Constructal view of scaling laws of river basins

River basins are examples of naturally organized flow architectures whose scaling properties have been noticed long ago. Based on data of geometric characteristics, Horton [Horton, R.E., 1932. Drainage basin characteristics. EOS Trans. AGU 13, 350–361.], Hack [Hack, J.T., 1957. Studies of longitudinal profiles in Virginia and Maryland. USGS Professional Papers 294-B, Washington DC, pp. 46–97.], and Melton [Melton, M.A, 1958. Correlation structure of morphometric properties of drainage systems and their controlling agents. J. of Geology 66, 35–56.] proposed scaling laws that are considered to describe rather accurately the actual river basins. What we show here is that these scaling laws can be anticipated based on Constructal Theory, which views the pathways by which drainage networks develop in a basin not as the result of chance but as flow architectures that originate naturally as the result of minimization of the overall resistance to flow (Constructal Law).     

Racism and Intolerance in Eastern Australia: a geographic perspective

Racism has become a fact of life in Australia over the past decade or so, yet there are relatively few studies of its nature or extent, and still fewer on its geography. Using a social constructivist approach, this study draws on a survey of 5056 respondents to investigate attitudes to racism and cultural diversity in New South Wales and Queensland, and of perceptions of out-groups as instances of ‘strangers in our midst’. On racism, results show the presence of a continuum of attitudes ranging from generally tolerant to generally intolerant, a presence which cuts across compositional (social or aspatial) characteristics to emphasise the existence of a distinctive geography, an everywhere different nature to racist and non-racist attitudes which transcends urban–rural and traditional social layers. On the other hand, perceptions of out-groups are not uniformly correlated with presence or absence of cultural diversity. In many cases, the ability to make judgements about significant ‘others’ or out-groups has been shown to relate more to abstract notions of self and national identity, reproduced in public by mainstream news media and political leaders. In particular, it may reflect an Anglo (or Anglo-Celtic) view on nationalism, which is a hallmark of the ‘new racism’: an assimilationist or ethnocultural view of Australian society which is different from the ‘civic nation’ ideal envisaged by multiculturalism. That the geography of attitudes and perceptions people have towards and about different cultural groups is so ‘everywhere different’ has important implications for attempts to address and redress issues of intolerance in Australia.     

Withered Geography

This commentary is a response to an article by Jay R. Harman in the November 2003 issue of The Professional Geographer. I argue that Harman's claim that scholarly disciplines offer social “returns” in a competitive “market” obscures the fundamentally political nature of how social resources are allocated and how social needs are defined. Harman would have us subordinate scholarly research to agendas set elsewhere, by politicians and other powerful interests, but I argue that such a vision would turn geographers into mere technicians. A healthier role for the discipline is for geographers to seek ways of asserting intellectual leadership and of shaping social agendas along more humane and socially just lines.     

SOCIAL RELATIONS SPATIALLY FIXED: CONSTRUCTION AND MAINTENANCE OF SCHOOL DISTRICTS IN SAN ANTONIO,TEXAS

ABSTRACT. More than 140 court cases filed in the United States between 1970 and 2003 argued that unacceptable and unconstitutional funding disparities exist among school districts in most states. In those arguments, stories, statistics, and maps are used to compare various school districts to prove that conditions are indeed unequal. Both sides—plaintiff and defendant—use such information to disprove each other's contentions. In so doing, each assumes that the political spaces of the school districts are absolute, timeless, and independent. Failure to recognize that these spaces—the school districts—are not objective but, in fact, constitutive of the class and race relations actually being argued and debated in court further legitimates local geographies of privilege and deprivation. I examine the formation of the school districts around San Antonio, Texas to illustrate that these districts are far from independent of one another and were formed to isolate privileged communities from the rest of the city. A relational view of space‐time allows such spaces as school districts to assume a political role, as opposed to the absolute, independent spaces they now represent.     

Spherical Slepian functions and the polar gap in geodesy

The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. We show that this potential-field estimation problem has deep-seated connections to Slepian's spatiospectral localization problem which seeks bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures such as bias, variance and mean squared error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of our method make the use of spherical Slepian functions in earth and planetary geodesy practical.