 4-9 τ AS msε σ AS = ( m + ms ) ε ASσ τ ε AS τ AS

42 4 4-8 τ ε AS 4-8 τ ε AS τ ε AS ( 10-1 J) τ AS = 3.0τ A 0.54 τ AS = 1.8τ A τ AS = τ A.8 τ AS = 0.7τ A τ AS = 1.8τ A τ AS = τ A 000ps 5000ps Density[1/Å 3 ] Tempeatue[K] K : Tempeatue jump 0.069K Position[Å] 4-10

43 43 1 ε AS τ AS = 0.7τ A 000ps 5000ps Density[1/Å 3 ] Tempeatue[K] K : Tempeatue jump.75k Position[Å] 4-11 τ AS = τ A τ AS = τ A

44 τ T jump R T q w L R τ AS ε AS ( 10-1 J) 4-9 τ AS T jump (K) q W (MW/m ) R T (m /MW) L R (Å) τ AS = 3.0τ A τ AS = 1.8τ A τ AS = τ A τ AS = 0.7τ A τ AS τ A ε τ AS τ A τ AS = τ A τ AS τ S τ AS τ A τ S τ A ε AS

45 45

46 46 τ 3 τ 1 τ

47 47 MD 4

48 48 [1] [] Mauyama, S. et al., Micoscale Themophysical Engineeing, -1(1998), 49. [3] Blöme, J. and Beylich, A. E., Poc. of Intenational Symp. on Raefied Gas Dynamics, (1996),39 [4] [5] [6] [7] [8]

LLG-R8.Nisus.pdf

LLG-R8.Nisus.pdf d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =