The City Is Here to Stay

It is not the aim of this article to analyze the modem American city\u27s ills and to provide a set of prescriptions, a healthful regimen for their cure. Growing out of an informal talk, this essay is a rather personal statement of an attitude, a most positive attitude, toward great cities. Though it is part credo and part panegyric, it will nonetheless seek to make some analytical points

Foreword—The United States Supreme Court’s “Environmental Term” (1991-1992)

This symposium collects, analyzes, and comments on the environmental law decisions of the 1991-92 term of the Supreme Court

Discretization of the velocity space in solution of the Boltzmann equation

We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a BGK collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers. Higher order approximations to the Boltzmann equation can be achieved by using more velocities in the quadrature