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

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Adakah lebuhraya punyai ingatan?

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Nak dibuat: Profil halaju: halaju purata di setiap lajur Lihat ‘pergerakan’ bhg perlahan (jika ada) Lihat masa hayat lwn kepadatan