461 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
Origin of complex crystal structures of elements at pressure
We present a unifying theory for the observed complex structures of the
sp-bonded elements under pressure based on nearly free electron picture (NFE).
In the intermediate pressure regime the dominant contribution to crystal
structure arises from Fermi-surface Brillouin zone (FSBZ) interactions -
structures which allow this are favoured. This simple theory explains the
observed crystal structures, transport properties, the evolution of internal
and unit cell parameters with pressure. We illustrate it with experimental data
for these elements and ab initio calculation for Li.Comment: 4 pages 5 figure
The role of van der Waals and exchange interactions in high-pressure solid hydrogen
We investigate the van der Waals interactions in solid molecular hydrogen structures. We calculate enthalpy and the Gibbs free energy to obtain zero and finite temperature phase diagrams, respectively. We employ density functional theory (DFT) to calculate the electronic structure and density functional perturbation theory (DFPT) with van der Waals (vdW) functionals to obtain phonon spectra. We focus on the solid molecular C2/c, Cmca-12, P63/m, Cmca, and Pbcn structures within the pressure range of 200 < P < 450 GPa. We propose two structures of the C2/c and Pbcn for phase III which are stabilized within different pressure range above 200 GPa. We find that vdW functionals have a big effect on vibrations and finite-temperature phase stability, however, different vdW functionals have different effects. We conclude that, in addition to the vdW interaction, a correct treatment of the high charge gradient limit is essential. We show that the dependence of molecular bond-lengths on exchange–correlation also has a considerable influence on the calculated metallization pressure, introducing errors of up to 100 GPa
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