Second order accurate upwind difference schemes for scalar conservation laws with source terms

A second order accurate, characteristic-based, finite difference scheme is developed for scalar conservation laws with source terms. The scheme is an extension of well-known second order scalar schemes for homogeneous conservation laws. Such schemes have proved immensely powerful when applied to homogeneous systems of conservation laws using flux-difference splitting. Many application areas, however, involve inhomogeneous systems of conservation laws with source terms, and the scheme presented here is applied to such systems in a subsequent paper.

The impact of minimum services laws on real estate brokerage competitive intensity

As many as fourteen US states have now mandated minimum service requirements for real estate brokerage relationships in residential transactions. This study attempts to determine whether these minimum service laws have any impact on brokerage competition. Federal government agencies allege such laws discourage competition because they limit the offering of nontraditional brokerage services. However, alternatively, a legislative “bright line” definition of the lowest level of acceptable service may reduce any perceived risk in offering non-traditional brokerage services and therefore encourage competition. Using several empirical strategies and state-level data over nine years (2000-08), we do not find any consistent and significant impact (positive/negative) of minimum services laws on number of licensees per 100 households, our proxy for competition. Interestingly, we also find that association strength, as measured by Realtor association membership penetration, has a strong deterring effect on competition.

Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.