X and the City: Modeling Aspects of Urban Life by Adam John A

Author:Adam, John A. [Adam, John A.]
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2012-05-26T20:00:00+00:00

It can be seen that if b < −, i.e., β < −1, then there are no points of inflection and ρ(r) decreases monotonically from the central business district outward (youthful city). If − < b < 0, (−1 < β < 0) or 0 < b (0 < β < 1) there is a single point of inflection (in early and late maturity, respectively). Finally, if b > (β > 1) there are two such points and the full density crater profile is evident (aging city).

There can be variations on this theme using the concept of a “traveling wave of metropolitan expansion.” We can illustrate the stages of city development by positing a traveling pulse of “shape” ρ(r) moving outward with speed v, that is,

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