Stability analysis of spectral methods for hyperbolic initial-boundary value systems

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations

Convergence of spectral methods for hyperbolic initial-boundary value systems

A convergence proof for spectral approximations is presented for hyperbolic systems with initial and boundary conditions. The Chebyshev collocation is treated in detail, but the final result is readily applicable to other spectral methods, such as Legendre collocation or tau-methods

Quadrature imposition of compatibility conditions in Chebyshev methods

Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied

Urban Resurgence and the Consumer City

Cities make it easier for humans to interact, and one of the main advantages of dense, urban areas is that they facilitate social interactions. This paper provides evidence suggesting that the resurgence of big cities in the 1990s is due, in part, to the increased demand for these interactions and due to the reduction in big city crime, which had made it difficult for urban residents to enjoy these social amenities. However, while density is correlated with consumer amenities, we show that it is not correlated with social capital and that there is no evidence that sprawl has hurt civic engagement.

Anomalous vortex ring velocities induced by thermally-excited Kelvin waves and counterflow effects in superfluids

Dynamical counterflow effects on vortex evolution under the truncated Gross-Pitaevskii equation are investigated. Standard longitudinal mutual friction effects are produced and a dilatation of vortex rings is obtained at large counterflow. A strong temperature-dependent anomalous slowdown of vortex rings is observed and attributed to the presence of thermally exited Kelvin waves. This generic effect of finite-temperature superfluids is estimated using energy equipartition and orders of magnitude are given for weakly interacting Bose-Einstein condensates and superfluid $^4{\rm He}$

Computational problems in autoregressive moving average (ARMA) models

The choice of the sampling interval and the selection of the order of the model in time series analysis are considered. Band limited (up to 15 Hz) random torque perturbations are applied to the human ankle joint. The applied torque input, the angular rotation output, and the electromyographic activity using surface electrodes from the extensor and flexor muscles of the ankle joint are recorded. Autoregressive moving average models are developed. A parameter constraining technique is applied to develop more reliable models. The asymptotic behavior of the system must be taken into account during parameter optimization to develop predictive models

The Economics of Place-Making Policies

place-making policy, macroeconomics, welfare, income, Empowerment Zones, productivity

The Economics of Place-Making Policies

Should the national government undertake policies aimed at strengthening the economies of particular localities or regions? Agglomeration economies and human capital spillovers suggest that such policies could enhance welfare. However, the mere existence of agglomeration externalities does not indicate which places should be subsidized. Without a better understanding of nonlinearities in these externalities, any government spatial policy is as likely to reduce as to increase welfare. Transportation spending has historically done much to make or break particular places, but current transportation spending subsidizes low-income, low-density places where agglomeration effects are likely to be weakest. Most large-scale place-oriented policies have had little discernable impact. Some targeted policies such as Empowerment Zones seem to have an effect but are expensive relative to their achievements. The greatest promise for a national place-based policy lies in impeding the tendency of highly productive areas to restrict their own growth through restrictions on land use.

The Wealth of Cities: Agglomeration Economies and Spatial Equilibrium in the United States

Empirical research on cities starts with a spatial equilibrium condition: workers and firms are assumed to be indifferent across space. This condition implies that research on cities is different from research on countries, and that work on places within countries needs to consider population, income and housing prices simultaneously. Housing supply elasticity will determine whether urban success shows up in more people or higher incomes. Urban economists generally accept the existence of agglomeration economies, which exist when productivity rises with density, but estimating the magnitude of those economies is difficult. Some manufacturing firms cluster to reduce the costs of moving goods, but this force no longer appears to be important in driving urban success. Instead, modern cities are far more dependent on the role that density can play in speeding the flow of ideas. Finally, urban economics has some insights to offer related topics such as growth theory, national income accounts, public economics and housing prices.