Dynamics of urban sprawl

This paper introduces a framework for understanding the dynamics of urban growth,particularly the continuing problem of urban sprawl. The models we present are based on transitions from vacant land to established development. We propose that the essential mechanism of transition is analogous to the way an epidemic is generated within a susceptible population, with waves of development being generated from the conversion of available land to new development and redevelopment through the aging process. We first outline the standard aggregate model in differential equation form, showing how different variants (including logistic, exponential, predator-prey models) can be derived for various urban growth situations. We then generalize the model to a spatial system and show how sprawl can be conceived as a process of both interaction/reaction and diffusion. We operationalize the model as a cellular automata (CA) which implies that diffusion is entirely local, and we then illustrate how waves of development and redevelopment characterizing both sprawl and aging of the existing urban stock, can be simulated.Finally we show how the model can be adapted to a real urban situation - the AnnArbor area in Eastern Michigan - where we demonstrate how waves of development are absorbed and modified by particular historical contingencies associated with the re-existing urban structure

A statistical model approximation for perovskite solid-solutions: a Raman study of lead-zirconate-titanate single crystal

Lead titanate (PbTiO3) is a classical example of a ferroelectric perovskite oxide illustrating a displacive phase transition accompanied by a softening of a symmetry-breaking mode. The underlying assumption justifying the soft-mode theory is that the crystal is macroscopically sufficiently uniform so that a meaningful free energy function can be formed. In contrast to PbTiO3, experimental studies show that the phase transition behaviour of lead-zirconate-titanate solid solution (PZT) is far more subtle. Most of the studies on the PZT system have been dedicated to ceramic or powder samples, in which case an unambiguous soft-mode study is not possible, as modes with different symmetries appear together. Our Raman scattering study on titanium-rich PZT single crystal shows that the phase transitions in PZT cannot be described by a simple soft-mode theory. In strong contrast to PbTiO3, splitting of transverse E-symmetry modes reveals that there are different locally-ordered regions. The role of crystal defects, random distribution of Ti and Zr at the B-cation site and Pb ions shifted away from their ideal positions, dictates the phase transition mechanism. A statistical model explaining the observed peak splitting and phase transformation to a complex state with spatially varying local order in the vicinity of the morphotropic phase boundary is given.Comment: Article contains four black-and-white figures, one colour figure and one Table. Symmetry analysis and details of the model are given in Appendices I and II, respectivel

Planetesimal collisions in binary systems

We study the collisional evolution of km-sized planetesimals in tight binary star systems to investigate whether accretion towards protoplanets can proceed despite the strong gravitational perturbations from the secondary star. The orbits of planetesimals are numerically integrated in two dimensions under the influence of the two stars and gas drag. The masses and orbits of the planetesimals are allowed to evolve due to collisions with other planetesimals and accretion of collisional debris. In addition, the mass in debris can evolve due to planetesimal-planetesimal collisions and the creation of new planetesimals. We show that it is possible in principle for km-sized planetesimals to grow by two orders of magnitude in size if the efficiency of planetesimal formation is relatively low. We discuss the limitations of our two-dimensional approach.Comment: 5 pages, 5 figures, accepted for publication in MNRA