Fizik Lalulintas Wan Ahmad Tajuddin Wan Abdullah Jabatan Fizik Universiti Malaya & Institut Ibnu Sina UTM http://fizik.um.edu.my/cgi-bin/hitkat?wat
Alam ini kompleks
Sistem kompleks Tak keseimbangan, pelesapan Banyak darjah kebebasan fungsi Lyapunov Tak linear pemetaan peta logistik xn+1 = axn(1-xn) Komputer: simulasi, pemetaan
Bawah ke Atas saling tindak tempatan, minimal ↓ fenomena sejagat
pemerihalan statistik Rawak Sistem besar Ergodik Entropi Perubahan fasa …
Automaton bersel (/Permainan Kehidupan) salingtindak (hidup/mati) sel/organisme dgn jiran, berruang unsur Boole di atas kekisi dengan salingtindak jiran terdekat 2 dimensi: h g f e p d c b a Keadaan p bergantung kepada keadaan-keadaan a, b, …, h (dan diri sendiri p). Dinamik automaton bersel 1 dimensi dgn s/t jiran terdekat – 4 jenis: Evolusi kepada keadaan homogen Evolusi kepada keadaan berkala/berkitar Evolusi kepada keadaan celaru Evolusi kepada keadaan dgn struktur-struktur kompleks bertempat, kadangkala hidup lama
1 dimensi dgn s/t jiran terdekat bergantung kpd jiran kiri, diri sendiri dan jiran kanan – 3 keadaan, - boleh diwakili nombor dedua 3 bit (no. perpuluhan 0-7: ada 8 kemungkinan). Atur nombor-nombor (keadaan-keadaan mungkin) ini secara menurun dan tuliskan keadaan terhasil bagi unsur tengah mengikut turutan – ini memberikan suatu nombor dedua 8 bit yg menentukan hukum bagi dinamik automaton bersel berkaitan. mis. 111 110 101 100 011 010 001 000 0 1 0 1 1 0 1 0 Hukum 90 (010110102 = 9010)
Lalulintas Lebuhraya Aliran berbiji Tindakan pemandu Satu hala Satu dimensi
Model automaton bersel Model mudah: 1 lorong, 1-dim Hukum 184 – 111 110 101 100 011 010 001 000 1 0 1 1 1 0 0 0 bergerak ke kanan satu tapak jika kosong - Bil./kepadatan kereta terabadi - Kelajuan maksimum m=1
Perubahan fasa pada rc = 1/2 (kinetik peringkat ke2) di mana Perubahan fasa pada rc = 1/2 (kinetik peringkat ke2) [peralihan mengejap]
Gambarajah fundamental arus lwn kepadatan j = vr r j Hukum 184: r
penumbesaran kelompok soliton
Pengaman/pengumuman Banyak lorong (- memotong) Banyak kelajuan (- brek dan pecut) Sikap pemandu Masukan kereta Hingar Perlanggaran …..
Model Malaysia (awalan) 3 lorong m=3 pecut jika boleh (kelajuan maksimum kalau boleh) brek jika terpaksa (brek ganas jika terpaksa) potong sebelah kanan jika lebih ruang (tak kesah kereta datang; tak balik ke lorong kiri) kereta masuk di suatu hujung, keluar di hujung bertentangan kebarangkalian kelajuan maksimum lebih besar lebih besar
0_0_0_0_0_______________________________ 0_0_0_0___0_____________________________ 0_0___0__0__0___________________________ _0__0_0_0_0_____________________________ 0_0_0_0_0___0___________________________ 00__0____0__0__0________________________ 0_0___0_0_0_0___________________________ 0__00_0_0_0___0_________________________ 000___0_____0__0__0_____________________ 00_0____0_0_0_0_________________________ 00____0_0_0_0___0_______________________ 0000__0_0______0__0__0__________________ 000_0_____0_0_0_0_______________________ 000_____0_0_0_0___0_____________________ 00000____00_______0__0__0_______________ 0000_0______0_0_0_0_____________________ 0000______0_0_0_0___0___________________ 000000_____00________0__0__0____________ _0000_0_______0_0_0_0___________________ 00000_______0_0_0_0___0_________________ _000000______00_________0__0__0_________ __0000_0________0_0_0_0_________________ _00000________0_0_0_0___0_______________ __000000_______00__________0__0__0______ 0__0000_0_________0_0_0_0_______________ 0_00000_________0_0_0_0___0_____________ 0__000000________00___________0__0__0___ 0_0_0000_0__________0_0_0_0_____________ 0_000000__________0_0_0_0___0___________ __0_000000_________00____________0__0__0 __0_00000_0___________0_0_0_0___________ _0_000000___________0_0_0_0___0_________ 0___0000000__________00_____________0__0 0___000000_0____________0_0_0_0_________ 0_0_000000____________0_0_0_0___0_______ ___0_0000000___________00______________0 0_0__000000_0_____________0_0_0_0_______ 00_0_000000_____________0_0_0_0___0_____ _____00000000____________00_____________
Adakah lebuhraya punyai ingatan?
__________0_____________________________ ________________________________________ 0_______________________________________ __0_____________________________________ ____0___________________________________ ______0_________________________________ ________0_______________________________ ____________0___________________________ ______________0_________________________ ________________0_______________________ 0_________0_____________________________ __________________0_____________________ ___0______0_____________________________ ____________________0___________________ ______0___0_____________________________ ______________________0_________________ _________00_____________________________ 0_______________________0_______________ __________0_____________________________ __0_________0___________________________ _0________________________0_____________ ____0__________0________________________ __0_________________________0___________ ______0___________0_____________________ ___0__________________________0_________ 0_________0_____________________________ ________0____________0__________________ ____0___________________________0_______ ___0______0_____________________________ __________0_____________0_______________ _____0____________________________0_____ ______0___0_____________________________ ____________0______________0____________ ______0_____________________________0___ _________0______________________________ ______________0_______________0_________ _______0______________________________0_ ____________0___________________________ ________________0________________0______ 0_______0_______________________________ _______________0________________________ 0_________________0_________________0___ _0_______0______________________________ 0_________________0_____________________ __0_________________0__________________0 0_0_______0_____________________________ ___0_________________0__________________ ____0_________________0_________________ 0_00_______0____________________________ ______0_________________0_______________ __000_______0___________________________ _________0_________________0____________ ________0_________________0_____________ ___000_______0__________________________ ____________0_________________0_________ __________0_________________0___________ ____000_______0_________________________ _______________0_________________0______ ____________0_________________0_________ _____000_______0________________________ __________________0_________________0___ ______________0_________________0_______ ______000_______0_______________________ _____________________0_________________0 ________________0_________________0_____ _______000_______0______________________ ________________________0_______________ ________000_______0_____________________ ___________________________0____________ ____________________0_________________0_ _________000_______0____________________ ______________________________0_________ ______________________0_________________ __________000_______0___________________ _________________________________0______ ___________000_______0__________________ ____________________________________0___ __________________________0_____________ ____________000_______0_________________ _______________________________________0 ____________________________0___________ _____________000_______0________________ ________________________________________ ______________000_______0_______________ 0_______________________________0_______ _______________000_______0______________ 0_______________________________________ __0_______________________________0_____ ________________000_______0_____________ _0______________________________________ ____0_______________________________0___ _________________000_______0____________ __0_____________________________________ ______0_______________________________0_ __________________000_______0___________
____000___0_____________________________ ____0_0000___0____0_0___0_000___________ 0______0000__________0________0_____0___ _____000__0_____________________________ 0_____00000___0_____0_0___0_000_________ _0______0000____________0________0_____0 0_____000_0_____________________________ 0_0_____0000___0______0_0___0_000_______ 0_0_____00000______________0________0___ ___0___0000_____________________________ 0__00____0000___0_______0_0___0_000_____ 00_0_____00000________________0________0 0_____0_000_____________________________ 0_0__00___0000___0________0_0___0_000___ 000_0_____00000__________________0______ _0______000_____________________________ __0_0__00_00000___0_________0_0___0_000_ 0000_0_____00000____________________0___ 0_0________0____________________________ 0___0_0__0000000___0__________0_0___0_00 _0000_0_____00000______________________0 00_0__________0_________________________ 0__0__0_0__000000___0___________0_0___0_ __0000_0____000000______________________ _00_0____________0______________________ 0_0___0_0_0_000000___0____________0_0___ 0__0000_0____000000_____________________ 0_00_0______________0___________________ ___00____00_0000000___0_____________0_0_ 00__0000_0____000000____________________ ___00_0________________0________________ ___0_00____00_000000___0______________0_ 000__0000_0___0000000___________________ 0___00_0__________________0_____________ ______000____00000000___0_______________ 0000__0000_0___0000000__________________ 00___00_0____________________0__________ 0_______000____0000000___0______________ 00000__0000_0__00000000_________________ __0___00_0______________________0_______ 0_00______000___0000000___0_____________ 000000__0000_0__00000000________________ ___0___00_0________________________0____ ___00_0_____000__0000000___0____________ _000000__0000_0__00000000_______________ 0___0___00_0__________________________0_ _____00__0____000_0000000___0___________ __000000__0000_0__00000000______________ ___0_0___00_0___________________________ 0______00___0___0000000000___0__________ ___000000__0000_0__00000000_____________ 0_____0___00_0__________________________ _0____0__00____0__000000000___0_________ 0___000000__0000_0_000000000____________ 00_____0___00_0_________________________ __0______0_00_____0000000000___0________ ___0_000000__0000_0_000000000___________ __0_____0___00_0________________________ 0_00________000____0000000000___0_______ 0____0000000__0000_0_000000000__________ 0__0_____0___00_0_______________________ 00__0_________000___0000000000___0______ 0_0__00000000__0000_0_000000000_________ 0_0_0_____0___00_0______________________ _00__0__________000__0000000000___0_____ _0__0_00000000__0000_0_000000000________ 0_0_00_____0___00_0_____________________ __00__0___________000_0000000000___0____ __0___000000000__0000_0_000000000_______ 0_0_0_0_____0___00_0____________________ ___00_00____________0000000000000___0___ ___0___000000000__0000_0_000000000______ 00__0_00_____0___00_0___________________ ____00_00____________0000000000000___0__ ____0___000000000__0000_0_000000000_____ 0_0___000_____0___00_0__________________ __0__00_00____________0000000000000___0_ 0____0___000000000__0000_0_000000000____ __00___000_____0___00_0_________________ ____0_00_00____________0000000000000___0 00____0___000000000__0000_0_000000000___ ____0___000_____0___00_0________________ ____0_000_00____________0000000000000___ _00____0___000000000__0000_0_000000000__ 0_________0_____________________________ 0_______________________________________ ________________________________________ 0_0_______0_____________________________ 0_0_____________________________________ _0__0_____0_____________________________ 0_0_0___________________________________ __0___0___0_____________________________ __0_0_0_________________________________ ___0____________________________________ 0__0____0_0_____________________________ 0___0_0_0_______________________________ 0_____0_________________________________ 0_0_0____00_____________________________ 0__0__0_0_0_____________________________ 00_______0______________________________ __0_00____0_____________________________ _0____0_0_000___________________________ 000_________0___________________________ 0___0_0___0_____________________________ __0___0__00_000_________________________ _000___________0________________________ 0__0__00__0_____________________________ ___0____0___0_000_______________________ __000_______0_____0_____________________ 00____0_0_0_____________________________ 0___0___0_0___0_000_____________________ ___000_________0_____0__________________ 000______00_____________________________ 0_0__0___00_0___0_000___________________ 0___000___________0_____0_______________ 0000______0_____________________________ __0_0_0___0_0_0___0_000_________________ ___0_000____0________0_____0____________ 0_000_____0_____________________________ ___00_00___0__0_0___0_000_______________ _____0000______0________0_____0_________ __0000____0_____________________________ _____0000___0___0_0___0_000_____________ ______0000________0________0_____0______
Nak dibuat: Profil halaju: halaju purata di setiap lajur Lihat ‘pergerakan’ bhg perlahan (jika ada) Lihat masa hayat lwn kepadatan