(ANAGISAWA Daichi) (NISHINARI Katsuhiro) 1 1 Helbing Social Force Model [1] Social Force Social Force [2][3] [3] 1

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1 No.17ME-S2 Reports of RIAM Symposium No.17ME-S2 Phenomena and Mathematical Theory of Nonlinear Waves and Nonlinear Dynamical Systems Proceedings of a symposium held at Chikushi Campus, Kyushu Universiy, Kasuga, Fukuoka, Japan, November 9-12, 25 Article No. 28 ANAGISAWA Daichi NISHINARI Katsuhiro Received February 13, 26 Research Institute for Applied Mechanics Kyushu University May, 26

2 (ANAGISAWA Daichi) (NISHINARI Katsuhiro) 1 1 Helbing Social Force Model [1] Social Force Social Force [2][3] [3] 1

3 (1) (2) (1) (1) (3) (1) (1) (1) (1) 1 ( FF) FF FF FF FF 2.1 FF ( 2) FF 3 O ( = U, D, R, L) FF p s(o ) = exp{k s (S O S )} (1) k s [, ): FF ( FF ) S Z (Z = O, U, D, R, L) [, ): Z FF( ) ( ) FF( ) 3 U L O R D 1 (O ) 2.2 ( ) 1 ( 4) FF FF p d1(o ) = exp(k d1 D 1, ) (2) k d1 [, ): FF ( FF ) 2

4 D 1, ( = U, D, R, L) [, ): Z FF.. ( 5) α δ FF FF D t+1 i j = (1 α)d t i j + α 4 (Dt i+1, j + Dt i 1, j + Dt i, j+1 + Dt i, j 1 ) (3) D t+1 i j = (1 α)(1 δ)d t i j D t+1 i j = (1 δ)d t i j (4) α(1 δ) + (D t i+1, j 4 + Dt i 1, j + Dt i, j+1 + Dt i, j 1 ) (5) ( (i, j) 6.) 4 D 1 = ( ) FF( ) = FF (α = δ =.2) (i 1, j + 1) (i, j + 1) (i + 1, j + 1) (i 1, j) (i, j) (i + 1, j) (i 1, j 1) (i, j 1) (i + 1, j 1) FF 2.2 FF FF FF 9% 3

5 3.1 FF 1 FF 4 FF 4 FF p d2(direction) = exp{k d2 (ΣD 2(direction) } (6) direction = {,,, }, k d2 3.2 = RoV( N) RoV 2 7,8 RoV = k v1 (i, j) ( 7 ) p v1,up = exp [ { k v1 Σ j+rov j) n= j+1 Σi+(n m=i (n j) man( m, n, 1 1 m i )}] 2 n j (7) p v1,right = exp [ { k v1 Σ j+rov j) n= j+1 Σi+(n m=i+1 man( m, n, 1 m i)}] 2 n j (8) k v1 :. man(m, n, x): (m, n) x p v2,direction = exp{k v2 ( direction )} (9) k v2 4

6 j+2 j+1 j i-2 i-1 i i+1 i+2 j+2 j+1 j i-2 i-1 i i+1 i (RoV = 2) (RoV = 2) 4 2,3 4 ( FF, FF,, ) , 2 9, 1 FF 4 ( SC) 1 1, 2 SC ( ) 1 2( ) 1 SC( ) 2 SC( 1, 2) k s 3 RoV 6 α.2 δ.2 µ (25, 1) (49, 27),(49, 28), (49, 29),(49, 3) ρ 6.%( ) 6.17%( 2334 ) FF ( ) 5 ( / ) 5

7 : FF 12 2: FF (k d1 = 1.5)(84/289) (k d2 = 1.5)(81/291) : 14 4: 15 FF (k v1 = 1.5)(81/295) (k v2 = 1.5)(83/289) (84/289) FF 1 4 ( ) 5 2 (2 x 23, 27 y 48) FF p u p u p r log ( ) p r p u 21 p r : FF 17 2: FF 18 3: (k d1 = 4)(59/288) (k d2 = 4)(71/231) (k v1 = 4)(76/291) 6

8 count(p d1 ) count(p d2 ) count(p v1 ) count(p v2 ) count(p) log(p r /p u ) 19 4: (k v2 = 4)(65/25) 2 FF (64/265) k turn ave ( 22, 23) 32 3 k d1 k d2 315 k d1 k d2 k v1 k v2 31 k v1 k v2 28 turn ave 35 3 turn ave k d1, k d2, k v1, k v k d1, k d2, k v1, k v2 22 ( 1) 23 ( 2) 4.3 ( 24, 25) k d1 k d1 k d2 8 k d2 2 k v1 Calculation Time (sec) k v1 k v2 Calculation Time (sec) 15 1 k v k d1, k d2, k v1, k v k d1, k d2, k v1, k v2 24 ( 1) 25 ( 2) ( 1) 1 ( 11 15) ( 13) 1 7

9 45 FF ( 15) 5.2 ( 2) ( 16 2) FF 21 FF log ( ) p r p u = pu p r p r p u log ( ) p r p u = pu p r FF n 3 ([ ].) 3 FF [ n [ 2] n 2] n RoV FF 4 FF FF FF( 16) FF( 17) FF FF FF FF FF 16 FF 1 FF 8

10 k d2 = 4 FF ( 13) 2 FF 1 FF 2 2 FF FF 1 1 FF 2 FF 1 2 FF 1 FF FF 1 2 FF 1 FF ( 22) k 2 k FF k d2 = , 25 FF FF 4 (RoV + 1) 2 1 FF 6 4 ( ) 4 9

11 4 4 FF FF ( 1 ) ( 2) ( 2 ) ( 1) 7 2 FF α, δ, RoV 4 FF ( ) ( FF ) ( ) [1] Dirk Helbing, Illés Farkas, Tamás Vicsek, Simulating dynamical features of escape panic, nature 28 September 2 [2] Ansgar Kirchner, Katsuhiro Nishinari, and Andreas Schadschneider, Friction effects and clogging in a cellular automaton model for pedestrian dynamics, PHSICAL REVIEW E 67, (23) [3] Katsuhiro NISHINARI, Ansgar KIRCHNER, Alireza NAMAZI, and Andreas SCHADSCHNEIDER, Nonmembers, Extended Floor Field CA Model for Evacuation Dynamics, IEICE TRANSACTIONS on Information and Systems VOL.E87-D NO.3 MARCH 24 1

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