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Fizik Lalulintas

Wan Ahmad Tajuddin Wan Abdullah Jabatan Fizik Universiti Malaya & Institut Ibnu Sina UTM http://fizik.um.edu.my/cgi-bin/hitkat?wat. Fizik Lalulintas. Alam ini kompleks. Komputer: simulasi, pemetaan. Sistem kompleks. Tak keseimbangan, pelesapan

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Fizik Lalulintas

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  1. Wan Ahmad Tajuddin Wan Abdullah Jabatan Fizik Universiti Malaya & Institut Ibnu Sina UTM http://fizik.um.edu.my/cgi-bin/hitkat?wat Fizik Lalulintas

  2. Alam ini kompleks

  3. Komputer: simulasi, pemetaan Sistem kompleks • Tak keseimbangan, pelesapan • Banyak darjah kebebasan fungsi Lyapunov • Tak linear pemetaan peta logistik xn+1 = axn(1-xn)

  4. Bawah ke Atassaling tindak tempatan, minimal↓fenomena sejagat

  5. Entropi Perubahan fasa … pemerihalan statistik Rawak Sistem besar Ergodik

  6. (/Permainan Kehidupan) salingtindak (hidup/mati) sel/organisme dgn jiran, berruang unsur Boole di atas kekisi dengan salingtindak jiran terdekat 2 dimensi: a b c d p e f g h Automaton bersel Keadaan p bergantung kepada keadaan-keadaan a, b, …, h(dan diri sendiri p). Dinamik automaton bersel1 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

  7. 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. 111110101100011010001000 0 1 0 1 1 0 1 0 Hukum 90 (010110102 = 9010)

  8. Lalulintas • Aliran berbiji • Tindakan pemandu Lebuhraya • Satu hala • Satu dimensi

  9. Model automaton bersel Model mudah: 1 lorong, 1-dim Hukum 184 – 111110101100011010001000 1 0 1 1 1 0 0 0 bergerak ke kanan satu tapak jika kosong - Bil./kepadatan kereta terabadi - Kelajuan maksimum m=1

  10. di mana Perubahan fasa pada rc = 1/2 (kinetik peringkat ke2) [peralihan mengejap]

  11. Gambarajah fundamentalarus lwn kepadatan j j = vr r j Hukum 184: r

  12. penumbesaran kelompok soliton

  13. Pengaman/pengumuman • Banyak lorong (- memotong) • Banyak kelajuan (- brek dan pecut) • Sikap pemandu • Masukan kereta • Hingar • Perlanggaran • …..

  14. 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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  16. Adakah lebuhraya punyai ingatan?

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

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