No abstract

A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak-Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into account business rule(s), like enterprise -enterprise short range location "interaction"(s), business plan(s) through spin-offs or merging and enterprise survival evolution law(s). It is numerically found that the model leads to a sort of phase transition for the fitness gap as a function of the selection pressure.

Among econophysics investigations, studies of religious groups have been of interest. On one hand, the present paper concerns the Antoinist community financial reports, -a community which appeared at the end of the 19-th century in Belgium. Several growth-decay regimes have been previously found over different time spans. However, there is common suspicion about sect finances. In that spirit, the Antoinist community yearly financial reports, income and expenses, are hereby examined along the so-called Benford's law. The latter is often used as a test about possible accounting wrongdoings. On the other hand, Benford's law is known to be invariant under scale and base transformation. Therefore, as a further test, of both such data and Benford's law use, the yearly financial reports are nonlinearly remapped through a sort of Theil transformation, i.e. based on a log-transformation. The resulting data is again analyzed along the Benford's law scheme. Bizarre, puzzling, features are seen. However, it is emphasized that such a non-linear transformation can shift the argument toward a more objective conclusion. In an Appendix, some brief discussion is made on why the original Theil mapping should not be used. In a second Appendix, an imperfect Benford's law-like form, -better suited for anomalous distributions, is presented.

We consider a lattice gas for which particles possessing magnetic moments can interact via magnetic long-range Kac potential and short-range intermolecular potential. From the exact equation of state of the lattice gas and the magnetization we construct and discuss phase diagrams in one and two dimensions. The appearance of any of the possible phases -nonmagnetic gas, nonmagnetic liquid, or magnetic liquid -is shown to depend crucially on the value of the parameter R, the ratio of the short-range (nonmagnetic) to long-range (magnetic) interaction strengths.

The frequency spectrum of clusters of small ionic particles is calculated when the particle mutual interaction is described by a dipole-dipole interaction Hamiltonian. The crystallites are spheres of known bulk dielectric properties. The actual geometry of the cluster is taken into account. Clusters of increasing size (pair, triplet, quadruplet, etc. ) have been solved analytically. As expected, the dipolar broadening of the frequency spectrum of (optically active or inactive) surface modes increases with cluster size and compactness. From the spectrum of few-particle clusters, one obtains the long-wavelength modes of large linear or planar aggregates of such clusters by application of the Bloch-Floquet theorem. Application is made to ir optical absorption of NiO. The present approach is intermediate between the continuum model of a structureless powder on the one hand and microscopic calculations for single microcrystals of prescribed shape on the other hand.