morphology of urban conglomerations: experimental and theoretical modeling, and implications for...
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Morphology of urban conglomerations:experimental and theoretical modeling,
and implications for everyday traffic
Massimo Pica Ciamarra
Dipartimento di Scienze FisicheUniversità di Napoli Federico IICrdc-AMRA
Antonio Coniglio
Physics and the city, Bologna, 15 Dic. 2005
Outline
Motivation
Urban morphology: empirical analysis
theoretical modeling
Evacuation
Conclusions
• Motivation • Urban morphology
• Evacuation • Conclusions
Mt. Vesuvius
• Motivation • Urban morphology
• Evacuation • Conclusions
People to be evacuated: 500.000
Eruption forecast
Mt. Vesuvius estimate: 14 days
-1980 Mt. St. Elena 24 h
- 1991 Mt. Pinatubo 48 h
- 1996 Mt. Ruapehu 6 days
- ??? Mt. Vesuvius 14 days
Population: 500.000
Mt. Vesuvius
Naples
Ercolano
Pompei
Evacuation time
Numbers
• People: 500.000• Safety distance: d = 50 Km
Evacuation time
v = 4 Km/h
T = 12h 30m
v = 20 Km/h
T = 2h 30m
v = 40 Km/h
T = 1h 15m
Congestion ?
no yes
?
• Motivation • Urban morphology
• Evacuation • Conclusions
The road network: Rome
20 Km
20 Km
1.5 Km
• Motivation • Urban morphology1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions
P.za Venezia
1.1 Km
A grid element
= # black pixels
# pixels
P.za N
avona
Via del C
orso
Via N
azio
nale
Campidoglio
1.5 Km
Maps: www.maporama.com
1px = 2 m2
• Motivation • Urban morphology1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions
0
Km7.8Nr
N
Nrrr
2Erfc
2)( 0max
0
0.3
0.2
0.1
10 20 30 400
)(r
(Km) r
Andamento di (r) per la città di Roma
Km7.1N
• Motivation • Urban morphology1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions
Cluster growth: background
• Motivation • Urban morphology 1. Empirical analysis
2. Theoretical modeling• Evacuation • Conclusions
DLA: T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981).M. Batty and P. Longley, Area 19, 215 (1987); M. Batty and P. Longley, Env. and Planning B 14, 123 (1987).M. Batty et. al., Env. and Planning A 21, 1447 (1989).
Diffusion-Limited Aggregate Eden Model
M. Eden, Proc. 4° Berkeley Symp. On Mat. Stat. and Probability, Univ. California. Press, (1961).J.D. Weeks et. al., J. Chem. Phys. 65, 712 (1976).L. Benguigui, Physica A 219, 13 (1995).
2
2
2Exp
2
1),(
N
N
N
rrNrP
r
'
N
Nr
N
N
Random walk cluster growth model
• Motivation • Urban morphology 1. Empirical analysis
2. Theoretical modeling• Evacuation • Conclusions
2
2
2Exp
2
1),(),(
N
N
N
RWCG
rrrNrP
rNrP
2
0
r
rN N
Assumptions:
1: 2:
Nrrandom walk with a driftMean: St. Dev.:
0v
rrrP N )(3:
2
1;0 NrrN 4
1';'0 NN
Growth probability
• Motivation • Urban morphology 1. Empirical analysis
2. Theoretical modeling• Evacuation • Conclusions
Probability of building a city unit in a point at a distance r form the center
rNrP /),(
),( Nr
Radial density
• Motivation • Urban morphology 1. Empirical analysis
2. Theoretical modeling• Evacuation • Conclusions
N
NN
RWCG
rr(n,r)dnP
rNr
2Erfc
22
1),( 0max
0
0
Evacuation and bottlenecks: Rome
(Km) r10 20 30 40
0.3
0.1
0.2
0.25
0.15
0.050
10
20
)(Km
)(2
rS
)(r
expansion compression expansion
)(2)( rrrS
• Motivation • Urban morphology
• Evacuation • Conclusions
Optimization of the evacuation process
One entry ?Two entries ?
• Motivation • Urban morphology
• Evacuation • Conclusions
Entry ramps
Qupstream Qexit
Qin
Qexit = Qupstream + Qin
Entry ramp model
p
If we can insert a car in the main flow without causing accidentsWe insert the car with probability p
p = 0: cars are never insertedp = 1: a car is inserted as soon as possible
M. Pica Ciamarra, Phys. Rev. E 72, 066102, (2005).
Simulation with the Extended Nagel - Schreckenberg modelKnospe et. al., Phys. Rev. E 70, 016115 (2004).
Qexit = Q(p1,…,pn)
• Motivation • Urban morphology
• Evacuation • Conclusions
p1
p2
0 10.50
1
0.5
Example: two entries – two lane road
1600
0
800
400
1200
Q (cars/h)
(p1, p2) (0.35,0.5)
Q1 900 cars/h
Q2 700 cars/h
Max:
• Motivation • Urban morphology
• Evacuation • Conclusions
Conclusions
1. Morphology of a city
Empirical study of digital maps (resolution: 2m2)
Simple model of cluster growth (anal. solvable)
Universality - Bottlenecks
2. Optimization of on-ramp entries
Simulation of the extended Nagel-Schreckenberg model
Control of the flux of entering cars
O posteri, o posteri si tratta di voiun giorno è lume all'altro
e il dì precedente è norma per il dì che segueudite
venti volte da che splende il solese non sbaglia la storia
arse il Vesuvio.Sempre con strage immane di chi a fuggir fu lento.
Affinché dopo l'ultimo lutto più non vi colpiscaio vi avviso.
Questo monte ha greve il seno di bitume,allume, zolfo, oro, argento, nitro, di fonte d'acque.
Presto o tardi si accende ma prima gemetrema, scuote il suolo mescola e fumo e fiamme e lampi
scuote l'aria, rimbomba, tuona, muggisce scaccia ai confini gli abitanti.Tu scappa finché lo puoi.
Ecco che scoppia e vomita di fuoco un fiumeche vien giù precipitando e sbarra la fuga a chi s'attarda
se ti coglie e' finita: sei mortodisprezzato apprese gli incauti e gli avidi
cui la casa e le suppellettili furono più care della vita.Ma tu, se hai senno, di un marmo che ti parla
di la voce non ti curar dei lari; senza indugi fuggi.
E. Fonseca y Zunica, Vicerè (1632)
Radial density (r)
Round cities
r
x
y
),( yx )(r• Motivation • Urban morphology
1. Empirical analysis2. Theoretical modeling• Evacuation • Conclusions
Deaths Volcano When Major Cause of Death (no starvation)
36,417 Krakatau, Indonesia 1883 Tsunami
29,025 Mt. Pelee, Martinique 1902 Ash town of Saint Pierre
25,000 Ruiz, Colombia 1985 Mudflows town of Armero
14,300 Unzen, Japan 1792 Volcano collapse, tsunami
5,110 Kelut, Indonesia 1919 Mudflows
4,011 Galunggung, Indonesia 1882 Mudflows
3,500 Vesuvius, Italy 1631 Mudflows, lava flows
3,360 Vesuvius, Italy 79 Ash flows and falls
2,957 Papandayan, Indonesia 1772 Ash flows
2,942 Lamington, Papua N.G. 1951 Ash flows
2,000 El Chichon, Mexico 1982 Ash flows
1,680 Soufriere, St Vincent 1902 Ash flows
1,475 Oshima, Japan 1741 Tsunami
1,377 Asama, Japan 1783 Ash flows, mudflows
1,335 Taal, Philippines 1911 Ash flows
1,200 Mayon, Philippines 1814 Mudflows
1,184 Agung, Indonesia 1963 Ash flows
1,000 Cotopaxi, Ecuador 1877 Mudflows
800 Pinatubo, Philippines 1991 Roof collapses and disease
Volcanic Hazards: A Sourcebook on the Effects of Eruptions, Russell J. Blong (Academic Press, 1984).