X and the City: Modeling Aspects of Urban Life (90 page)

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Biometrika
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acceleration “noise,”
85
–87

accidents, car,
12
,
77

avoiding,
80
–85

advection-diffusion,
183

air pollution,
179
,
191

its effect on visibility,
191

air travel,
7
–10,
13

analogies,
2
–3

asteroids,
248

capture cross section for,
303

close encounters with,
303
–7

collisions with,
249

Astronomy Picture of the Day (APOD),
248

bamboo, growth of,
42

bedbugs,
142

beltways,
133

M25 in UK,
125
,
133

Brownian motion,
181

buses, bunching of,
64

cancer.
See
tumors

Central Park: jogging in,
49
–51

squirrels in,
47

sunbathing in,
48
–49

circumhorizontal arc,
301

cities: Bessel,
163
–64

equilibrium models of,
159

scaling in,
171

Cobb-Douglas production function,
30

comet, Shoemaker-Levy,
247

concert halls,
19
–21

dental offices, number of,
16

dewbows,
230

diamond dust,
229
,
301

Dido, princess,
4
–5

and the sinc function,
263
–68

theorems for,
261
–62

differential equations: Bernoulli,
172

delay-,
108

diffusion,
182
–83,
188
,
293
–95

nonlinear,
137
,
140

diffusion equation,
293

and diffusion coefficient,
294
.
See also
differential equations

dimension: Hausdorff-Besicovitch,
288

topological,
288

distributions: exponential,
91

negative exponential,
91
,
96

Poisson (
see
Poisson distribution)

doomsday,
136
,
139
,
176

earthquakes, in Virginia,
25

ellipses,
219
–20

expectation value,
95

eruption of,
180

flashlight beams,
242
–43

fractal,
3

box-,
289

Cantor dust,
290

and fractal dimension,
3
,
169
–70,
288
–90

Koch snowflake,
289

Menger sponge,
290

Sierpinski triangle,
289

fruit,
36
–37

gaps, at school crossings,
92
–94

gasoline, consumption of,
74
–76

geometrical optics,
193

Goldilocks principle,
11
,
17
,
39
,
251

grass seed,
42
–43

halos: ice crystal,
204
,
224

in lighthouse beams,
239
–240

harmonic mean,
74

headway,
88
,
94

heat island, urban,
58
,
61

houses of worship,
16
–17

hyperbolic orbit,
304

isoperimetric inequality,
261

isoperimetric theorem,
261

jogging,
49
–51

Lagrange multipliers,
31
,
277

leaves,
45

light: and diffraction,
192
–93

and light bulbs,
222

and light pillars,
222
–23

and polarization,
198
–200

reflection and refraction of,
192

and scattering of (
see
scattering)

wavelengths of,
192
–93

London, population of,
144

M25 motorway,
105
,
133

malls,
25
–27

Malthusian growth,
137

Mandelbrot set,
287

Manhattan distance,
270

Manhattan metric,
26

maps,
10
–11

mathematical models: continuum,
136
,
284

deterministic vs. probabilistic,
89

incorporating reaction time,
117
–20

kinematic vs. dynamic,
89
–90,
99

metaphors,
2
–3

meteor crater (Winslow, Arizona),
249
–50,
252
–53

Minnaert, Marcel,
216
,
225

and “apples,”
224

and “cigars,”
224
–25

moonbows,
230

mortgages,
32
–33

museums,
17
–19

normal distribution,
184

Old Dominion University,
253

orchids, maturation of,
43
–44

overtaking (passing),
88

pedestrians,
72

petrol.
See
gasoline consumption

Poisson distribution,
28
,
91
,
273

derivation of,
274
–75

population: of certain cities,
151
–52

and population densities,
152

population growth: exponential,
136

Gompertz-like,
173

logistic,
140

Malthusian,
137

post office,
27
–28

probability: density function of,
94

geometric,
29
,
281
–82