552 research outputs found
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
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