Boom and bust in continuous time evolving economic model

We show that a simple model of a spatially resolved evolving economic system, which has a steady state under simultaneous updating, shows stable oscillations in price when updated asynchronously. The oscillations arise from a gradual decline of the mean price due to competition among sellers competing for the same resource. This lowers profitability and hence population but is followed by a sharp rise as speculative sellers invade the large un-inhabited areas. This cycle then begins again.Comment: 7 pages, 9 figures, epjb style. New references. Section on avoiding boom and bust. Fix bibliograph

Ab initio studies of structural instabilities in magnesium silicate perovskite

Density-functional simulations are used to calculate structural properties and high-symmetry phonons of the hypothetical cubic phase, the stable orthorhombic phase and an intermediate tetragonal phase of magnesium silicate perovskite. We show that the structure of the stable phase is well described by freezing in a small number of unstable phonons into the cubic phase. We use the frequencies of these unstable modes to estimate transition temperatures for cubic--tetragonal and tetragonal--orthorhombic phase transitions. These are investigated further to find that the coupling with the strain suggests that phonons give a better representation than rigid unit modes. The phonons of an intermediate tetragonal phase were found to be stable except for two rotational modes. The eigenvectors of the most unstable mode of each of the cubic and tetragonal phases account for all the positional parameters of the orthorhombic phase. The phase boundary for the orthorhombic--tetragonal transition intersects possible mantle geotherms, suggesting that the tetragonal phase may be present in the lower mantle.Comment: 16 pages, REVTEX, 7 postscript figures (Fig 1 very large, contact Authors if required); submitted to Physics and Chemistry of Mineral

Temperature dependence in interatomic potentials and an improved potential for Ti

The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic potentials which are used in molecular dynamics, as a model for the forces on a system. These forces should be the derivative of the free energy of the electronic system, which includes contributions from the entropy of the electronic states. This free energy is weakly temperature dependent, and although this can be safely neglected in many cases there are some systems where the electronic entropy plays a significant role. Here a method is proposed to incorporate electronic entropy in the Sommerfeld approximation into empirical potentials. The method is applied as a correction to an existing potential for titanium. Thermal properties of the new model are calculated, and a simple method for fixing the melting point and solid-solid phase transition temperature for existing models fitted to zero temperature data is presented.Comment: CCP 201