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1 No.18ME-S5 Reports of RIAM Symposium No.18ME-S5 Crossover among theoretical, numerical and experimental studies on nonlinear waves Proceedings of a symposium held at Chikushi Campus, Kyushu Universiy, Kasuga, Fukuoka, Japan, November 6-8, 26 Article No. 33 Received February 28, 27 Research Institute for Applied Mechanics Kyushu University May, 27

2 PL2N.K*1k[o=] SMd"kZlR &2gX})X&fJ 27 / 2 n 25 5W 2o`N?3R,PL*+DS>*K.lF$kOGN"/i9?js".lNZj".lNi$U?$`"b)YhGN[o=]rtM7_el<7gsGrO7?# 1 O8aK =e*}xk*1k@$j_c/9np]o"4.ndrl.+i8*dnn8d^g=n g-j-,jr+;f$k [1]#3liNOXOF-Nd.NHcCF"?}xKjv9k NG?kp\6},J$3HKg-JC',"j"=l,NKs~A*}XNg-JUmsF# "r.7f$kh@(kg"m&#l}g3li@$j_c/9nt=]ko&l-"aw,+u1ilk3h,?$#c(punfn4rm(k#okhk.l,"kh-uns zlkhcf4ko-zzo,88"4.k/i9?js,/3k#>}grl.k*$f b"b.;)k*1kvn/i9?js,+u1il"b] OV O? [2] \@8GO2o`N?3R,._9kOK*1k"PLWMN.lrM(k#33G@&2 o`ho"kb.y,[jk2o`n?3rg_$ksm9kbnrx9 (^.1 )#3NH-. ^ 1: PL2P. l,zk=]jz.uvk*hsz.uvk+\9k^gn/i9?jsn}w*-ake \9k#3Nh&JPL2N.,[j7F$kNO"J<Nh&J+3OG"k#(1) 4-U NfK2o`N?3R,8_7"KB.Y,[JkH$&roG*_$WM7g&O#3NH -KB.YN?QMG/B8OG+kH"PL*KWM9k2N3ROHM(k3H,G1

3 k#(2) _C/9OPL2N.H_J;k#(3) rl.#v~,#t"k;)g"dr.y,.$vhy $V,._9klgb"V1N,r1"&3H,SM*WMHM(kH1MK_J93H,G -k#(4) btt. [3]#b;*$FPLNMN.lbPL2P.HM(k3H,G-k# 3li[JkOr7&lg"OXr-R9kbGkO=l>l,ZKM(J1lPJiJ$ G"m&,"33G&LN-AG"k 1) KB.Y,PL*J}~ 2) _$KSM*KWM H$&2Dr~?7?eG"JkY/J1JVGgxst*WJbGkrM(?$#=3G" aghje2k# 2 ;k*<h^hsbgk PL2P.r7_el<7gs9k?aK"\@8GO1DN;k*<H^HsbGkrs P9k#^:33GO2!5Orhje2k3HH9k#JT}~H#}~K5}JRr_1 F"#}~N<KOS>*JI,"j"JT}~O=,9$H7F~ *-&ror>j9k# \@8GO#}=1, JT}~}=1 H7?# \ (fl&) }~KJ`3RJ\JT3R)"]}~ (18) KJ`3RJ]JT3R) 2o`N 3RrljtQU7F"i roh7fjrkis@`k[v9k#"k~on[v+i!n (1) }N5$H (JT}~NlDhN5$H),u$F$?i=3K=N^^J` (2) }N5$H,I,CF$F"&}N5$H8}5$H,>}u$F$?i"2DN &ARHDris@`K*sGJ` (3) }N5$H,I,CF$F"&}"8}IAi+N1DN5$H,u$F$?i= 3KJ` (4) }"&}"8}N5$H,I,CF$?iJ^J$# J#de}KOJaJ$H>j) (5) Js@,">N3RH-go;7?lgOJak3RrlDis@`K*P7F"*Pl J+C?3RO5NLVKa9 33GmU9Y-3HO"@$J_/9OLVps+ih^kH$&3HG"k#3lOOX N)l+i9kH7-`O5k7?3HKjv9k,"4-.K*$FO9H</9awH7 FNilF$k# 2

4 (^.2)#p\^OrL.G Q$ilk5G"j"#4KV>)Y"D4KV.Lr(7?iUG"k#33GO]J T3Rt n r, 1, 3, 6, 9 NlgK"\JT3RtH\JT3RtN.LrX8r=7?#?@ 7V.LWHO33GO 5?$`9FCWNVK"~ -&Ni$sr6(?3RNmtH 7?#n = Nlg,rL.KP~9k,"33Gb1T</,B=5lF$k# ^ 2: p\^ 3 /i9?jsh.lni$u?$`}w \JT3Rt N = 4, ]JT3Rt n = 2 NH-N"7_el<7gsNkLr(9J^.36K#?@7 O\JT3R"{O]JT3Rr"io9bNH9k#\JT3RKm\9kH" ~VNPaHHbK/i9?<,A.5l=l,gN"pg=7F"D$KOPL3RN?a K.l,9HCW9kuVJZ.uVKKYk#3N/i9?<Npg==]rjL*K_k?a"/i9?<Xtr3~9k# /i9?<ojt}~n.lnzj,6xjng"/i9?<xtrjt}~nlvx8n _rm89k#\jt3rn/i9?<xto"\jt3rn4fnz"<rhcf"jt} ~NB8M,18Ji+2, JT}~NB8M,,lDc$Ji+1 H7FgWrHC?bNH9 k#3lo"jt}~k\jt3r,8^kmrrjl=7?bnh$(k# /i9?<xtn~vq=ric?nr^.7 K(9#?@7 N = 4, n = 2 G"k#^h j"7_el<7gs9?<h>e+i"/i9?<xt,}c7f$k#d^j3lo/i 9?<,~VHbKpg=dgN,/-F$kH$&vBHgW7F$k#G**KO.l, 9HCW7FZ.uVKJkNG"/i9?<XtbljMK_^CF$k#!K"\JT3 3

5 3: ˆ ƒ 4: T=8 ˆ ˆ 5: T=16 ˆ 6: T=276 4

6 Rt N, ]JT3Rt n r=l>l"33, 1 H:i7F"/i9?<XtN@$J_C/9r =7?N,^.8 G"k# 33GmU9Y-O#4N~V91<k,^.7 HO 1 \g-$h$ N X^[w Ô T ^ 7: /i9?<xt@$j_c/9 (\JT3Rt=4 ]JT3Rt=2) N X^[w Ô T ^ 8: /i9?<xt@$j_c/9 (\JT3Rt=33 ]JT3Rt=1) &3HG"k#D^j^ 6 O~V T 25 H$&9~VKo?CF/i9?<=,J+J+ JT7J$NG"k#3lO"3Rt,/J$H$&vB,G>K?G5l?kLG"j+3 J3HG"k#H3m,"3NH-bG**KOZ.uVKYCF.lO9HCW9k#3l r/i9?<n)lg+kh T 25 G/i9?<,v3/87F"=l,.97FD$K OZ.uVrb?i9HM(ilk# Je2DNlgNg-Jc$O"/i9?<=,>AK/3k+]+G"k#3Nc$rh j@i+k9k?ak".lni$u?$`rja9k#d^j"i uv+iz.uvkjc 5

7 F.l,_^k^GN~VH9k#3Ni$U?$`O?H(\JT3Rt N, ]JT3Rt n 18@H7Fb"7_el<7gsN?SK[JkM,PF/k#D^j.lNi$U?$ `KOIi.,"kNG"J<Ki$U?$`N}WrrO9k# /i9?<=,>ak/3c?tnlgn"i$u?$`nqy,[r(7?n,^.9 G "k#?@7 n = 4, N = 4#8OD4N_rPtK7?"semi-log iug"k,@i+x êì Ct^C px v +is±q N=4 is±q n=4 linear XP[ 5 semi@logxp[ Ct^C T Ct^C T 5 6 ^ 9: i$u?$`qy,[ 1 txt*:j,+ilk#d^ji$u?$` T HQY P HNX8O P (T ) e γt, (T 2) H>A5lk#3NvBOTNlg"vBei$U?$`O-BG"kH$3Hr(9#3 lo">ak/i9?<=,/3kh$&3hh7b7j$klg"k#!k/i9?<=, J+J+JT7J$eTNlgNQY,[r(9#33GO\JT3RtOQ(:KPL3R Ntr4,N1:i7F n = 1, N = 4 H7?#3NH-"2DN~VNhKhk,[Nc $,+il?#t <= 2 K*$FO"TH1MXtXt*:j,+il?#(^.1) l}" 9~VNh T > 2 K*$FOQY P,J+J+:j;:K"i$U?$`N9$$YsH,Q/9k#3lr>PtK9kH[\>~HJkNG"QYXtOUY-* P (T ) T γ, γ 5 HJk3H,o+k#^ 11 OIi.,c7$,"3lO$YsHt,4//tG"k3HN= lg"k#"s5svktr?/9k3hkhcfrc5lk#3n=]r/i9?<n)l GM(kH"/i9?<Xt,i M+iJ+J+Q=;:KJv3I3+GG-k^GK9 ~VHI^CF$?^.8 KP~9k#3NQY,[N6kq$O long time tail G"j"+*9 N$&GOVguVN~V,[G=lk3H,NilF$k# 6

8 œ ( œ ) + š N=4 š n=1 5 4 linear ƒˆˆ 1 semi logƒˆˆ T T 1: ˆ 2(Š Š) œ ( œ ) + š N=4 š n=1 8 T log logƒˆˆ ƒ T 11: ˆ 2( Š) 7

9 \angek"/i9?jsh long time tail $#?H(P\JT3R,#t#BSKJC?H9k#9kH]JT3ROJT,VmC/5 lf"\jt3rn#sn<ko_p93hkhk#1~k#sne}kour (void),8^ lk#=nh-em+ihk\jt3ro"#+ihk]jt3rkk^lf void K~CF7 ^&#ki=lio#shgn7f/i9?<n.9rb?i93hhjk# /i9?jsn?ako3rn#s,8.5lk3h,ewg"k,"lyds,g-? H-3lbBj*K]?lk#3Rt,fS*/J$lg"#s,8.5lkKDs,8. 5lkH9~VKo?CF"PLWMN!q,:ol3l,kL*K9~VNi$U?$`B =7"P (T ) N long time tail rb?i9h=[5lk# 4 b))ynhk*1k[o=] ^ 3 Np\^G n = 9 NH-"N 8 Go:+J,iT</,"k3HKe\7?$#3 RN)Y,soKb$lg".LKU>=]"D^j\h)YHbK.L,:kY-,"UK }(F$kH$&=],/-F$kNG"k#\@8GO3N=]rV[o=]WHFV3H H7?$#3N[o=]rhj@N=9k?aKVZ.N(Wr3~9k#Z.N(HOlj ~V (33GO 5 H7?) ^GK"Z.uV,/3kN(H7"3lO7_el<7gsN "s5svk}w+i@ilkbng"k#]jt3rt n, 1, 2, 3 NlgN\JT3Rt N HZ.N(HNX8r(7?N,^.12 G"k#N HHbKZ.N(,}(kNOv3G" 5,stepÜÅÉØ óôéèém A T u Í1 1 n=3 pjbn m.8.6 t]»û iùí»û) n=2 n= {is±q 8 1 ^ 12: Z./8( k,"n,g-/jj")y,b/jkhukz.n(,:kh$&u>=],/3cf$k N,+Fhlk#n = 1 NH-b)YNhK*$F"\JT3RN.Lr=7?N,^.13 G 8

10 ^ 13: Z./8( "k#.lkx7fbu>=],/3cf$kn,o+k#3n[o-no?f(/3kng (94 99),]JT3RNt (1 3) h5]*kg-$ng"tr[9h3r"etrt c*hfv3hk9k#[9h3r+n,b)yg,[7f$kng"/i9?n/8!=n H3mGRY?u& (void),/87fb>akcg9k#=nkl"tc*n/i9?<=, klpl3rnpipikjc?u7g[9h3rnjt,"cf9`<:kjkh$&a+ K:`G"k# 5 ^HaH]j \@8GO"PL*K.lk2o`N3ROr7C?#.NfN3R"4.N"rL."bT T.JI-OON,QrknK~l?eGGbJ1@HWolk";k*<H^HsNbGk rnq7?#3rtkbhk,"7_el<7gsnkl"1o3rn/i9?js,/# 7"D$KO.l,9HCW7F7^&Z.uVKYk3H,o+C?#5iK/i9?js N/#rjL=9k?aK"Xtr3~7F=N~VQ=rIC?#kL"2DNC'*J lgr+p93h,g-?#h1nlgo/i9?<n/8"pg=,>ak/3jfs*; ~VG.l,_^k (^.7)#h2KlgO"3Rt,/J$lg/i9?<N/8,J+J+ /3i:""kH-v3/87?H-K.97Z.uVKYkQ?<sG"k (^.8)#3li N.lN}3~V"D^ji$U?$`NQYr}W*KW,7?kL"TOXtXt*K :j9k3h,o+c? (^.9)#l}eTO"i$U?$`,;$$YsHKX7FOXtX t*:jr(7?, (^.1)"9~VNhKX7FOUY-G:j9k3H,o+C? (^.11)# 9

11 XtOs-5#i$U?$`NXtXt*:jH1MN=],"HiCWI-s/KhCFA. 5lk=3N.lK*$FB3*K+P5l?3HO=#<$ ri$u?$`hra9lp"g*lvn,[xthjfs9k3h,g-k#^?"9~v hk*1k long time tail =]OVg*+*9N`BjuVG+ilk3H,"k#!Kl}N3Rt,5]*K?/"R}N3RrTc**JH_J;"+D4NH7FN) Y, 1 Q<;sHa/KJkH".l,UK%J9kH$&U>=]r+$@5l?#3l Oo1*KOV[o=]WHM(Fbh$,"Tc*,uaru1F/i9?<=,^)5l kh>j9lp}rg-k# \@8GO"\}~3Rt N "]}~3Rt n,4/bil?lgnc'*"5?*j=] rrp7?@1g"k,#n n N2!5LNI3G(BKZ.uVKJk+"I3G long time tail =],"kn+""k$oi3gz.o/3ij$n+"h$& global j^nroo #en]jh7?$# \bgkgn@$j_c/9nk<ko$/igbq9,g-k#c(p#k9i$i9k" -g&]n%hk<knha}"7-zln3~jig"k#3linlgb]jh7fn9 Y-G"k,"\@8GRY?C'*J=]O"j-*KO]?lkH.8k# 2M8% N1OM.Schreckenberg et al(ed), Pedestrian and Evacuation Dynamics, Springer(22) N2O~ZJl>, \*}Xqo 55(2)p166 N3OT.Iizuka, Traffic and Granular Flow G3 (ed.s.p.hoogendoorn, Springer)(23)p393 N4Oe#gX!<nQR!$N@8Vs.,4NN=3K*1k77$J=$W(25) 1

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