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	Clark Density Model	Urban Density Gradient Model
分野	Human Geography	Human Geography
系統	Regression model	Regression model
提唱年	1951	1951
提唱者	Colin Clark	Colin Clark; Edwin Mills & Richard Muth (theory); Bruce Newling (quadratic form)
種類	Empirical regression model of urban population density decline with distance	Family of functional models of urban population density as a function of distance from the centre
原典	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.
別名	Clark's Law, Negative-Exponential Density Model, Exponential Population Density Gradient, Clark Density Gradient	Urban Density Function, Population Density Gradient, Density-Distance Function, Monocentric Density Model
関連	4	4
概要	The Clark density model is the classic empirical description of how urban population density falls with distance from the city centre, formulated by the economist Colin Clark in 1951. It states that density declines exponentially outward from a central peak, so that plotting the logarithm of density against distance yields a straight line whose slope is the density gradient. This negative-exponential 'law' became the standard model of urban spatial structure and the empirical foundation for later monocentric-city theory.	The urban density gradient model is the broad family of functional relationships that describe how population density varies with distance from a city's centre. Its canonical member is Colin Clark's 1951 negative-exponential form, but the family also includes Bruce Newling's quadratic-exponential function that permits a density crater at the core, simpler linear and Smeed forms, and the economic micro-foundation supplied by the Muth-Mills monocentric city model. Together these give planners and economists a compact, comparable language for urban spatial structure.